Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis...

206
STRUCTURAL DAMAGE IDENTIFICATION USING EXPERIMENTAL MODAL PARAMETERS VIA CORRELATION APPROACH Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School of Civil Engineering and Built Environment Science and Engineering Faculty Queensland University of Technology 2018

Transcript of Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis...

Page 1: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

STRUCTURAL DAMAGE IDENTIFICATION

USING EXPERIMENTAL MODAL

PARAMETERS VIA CORRELATION

APPROACH

Khac-Duy Nguyen

M.E., B.E

A Thesis submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Civil Engineering and Built Environment

Science and Engineering Faculty

Queensland University of Technology

2018

Page 2: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School
Page 3: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page i

© 2017 Khac-Duy Nguyen Page i

Keywords

Structural health monitoring, vibration-based, damage identification,

correlation approach, genetic algorithm, optimisation-based, modal strain energy,

geometric modal strain energy, sensitivity-weighted search space, benchmark

structures, spring-mass system, three story shear building, complex truss structure, I-

40 Bridge.

Page 4: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page ii

© 2017 Khac-Duy Nguyen Page ii

Page 5: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page iii

© 2017 Khac-Duy Nguyen Page iii

Abstract

Damage identification is an important step within structural health monitoring

(SHM) for the assessment of the structural safety. To date, a large number of damage

identification algorithms have been proposed. Among those, methods using vibration

characteristics have been intensively investigated and widely applied to various

practical applications of our infrastructure. Feasibility of vibration-based damage

identification methods generally rely on vibration measurement and physical damage

detection models. However, the vibration features are normally measured with some

errors, and the damage identification models are inevitably established with some

differences compared to the real structures. Therefore, there is a demand to continue

discovering new vibration features which are highly sensitive to damage but little

affected by measurement and modelling uncertainties.

It is well-know that both modal strain energy and eigenvalue can be used as

damage indicators. While modal strain energy is more sensitive to elemental damage

but less accurately estimated, eigenvalue is measured with better accuracy but less

sensitive to damage. It is reasonably expected that combined use of them will give

more reliable damage identification results. This study presents new damage

identification algorithms based on modal strain energy-eigenvalue ratio (MSEE).

Firstly, a method using a simplified term of MSEE called geometric modal strain

energy-eigenvalue ratio (GMSEE) is developed. Damage is identified by optimizing

the correlation level between a measured GMSEE change vector and a numerical

one. The method requires only measured modal parameters (i.e., natural frequency

and mode shape) and geometric information of the structural element. Secondly, a

modification of this method is presented considering use of the full term of MSEE.

The modified method is capable for damage identification with fewer modes

compared with the original one although it requires both material and sectional

Page 6: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page iv

© 2017 Khac-Duy Nguyen Page iv

properties of the structural element. Thirdly, in order to enhance the efficiency of the

proposed algorithms, an enhanced technique is proposed for the optimisation

procedure. The technique refers sensitivity-weighted search space which is able to

reduce the effect of measurement noise on low-sensitivity elements.

Performance of the proposed damage identification algorithms and enhanced

technique has been validated with a simple numerical model and some experimental

models of various scales from small to large. It has been found that the modal strain

energy-eigenvalue ratio is a sensitive damage indicator for large structures and the

enhanced technique significantly improve the effectiveness of the damage

identification methods proposed in this study. Results obtained in this study show the

high capability of the proposed damage identification algorithms for damage

identification where uncertainties associated with measurement and structural

identification are present. Also, the results show a great promise of the proposed

damage identification algorithms in practical applications for real structures. In

summary, this thesis provides an efficient damage identification scheme for

structural health monitoring of infrastructure.

Page 7: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page v

© 2017 Khac-Duy Nguyen Page v

Table of Contents

Keywords........................................................................................................................................... i

Abstract ............................................................................................................................................iii

Table of Contents ............................................................................................................................. v

List of Figures ................................................................................................................................... ix

List of Tables .................................................................................................................................... xv

List of Abbreviations ...................................................................................................................... xvii

List of Symbols ................................................................................................................................ xix

Statement of Original Authorship .................................................................................................. xxiii

Acknowledgments ......................................................................................................................... xxv

CHAPTER 1: INTRODUCTION ............................................................................................................ 1

1.1 Background ............................................................................................................................ 1

1.2 Research Problems ................................................................................................................ 2

1.3 Research Aim and Objectives ................................................................................................. 3

1.4 Significance of the Study ........................................................................................................ 3

1.5 Scope of the Study ................................................................................................................. 4

1.6 Thesis Outline ........................................................................................................................ 4

CHAPTER 2: LITERATURE REVIEW .................................................................................................... 9

2.1 Introduction to Damage Identification .................................................................................... 9

2.2 Vibration-based Damage Identification ................................................................................ 11 2.2.1 Natural Frequency-based Damage Identification Methods ......................................... 11

2.3 Mode Shape-based Damage Identification Methods ............................................................. 13 2.3.1 Methods based on Direct Use of Mode Shape Change ............................................... 13 2.3.2 Modal Flexibility-based Methods ............................................................................... 14 2.3.3 Mode Shape Curvature-based Methods ..................................................................... 16 2.3.4 Modal Strain Energy-based Methods ......................................................................... 18

2.4 Signal-based Damage Identification Methods ....................................................................... 21

2.5 Incoporating Soft Computing Approaches for Damage Identification .................................... 23 2.5.1 Damage Identification incorporating Evolutionary Computation ................................ 23 2.5.1.1 Genetic Algorithm ..................................................................................................... 24 2.5.1.2 Other Evolutionary Computation Methods ................................................................ 26 2.5.2 Damage Identification using Artificial Neural Networks .............................................. 27

2.6 Practical Issues ..................................................................................................................... 29 2.6.1 Measurement Errors ................................................................................................. 29 2.6.2 Modelling Errors........................................................................................................ 30 2.6.3 Ill-Posed Problem ...................................................................................................... 31

2.7 Summary of Literature Review ............................................................................................. 32

CHAPTER 3: GEOMETRIC MODAL STRAIN ENERGY-EIGENVALUE RATIO (GMSEE) CORRELATION METHOD ........................................................................................................................................ 35

3.1 Conventional Correlation-based Damage Identification Methods ........................................... 35 3.1.1 Conventional Correlation-based Damage Identification Methods ............................... 35

Page 8: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page vi

© 2017 Khac-Duy Nguyen Page vi

3.2 Theoretical Development of GMSEE Correlation Method ...................................................... 37 3.2.1 Sensitivity Analysis of GMSEE .................................................................................... 37 3.2.2 Locating damage using GMSEE change vector ............................................................ 40 3.2.3 Quantifying Damage .................................................................................................. 42 3.2.3.1 Quantifying Damage using Natural Frequency Change ............................................... 42 3.2.3.2 Quantifying Damage using GMSEE Change................................................................. 43

3.3 Summary of GMSEE Correlation Damage Identification Method ........................................... 43

3.4 idenfication of Correlative Damage Vector using Genetic Algorithm ..................................... 45

3.5 Numerical Verification.......................................................................................................... 46 3.5.1 Damage Identification with Noise-free Modal Data .................................................... 47 3.5.2 Damage Identification with Measurement Noise ....................................................... 50

3.6 Experimental Verification ..................................................................................................... 60 3.6.1 Case Study 1: LANL 8-DOF System.............................................................................. 60 3.6.2 Case Study 2: LANL Three-story Building Model ......................................................... 62

3.7 Conclusions .......................................................................................................................... 69

CHAPTER 4: MODAL STRAIN ENERGY-EIGENVALUE RATIO (MSEE) CORRELATION METHOD .......... 71

4.1 Sensitivity Analysis for Modal Strain Energy-Eigenvalue Ratio (MSEE) ................................... 71 4.1.1 Change in Elemental MSEE ........................................................................................ 71 4.1.2 Change in Total MSEE ................................................................................................ 72

4.2 Damage Identification using MSEE Change ........................................................................... 73

4.3 Summary of MSEE Correlation Damage Identification Method.............................................. 75

4.4 Numerical Verification.......................................................................................................... 76 4.4.1 Damage Identification with Noise-free Modal Data .................................................... 76 4.4.2 Damage Identification with Measurement Noise ....................................................... 78 4.4.2.1 Damage Identification Results using 8 modes ............................................................ 78 4.4.2.2 Damage Identification Results using 4 modes ............................................................ 86 4.4.3 Damage Identification with Modelling Errors ............................................................. 94

4.5 Experimental Verification ..................................................................................................... 99

4.6 Conclusions ........................................................................................................................ 103

CHAPTER 5: SENSITIVITY-WEIGHTED SEARCH SPACE FOR CORRELATION-BASED DAMAGE IDENTIFICATION ........................................................................................................................... 105

5.1 Theoretical Development of Sensitivity-Weighted Search Space ......................................... 105

5.2 Numerical Verification........................................................................................................ 107

5.3 Conclusions ........................................................................................................................ 110

CHAPTER 6: EXPERIMENTAL VALIDATION FOR A COMPLEX TRUSS STRUCTURE........................... 111

6.1 Introduction of Laboratory Through-Truss Bridge Model .................................................... 111

6.2 Experimental Setup ............................................................................................................ 114

6.3 Modal Extraction and Verification ...................................................................................... 119 6.3.1 Modal Extraction ..................................................................................................... 119 6.3.2 Modal Verification ................................................................................................... 127

6.4 Damage Identification for QUT Through-Truss Bridge Model .............................................. 131 6.4.1 Damage Identification using GMSEE Method ........................................................... 134 6.4.2 Damage Identification using MSEE Method.............................................................. 138

6.5 Conclusions ........................................................................................................................ 143

Page 9: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page vii

© 2017 Khac-Duy Nguyen Page vii

CHAPTER 7: EXPERIMENTAL VALIDATION FOR A REAL BRIDGE .................................................... 147

7.1 Experiment Description and Modal Properties ................................................................... 147

7.2 Damage Identification using GMSEE Correlation Method.................................................... 150

7.3 Damage Identification using MSEE Correlation Method ...................................................... 155

7.4 Conclusions ........................................................................................................................ 159

CHAPTER 8: CONCLUSIONS AND FUTURE STUDIES ...................................................................... 161

8.1 Summary and Conclusions ................................................................................................. 161

8.2 Future Studies .................................................................................................................... 167

REFERENCES ................................................................................................................................. 169

APPENDICES ................................................................................................................................. 177

Appendix – A: Examples of Geometric Quantity of Stiffness Matrix................................................ 177

Appendix – B: Publications Derived from This Project .................................................................... 178

Page 10: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page viii

© 2017 Khac-Duy Nguyen Page viii

Page 11: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page ix

© 2017 Khac-Duy Nguyen Page ix

List of Figures

Figure 2-1. Four diagnostic levels in damage identification process [adapted from

Rytter (1993)] ................................................................................................................... 10

Figure 3-1. Schematic of GMSEE correlation-based damage identification method ........... 44

Figure 3-2. Two-dimensional truss bridge (Rahai et al. 2007) ............................................ 46

Figure 3-3. Damage identification result for 2-D truss model: Case 1: D9 = 20% ............. 49

Figure 3-4. Damage identification result for 2-D truss model: Case 2: D4 = 20%,

D11 = 30% ...................................................................................................................... 49

Figure 3-5. Damage identification result for 2-D truss model: Case 3: D7 = 20%, D8

= 25%, D10 = 30% .......................................................................................................... 49

Figure 3-6. Detection probability results for 2-D truss model under noise: Case 1 .............. 53

Figure 3-7. Detection probability results for 2-D truss model under noise: Case 2 .............. 54

Figure 3-8. Detection probability results for 2-D truss model under noise: Case 3 .............. 55

Figure 3-9. Average damage extent results for 2-D truss model under noise: Case 1 ........... 57

Figure 3-10. Average damage extent results for 2-D truss model under noise: Case 2 ......... 58

Figure 3-11. Average damage extent results for 2-D truss model under noise: Case 3 ......... 59

Figure 3-12. LANL 8-DOF system (Duffey et al. 2001)..................................................... 61

Figure 3-13. Damage identification result for 8-DOF system by GMSEE correlation

method .............................................................................................................................. 62

Figure 3-14. 4-DOF three-story building from LANL ........................................................ 63

Figure 3-15. Basic dimensions of the three story building model ....................................... 64

Figure 3-16. Modal parameters of baseline model .............................................................. 66

Figure 3-17. Damage probability results for the shear building by GMSEE method ........... 67

Figure 3-18. Average damage extent results for the shear building by GMSEE method ...... 68

Figure 4-1. Schematic of MSEE correlation-based damage identification method .............. 75

Figure 4-2. Damage identification results for the 2-D truss model by MSE, GMSEE

and MSEE methods using first 4 modes............................................................................. 77

Page 12: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page x

© 2017 Khac-Duy Nguyen Page x

Figure 4-3. Detection probability results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 1 .................................................... 79

Figure 4-4. Detection probability results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 2 .................................................... 80

Figure 4-5. Detection probability results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 3 .................................................... 81

Figure 4-6. Average damage extent results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 1 .................................................... 83

Figure 4-7. Average damage extent results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 2 .................................................... 84

Figure 4-8. Average damage extent results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 3 .................................................... 85

Figure 4-9. Detection probability results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 1 .................................................................. 87

Figure 4-10. Detection probability results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 2 .................................................................. 88

Figure 4-11. Detection probability results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 3 .................................................................. 89

Figure 4-12. Average damage extent results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 1 .................................................................. 91

Figure 4-13. Average damage extent results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 2 .................................................................. 92

Figure 4-14. Average damage extent results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 3 .................................................................. 93

Figure 4-15. Damage identification results for the 2-D truss model by MSE and MSEE

methods considering modelling errors: Case 1 ................................................................... 96

Figure 4-16. Damage identification results for the 2-D truss model by MSE and MSEE

methods considering modelling errors: Case 2 ................................................................... 97

Figure 4-17. Damage identification results for the 2-D truss model by MSE and MSEE

methods considering modelling errors: Case 3 ................................................................... 98

Figure 4-18. Damage identification for the 8-DOF system by MSEE method .................... 99

Figure 4-19. Detection probability results for the shear building by GMSEE and

Page 13: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xi

© 2017 Khac-Duy Nguyen Page xi

MSEE methods. .............................................................................................................. 101

Figure 4-20. Average damage extent results for the shear building by GMSEE and

MSEE methods ............................................................................................................... 102

Figure 5-1. Average MSEE sensitivity of the first 4 modes of the 2-D truss model ........... 108

Figure 5-2. Sensitivity-weighted search space of all elements of the 2-D truss model ....... 108

Figure 5-3. Damage identification results using MSEE method for a noised data in

Case 2 of the 2-D truss model .......................................................................................... 109

Figure 6-1. QUT steel through-truss bridge model ........................................................... 112

Figure 6-2. Dimensions of QUT steel through-truss bridge model .................................... 113

Figure 6-3 Joint connections at some typical positions ..................................................... 113

Figure 6-4. Sensor layouts for vibration measurement of the QUT through-truss bridge

model ........................................................................................................................ 115-116

Figure 6-5. Measured DOFs for the QUT through-truss bridge model .............................. 117

Figure 6-6 Sensors at some typical joints of the QUT through-truss bridge model ............ 117

Figure 6-7 Representative acceleration time-series of layout 1 of the QUT through-

truss bridge model ........................................................................................................... 118

Figure 6-8. Element numbering for the examined truss plane of the QUT through-truss

bridge model ................................................................................................................... 119

Figure 6-9 SVD diagram and the identified natural frequencies for the QUT through-

truss bridge model ........................................................................................................... 121

Figure 6-10 Modal strain energy of the unselected mode at 7Hz from two different

data sets .......................................................................................................................... 124

Figure 6-11 Modal strain energy of the unselected mode at 62.125Hz .............................. 124

Figure 6-12 Modal strain energy for the first selected mode (15.375Hz) from 2

different data sets ............................................................................................................ 125

Figure 6-13 Modal strain energy for the second selected mode (30.25Hz) from 2

different data sets ............................................................................................................ 125

Figure 6-14 Modal strain energy for the third selected mode (58.75Hz) from 2

different data sets ............................................................................................................ 126

Figure 6-15 Experimental mode shapes identified by FDD method .................................. 126

Page 14: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xii

© 2017 Khac-Duy Nguyen Page xii

Figure 6-16 FE model of the QUT through-truss bridge model .........................................127

Figure 6-17. Comparison of two FE models of a bottom chord for refining member’s

stiffness ...........................................................................................................................128

Figure 6-18. Three identical modes obtained from the FE model of the QUT through-

truss bridge structure ........................................................................................................130

Figure 6-19. Spring-in-series model of bolted truss element .............................................131

Figure 6-20. Illustration of damaged elements on the QUT through-truss bridge model

........................................................................................................................................133

Figure 6-21. Sensitivity-weighted search space of all elements of the examined plane

of the QUT through-truss bridge model ............................................................................134

Figure 6-22. Damage identification results for state 1-1 using GMSEE method with

sensitivity-weighted search space .....................................................................................136

Figure 6-23. Damage identification results for state 1-2 using GMSEE method with

sensitivity-weighted search space .....................................................................................136

Figure 6-24. Damage identification results for state 2-1 using GMSEE method with

sensitivity-weighted search space .....................................................................................136

Figure 6-25. Damage identification results for state 1-1 using GMSEE with

conventional search space ................................................................................................137

Figure 6-26. Damage identification results for state 1-2 using GMSEE with

conventional search space ................................................................................................137

Figure 6-27. Damage identification results for state 2-1 using GMSEE method with

conventional search space ................................................................................................138

Figure 6-28. Damage identification results for state 1-1 using MSEE method with

sensitivity-weighted search space .....................................................................................139

Figure 6-29. Damage identification results for state 1-2 using MSEE method with

sensitivity-weighted search space .....................................................................................139

Figure 6-30. Damage identification results for state 2-1 using MSEE method with

sensitivity-weighted search space .....................................................................................139

Figure 6-31. Damage identification results for state 1-1 using MSEE method with

conventional search space ................................................................................................141

Figure 6-32. Damage identification results for state 1-2 using MSEE method with

conventional search space ................................................................................................141

Page 15: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xiii

© 2017 Khac-Duy Nguyen Page xiii

Figure 6-33. Damage identification results for state 2-1 using MSEE method with

conventional search space ............................................................................................... 141

Figure 6-34. Damage identification results by traditional MSE method using only 3

experimental modes ........................................................................................................ 142

Figure 6-35. Damage identification results by traditional MSE method using 3

experimental modes together with 100 numerical modes ................................................. 143

Figure 7-1. I-40 Bridge over Rio Grande in Albuquerque, NM, USA (Farrar et al.

1994) .............................................................................................................................. 148

Figure 7-2. Sensor layout and location of damage ............................................................ 149

Figure 7-3. Four damage levels: cuts at the middle span of on the north plate girder ........ 149

Figure 7-4. Variation in stiffness around the crack ........................................................... 151

Figure 7-5. Result for damage case E-3 by GMSEE correlation method with

sensitivity-weighted search space .................................................................................... 153

Figure 7-6. Result for damage case E-4 by GMSEE correlation method with

sensitivity-weighted search space .................................................................................... 153

Figure 7-7. Result for damage case E-3 by GMSEE correlation method with

conventional search space ............................................................................................... 154

Figure 7-8. Result for damage case E-4 by GMSEE correlation method with

conventional search space ............................................................................................... 154

Figure 7-9. Result for damage case E-3 by MSEE correlation method with sensitivity-

weighted search space ..................................................................................................... 157

Figure 7-10. Result for damage case E-4 by MSEE correlation method with

sensitivity-weighted search space .................................................................................... 157

Figure 7-11. Result for damage case E-3 by MSEE correlation method with

conventional search space ............................................................................................... 158

Figure 7-12. Result for damage case E-4 by MSEE correlation method with

conventional search space ............................................................................................... 158

Page 16: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xiv

© 2017 Khac-Duy Nguyen Page xiv

Page 17: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xv

© 2017 Khac-Duy Nguyen Page xv

List of Tables

Table 3-1. Damage scenarios for 2-D truss model .............................................................. 46

Table 3-2. Quantification of damage extent prediction error caused by measurement

noise ................................................................................................................................. 60

Table 3-3. Damage states of the three-story shear building model ...................................... 65

Table 4-1. Quantification of damage extent prediction error caused by measurement

noise using 8 modes .......................................................................................................... 86

Table 4-2. Quantification of damage extent prediction error caused by measurement

noise using 4 modes .......................................................................................................... 94

Table 6-1. Details of structural members of QUT steel through-truss bridge model .......... 114

Table 6-2. Summary of mode selection for the QUT through-truss bridge model.............. 123

Table 6-3. Comparison of natural frequencies obtained from experimental model and

FE model of the QUT through-truss bridge structure ....................................................... 130

Table 6-4. Damage scenarios for the QUT through-truss bridge structure ......................... 132

Table 6-5. Natural frequencies of the QUT through-truss bridge structure at

undamaged and damaged states ....................................................................................... 133

Table 6-6. Summary of damage identification results for the QUT through-truss bridge

model (with the use of sensitivity-weighted search space) ............................................... 140

Table 7-1. Natural frequencies of the I-40 Bridge ............................................................ 149

Table 7-2. MAC values after the introduction of damage ................................................. 150

Table 7-3. Equivalent stiffness reduction ......................................................................... 151

Page 18: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xvi

© 2017 Khac-Duy Nguyen Page xvi

Page 19: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xvii

© 2017 Khac-Duy Nguyen Page xvii

List of Abbreviations

2D Two Dimensional

ANN Artificial Neural Network

AR Autoregressive

ARX Autoregressive with Exogenous Inputs

ACF Autocorrelation Function

CCF Cross-correlation Function

CDF Curvature Damage Factor

COMAC Coordinate Modal Assurance Criteria

CS Cuckoo Search

CWT Continuous Wavelet Transform

DOF Degree of Freedom

FDD Frequency Domain Decomposition

FE Finite Element

FRF Frequency Response Function

GA Genetic Algorithm

GMSE Geometric Modal Strain Energy

GMSEE Geometric Modal Strain Energy-Eigenvalue ratio

HS Harmony Search

MAC Modal Assurance Criteria

MDLAC Multiple Damage Location Assurance Criteria

ML-GA Multi-layer Genetic Algorithm

MSE Modal Strain Energy

MSEE Modal Strain Energy-Eigenvalue ratio

PCA Principal Component Analysis

PSO Particle Swarm Optimisation

RFC Relative Flexibility Change

SHM Structural Health Monitoring

STFT Short-time Fourier Transform

WT Wavelet Transform

VBDI Vibration-based Damage Identification

Page 20: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xviii

© 2017 Khac-Duy Nguyen Page xviii

Page 21: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xix

© 2017 Khac-Duy Nguyen Page xix

List of Symbols

C Damage scaling coefficient

ijF Fraction of modal strain energy of the jth element for the ith mode

u

iiF Diagonal component of flexibility matrix before damage

d

iiF Diagonal component of flexibility matrix after damage

ijG Geometric modal strain energy-eigenvalue ratio (GMSEE) of the

jth element for the ith mode

H Girder height

K System stiffness matrix

jK Stiffness matrix of element j

0jK Geometric quantity of stiffness matrix of element j

M System mass matrix

MDLAC Multiple damage location assurance criterion

MSE MSE vector for all modes

iMSE MSE vector for mode i

,1iMSE First data set of the ith MSE data

,2iMSE Second data set of the ith MSE data

ijMSEE MSEE component of mode i and element j

MSEMAC Modal assurance criteria of MSE

N Number of MSE values in MSE vector

fS Sensitivity matrix of natural frequency

GMSEES Sensitivity matrix of GMSEE

GMSEEiS Sub-sensitivity matrix of GMSEE for mode i

GMSEEavgS Average sensitivity matrix of GMSEE

GMSEEuS Sensitivity matrix of GMSEE at undamaged state

GMSEEdS Sensitivity matrix of GMSEE at damaged state

MSEEavgS Average sensitivity matrix of MSEE

Page 22: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xx

© 2017 Khac-Duy Nguyen Page xx

MSEEuS Sensitivity matrix of MSEE at undamaged state

MSEEdS Sensitivity matrix of MSEE at damaged state

MSEEiS Sub-sensitivity matrix of MSEE for mode i

MSEEijS Sensitivity coefficient of MSEE for mode i and element j

meanjS Average sensitivity of element j to damage

iTMSEE Total MSEE of mode i

ijU Modal strain energy of the jth element for the ith mode

iU Total modal strain energy for the ith mode

ijU Geometric modal strain energy of the jth element for the ith mode

if Natural frequency of mode i

if Noised natural frequency of mode i

jk Stiffness constant of the jth element

k(x) Stiffness constant of the element at location x

joint-1k Tangential contact stiffness at the first end of a truss bar

joint-2k Tangential contact stiffness at the second end of a truss bar

bark Axial stiffness of a truss bar

ek Equivalent stiffness of a truss member

jl Length of element j

n number of elements

m number of modes

n Number of MSE values being greater than the mean value of

MSE vector

MSEp Percentage of MSE greater than its mean value

jx Damage extent variable of element j

j Damage index for element j

ij , f

i Independent random number in range of [-1, 1]

ΔG Measured GMSEE change vector

Δ iG Measured GMSEE change vector for mode i

Page 23: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xxi

© 2017 Khac-Duy Nguyen Page xxi

ΔMSEE Measured MSEE change vector

iΔMSEE Measured MSEE change vector for mode i

Δ iTMSEE Measured total MSEE change of mode i

δG Analytical GMSEE change vector

δ iG Analytical GMSEE change vector for mode i

δD Damage vector

jD Damage extent at element j

δMSEE Analytical MSEE change vector

iδMSEE Analytical MSEE change vector for mode i

iTMSEE Analytical total MSEE change of mode i

i Eigenvalue of mode i

u Mean value of damage extent at undamaged state

Damage extent threshold

u Standard deviation of damage extent at undamaged state

Noise level of mode shape

f Noise level of natural frequency

Φ Mode shape matrix

iΦ Mode shape vector of mode i

ij Mode shape component of mode i for element j

ij Noised mode shape component of mode i for element j

"( )i x Modal curvature at location x for mode i

Page 24: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xxii

© 2017 Khac-Duy Nguyen Page xxii

Page 25: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xxiii

© 2017 Khac-Duy Nguyen Page xxiii

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To the

best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.

Signature: QUT Verified Signature

Date: March 2018

Page 26: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xxiv

© 2017 Khac-Duy Nguyen Page xxiv

Page 27: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xxv

© 2017 Khac-Duy Nguyen Page xxv

Acknowledgments

First of all, I would like to thank my principal supervisor, Prof. Tommy Chan

for his endless support and guidance of my research throughout my PhD study.

During my candidature, I have benefited from his enthusiasm, high sense of

responsibility and invaluable advice to my research. His logical, detailed and

constructive comments have helped me complete my research successfully. I also

thank him for being always available for me to keep in touch no matter where he is

(in Australia or overseas). He is my ultimate role model as researcher, advisor,

lecturer and mentor.

I would like to thank my first associate supervisor, Prof. David Thambiratnam

for his care, encouragement and advice on my study. Moreover, I appreciate his

careful editing for my papers, making them more readable as well as his willingness

to share his academic and life experience with me.

I would also like to thank Dr. Andy Nguyen as my second associate

supervisor. He has shared with me his fruitful experience on how to keep a PhD

study on track as well as helped me a lot with my study and life settlement since my

first day at QUT. I thank him for his constant support and advice on my research. I

have also learnt a lot from his expertness on modal testing and sensor technology as

well as his great passion for research.

Special thanks are extended to my M.S. supervisor, Prof. Jeong-Tae Kim at

Pukyong National University, South Korea. He has given me the beginning lessons

on structural dynamics, modal testing and analysis, structural health monitoring, and

damage identification. Without his guidance, I would not be able to achieve much in

my research project.

My experimental tests on the QUT through-truss bridge would not have been

possible without the support of Banyo staff members, especially Mr. Barry Hume.

His support made my tests become easier and more professional. I also greatly

acknowledge Mr. Craig Cowled for his design and fabrication of this truss bridge

model.

My sincere thanks also spread to Mehran Aflatooni, Tharindu Kodikara, Zhi

Xin Tan, Ngoc Thach Le, Shojaeddin Jamali, Parviz Moradi, Ziru Xiang, Manal

Page 28: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Structural Damage Identification using Experimental Modal Parameters via Correlation Approach Page xxvi

© 2017 Khac-Duy Nguyen Page xxvi

Hussin, Thisara Pathirage, Thuy Nguyen, Benyamin Monavari, Hossein Moravej and

other fellows in the SHM research team at QUT for their help, debates and feedbacks

on my work. It was my honour to be a member of such a friendly, dynamic and

knowledgeable group.

I would like to express my appreciation to Queensland University of

Technology for the scholarships that supported during my candidature, and also for

providing the research facilities and technical support. I would also like to thank Dr.

Chaminda Gallage and Dr. Jason Watson for being panel members of my final

seminar and for their recommendations for making this thesis better. I sincerely

thank QUT Research Student Centre and HDR Student Support Team (especially

Ms. Tiziana La Mendola) for their direct and indirect support during my PhD

candidature. My gratitude is also given to the Los Alamos National Laboratory, USA

for providing experimental data used in this research.

Last but not least, I would like to thank my parents for giving me the birth,

for their unconditional love and support during my study abroad. My strength to

complete this research through to the end is from them. I also thank all my relatives

and friends who have helped, concerned and loved me in millions of ways in the past

years.

Page 29: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 1

© 2017 Khac-Duy Nguyen Page 1

1Chapter 1: Introduction

1.1 BACKGROUND

Structural safety is an essential issue for all civil structures such as bridges,

buildings, offshore platforms and nuclear power plants. In many developed countries,

the budget for the maintenance of structures has been annually expended. Despite

these efforts, damage in these structures seems to be inevitable since bridges are

subjected to various extreme loadings and environmental impacts that might have

been underestimated in the design process. Moreover, many bridges which were

constructed long time ago are becoming aged and their load-carrying capability has

declined. Therefore, it is important to detect early any abnormal behaviour or

damage in structures so that their lives can be prolonged by taking appropriate

actions.

Recently, the structural health monitoring (SHM) technology has drawn a

serious attention from researchers as an economic, efficient and intelligent way for

the maintenance of structures. SHM refers to a non-destructive structural evaluation

process of tracking and assessing the safety and performance of the structure using

an on-structure sensing system (Aktan et al. 2000, Chan and Thambiratnam 2011).

Over the past three decades, a large amount of research focusing on the first function

of SHM (i.e., structural safety) has been conducted. It is very important to have a

reliable damage detection procedure because if damage is not detected correctly, it can

eventually lead to local failure of the structural elements and in consequence to the collapse

of the whole structure. Damage detection methods are often classified based on type of

structural features used, such as natural frequency, mode shape, displacement, strain,

curvature, flexibility, strain energy or damage identification techniques such as

damage index, feature correlation, neural networks, etc. Most of these approaches are

based on vibration measurement.

Page 30: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 2

© 2017 Khac-Duy Nguyen Page 2

Among these techniques, modal vector correlation-based methods have been

found to be effective for locating damage as well as estimating damage extent since

they integrate advanced optimisation techniques to solve the damage problem.

Several correlation methods have been developed using changes in either natural

frequency (Messina et al. 1998) or mode shape (Shi et al. 2000b) or elemental modal

strain energy (Wang et al. 2012). However, these methods still have some limitations

as highlighted as follows. While the frequency correlation method requires the

availability of a sufficient set of natural frequencies, the accuracy of the other

methods relies very much on the number of analytical mode shapes used and the

degree of matching between numerical models and real structures. Therefore, when

dealing with a large number of structural members in a complex structure, the

existing correlation-based methods may become less practical, less accurate and may

generate high degree of false detection. Also, solving techniques for the correlation-

based methods need to be improved when dealing with high measurement noise

usually associated with real structures.

1.2 RESEARCH PROBLEMS

From the above presentation, it is evident that developing an effective

damage identification method is essential for the maintenance of structures. Degrees

of false-positive and false-negative detection need to be reduced, and accuracy of

predicting the damage extent needs to be improved, especially when noise is

introduced in measurement. The following research problems are identified:

1. How to develop a vibration-based damage indicator that is practical, suitable

for identifying damage via the correlation technique, accurate for both single

and multiple damage cases and suitable in the presence of measurement and

modelling uncertainties?

2. How to improve the damage detection accuracy when dealing with

structures having large number of degrees of freedom compared to the

Page 31: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 3

© 2017 Khac-Duy Nguyen Page 3

number of modes that could be measured?

3. How to minimize false detection caused by high measurement noise?

1.3 RESEARCH AIM AND OBJECTIVES

The main aim of this study is to develop new vibration based damage

identification methods for civil structures by using correlation of modal parameters

together with optimisation approaches. The proposed method is aimed at improving

the accuracy of damage detection, reducing the degree of false detection and

increasing practicality. The objectives of this research are as follows:

1. To investigate what vibration parameters and what approaches to be selected

for the development of new damage identification scheme.

2. To develop a sensitivity-based and correlation-based method using vibration

parameter incorporating both natural frequency and mode shape terms. Also,

it is needed to develop a method to estimate damage extent using the

proposed vibration parameter.

3. To improve the proposed method for the case where only fewer modes can

be measured.

4. To develop a technique that can reduce false detection associated with

measurement noise.

1.4 SIGNIFICANCE OF THE STUDY

This research deals with the general problem of structural damage

identification including locating the damage and estimating its severity. The research

is significant because it will overcome the several of the existing issues to provide

safer structures. The issues are: (i) existing damage detection methods have troubles

with accuracy in locating the damage, estimating its severity and false alarms, (ii)

there are certain differences between all real structures and their numerical models,

Page 32: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 4

© 2017 Khac-Duy Nguyen Page 4

(iii) vibration parameters of structures are measured with a certain degree of error,

(iv) only few modal parameters of a structure can be measured and reliable for the

use of damage identification purpose; and (v) findings of this work may lead to

more understanding of the impact of structural damage on structural behaviour.

1.5 SCOPE OF THE STUDY

The methodology of this study is derived for the damage which results in a

reduction of structural stiffness. For real world applications, stiffness reduction is

generally used to represent other damage types such as crack, corrosion and material

degradation. The feasibility of the methodology is validated using a physical spring-

mass system, a multi-story building model, a plate-girder bridge and truss bridge

models. However, the methodology can also be applied to other kinds of civil

structures such as beam-type bridges and frame structures. It should be noted that

this study does not examine effects of environmental factors on vibration parameters

of structures as there is already a large amount of research on compensation for

changes in vibration characteristics due to changes in environmental conditions.

Those environmental effect studies can be used in conjunction with this study for

better damage identification.

1.6 THESIS OUTLINE

The research focuses of the development and application of damage

identification algorithms for structures. The contributions of the research are in the

development of damage identification methods using experimental modal

parameters, development of a technique dealing with structures consisting of a large

number of degrees of freedom, and verification of the proposed methods and the

technique for a large complicated truss structure. This section summarizes the

overview of the thesis on each of the remaining chapters.

Chapter 2 reviewed the recent literature on vibration-based damage

identification algorithms and application of soft computing approaches for the

Page 33: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 5

© 2017 Khac-Duy Nguyen Page 5

damage identification problem. From the review of vibration-based damage

identification algorithms, it is found that using both natural frequency and mode

shape information would give better damage results. Also, modal strain energy-based

methods have shown to be effective to locate damage and to estimate damage

severity. Modal strain energy and natural frequency are used as key parameters for

the damage identification algorithms developed in this research. Additionally, the

modal vector correlation-based technique is found to be effective to locate damage

and hence is employed to formulate objective functions in this research. From the

review of soft computing approaches, evolutionary optimisation techniques have

shown excellent performance in solving damage identification problems. One of

these algorithms, the genetic algorithm (GA) is utilized as a basic technique in the

damage identification framework developed in this research.

Chapter 3 and 4 describe the development of damage identification

algorithms. The algorithms are based on a new damage indicator called modal strain

energy-eigenvalue ratio. Chapter 3 provides detail of a correlation-based method

using geometric modal strain energy-eigenvalue ratio (GMSEE) and its validation

for simple numerical and experimental models. The sensitivity of GMSEE to

structural stiffness reduction is derived using measured modal parameters and

geometric information of structural elements such as length and/or thickness

depending upon structure types. Unscaled damage extent information can be

identified from optimizing the correlation level between the measured GMSEE

change vector and numerical GMSEE change vector. Herein, genetic algorithm (GA)

can be embedded as a search engine to find an optimal solution. Then, final damage

extent information is identified using a scale factor calculated from the total change

in GMSEE. Due to an assumption that the fractional modal strain energy does not

change after a damage episode, the method still requires a good number of measured

modes. The algorithm was validated for a numerical 2-D truss model and two simple

laboratory models.

Page 34: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 6

© 2017 Khac-Duy Nguyen Page 6

In Chapter 4, an improvement made for the method developed in Chapter 3 is

presented regarding the capability for damage identification with fewer modes.

Herein, change in modal strain energy-eigenvalue ratio (MSEE) is utilized instead of

change in geometric modal strain energy-eigenvalue ratio (GMSEE). A new vector

form consisting of individual MSEE of each member and total MSEE is used to

formulate the objective function showing the correlation level between the measured

MSEE change and analytical MSEE change. The new approach can reduce the effect

caused by the assumption made in the original method made in Chapter 3; and hence

can reduce the number of modes used. However, this method will require full

information of structural elements including both geometric and material properties.

In summary, both methods developed in Chapter 3 and 4 are useful depending upon

particular cases where either full information of structural elements or sufficient

information of vibration modes is provided.

Chapter 5 presents a technique to improve damage identification capability

for large structures where measurement noise associated with these structures is

significant. The technique is based on the observation that damage identification is

only reliable for elements with high vibration stress. A search technique considering

sensitivity of individual structural element is developed wherein the search space of

an element is weighted with its sensitivity. The hidden concept behind this technique

is that the importance of each element is treated unequally; the higher sensitivity the

element has, the broader its search space is. This technique is tested for the

numerical 2D truss model in condition of high measurement noise.

Chapter 6 describes the validation of the developed damage identification

algorithms for a complex truss model with 100 degrees of freedom assessed. First of

all, vibration tests were conducted using a wired sensing system with 18

accelerometers. A major number of DOFs were measured by multiple roving setups.

Vibration characteristic of unmeasured DOFs were obtained by simple interpolation

Page 35: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 7

© 2017 Khac-Duy Nguyen Page 7

from the measured ones. Subsequently, modal parameters extracted from the

measured responses were verified with a FE model. Then, some damage scenarios

were simulated on the experiment model by introducing bolt loose to selected truss

elements. Finally, damage identification for the truss model was performed using the

proposed damage indemnification algorithms.

Chapter 7 provides the validation of the developed damage identification

algorithms for a benchmark full-scale bridge. The validation study used existing

experimental data of the I-40 Bridge provided by the Los Alamos National

Laboratory. For higher resolution of damage identification results, mode shapes of

unmeasured locations were estimated using cubic interpolation technique. In order to

reduce fitting errors associated with high order curves of the whole mode shapes, the

interpolation task was performed individually for each span. Results showed the

potential of the developed damage identification algorithms for real applications.

Chapter 8 summarizes the findings and conclusions of the thesis as well as

recommendations for future work. This research presents the development of

damage identification algorithms for structures based on modal vector correlation

principal. A sensitivity-weighted search space concept is developed, which is

effective for large structures with high measurement noise. Validation has been

performed for several structures with various scales from small to large. The future

work includes the issues for improving the damage identification algorithms

developed in this thesis, as well as the potentials to extend the research to various

applications.

Page 36: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 1: Introduction Page 8

© 2017 Khac-Duy Nguyen Page 8

Page 37: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 9

© 2017 Khac-Duy Nguyen Page 9

2Chapter 2: Literature Review

This section first provides the concept of damage identification. Then it

reviews theory of existing vibration-based damage identification (VBDI) methods and

their applications. Herein, VBDI methods are categorized into three groups: 1)

methods using change in natural frequency, 2) methods using change in mode shape

and its secondary features such as modal curvature, modal flexibility and modal strain

energy, and 3) methods based on vibration signals. Some soft computing techniques

used to solve the damage identification problem using vibration features are introduced

in this section, including some evolutionary optimisation algorithms such as genetic

algorithm, particle swarm optimisation, harmony search and cuckoo search, and

Artificial Neural Networks. Some practical issues are also discussed in this chapter.

2.1 INTRODUCTION TO DAMAGE IDENTIFICATION

In a structural system, damage can be defined as changes to the material

and/or geometric properties, which adversely affects the current or future

performance of the system (Sohn et al. 2003). Damage is typically categorized into

linear and nonlinear. Linear damage refers to the case when the initially linear-elastic

structure behaves in a linear manner after the occurrence of damage. Conversely, the

behaviour of a linear-elastic structure becomes nonlinear after a nonlinear damage

has been introduced. For example, linear damage is associated with section corrosion

or material degradation, while nonlinear damage is associated with fatigue crack,

frozen bearings or loose connections. The damage identification algorithms in this

study are developed under the phenomena of linear damage. For simplification, any

damage introduced in this study is assumed as linear damage.

Damage identification in a structural system is a process of examining

changes in measured response of the system to detect, locate and characterize

damage in the system (Farrar and Doebling 1997). According to Rytter (1993), the

Page 38: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 10

© 2017 Khac-Duy Nguyen Page 10

damage identification process can be illustrated in four levels as shown in Fig.2-1.

Level 1 gives the information whether damage is present in the structure. Level 2

and 3 provides information about the location and the size of the damage. The most

sophisticated level is the prognosis of the remaining life, which requires a

comprehensive interpretation of the impact of the discovered damage on the

structure.

Figure 2-1. Four diagnostic levels in damage identification process [adapted from

Rytter (1993)]

Over the past three decades, a large amount of research on vibration-based

damage identification (VBDI) has been conducted due to their reliability,

practicability and cost effectiveness (Doebling et al. 1998, Wang and Chan 2009,

Fan and Qiao 2010). The basic concept of the VBDI is to examine the correlation

between the change in structural properties (e.g., mass, stiffness, damping or

boundary condition) and the change in modal parameters which can be obtained by

measuring dynamic responses of the structure. In the following sections, the

common VBDI algorithms are reviewed.

Page 39: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 11

© 2017 Khac-Duy Nguyen Page 11

2.2 VIBRATION-BASED DAMAGE IDENTIFICATION

2.2.1 Natural Frequency-based Damage Identification Methods

Natural frequency has been widely used for damage diagnosis by many

researchers. Natural frequency is a global parameter of structures so that the change

in local members would be reflected by the change in natural frequency. Using

natural frequency change as a damage indicator is very efficient since natural

frequency can be quickly extracted from a vibration signal at a single location. The

degree of natural frequency change is dependent on the position of the damage

relative to the mode shape (Rytter and Kirkegaard 1994). It has been reported that

the measurement of natural frequency is reliable (Salawu 1997, Doebling et al.

1998) and less affected by random error sources than other modal parameters (Farrat

et al. 1997, Doebling et al. 1997).

On the contrary, Doebling et al. (1996) criticized in his review that natural

frequency change has low sensitivity to damage so the corresponding detection

methods require either very precise measurements or large levels of damage. He

used the data obtained from the test on the I-40 Bridge (Farrar et al. 1994) to

demonstrate his opinion. However, changes in the natural frequencies of the bridge

due to environmental variations were not controlled. Also, significant reductions of

resonant frequencies (exceeding 5%) were observed after the bending stiffness of the

bridge cross section was reduced by 21%.

Gudmundson (1982) mathematically formulated the changes in natural

frequencies of beams due to cracks, notches or other small geometrical changes. It

has been found that the predictions for geometrical changes close to supports are as

not as good as for the changes in other positions. That is due to the fact that vibration

behaviours of the regions close to supports are influenced by the nonlinear stress

intensity. The method was proved to be accurate for up to 10% change in natural

frequency when damage occurred closely to supports. Apart from those cases, the

prediction of natural frequency changes due to geometrical changes was very

Page 40: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 12

© 2017 Khac-Duy Nguyen Page 12

accurate.

Kim et al. (2003a) developed a direct damage index method for beam like

structures using the ratio of fractional changes in frequency for two modes. The

method was found to be practical as it needs only the measured modal parameters

and stiffness matrix. Also, damage severity was also accurately predicted by

correlating the size of fatigue crack to the change in natural frequencies. However,

the method is capable for only single damage scenarios.

As one of the earliest works for the forward methods, Cawley and Adams

(1979) proposed an optimisation-based method using the ratio of frequency changes

in two modes together with sensitivity analysis for localizing damage and

quantifying damage. The method was found sensitive to detect damage location in

aluminum plates and cross-ply carbon-fiber-reinforced plastic plate all but with

erroneous prediction of damage amount.

Messina et al. (1998) proposed a forward method to locate damage and

estimate damage severity using the Multiple Damage Location Assurance Criterion

(MDLAC) that is a correlation factor between the change of a measured natural

frequency set and that of the corresponding numerical natural frequency set. Damage

location is identified by searching the numerical damage set which gives the largest

MDLAC. Also, the first order and second order sensitivity matrices have been

derived for damage extent estimation. It was found that the both methods could

estimate damage extent accurately, and the second order method with a much higher

calculation effort gave only a little improvement in accuracy.

In summary, the natural frequency-based methods are simple, cost efficient

and reliable. Relying on natural frequency change, the existence of damage, the

location and severity of damage can be accurately predicted. However, the methods

cannot distinguish damage at symmetric locations in a symmetric structure (Cawley

and Adams 1979, Shih 2009). It is found that the direct method can only deal with

Page 41: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 13

© 2017 Khac-Duy Nguyen Page 13

single damage cases. Although the correlation-based method proposed by Messina et

al. (1998) enables to detect multiple-damage, the method much relies on the

availability of a sufficient set of natural frequencies. That is due to the fact that the

change of natural frequencies in different multiple-damage scenarios might be the

same.

2.3 MODE SHAPE-BASED DAMAGE IDENTIFICATION METHODS

2.3.1 Methods based on Direct Use of Mode Shape Change

Mode shape is a modal parameter which represents the relative deformation

of a structure in modal domain. West (1986) probably presented the first systematic

use of mode shape information for detecting damage based on only measurements of

mode shape sets before and after a damage episode. The statistical term named

modal assurance criteria (MAC) was used to determine the degree of correlation

between modes before and after a damage episode:

( )

( )( )

2*

* *( , )

T

i j

T T

i i j j

MAC i j =Φ Φ

Φ Φ Φ Φ (2-1)

where iΦ is the ith mode shape vector of the structure in the undamaged state, and

*

jΦ is the jth mode shape vector of the structure in the damaged state. The MAC

takes on values from zero representing no correlation, to one representing full

correlation. The change in MAC across the different partitioning techniques is used

to localize the structural damage.

Since the MAC does not give spatial information of structural damage, it is

hard to determine the damage location. An improvement of the modal assurance

criterion is the coordinate modal assurance criterion (COMAC) proposed by Lieven

and Ewins (1988). The COMAC identifies spatially which degree-of-freedom (DOF)

contributes negatively to a low value of MAC; then the damage is located at the

position corresponding to that DOF. The COMAC is calculated as follows:

Page 42: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 14

© 2017 Khac-Duy Nguyen Page 14

( )2

*

1

2 *2

1 1

( )

m

ki ki

k

m md

ki ki

k k

COMAC k =

= =

=

(2-2)

where ki is the undamaged mode shape value of the kth DOF corresponding to the

ith mode; *

ki is the damaged mode shape value of the kth DOF corresponding to the

ith mode; and m is the highest mode number of interest.

Ko et al. (1994) proposed a method to locate damage by combining

sensitivity analysis, MAC calculation and COMAC calculation. Sensitivity analysis

is carried out to narrow the set of mode shapes used in MAC and COMAC analysis.

It was observed that the method can better detect the damage location by using the

selected modes rather than by using all the modes. However, damage location should

be assumed for the selection of mode shapes.

Inherited from the MDLAC method proposed by Messina et al. (1998), Shi et

al. (2000b) modified the MDLAC method by using mode shape changes instead of

natural frequency changes. They succeeded to detect single-damage and multiple-

damage cases in a truss structure. It was observed that the damage detection results

using the modified MDLAC contain less false-positive detection than those using the

original MDLAC with natural frequency changes. Also, the modified MDLAC

method requires much fewer modes than the original one. However, the accuracy of

the method relies on the number of analytical mode shapes used and the degree of

matching between the analytical mode shapes and the experimental mode shapes

including the measured and unmeasured ones.

2.3.2 Modal Flexibility-based Methods

Damage detection based on changes in modal flexibility was first proposed

by Pandey and Biswas (1994). The flexibility matrix is obtained from measured

natural frequencies and mass-normalized mode shapes as follows:

Page 43: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 15

© 2017 Khac-Duy Nguyen Page 15

2

1

1m1 T T

i i

i iω=

= =-F ΦΩ Φ ΦΦ (2-3)

where 1 2[ , ,..., ]n=Φ Φ Φ Φ is the mode shape matrix, iΦ is the ith mode shape,

2( )idiag= Ω is the diagonal matrix containing the eigen-frequencies, and m is the

number of modes. The damage location can be determined by comparing the

damaged flexibility to the undamaged flexibility. A merit of the method is that

damage can be estimated from a few of the lower vibration modes which can be

easily measured. That is due to the fact that the flexibility of a structure converges

rapidly with increasing frequency, and hence, a good estimation of the flexibility

matrix can be obtained from only a few lower modes. However, mode shapes are

required to be mass-normalized that requires an accurate mass matrix from a

numerical model. Another drawback of the method is that the change in flexibility

matrix itself does not provide the information of damage extent.

Zhao and DeWolf (1999) compared the sensitivities of natural frequencies,

mode shapes and modal flexibility to structural stiffness reduction for a five degree

spring-mass system. It was found that modal flexibility (which is a function of both

natural frequencies and mode shapes) is more sensitive to damage than either natural

frequencies or mode shapes.

Ni et al. (2008) applied the flexibility method to detect damage in the Ting

Kau cable stayed Bridge. They defined the relative flexibility change (RFC) index to

identify damage location:

u d

ii ii

i u

ii

F FRFC

F

−= (2-4)

where iRFC is the relative flexibility change at the ith DOF; u

iiF and d

iiF are the

diagonal component of the flexibilities matrix before and after damage, respectively.

It was found that the RFC performs well for locating single damage cases but may

Page 44: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 16

© 2017 Khac-Duy Nguyen Page 16

provide false-positive identification for multiple-damage cases. Also, the RFC index

performance is significantly reduced by introducing ambient conditions.

Shih (2009) combined the modal flexibility change and a modal strain

energy-based damage index to detect damaged elements in truss bridges using a few

lower modes. The method was found effective to locate single and multiple damage

cases. However, the method was only verified on a numerical truss bridge, in which

no systematic and measurement errors were considered. Also, simultaneous use of

two methods to assess damage in same elements may lead to conflict in the damage

decision and can result in more false-positive or false-negative detections.

Chen and Nagarajaiah (2007) developed a forward method based on modal

flexibility correlation. Damage is identified by minimizing the difference between an

analytical flexibility matrix and the measured flexibility matrix using sensitivity

analysis and Gauss-Newton optimisation algorithm. The method was verified by

simulation examples on a three-bay cantilever truss structure and a six-bay simply-

supported truss structure. It was found that the method is successful to detect damaged

elements, even if the identified modes are corrupted by light noise (1% for natural

frequencies and 3% for mode shapes). However, the authors noted that the accuracy of

the method would be affected by high noise level of the identified modes.

Koo et al. (2010) proposed another forward method for shear buildings by

using deflections obtained from modal flexibility. The method was found to be

successful to estimate the location and extent of damage by incorporating with an FE

model and an optimisation process. However, the feasibility of the method was

verified only by a numerical study and limited to shear buildings.

2.3.3 Mode Shape Curvature-based Methods

Mode shape curvature is the second derivative of mode shape, and therefore

it has a direct relationship with bending strain mode shape in beams, plates and

shells. Curvature-based methods are capable of locating damage but they are only

Page 45: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 17

© 2017 Khac-Duy Nguyen Page 17

suitable for flexural members. Pandey et al. (1991) first proposed the use of mode

shape curvature to locate the damage for a cantilever beam and a simply-supported

beam. Mode shape curvature can be computed from displacement mode shapes by a

central difference approximation as:

, 1 , , 1"

, 2

2i j i j i j

i j

jl

+ − − + = (2-5)

where ,i j is the component at node j of the ith displacement mode shape, and

jl is

the distance between two nodes. They demonstrated that absolute changes in mode

shape curvatures are useful to locate damage, and the intensity of damage is

proportional to the changes in mode shape curvatures.

Abdel Wahab and De Roeck (1999) applied the method of Pandey et al.

(1991) with a small modification making use of all measured modes to detect

damage in the pre-stressed concrete bridge Z24. The curvature damage factor (CDF)

was proposed to locate damage as follows:

" *"

1

1 m

j ij ij

i

CDFm =

= − (2-6)

where m is the total number of modes to be considered; "

ij and *"

ij is the

component at node j of the ith mode shape curvature of the intact structure and that of

the damaged structure, respectively. They found that when more than one fault exists

in the structure, it is impossible to locate damage by using only one single mode, but

the combination of all modes (e.g., CDF) gives a clear identification of these

locations.

Ni et al. (2000) developed a damage index using the mode shape curvature

change rate for damage detection. The mode shape curvature change rate for the ith

mode is calculated as:

Page 46: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 18

© 2017 Khac-Duy Nguyen Page 18

*" "

*" "( )

ij ij

i

ij ij

j

Index j −

= −

(2-7)

Then, a Z-value of mode shape curvature change rate for the ith mode is

obtained as:

( )

( )( )

i ii

i

index indexZ j

index

−=

(2-8)

where and represent the mean and the standard deviation of the index vector.

Based on the Neyman-Pearson criterion, a damage is identified at location j if

( ) 3iZ j . Numerical damage identification results for the Tsing Ma Bridge showed

that the Z-value diagrams obtained from longitudinal modal curvatures can correctly

indicate damaged segments of deck. However, several false positive detections were

also observed using the Z-value indicator. Also, the method was only verified with

single damage cases at noise-free condition.

2.3.4 Modal Strain Energy-based Methods

Modal strain energy (MSE) is known as a damage sensitivity parameter and

is widely used to formulate damage detection methods. The first damage detection

method based on change in MSE was developed by Stubbs et al. (1992). The ith MSE

of an arbitrary structure can be obtained as follows:

T

i i iK =Φ KΦ (2-9)

where K is the system stiffness matrix. The method relies on the assumption that the

change in elemental fraction of modal strain energy of the ith mode before and after

damage is negligible. The idea behind this assumption is that the eigenvalues of the

structure can be assumed to be linear to damage (Messina et al. 1998). It has been

reported by the authors that this assumption is reasonable for small damage but gives

significant error for large damage. . A damage index j of the ith element is obtained

as follows:

Page 47: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 19

© 2017 Khac-Duy Nguyen Page 19

* *

0

1

**

0

1

mT

i j i ij i

j mTji j i i

i

KE

EK

=

=

= =

Φ K Φ

Φ K Φ

(2-10)

where jE is the parameter representing material stiffness properties of the jth

element; 0jK is the geometric quantities of the stiffness matrix of the jth element; m

is the number of modes; the asterisk (*) denotes the damage state.

Kim and Stubbs (2002) modified the original damage index to overcome the

singularity problem associated with zero-modal strain energy of elements at nodal

points of a mode. The modified damage index is as follows:

* * * *

0 0

1 1

**

0 0

1 1

m nT T

i j i i k i ij i k

j m nT Tji j i i k i i

i k

KE

EK

= =

= =

+

= =

+

Φ K Φ Φ K Φ

Φ K Φ Φ K Φ

(2-11)

where n is the number of elements. They found that the modified damage index can

significantly reduce false-positive detection compared with the original one.

Kim and Stubbs (2002) also proposed an improved damage index utilizing

changes in both natural frequency and modal strain energy. The improved damage

index is calculated as follows:

* *

0

1

*

0

1

/

nT

i j ij i

j nTj

i i i j i

i

E

EK g nd

=

=

= =

+

Φ K Φ

Φ K Φ

(2-12)

where 2 2( / )i i ig ω ω= is the relative change in the ith eigenvalue; and nd is the

number of damage in the structure. It was found that damage severity is predicted

more accurately by using the improved damage index than by using the original and

the modified ones. However, the improved damage index method has several

limitations as: the number of damage locations must be known, these locations

Page 48: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 20

© 2017 Khac-Duy Nguyen Page 20

should be symmetric, and damage extents at these locations should be equivalent.

The performance of the method was actually proved only for this kind of damage.

Shi et al. (1998) used elemental modal strain energy change ratio as a

damage indicator. They found that this parameter is an efficient indicator in locating

structural damage. Shi et al. (2000a) further expand the method to quantify damage

extent by analyzing the sensitivity to local damage. They evaluated the method on an

FEM model of a fixed-supported beam and on a two-story frame structure model. It

was found that damage quantification is successful to quantify single damage with

7% noise but not good for multiple damage under the same noise level. Also, they

noted that the accuracy of damage extent estimation significantly relies on the

number of numerical modes used and modeling accuracy for higher modes.

Hu et al. (2006) developed a damage detection method based on cross modal

strain energy. Damage extent is calculated by a least square approach using both

changes in natural frequencies and mode shapes. The method was verified on a FEM

of a five story frame structure. It was observed that the method is able to detect small

damage (5% stiffness reduction) under mild noise environment. However, its

accuracy is significantly affected by high-noise measurements. Also, the method

faces with singularity problem which requires proper selections of modes.

Shih et al. (2009) studied on the application of MSE-based damage index

methods and found that their performance on damage quantification is only feasible

for single damage cases. Moreover, it was reported that the relatively small damage

is hard to be detected by these indices when multiple damage is introduce

(Wahalathantri et al. 2010).

Wang et al. (2012) proposed a new MDLAC using modal strain energy

change for damage detection. A mode selection algorithm was also proposed to

select the modes which are the most potential to indicate damage. The correlation

coefficient is calculated as follows:

Page 49: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 21

© 2017 Khac-Duy Nguyen Page 21

2

. ( )( )

. ( ). ( )

T

MSE

T TMDLAC

=

MSE δMSE δDδD

MSE MSE δMSE δD δMSE δD (2-13)

where 1 2[ , ,..., ,..., ]T

i m=MSE MSE MSE MSE MSE is the elemental modal strain

energy vector, iMSE is the elemental modal strain energy vector for the selected

mode ith, and m is the number of selected modes. The method was successful to

detect single damage on a lab-scale complicated steel truss. However, high degree of

false-positive detection was also observed in the damage detection result. Also, as

numerical mode shapes of many sampled FE models are calculated, a huge

computation resource must be used. Besides, this method relies much on the

accuracy of the established FE model compared to the real structure.

2.4 SIGNAL-BASED DAMAGE IDENTIFICATION METHODS

Different from modal-based damage detection methods that need the

extraction of modal information from measured signals, signal-based methods

directly use experimental signals or their features to determine damage information.

Sohn et al. (2000) developed an autoregressive (AR) model of time history

responses for damage detection purposes. In the damage detection procedure, time

series are compressed using principal component analysis (PCA) to reduce their

dimension prior to be used to construct the AR model. AR coefficients which are

considered as damage-sensitive features are estimated from smaller windows of the

compressed time signals. The multidimensional space AR coefficients are then

projected into 1D space vector using Bayes’ theorem since the sensitivities of the AR

coefficients to damage are different each other. The occurrence of damage is realized

through an outlier analysis known as X-bar control chart of the projected AR

coefficients. Feasibility of the method was verified by an experiment on concrete

columns. The occurrence of damage was successfully detected and false-positive

indication of damage was minimized.

Page 50: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 22

© 2017 Khac-Duy Nguyen Page 22

Sohn and Farrar (2001) extended the study of Sohn et al. (2000) for damage

location problems using a two-stage prediction model combining AR and

autoregressive with exogenous inputs (ARX) models. Spatial time series are first

used to construct the AR models. The errors between the measurements and the

predictions by the AR models are assumed to be mainly caused by the unknown

external inputs, and therefore, can be predicted by another AR models, so-called

ARX. The final errors between measurements and the predictions by the ARX

models are considered as the damage sensitive feature. The ratio of the final error in

a damage state to that in the undamaged state is used as a damage locating index. It

was found that the method is promising for automated continuous SHM systems

since it is simple and does not require much interaction with users.

Liu et al. (2009) developed a decentralized damage detection method called

ACF-CCF using the autocorrelation function (ACF) of individual sensors and the

cross-correlation function (CCF) of designed node pairs. The occurrence of damage

is realized by the change in ACF. Once damage is alerted, the location of damage can

be determined as at the region of the node pair on which the change in CCF is

observed. It is found that the method can accurately detect damage regions with

small degree of false-positive detection. From experimental results, Jayawardhana et

al. (2011) demonstrated that the ACF-CCF method is a better method compared with

the AR-ARX method regarding time consuming and damage detection accuracy.

Jayawardhana et al. (2013) applied a noise filtering technique, named discrete-

time Wiener filter, for damage alert and location. The idea of the Wiener filter-based

method is that the error obtained after filtering the signal at a damaged state is different

from that at the undamaged state. The CCF of the error is also applied to locate

damage, as similar with the means presented by Liu et al. (2009). It was found that the

method is effective to realize damage occurrence as well as to locate damaged regions

at noise-presented condition. However, the method requires the same operational and

environmental conditions before and after a damage episode.

Page 51: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 23

© 2017 Khac-Duy Nguyen Page 23

Wavelet transform-based methods are also effective signal based damage

detection methods. Wavelet transforms (WTs) are time-frequency transformation

tools based on windowing techniques with various time intervals. The tools can

simultaneously perform low frequency responses with high resolution using large

windows, and high frequency responses with low resolution using small windows.

Compared to the short-time Fourier Transform (STFT), WTs can provide more

accurately the location of a transient signal (observed in the high frequency diagram)

while the low frequency response is also obtained with equivalent accuracy. Hou et

al. (2000) showed that location of damage can be detected by spikes in the details of

the wavelet transform of a response data. Fan and Qiao (2009) applied a 2-D

continuous wavelet transform (CWT) on mode shapes for damage detection in plate-

type structures. It was found that the method is superior in noise immunity and

robust under limited sensor data.

2.5 INCOPORATING SOFT COMPUTING APPROACHES FOR DAMAGE IDENTIFICATION

In order to deal with more complicated damage situations in more complex

structures, it is essential to incorporate the existing damage algorithms with powerful

computation tools. Soft computing approaches can provide effective computation to

solve damage detection problems. The idea of soft computing was initiated by Zadeh

(1994). Different from hard computing, the soft computing is tolerance of

imprecision, uncertainty, partial truth and approximation. It aims at achieving close

resemblance with human like decision making. Soft computing is used when there is

a lack of information about a problem itself. The followings are several soft

computing approaches used for solving damage detection problems.

2.5.1 Damage Identification incorporating Evolutionary Computation

Evolutionary computation is a family of optimization algorithms inspired by

biological evolution. The evolutionary computation techniques include genetic

algorithm (GA), particle swarm optimisation (PSO), harmony search (HS), cuckoo

Page 52: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 24

© 2017 Khac-Duy Nguyen Page 24

search (CS), etc. Evolution computation techniques can be used to identify structural

damage by minimising the difference between the changes in experimental modal

parameters and those of a theoretical model. The following sections will focus on

applications of the evolutionary computation techniques on damage identification.

2.5.1.1 Genetic Algorithm

Genetic algorithm (GA) is one of the most widely used and powerful

optimisation tools for damage detection problems. The method is based on the

mechanism of biological evolution by the repetitive process of encoding, selection,

crossover and mutation (Goldberg 1989). In the method, a population of a structural

property such as structural stiffness is established for damaged structures. Each

member of the population is encoded into a binary string or a real number.

Subsequent generations are generated from those members based on the principle

“survival of the fittest”. Different from traditional optimisation techniques, GA

evaluates many solutions simultaneously, that potentially avoid convergence to a

non-global optimum.

Friswell et al. (1998) presented a combined genetic and sensitivity algorithm

for damage detection. In order to reduce the effect of systematic error, changes in

frequency from the undamaged to the damaged structure is considered instead of

natural frequency of the damaged structure. The GA is used to locate damage by

assuming that damage occurs at a single location and introducing into the objective

function a term considering other damage locations. The sensitivity analysis is then

used to estimate damage extent of the identified damaged elements. The method was

successful to locate damage for a numerical cantilever beam and an experimental

cantilever plate.

Hao and Xia (2002) investigated the performance of several damage objective

functions using three criteria, which are change in natural frequency, change in mode

shape and the combination of the two. They found that using change in natural

frequencies provides better damage prediction results than using change in mode

shapes. It was also observed that the performance of damage detection by combining

Page 53: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 25

© 2017 Khac-Duy Nguyen Page 25

two parameters is significantly affected by the relative weight of mode shape to

natural frequency.

Kim et al. (2007) examined the feasibility of using modal strain energy for

updating damage parameters using GA. They demonstrated that neither mode shape

nor modal strain energy can detect locations of saw cuts in a free-free beam model.

Also it has been reported that the combination of natural frequency and modal strain

energy is the most effective parameter for damage parameter updating.

Gomes and Silva (2008) compared GA-based and modal sensitivity-based

method in structural damage detection. They found that damaged members are

successfully located by both the modal sensitivity and GA with equivalent degrees of

accuracy. Regarding damage extent prediction, while the sensitivity-based method

has limitation on dealing with large amount of damage due to its assumptions and

simplification, the GA-based method which does not use such simplifications cannot

correctly converge to the actual damage extent.

Wang (2012) proposed a multi-layer genetic algorithm (ML-GA) method

using correlation of modal strain energy vector as the objective function. The method

is developed to overcome ill-conditioned problems that happen when the number of

damage parameters is very large. In the method, the damage parameter updating

process is divided into multiple layers. In the first layer, the damage parameters are

categorized into major groups and the optimisation is done for each group. In the

subsequent layers, the optimisation is done for a larger group with the starting point

inherited from the previous layers. The process ends up at the final layer where one

group includes all damage parameters. The method was successful in identifying the

damaged member of a complicated truss bridge model with significant reduction of

computation cost. However, high degree of false-positive detection was still

observed. Also, the damage extent prediction needs to be improved.

Page 54: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 26

© 2017 Khac-Duy Nguyen Page 26

2.5.1.2 Other Evolutionary Computation Methods

Kennedy and Eberhart (1995) developed a population-based global

optimisation technique, called Particle Swarm Optimisation (PSO). PSO is loosely

modeled on the basis of social behavior, such as bird flocking or fish schooling. The

technique has many similarities with GA such as the concepts of stochastic process,

crossover operation and fitness. However, instead of using genetic operators, the

individuals in a population are generated by cooperation and competition. PSO is

flying potential solution through hyperspace, accelerating toward “better” solutions.

Kang et al. (2012) attempted to apply PSO for solving structural damage detection

problems. The method was successful to locate damage and estimate damage extent

for a simply supported beam and a truss structure, even at 10% noise of mode shape

measurement. Seyedpoor (2012) proposed a two stage damage detection method

using modal strain energy damage index for locating damage and PSO for damage

extent estimation. The method showed the high efficiency on identifying the location

and extent of multiple structural damages for beams and truss structures.

Geem et al. (2001) developed a music-based meta-heuristic optimisation

algorithm, named Harmony Search (HS). It is inspired by the improvisation process

of musicians that searches for a perfect state of harmony. The process starts with an

initial random harmony memory which comprises of many harmonies in the form of

vectors. A new harmony is improvised from the harmony memory with a harmony

memory considering rate, together with a pitch adjusting process. That harmony will

replace the minimum harmony from the harmony memory if it is better than the

minimum one. Similar to GA, HS algorithm can solve continuous variable problems

as well as discrete variable problems. Differently from GA that considers only two

parent strings to produce new strings in the next generation, HS makes a new vector

after considering all existing vectors. Miguel et al. (2012) applied the HS algorithm

to structural damage detection problems. The HS algorithm was examined for three

criteria which are frequency and mode shape changes, dynamic residual force vector,

Page 55: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 27

© 2017 Khac-Duy Nguyen Page 27

modal flexibility change. It was found that damage location and damage extent of a

numerical cantilever beam is identified correctly even in noise condition of up to

5%.

Cuckoo Search (CS) is a promising evolutionary optimisation algorithm

recently developed by Yang and Deb (2009). The algorithm is inspired by the special

lifestyle of some cuckoo species that lay their eggs in the nests of other host birds of

other species. The reproduction procedure is based on the obligate brood parasitism,

which means the cuckoo eggs are not detected by the host birds and can become

mature cuckoos. In the algorithm, each egg in a nest represents a solution, and a

cuckoo egg represents a new solution. CS aims at replacing a not-so-good solution in

the nests by using the new potentially better solutions (cuckoo eggs). Hosseinzadeh

et al. (2014) attempted to use the CS algorithm for detecting damage in several

structure types such as beams, truss bridges and shear buildings. The results showed

that CS is an effective, robust and speedy optimisation method for structural damage

problems.

There has still been an argument on which algorithm is the best among GA,

PSO, CS and HS. It is very hard to make a comprehensive comparison as these

algorithms used different solver parameters; and for each algorithm, different

settings of solver parameters give different performances. Particularly for the

damage identification problem, it is observed that GA was the most widely used

technique and has also demonstrated its effectiveness for a variety of structures as

well as damage.

2.5.2 Damage Identification using Artificial Neural Networks

Artificial neural networks (ANNs) are computational models inspired by the

structure and functions of biological neural networks. An ANN comprised of a large

number of highly connected simple processing units, so-called neurons (Wu et al.

1992). The strength of the connections between the neurons is represented by

weights. ANNs are capable of machine learning and pattern recognition. One of the

powerful characteristics of ANNs is the capability of modeling non-linear

Page 56: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 28

© 2017 Khac-Duy Nguyen Page 28

relationships, and therefore, they can produce correct or nearly correct outputs in the

presence of incomplete inputs or in the presence of noise (Balageas et al. 2006,

Dackermann 2010).

In damage detection problems, ANNs are trained to recognize the structural

response features (frequencies, mode shapes, frequency response, etc.) of an

undamaged structure as well as those of the structure sustaining damage. Wu et al.

(1992) might be the pioneers introducing ANNs in structural damage detection. They

used Fourier spectrum portions as inputs of a single-layer perceptron neural network

and found that the ANN are capable of identifying damaged members and the extent

of the damage from patterns in the frequency response of the structure.

Pandey and Barai (1995) adopted a multi-layer perceptron ANN to identify

damage in a truss bridge. They concluded that the performance of the network with

two hidden layers is better than that with one single layer. It was also demonstrated

that only a few measurements are needed to train the network for damage

identification.

Ko et al. (2000) applied two special kinds of ANNs which are auto-

associative neural network and probabilistic neural network for the detection of

damage occurrence and location in the Tsing Ma Bridge. It was found that the

occurrence and location of damage can be detected only in low noise conditions.

Bandara et al. (2014) proposed a damage detection method by combining

ANNs, principal component analysis (PCA) and frequency response functions

(FRFs). FRFs are used as inputs of a neural network. PCA is used to reduce the size

of the FRF data inputting into the neural network. Numerical results for a two-story

framed structure demonstrated that the method can deal with single and multiple

damage cases in noise levels up to 10%. It was also found that two hidden layers are

sufficient for a neural network to deal with damage identification problems.

Most of the studies showed the excellent performance of ANNs when dealing

Page 57: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 29

© 2017 Khac-Duy Nguyen Page 29

with non-linear and noise-infested damage identification problems. Also,

incorporating ANNs do not require physical relationship between damage and

measured features. However, there are two critical reasons that limit the application

of ANNs. Firstly, the techniques require a large amount of training data for that their

verification has only been conducted for small structures. Secondly, the techniques

require a very accurate numerical model for generating training data since damage

simulation on real structures is prohibited.

2.6 PRACTICAL ISSUES

2.6.1 Measurement Errors

In practice, measurement errors can be caused by errors in measurement

equipment (e.g., sensors, data acquisition devices), system synchronization errors,

and calculation errors associated with modal extraction techniques, etc. The errors

existing in the measured data limit the successful use of damage identification

methods (Friswell et al. 1997). For instance, existence of measurement noise may

state certain less pronounced damaged elements undetectable (false-negative

detection), while identifying some undamaged structural elements as damaged

(false-positive detection) (Farrar and Doebling 1998).

Another source of measurement error is the change in environmental

conditions temperature, humidity, wind effect and traffic effect (Aktan et al. 1994,

Salawu 1997). It has been noted that the change by about 5% might be required to be

able to detect the damage in structures (Salawu 1997). In order to increase the

accuracy of damage detection results, many researchers have attempted to

discriminate the changes in modal parameters due to environmental effects from

those due to damage effect. Ni et al. (2005) modelled temperature effects on modal

frequencies of the Ting Kau Bridge using long-term structural health monitoring

data. The support vector machine (SVM) technique was applied to quantify the

effect of temperature on modal frequencies. It shows that the SVM models exhibit

good capabilities for mapping between the temperature and modal frequencies. Kim

Page 58: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 30

© 2017 Khac-Duy Nguyen Page 30

et al. (2003b, 2007) presented vibration-based damage monitoring scheme to give

warming of damage occurrence, damage location and damage severity under

temperature variation conditions using a pattern recognition technique. Peeters and

De Roeck (2001) utilized an ARX model to estimate the effect of temperature

change in natural frequencies and shown the possibility of damage identification

under temperature variation conditions. Cross et al. (2013) attempted to estimate the

effects of temperature, traffic load and wind speed to natural frequencies of the

Tamar Bridge. It was found that the model was accurate for the first mode but less

accurate for higher modes. Most of the previous studies showed that the fluctuation

in natural frequencies after compensated with the change in environmental factors

can be considered as random errors.

Effect of measurement error in damage identification has been studied by

many researchers. Some researchers evaluated measurement noise effect using

deterministic analysis (Shi et al. 2000, Ren and De Roeck 2002). However, this kind

of analysis is not very reliable as only one noised dataset is considered, and different

dataset will give different results. Some other researchers used statistical analysis to

evaluate noise effect (Xia et al. 2002; Xia and Hong, 2003). It has been shown that

the presence of noise reduces the detection probability of actual damage while

increases the probability of false-positive detection. An et al. (2006) suggested a

60%-threshold for detection probability to discriminate the damaged elements. This

threshold has been found appropriate to avoid both false negative and false positive

elements.

2.6.2 Modelling Errors

Many damage identification methods rely on the finite element (FE) model.

However, in practice, it is very hard to obtain an accurate FE model due to the

uncertainties in structural material properties, structural geometric properties,

boundary conditions, structural types, etc. Hence, the damage identification methods

will have great difficulty in distinguishing between the actual damage sites and false

Page 59: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 31

© 2017 Khac-Duy Nguyen Page 31

detection. One possible solution is to update the FE model of the structure to produce

a reliable model (Friswell and Mottershead 1995). Obviously, the quality of the

damage identification results is critically dependent upon the degree of matching

between the FE model and the actual model.

One possible solution is to update the FE model of the structure to produce a

reliable model. However, it was found that the difference between the actual modal

parameters and the updated ones were still significant, especially for large scale

structures. For example, errors of up to 11% in natural frequencies were observed for

the FE model of the Kap Shui Mun Bridge located in Hong Kong after model

updating (Zhang et al. 2000). Also, the updated FE model of the Saftu Link cable-

stayed bridge in Singapore had significant errors in natural frequencies of up to 9%

(Brownjohn and Xia 2000). Moreover, it is worth noting that the number of possible

structural parameters is significantly larger than the number of measured modes.

Therefore, the update of modal parameters does not guarantee the better FE model.

2.6.3 Ill-Posed Problem

The damage identification problem is often ill-posed due to calculation errors

or other uncertainties, which leads to non-uniqueness of the solutions of damage

location and severity. Salawu (1997) reported that the damage identification is only

reliable for elements with high strain energy since only very small change in modal

parameters will be a result of a very large change in structural stiffness of low-strain-

energy elements. The accuracy of damage prediction is higher for the damage

occurring at sections of high modal strain amplitude than for the one at sections of

low modal strain amplitude (Salane and Baldwin 1990). Hsu and Loh (2006)

conducted a damage identification study for a frame structure and reported about

abnormal results at the elements with MSE close to zero. In order to avoid these

false errors, they suggested a criterion for ignoring the elements with low level of

MSE. In another study for beam structures, Wahalathantri et al. (2012) showed some

false errors in the elements close to nodal points. They suggested multiplying the

Page 60: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 32

© 2017 Khac-Duy Nguyen Page 32

damage results by a modification function as a form of normalized modal strain

energy curve.

2.7 SUMMARY OF LITERATURE REVIEW

From the review of literature, the following summary has been drawn:

1) Both natural frequency and mode shape represent information of

structural characteristics. While natural frequency contains global

structural information, mode shape contains spatial structural

information. Use of natural frequencies has limitation on locating

damage but it can be generally measured with higher degree of accuracy.

Use of mode shapes is very suitable for damage identification but the

estimation of mode shapes is more sensitive to noise.

2) Modal strain energy is found to be more sensitive to damage than other

spatial modal parameters such as mode shape, modal curvature and

modal flexibility, but it is more affected by noise and incomplete data.

3) It has been shown that using changes in both natural frequency and mode

shape is more effective for damage identification than using only mode

shape or natural frequency. Use of both parameters would give better

results in case of measurement noise (mainly associated with

experimental mode shapes) and modelling errors (mainly associated with

analytical mode shapes).

4) Damage index-based methods are practical since they use only measured

modal parameters and simple computation to identify damage. However,

these methods are potential to false-positive as well as false-negative

detections.

Page 61: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 33

© 2017 Khac-Duy Nguyen Page 33

5) Correlation-based methods are found to be very effective to identify

damage in single and multiple damage cases. However, sensitivity

analysis of spatial modal parameters relies much on the matching

between numerical mode shapes and experimental ones, and mass-

normalized mode shapes are required. Therefore, errors in analytical

mode shapes may significantly affect the accuracy of the damage

detection methods based on sensitivity of modal strain energy.

6) It is shown that signal-based methods are simple and straightforward, but

cannot provide information of damage extents. Therefore, those methods

are suitable for online SHM and can be used as the first step in the

damage identification processes.

7) Using evolutionary optimisation techniques is an excellent way to solve

damage identification problem. Amongst the optimisation methods, GA

is the most widely used tool for damage detection because of its ease and

powerful performance. However, there are several problems that need to

be overcome. First, the computational process takes a long time to

converge. Second, if more elements are included in the damage search,

more local optima results associated with false detection can be

observed. Third, the selection of modal parameters for the objective

function may affect the accuracy of the damage detection.

8) ANNs is found to be excellent to solve non-linear and noise-infested

damage identification problems. Despite this, their practicality is very

limited since they require a large amount of training data and good

numerical models that accurately reflect the dynamic properties of the

real structures.

Page 62: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 2: Literature Review Page 34

© 2017 Khac-Duy Nguyen Page 34

9) Many existing damage identification methods have shown their

capability to cope with level 2 and level 3 of the damage identification

problem. However, these methods have mostly been validated with

numerical models or simple experimental structures. Only few studies

have been conducted for complex structures.

10) It has been shown that measurement and modelling uncertainties

significantly affect damage identification results. Also, calculation error

associated with low-strain-energy elements is another source of

uncertainty in damage identification.

Based on the above literature review, this research explores two effective

damage identification methods based on a new vibration parameter formulated from

modal strain energy and natural frequency. The correlation approach is selected to

formulate the damage identification problem. Also, genetic algorithm (GA) is

selected as an optimisation tool to provide the optimal solution of damage state. The

next chapter will present the development of a damage identification method using

geometric modal strain energy-eigenvalue ratio via correlation approach.

Page 63: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 35

© 2017 Khac-Duy Nguyen Page 35

3Chapter 3: Geometric Modal Strain Energy-

Eigenvalue Ratio (GMSEE) Correlation Method

This chapter describes the development of a correlation-based method using

geometric modal strain energy-eigenvalue ratio (GMSEE). The method utilizes

measured modal parameters (i.e., natural frequency and mode shape) and geometric

information of structural elements such as length and/or thickness depending upon

structure types. This method is able to identify damage location and to estimate

damage extent. The method does not requires modal information obtained from

numerical model; therefore, false detection caused by differences in numerical model

and experimental model can be reduced. This chapter summarizes the theoretical

development, numerical verification, and experimental validation for simple

laboratory models.

3.1 CONVENTIONAL CORRELATION-BASED DAMAGE IDENTIFICATION METHODS

3.1.1 Conventional Correlation-based Damage Identification Methods

Messina et al. (1998) developed a sensitivity- and statistical-based criterion

called multiple damage location assurance criterion (MDLAC) using change in

natural frequency to locate damage as well as to estimate the correlative damage

extent. With similar forms, Shi et al. (2000b) and Wang et al. (2012) employed the

formulation to detect damage using mode shape change and elemental modal strain

energy (MSE) change, respectively. The general formula of the criterion is as

follows:

( ) ( )

2T

Z

T T

. ( )MDLAC ( )

. . ( ) . ( )=

ΔZ δZ δDδD

ΔZ ΔZ ΔZ δD ΔZ δD (3-1)

Page 64: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 36

© 2017 Khac-Duy Nguyen Page 36

where Z represents for a modal feature such as natural frequency, mode shape or

MSE; ΔZ is the measured modal feature change vector; δZ is the analytical modal

feature change vector for a known relative damage extentδD . The damage sites can

be identified by searching the largest MDLAC value using an optimisation

algorithm. The following modal features can be used in Eq. (1) for identifying

damage.

Natural Frequency Change

If natural frequency is used, δZ can be calculated based on the following

sensitivity equation (Messina et al. 1998):

2

1.

8

T

i i k i

T

k i i i

f

D f

=

Φ K Φ

Φ MΦ (3-2)

where if is the analytical frequency change of the ith mode for a known damage size

kD at location k; iΦ is the ith mode shape; kK is the kth elemental stiffness matrix;

and M is the system mass matrix. For this method, the sizes of δZ and ΔZ are

equal to the number of measured modes.

Mode Shape Change (MSC)

If mode shape is used, the sensitivity of the ith mode shape to a known

damage size kD at element k is given by (Shi et al. 2000b):

1

( )Tn

i r k ir

rk r i

r iD =

= −

Φ Φ K ΦΦ (3-3)

where iΦ is the ith analytical mode shape change for a damage kD ; i is the ith

eigenvalue; and n is the number of numerical modes used in the calculation (n

should be equal to the total number of degrees-of-freedom (DOFs) of the system).

For the MSC correlation method, the sizes of δZ and ΔZ are equal to the product of

the number of measured modes and the number of degrees of freedom.

Page 65: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 37

© 2017 Khac-Duy Nguyen Page 37

Modal Strain Energy Change (MSEC)

If MSE is used, the sensitivity equation can be expressed as follows (Shi et

al. 2000a)

T

T

1

2 ( )n

ij r k ii j r

k r ir

Ur i

D =

= −

Φ K ΦΦ K Φ (3-4)

where ijU is the analytical MSE change of the jth element for the ith mode regarding a

damage kD at element k; and n is the number of numerical modes used in the

calculation. For the MSEC correlation method, the sizes of δZ and ΔZ are equal to

the product of the number of measured modes and the number of elements.

3.2 THEORETICAL DEVELOPMENT OF GMSEE CORRELATION METHOD

Despite their effectiveness on damage identification, the conventional

correlation-based methods still have some limitations as highlighted as follows. The

frequency-based correlation method is found effective for single damage cases, but

its accuracy is limited for multiple damage cases and its requirement on the

availability of a sufficient set of natural frequencies. On the other hand, spatial

modal-based correlation methods using mode shape or modal strain energy are found

more effective than the frequency-based method for multiple damage cases.

However, the accuracy of these methods relies very much on the number of

analytical mode shapes used and the degree of matching between numerical models

and experimental models which is not generally guaranteed for real structures. In

order to overcome the above limitations of the existing methods, a novel modal

vector correlation method is developed using measured modal parameters and

geometric information of structures.

3.2.1 Sensitivity Analysis of GMSEE

For a linear structure, the fractions of modal strain energies at undamaged

and damaged states are given as follows, respectively (Kim and Stubbs 1995):

Page 66: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 38

© 2017 Khac-Duy Nguyen Page 38

ij

ij

i

UF

U= (3-5)

*d

d

ij ij

ij

i i

U UF

U U

+=

+ (3-6)

where ijF and *

ijF are respectively the fraction of MSE of the jth element for the ith

mode at undamaged and damaged states; Tij i j iU =Φ K Φ is the MSE of the jth

element for the ith mode at undamaged state; Ti i iU =Φ KΦ is the total MSE for the

ith mode at undamaged state; iΦ is the mode shape vector of the ith mode; jK is the jth

elemental stiffness matrix; and K is the system stiffness matrix; d ijU and d iU are

the changes in the jth elemental MSE and the total MSE for the ith mode.

It has been reported that the fractional MSE can be assumed to be unchanged

after damage ( *ij ijF F ) (Kim an Stubbs, 1995, Stubbs and Osegueda 1990). Thus,

Eqs. (3-5) and (3-6) can be combined to the following equation:

d

d

ij ij ij

i i i

U U U

U U U

+=

+ (3-7)

By expanding and rearranging Eq. (3-7), the following expression can be

obtained:

d

d 0iij ij

i

UU U

U− = (3-8)

By neglecting change of mass after damage, the term d /i iU U can be

expressed by the change in eigenvalue (Kim and Stubbs 2002) as follows:

d di i

i i

U

U

= (3-9)

where 2(2 )i if = is the eigenvalue of the ith mode, and d i is the change in the ith

eigenvalue. By substituting Eq. (3-9) into Eq. (3-8), we obtain:

Page 67: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 39

© 2017 Khac-Duy Nguyen Page 39

d

d 0iij ij

i

U U

− = (3-10)

According to Kim and Stubbs (1995), by taking the rigidity term out of the

elemental stiffness matrix, the elemental MSE at undamaged and damaged states can

be expressed in terms of elemental geometric MSE as follows:

ijij jU k U= (3-11)

* d ( d )( d )ij ijij ij ij j jU U U k k U U= + = + + (3-12)

where T0ij i j iU =Φ K Φ is the geometric MSE of the jth element for the ith mode at

undamaged state; jk is the stiffness constant of the jth element at undamaged state;

0jK contains only the geometric quantity of the jth elemental stiffness matrix; d jk

and d ijU are the change in stiffness constant of the jth element and the change in

geometric MSE of the jth element for the ith mode. Note that, the stiffness constant of

an element is the resistance of the element against external forces, which is

proportional to material properties (e.g., elastic modulus) and cross sectional

properties (e.g., 2nd moment of area for beam elements, cross-sectional area for truss

elements or plate thickness for plate elements). Examples of geometric quantity of

stiffness matrix for some element types are provided in Appendix-A. By substituting

Eq. (3-11) and (3-12) into Eq. (3-10), we obtain:

( )( ) dd d 0i

ij ij ij ijj j j j

i

k k U U k U k U

+ + − − = (3-13)

By expanding, rearranging and neglecting high order terms, Eq. (3-13) leads

to:

d

d diij ij ijj j j

i

U k U k U k

− = − (3-14)

By dividing two sides of Eq. (3-14) by i and jk , the following equation is

Page 68: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 40

© 2017 Khac-Duy Nguyen Page 40

obtained:

2

ddd ij ij jiij

i i ji

kU UU

k

− = − (3-15)

Equation (3-15) can be rewritten in term of change in ratio of geometric MSE

to eigenvalue (GMSEE) as follows:

T0

d d dij i j i

ij j j

i i

UG D D

= − = −

Φ K Φ

or

T0d

d

ijij i j i

j i i

G U

D = − = −

Φ K Φ (3-16)

where ijij iG U = is the GMSEE of the jth element and the ith mode; and

d d /j j jD k k= is the relative reduction of stiffness of element j.

3.2.2 Locating damage using GMSEE change vector

Following the principle of the correlation-based methods, the damage

identification problem can be transformed to an optimization problem searching for

the best correlation between the measured GMSEE change vector and the analytical

one. As an expansion of the Eq. (3-1), the MDLAC function for GMSEE is defined

as follows:

( ) ( )

2T

GMSEE

T T

Δ .δMDLAC (δ )

Δ .Δ . δ .δ=

G GD

G G G G (3-17)

where ΔG is the measured GMSEE change vector; and δG is the analytical

GMSEE change vector for a known damage vector δD . MDLAC values range from

0 to 1, indicating correlation level from no correlation to exact correlation between

the patterns of GMSEE changes. The damaged elements and their correlative damage

extents can be identified by searching the largest MDLAC value using an

Page 69: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 41

© 2017 Khac-Duy Nguyen Page 41

optimisation algorithm. If m modes are used, the measured and analytical GMSEE

change vectors are given by the following expressions:

...

Δ Δ

...

Δ

i

m

=

G

G G

G

(3-18)

1

...

...

i

m

=

δG

δG δG

δG

(3-19)

where Δ iG is the measured GMSEE change vector for the ith mode which can be

calculated directly from measured modal data and geometric stiffness matrix; δ iG is

the analytical GMSEE change vector for the ith mode and is calculated based on a

sensitivity matrix as follows:

1

1

2

2

d0 ... 0

d

d0 ... 0

dδ δ

... ... ... ...

d0 0 ...

d

i

i

i

in

n

GD

GD

GD

=

G D

or GMSEEδ δi i=G S D (3-20)

where GMSEEiS is the sub-sensitivity matrix of GMSEE for the ith mode; and n is the

number of structural elements. Values of the diagonal entries of the above matrix are

calculated by Eq. (3-16). For convenience, the analytical GMSEE change vector for

all measured modes described in Eq. (3-19) can be rewritten in the following

expression:

Page 70: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 42

© 2017 Khac-Duy Nguyen Page 42

GMSEE1

GMSEE2

GMSEE

δ δ...

m

=

S

SG D

S

or GMSEEδ δ=G S D (3-21)

where GMSEES is the sensitivity matrix of GMSEE for all measured modes.

3.2.3 Quantifying Damage

As δD obtained from maximizing MDLAC value described in equation (3-

17) is a correlative vector, it means different scales of δD will give the same value of

MDLAC. Therefore, the damage scaling coefficient, C, such that .δC D gives the

actual damage extent in percentage, must be obtained. The followings present two

algorithms used to calculate this coefficient.

3.2.3.1 Quantifying Damage using Natural Frequency Change

Conventionally, the damage scaling coefficient can be obtained using changes

in measured natural frequencies with the first-order approximation as described in

Messina et al. (1998). In this study, their equation is little modified for using all the

measured natural frequencies as follows:

f

Δ

[ .δ ]C =

f

S D (3-22)

where Δf is the measured frequency change vector; and fS is the sensitivity matrix

of natural frequency in which its entries can be calculated as follows:

T

T.

2

i j ii i

j i i

f f

D

=

Φ K Φ

Φ KΦ (3-23)

where if is the analytical frequency change of the ith mode for a known damage size

jD at element j.

Page 71: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 43

© 2017 Khac-Duy Nguyen Page 43

3.2.3.2 Quantifying Damage using GMSEE Change

Since GMSEE change is used for estimating damage location and correlative

damage extent, it would be more logical to use this parameter for damage extent

estimation. Based on the calculation of GMSEE sensitivity, the following equation

can be used for the prediction of the damage scaling coefficient, C:

GMSEEavg

Δ

[ .δ ]C =

G

S D (3-24)

where GMSEEavgS is the average sensitivity matrix obtained from the pre-damaged

sensitivity matrix GMSEEuS calculated with modal information at undamaged state, and

the post-damaged sensitivity matrix GMSEEdS calculated with modal information at

damaged state. It is worth noting that unlike the frequency sensitivity-based method,

the damage extent estimation method based on GMSEE sensitivity does not require

information of material and cross sectional properties which are generally obtained

with certain errors.

3.3 SUMMARY OF GMSEE CORRELATION DAMAGE IDENTIFICATION METHOD

Figure 3-1 illustrates the schematic of the proposed GMSEE correlation-

based damage identification method. Firstly, one set of vibration responses is

measured as a baseline (undamaged state) and another set is measured later to check

for its damage status (damaged state). Natural frequencies and mode shapes for each

state are extracted from the corresponding vibration response set. Secondly, a

damage detection model is established based on a numerical model (e.g., FEM,

Euler-Bernoulli beam, shear-beam, etc.) but including only necessary information

(e.g., element types and geometries) for the calculation of elemental geometric

stiffness matrices. The measured GMSEE change is then calculated based on the

experimental modal parameters and the elemental geometric stiffness matrices. The

sensitivity matrix of GMSEE is also calculated using the experimental modal

Page 72: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 44

© 2017 Khac-Duy Nguyen Page 44

parameters and the elemental geometric stiffness matrices, as described in equations

(3-16), (3-20) and (3-21). Subsequently, an optimisation process is run to find the

correlative elemental stiffness reduction vector which gives the best correlation

between the analytical GMSEE change vector and the measured one. Note that the

analytical GMSEE change vector is calculated using the sensitivity matrix

established before. Lastly, the damage scaling coefficient C is calculated based on

either equation (3-22) or equation (3-24), and the estimated damage extent is

obtained.

Compared to other correlation-based methods, the proposed GMSEE

correlation-based method has some advantages as follows: 1) the calculation of

measured and analytical GMSEE change vectors does not require information of

material and sectional properties of elements, making it more practical as well as

avoiding numerical errors; 2) mode shapes are not required to be mass-normalized

which also reduces the effect of numerical errors on damage identification; and 3)

the method does not use numerical modal information; therefore, false detection

caused by differences in numerical and experimental modal parameters is eliminated.

Figure 3-1. Schematic of GMSEE correlation-based damage identification method.

Page 73: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 45

© 2017 Khac-Duy Nguyen Page 45

3.4 IDENFICATION OF CORRELATIVE DAMAGE VECTOR USING GENETIC ALGORITHM

As stated in chapter 2.5.1.1, Genetic algorithm (GA) is one of the most

widely used and powerful optimisation tools for solving the damage identification

problems (Wang et al. 2012, Chou and Ghaboussi 2001, Hao and Xia 2002). It is

based on the mechanism of biological evolution by a repetitive process of

reproduction, crossover, mutation and selection (Goldberg 1989). In GA, a

population of candidate solutions is evolved toward better solutions. Each candidate

solution can be represented in a form of a string or chromosome. Selection is a

process of selecting a portion of the existing population to breed to a new generation.

A fitness-based process is employed to decide which individual solutions are

selected. The fitter solutions measured by a fitness function are typically selected.

Crossover is a process of taking parent solutions and producing a child solution from

them. Crossover can make a child solution with better fitness compared to its parents.

Mutation is a process of altering one or more gene values in a chromosome. Mutation

can change a candidate solution to a new one with better fitness.

The classic binary-coded GA transforms unknown variables to a binary string

(chromosome or representation). For the damage identification problem, we can

consider the damage extent in percentage and convert it to a binary number. It has

been reported that the binary-coded GA is efficient for finding the solutions.

However, it is not convenient to use as not only it requires the variables to be

encoded to a binary string but also it must decode the string into candidate solutions,

evaluate and return the resulting fitness back to the binary-coded string representing

the evaluated candidate solutions. Also, as the number of variables increase, the size

of the chromosome becomes very large and can lead to poor performance (Yi et al.

2009).

A more convenient encoding type, called real-coded GA, simply describes a

chromosome as a row of real values in which each value represents the candidate

solution of each variable. It does not require such mapping of variables-gene-

Page 74: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 46

© 2017 Khac-Duy Nguyen Page 46

candidate solutions. Moreover, as the size of the chromosome is the same as the size

of the solution vector, the real-coded GA is capable of searching a large solution

domain. This study adapted the real-coded GA as a search engine for the correlative

damage vector.

3.5 NUMERICAL VERIFICATION

A 2-D numerical truss model presented in Rahai et al. (2007), as shown in

figure 3-2, is used to evaluate the feasibility of the proposed method. The finite

element (FE) model of the truss consists of 25 bar elements of various cross

sectional areas, and 21 active degrees of freedom (DOFs). More details of the

structure can be found in the reference cited above. Damage in the structure is

simulated as a stiffness reduction of individual elements. As shown in Table 3-1,

three damage scenarios are considered with different locations of damage, number of

damaged elements and damage severities.

Figure 3-2. Two-dimensional truss bridge [adapted from Rahai et al. 2007].

Table 3-1. Damage scenarios for 2-D truss model.

Damage

Scenario Damaged elements Cross-sectional area reduction

Case 1 9 20%

Case 2 4

11

20%

30%

Case 3

7

8

10

20%

25%

30%

Page 75: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 47

© 2017 Khac-Duy Nguyen Page 47

3.5.1 Damage Identification with Noise-free Modal Data

Performance of the proposed GMSEE correlation-based method is compared

with the conventional correlation-based method using modal strain energy (MSE)

change (Wang et al. 2012). For the GMSEE correlation-based method, analytical and

measured GMSEE change vectors of the first 8 modes are calculated. Note that, the

sensitivity matrix of GMSEE is obtained using only the corresponding modes. For

the MSE correlation-based method, analytical and measured MSE change vectors of

the first 8 modes are also calculated. However, different from the GMSEE method,

the MSE sensitivity matrix is obtained by using 21 numerical modes, which are all

the modes of the FE model. This gives the best accuracy for the MSE sensitivity

estimation.

For each method, the correlative damage vector is determined by searching

the greatest MDLAC value using the genetic algorithm (GA). In this study, the GA

optimisation toolbox embedded in MATLAB software package (MATLAB 2012) is

utilized to solve the optimisation problem. The solver parameters are set as follows.

The number of variables is 25 corresponding to the total number of truss elements

The range of the variables is [-1; -1E-10] corresponding to the possible range of

damage extent. The population size should be set large enough in order to reach the

global optimum, but should not be very large as the convergence time will increase.

Herein the population size is set as 200 as of eight time of the number of dimensions

(i.e., 25). The crossover fraction rate does not need to be set very high due to that a

large population size has been defined. In this study, it is set as 0.5. The convergence

tolerance is used as the condition to stop the GA process. , and this parameter should

be small enough to avoid premature convergence. In this study, it is set as 1E-10 . As

this is a constrained optimisation problem, the adaptive feasible mutation function

integrated in the toolbox is used for generating mutated individuals.

Damage identification results by the two correlation-based methods are

illustrated in Figs. 3-3 to 3-5, in which the results of the GMSEE correlation method

Page 76: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 48

© 2017 Khac-Duy Nguyen Page 48

using the frequency-based quantification technique (using Eq. 3-22) and GMSEE-

based quantification technique (using Eq. 3-24) are separated. For the single damage

case (Case 1), excellent results are obtained by both correlation methods. As shown

in Fig 3-3, it can be seen that both methods predict very similar results with accurate

damage location and accurate damage level. Also, both quantification techniques

used in the GMSEE method give the same prediction of damage extent. For the

double damage case (Case 2), although the MSE correlation method is successful in

locating the actual damaged elements, some false indications of damage are

observed (Figure 3-4). Moreover, the damage extents of the actual damaged

elements are quite underestimated which is 9.4% for element 4 and 23.3% for

element 11. Compared to the MSE correlation method, the GMSEE correlation

method gives better prediction for this damage case. The proposed method predicts

very well the locations of damage with no false indications. Regarding damage

extent estimation, the GMSEE method with any of the two quantification techniques

gives better accuracy for the small damage in element 4, and comparable accuracy

for the damage in element 11. For the triple damage case (Case 3), both correlation

methods correctly predict the locations of damaged elements (Fig 3-5). It is found

that the damage extents predicted by the MSE method are little more accurate than

those obtained by the GMSEE method. Regarding false identification, although both

methods generate some small false indications and those obtained from the GMSEE

method slightly higher possibility of damage, their damage levels are negligible. It is

also observed that the two quantification techniques using the GMSEE method give

very identical results. From this comparison, the proposed GMSEE method shows its

high capability of identifying damage with less modeling effort. Also, it can be

concluded that the GMSEE-based quantification technique can be used as an

alternative way for damage extent estimation in correlation-based methods.

Page 77: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 49

© 2017 Khac-Duy Nguyen Page 49

Figure 3-3. Damage identification result for 2-D truss model: Case 1: D9 = 20%.

Figure 3-4. Damage identification result for 2-D truss model: Case 2: D4 = 20%,

D11 = 30%.

Figure 3-5. Damage identification result for 2-D truss model: Case 3: D7 = 20%,

D8 = 25%, D10 = 30%.

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt (%

)

MSE Method

GMSEE Method, Frequency-based Quantification

GMSEE Method, GMSEE-based Quantification

Actual Damage

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age

Exte

nt (%

)

MSE Method

GMSEE Method, Frequency-based Quantification

GMSEE Method, GMSEE-based Quantification

Actual Damage

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt (%

)

MSE Method

GMSEE Method, Frequency-based Quantification

GMSEE Method, GMSEE-based Quantification

Actual Damage

Page 78: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 50

© 2017 Khac-Duy Nguyen Page 50

3.5.2 Damage Identification with Measurement Noise

In practice, measurement noise is unavoidable, and therefore, its effect on

damage identification performance should be considered. In this section, the

performance of the GMSEE correlation method under noise condition is examined

and compared with the results obtained by the MSE correlation method.

It was reported that natural frequency is measured with much higher

precision than mode shape (Doebling et al. 1998). Therefore, in this study, three

noise levels of 2% (noise level 1), 5% (noise level 2) and 7% (noise level 3) are

considered for mode shapes, and the corresponding noise levels for natural

frequencies are 0.5%, 1% and 1.25%. It has been reported that these noise levels are

reasonable for mode shapes and natural frequencies (Shi et al. 2000a, Shi et al.

2000b). Noise-contaminated mode shape and noise-contaminated natural frequency

can be simulated as follows (Ren and De Roeck 2002):

(1 )ij ij ij = + (3-25)

(1 )f f

i iif f = + (3-26)

where ij and ij are the mode shape components with noise and without noise,

respectively; if and if are the ith natural frequencies with and without noise,

respectively; and f are the noise levels of mode shapes and natural frequencies,

respectively; ij and f

i are independent random numbers in the range of [-1, 1]. In

order to evaluate the effect of different noise levels on damage identification

performance, the same sets of ij and f

i are used for different noise levels. Note

that, noise is added to modal parameters of both undamaged and damaged models.

Statistical damage identification following the procedure proposed by An et

al (2014) is performed to evaluate the robustness of the improved method under

noise condition. Firstly, at each noise level, 100 identification results are generated

Page 79: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 51

© 2017 Khac-Duy Nguyen Page 51

for each damage case. Secondly, a damage extent threshold is determined by

examining 100 identification results of the undamaged state under noise.

Considering the predicted damage extents at the undamaged state are a normal

distribution, the following equation is used to calculate the damage extent threshold

with capability of preventing 90% of false detection (Xia et al. 2002):

1.3u u = + (3-27)

where is the damage extent threshold; u and u is respectively the mean value

and the standard deviation of the damage extent distribution of all elements for all

damage identification results at undamaged state. For this truss model, the damage

thresholds are found to be 1.3% for noise level 1, 2.7% for noise level 2, and 4.4%

for noise level 3. Finally, detection probability for each element is estimated by

taking the ratio of number of times that its damage extent exceeds the threshold to

the total number of identification results (i.e., 100). Note that, the GMSEE-based

quantification technique is used to obtain the damage scaling coefficient as it has

similar performance with the frequency-based quantification technique.

Detection probability results by the GMSEE correlation method are

illustrated in Figs. 3-6 to 3-8. Normally, decision can be made on the favour of the

trend with higher probability. That means an element with probability of more than

50% can be considered as damaged. In this study, to be more confident in decision

making, a probability threshold of 60% is used to decide whether or not an element

is damaged. It has been reported that 60% is an appropriate level to avoid both false

negative and false positive elements (An et al. 2014). It is shown that the detection

probabilities of the actual damaged elements in the three damage cases tend to

reduce when measurement noise increases. All actual damaged elements are

successfully detected by the proposed method at the first two noise levels. At the

third noise level, only good results are obtained for Case 3. For Case 2, although

actual damaged elements (elements 4 and 11) are successfully detected, their

Page 80: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 52

© 2017 Khac-Duy Nguyen Page 52

detection probabilities are quite low. For the single damage case, the damage at

element 9 is not able to be detected at the highest noise level. It is also observed that

the false detection probabilities increase with the noise level. However, the

probabilities of the false elements do not exceed the probability threshold in all three

damage cases. For comparison purpose, results by the MSE correlation method are

also illustrated in Figs. 3-6 to 3-8. It is obvious that the detection probabilities of the

actual damaged elements by the MSE method are similar to those by the GMSEE

method in the first noise level. For Case 2, as noise increases, higher probabilities are

obtained for the actual damaged elements (elements 4 and 11) by using the MSE

method, especially at the highest noise level. However, for this damage case, the

false-positive detection probabilities obtained from the MSE method are

significantly higher than those obtained from the GMSEE method. For the single

damage case (Case 1), the proposed GMSEE method gives higher damage

probability for the actual damage (element 9). For Case 3, both methods have

comparable results when the measurement noise increases.

Page 81: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 53

© 2017 Khac-Duy Nguyen Page 53

(a) Frequency noise = 0.5%, mode shape noise = 2%

(b) Frequency noise = 1%, mode shape noise = 5%

(c) Frequency noise = 1.25%, mode shape noise = 7%

Figure 3-6. Detection probability results for 2-D truss model under noise: Case 1

(actual damage: element 9)

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

Page 82: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 54

© 2017 Khac-Duy Nguyen Page 54

(a) Frequency noise = 0.5%, mode shape noise = 2%

(b) Frequency noise = 1%, mode shape noise = 5%

(c) Frequency noise = 1.25%, mode shape noise = 7%

Figure 3-7. Detection probability results for 2-D truss model under noise: Case 2

(actual damage: elements 4 and 11)

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

Page 83: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 55

© 2017 Khac-Duy Nguyen Page 55

(a) Frequency noise = 0.5%, mode shape noise = 2%

(b) Frequency noise = 1%, mode shape noise = 5%

(c) Frequency noise = 1.25%, mode shape noise = 7%

Figure 3-8. Detection probability results for 2-D truss model under noise: Case 3

(actual damage: elements 7, 8 and 10)

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

rob

ab

ility

(%

)

MSE Method

GMSEE Method

Page 84: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 56

© 2017 Khac-Duy Nguyen Page 56

It is also important to evaluate the effect of noise on damage quantification.

Figures 3-9 to 3-11 show the damage extent results by the GMSEE and MSE

correlation methods by taking the average of all identification results in each case. It

is shown that the actual damaged elements are better distinguished from the

undamaged ones by the proposed GMSEE method than the MSE method.

Particularly for Case 1, it is very hard to distinguish the damaged element (element

9) by the MSE method at the highest noise level while the proposed GMSEE method

is still able to show the damaged element. It is also found that the average damage

extents of the actual damaged elements by both methods become less accurate when

noise increases. Table 3-2 shows the errors of damage extents for the actual damaged

elements compared to the predictions at the noise-free condition. The results by the

GMSEE method have acceptable errors at the low noise level. At the second noise

level, the estimations are significantly affected for Case 1 and Case 3. At the third

noise level, the estimations are significantly affected for all three damage cases.

Despite that, the GMSEE method seems to be less affected by noise than the MSE

method. Except for the higher errors observed in some cases (element 10 in Case 3,

element 4 in Case 2 at high noise levels), most of the estimations by the GMSEE

method have smaller or similar levels of errors compared to those from the MSE

method. In particular, the GMSEE method gives much smaller errors for element 9

in Case 1, element 11 in Case 2 (at noise levels 1 and 2), and element 8 in Case 3.

Moreover, by taking the average errors for all damage cases, it is shown that the

results by the GMSEE method are generally better than those from the MSE method.

In summary, the proposed GMSEE correlation method can be considered as a robust

method when modal data is polluted by noise.

Page 85: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 57

© 2017 Khac-Duy Nguyen Page 57

(a) Frequency noise = 0.5%, mode shape noise = 2%

(b) Frequency noise = 1%, mode shape noise = 5%

(c) Frequency noise = 1.25%, mode shape noise = 7%

Figure 3-9. Average damage extent results for 2-D truss model under noise: Case 1

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

Page 86: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 58

© 2017 Khac-Duy Nguyen Page 58

(a) Frequency noise = 0.5%, mode shape noise = 2%

(b) Frequency noise = 1%, mode shape noise = 5%

(c) Frequency noise = 1.25%, mode shape noise = 7%

Figure 3-10. Average damage extent results for 2-D truss model under noise: Case 2

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

Page 87: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 59

© 2017 Khac-Duy Nguyen Page 59

(a) Frequency noise = 0.5%, mode shape noise = 2%

(b) Frequency noise = 1%, mode shape noise = 5%

(c) Frequency noise = 1.25%, mode shape noise = 7%

Figure 3-11. Average damage extent results for 2-D truss model under noise: Case 3

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

ma

ge

Exte

nt (%

)

MSE Method

GMSEE Method

Page 88: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 60

© 2017 Khac-Duy Nguyen Page 60

Table 3-2. Quantification of damage extent prediction error caused by measurement

noise

Damage

scenario

Damaged

elements

Error by MSE correlation (%) Error by GMSEE correlation (%)

Noise 1 Noise 2 Noise 3 Noise 1 Noise 2 Noise 3

Case 1 9 7.16 13.58 19.34 3.79 9.34 13.16

Case 2 4

11

2.76

9.34

1.74

6.61

2.48

9.40

0.09

2.91

2.99

1.06

5.30

10.7

Case 3

7

8

10

0.04

2.61

0.08

2.20

5.23

7.04

6.50

10.80

13.10

0.94

0.32

3.82

3.05

1.62

11.00

0.10

5.00

14.50

Average error 3.67 6.07 10.27 1.98 4.84 8.13

Noise 1: Frequency noise = 0.5%, mode shape noise = 2%; Noise 2: Frequency noise = 1%,

mode shape noise = 5%; Noise 3: Frequency noise = 1.25%, mode shape noise = 7%.

3.6 EXPERIMENTAL VERIFICATION

It is important to evaluate the performance of the GMSEE correlation method

for experimental models. Herein, damage identification has been carried out for an 8

degree-of-freedom (DOF) system and a three-story shear building model. Both

experiments have been conducted by the Los Alamos National Laboratory (LANL),

USA. In the following experimental case studies, GMSEE change vector is used to

obtain the damage scaling coefficient as described in Eq. (3-24) since this technique

does not require information of structural stiffness.

3.6.1 Case Study 1: LANL 8-DOF System

Figure 3-12 shows the experimental set up of an 8-DOF system carried out by

the LANL to study the effectiveness of various vibration-based damage detection

methods. The system is constructed by a series of eight translating masses connected

by springs. Each mass is an aluminum disc with a center hole. The masses slide on a

highly polished steel rod that constrains them to move only in the translational

direction. At the undamaged state, all springs are identical and have a linear spring

constant. Damage is simulated by replacing the fifth spring with another spring

Page 89: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 61

© 2017 Khac-Duy Nguyen Page 61

which has stiffness 14% lower than the original one. Horizontal acceleration

responses are measured at each mass, giving a total of eight measured DOFs. The

structure is excited by a random force generated by an electro-dynamic shaker.

Natural frequencies and mode shapes of the first three modes have been used for

damage identification. It is worth noting that the examined damage case is the most

challenging case compared to damages at the extreme ends of the system (i.e.,

springs 1 and 7), as mentioned in Duffey et al. (2001). They also reported that

damage at the level of 14% was more difficult to detect than that at lower and higher

levels.

Figure 3-13 shows the damage identification results obtained by using the

GMSEE correlation method. It is obvious that the damaged spring has been

successfully identified. The estimated severity (67.8%) is found to be quite different

from the simulation (14%). This difference could be caused by the change in friction

between the masses and the steel rod after the spring was replaced. It is well-known

that friction is a source of damping which affects vibration behavior of the structure.

This has been previously reported in the reference (Duffey et al. 2001). Also, no

false alarms have been observed in the damage results predicted by the proposed

method.

Figure 3-12. LANL 8-DOF system (Duffey et al. 2001)

Page 90: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 62

© 2017 Khac-Duy Nguyen Page 62

Figure 3-13. Damage identification result for 8-DOF system by GMSEE correlation

method.

3.6.2 Case Study 2: LANL Three-story Building Model

Figure 3-14 shows the experimental set up of a 4-DOF shear building model

carried out by the LANL. The model consists of aluminium columns and plates

jointed by bolts with a rigid base sliding on rails that allows movement in the x-

direction only. At each floor, the top and bottom plates (30.5x30.5x2.5cm) are

connected by four aluminium columns (17.7x2.5x0.6cm), forming a 4-DOF system

(with 3 active DOFs). Also, there is a centre column (15.0x2.5x2.5cm) suspended

from the top floor, which is used to as a source of inducing nonlinear behaviours to

the system when it hit a bumper mounted on the second floor. The distance between

the suspended column and the bumper can be adjusted to vary the extent of the

nonlinearity. An electromagnetic shaker was used to give excitation to the base floor

of the system. Four accelerometers with a nominal sensitivity of 1000 mV/g were

mounted to the centre lines of four aluminium floor plates to measure vibration

response of the system in x-direction.

1 2 3 4 5 6 70

20

40

60

80

100

Element Number

Dam

age E

xte

nt (%

)

Page 91: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 63

© 2017 Khac-Duy Nguyen Page 63

(a) Three-story frame structure (b) Bumper and suspended column

at top floor

Figure 3-14. 4-DOF three-story building from LANL (Figueiredo et al. 2009)

Page 92: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 64

© 2017 Khac-Duy Nguyen Page 64

Figure 3-15. Basic dimensions of the three story builing model (Figueiredo et al.

2009)

A total of 7 states including the baseline state and the column damage states

are studied. The details of each state condition are provided in Table 3-3. For

example, state 2 refers to a 50% stiffness reduction in the column located between

the base and the first floor, in the intersection of plane B and D which is defined in

Fig. 3-15. For each state, floor’s equivalent damage extent is provided in Table 3-3,

which introduces the average reduction of stiffness of all four columns in each floor.

For example, 50% stiffness reduction in column 1BD (column BD in level 1) is

equivalent to 12.5% stiffness reduction in the first floor. It is worth noting that there

was no impact between the bumper and the suspended column during the excitation

to avoid nonlinear behaviour of the structure.

Page 93: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 65

© 2017 Khac-Duy Nguyen Page 65

Table 3-3. Damage states of the three-story shear building model

State State condition Floor’s equivalent

stiffness reduction

State 1 Baseline condition 0

State 2 Column 1BD – 50% stiffness reduction 12.5%

State 3 Column 1AD + 1BD – 50% stiffness reduction 25%

State 4 Column 2BD – 50% stiffness reduction 12.5%

State 5 Column 2AD + 2BD – 50% stiffness reduction 25%

State 6 Column 3BD – 50% stiffness reduction 12.5%

State 7 Column 3AD + 3BD – 50% stiffness reduction 25%

Up to three vibration modes were extracted from the acceleration responses

using the frequency domain decomposition (FDD) approach. Mode shapes and

natural frequencies of the these modes for baseline condition are provided in Figure

3-16. In order to increase the difficulty level for the damage identification task, only

the first mode is used. Statistical damage identification was also conducted for this

experiment. For the undamaged state and each damaged state, 5 data sets of the first

vibration mode were extracted. As a result, 25 damage identification results can be

obtained for each damage state. Also, by cross-checking among the undamaged data

sets, 20 damage identification results can be obtained for the baseline state. From the

baseline results, a threshold of 10% was determined based on Eq. (3-27).

Figure 3-17 shows the damage identification results obtained by using the

GMSEE correlation method. As shown in Fig. 3-17(c)-(f), excellent results are

obtained by the GMSEE method for damage states 3-4 referring stiffness reduction

in floor 2 and damage states 5-6 referring stiffness reduction in floor 3. Detection

probability of the actual damage is found 100% in these damage states. Regarding

the damage states in the first floor, as shown in Fig. 3-17(a)-(b), the proposed

method is only able to detect damage confidently for the more severe damage case.

For state 1 with 12.5% damage in the first floor, the GMSEE method gives a low

damage probability (about 55%) for the actual damaged floor. For the greater

Page 94: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 66

© 2017 Khac-Duy Nguyen Page 66

damage state in the first floor, the original method shows a higher detection

probability of about 65% for the first floor but there are some false errors of about

15% and 40% in the second and the third floors, respectively.

Average damage extent results are shown in Fig. 3-18. It can be seen that the

damage extents estimated by the proposed method match well with the actual

damage extents for the first two states, as shown in Fig. 3-18(a-b). Results for other

states show overestimation by about 10%-30%. However, these errors can be

considered to be acceptable for this experiment since the replacement of column

members might cause some model uncertainties such as change in joint stiffness.

Besides, the baseline condition might be changed after the damaged column was

replaced back with the intact column, but only one baseline state was examined for

all damage states. Regarding the change of damage extent, the GMSEE method is

able to indicate the increasing trend of damage extent in each floor shown in each

pair of the plots in Fig. 3-18: (a) and (b), (c) and (d), and (e) and (f).

(a) Mode 1 (30.87 Hz) (b) Mode 2 (53.55 Hz) (c) Mode 3 (71.19 Hz)

Figure 3-16. Modal parameters of baseline model

-1 -0.5 0 0.5 1Base

Floor 1

Floor 2

Floor 3

-1 -0.5 0 0.5 1Base

Floor 1

Floor 2

Floor 3

-1 -0.5 0 0.5 1Base

Floor 1

Floor 2

Floor 3

Page 95: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 67

© 2017 Khac-Duy Nguyen Page 67

(a) State 2: damage at 1st floor (12.5%) (b) State 3: damage at 1st floor (25%)

(c) State 4: damage at 2nd floor (12.5%) (d) State 5: damage at 2nd floor (25%)

(e) State 6: damage at 3rd floor (12.5%) (f) State 7: damage at 3rd floor (25%)

Figure 3-17. Damage probability results for the shear building by GMSEE method

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

Page 96: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 68

© 2017 Khac-Duy Nguyen Page 68

(a) State 2: damage at 1st floor (12.5%) (b) State 3: damage at 1st floor (25%)

(c) State 4: damage at 2nd floor (12.5%) (d) State 5: damage at 2nd floor (25%)

(e) State 6: damage at 3rd floor (12.5%) (f) State 7: damage at 3rd floor (25%)

Figure 3-18. Average damage extent results for the shear building by GMSEE method

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

Actual Damage

Page 97: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 69

© 2017 Khac-Duy Nguyen Page 69

3.7 CONCLUSIONS

The GMSEE correlation method was developed for locating damage and

estimating damage extent in structures. The performance of the method was verified

through numerical simulations and laboratory experiments. Results from the

numerical study showed that the proposed method could predict damage location and

damage extent with reasonable accuracy compared to the MSE correlation method.

Also, the GMSEE correlation demonstrated its robustness under noise conditions.

Performance of the proposed method was equivalent with the MSE correlation

method with regard to damage detection probability and false alarm probability.

Although the GMSEE method gave worse results for the double-damage case,

similar or better results were obtained by the proposed method for the single-damage

and the triple-damage cases. It is worth noting that the proposed GMSEE method is

more practical than the traditional MSE method because mode shapes are not

necessary to be mass-normalized, only geometric information of structural elements

is required, and only experimental modal information is required. Moreover, damage

quantification results from the proposed method were found to be less affected by

noise than those from the existing method. By applying this method to the

experimental models, the actual damaged elements were accurately located and their

damage extents were somewhat successfully quantified. Apart from the small

damage case in the first floor of the shear building model, other damage elements

were successfully located by the GMSEE method. Also, damage trends were

successfully detected by the proposed method.

Page 98: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 3: Geometric Modal Strain Energy-Eigenvalue Ratio (GMSEE) Correlation Method Page 70

© 2017 Khac-Duy Nguyen Page 70

Page 99: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 71

© 2017 Khac-Duy Nguyen Page 71

4Chapter 4: Modal Strain Energy-Eigenvalue

Ratio (MSEE) Correlation Method

The GMSEE correlation method proposed in Chapter 3 is based on the

assumption that the fractional modal strain energy is unchanged after damage. In

order to dominate the errors caused from this assumption, a good number of modes

should be used for constructing the GMSEE change vector. This chapter describes a

modified version of the correlation method proposed in Chapter 3, which is able to

reduce fault detection caused by the above assumption. The modified method uses

modal strain energy-eigenvalue ratio (MSEE) instead of geometric modal strain

energy-eigenvalue ratio (GMSEE). Similar to the original method, the MSEE

correlation method does not require numerical modal information. However, the

method needs information of elements’ rigidity. This chapter summarizes the

theoretical development for the MSEE correlation method, numerical verification,

and experimental validation for simple laboratory models.

4.1 SENSITIVITY ANALYSIS FOR MODAL STRAIN ENERGY-EIGENVALUE RATIO (MSEE)

4.1.1 Change in Elemental MSEE

By multiplying two sides of Eq. (3-16) by the jth stiffness constant kj, we have

the change in modal strain energy-eigenvalue ratio (MSEE):

T

d d di j i MSEE

ij j ij j

i

MSEE D S D

= − = −Φ K Φ

(4-1)

where Tij i j i iMSEE =Φ K Φ is the MSEE of the jth element and the ith mode; and

MSEEijS is the sensitivity coefficient for element j.

Page 100: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 72

© 2017 Khac-Duy Nguyen Page 72

4.1.2 Change in Total MSEE

It should be noted that Eq. (3-16) is a simplified expression of the following

equation by ignoring the change in fractional modal strain energy:

TT0

d d di j ii i

ij ij j

i j i

G F Dk

= −Φ K ΦΦ KΦ

(4-2)

By multiplying two sides of Eq. (4-2) by the jth stiffness constant kj, and

taking the summation for all elements, we have the change in total modal strain

energy-eigenvalue ratio:

TT

1 1 1

d d dn n n

i j ii iij ij j

j j ji i

MSEE F D = = =

= − Φ K ΦΦ KΦ

(4-3)

Considering the fact that the total change in fractional modal strain energy is

zero (1

d 0n

ij

j

F=

= ), Eq. (4-3) can be rewritten as follows:

T

1 1

d dn n

i j i MSEEi j ij j

j ji

TMSEE D S dD= =

= − = − Φ K Φ

(4-4)

where iTMSEE is the total modal strain energy-eigenvalue ratio (total MSEE) of

mode i and can be calculated from measured mode shape and eigenvalue as

Ti i i iTMSEE =Φ KΦ .

Different from the calculation for the elemental MSEE change in Eq. (4-1),

the equation for the total MSEE change is an exact expression without considering

the assumption that the fractional modal strain energy is unchanged. However, the

total MSEE is a global parameter which is less sensitive to stiffness reduction in each

member. Therefore, an appropriately combined use of these two parameters may help

to improve the damage prediction. The following section will present a combined use

of these two parameters for damage identification.

Page 101: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 73

© 2017 Khac-Duy Nguyen Page 73

4.2 DAMAGE IDENTIFICATION USING MSEE CHANGE

For locating damage, the multiple damage location assurance criterion

(MDLAC) is modified for MSEE change vector as follows:

( ) ( )

2T

MSEE

T T

Δ .δMDLAC (δ )

Δ .Δ . δ .δ=

MSEE MSEED

MSEE MSEE MSEE MSEE (4-5)

where ΔMSEE is the measured MSEE change vector including the elemental MSEE

change vector and the total MSEE change; and δMSEE is the analytical MSEE

change vector for a known damage vector δD . These vectors can be expressed as

follows:

1

...

Δ

...

Δ

i

i

m

m

TMSEE

TMSEE

TMSEE

=

ΔMSEE

ΔMSEEΔMSEE

ΔMSEE

(4-6)

1

1

...

...

i

i

m

m

TMSEE

TMSEE

TMSEE

=

δMSEE

δMSEEδMSEE

δMSEE

(4-7)

where Δ iMSEE is the measured elemental MSEE change vector for the ith mode

which can be calculated directly from measured modal data and elemental stiffness

matrix; iTMSEE is the measured total MSEE change vector for the ith mode which

can be calculated directly from measured modal data and system stiffness matrix;

Page 102: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 74

© 2017 Khac-Duy Nguyen Page 74

δ iMSEE is the analytical elemental MSEE change vector for the ith mode; and

iTMSEE is the analytical total MSEE change vector for the ith mode which is

calculated by Eq. (4-4). Herein, δ iMSEE is calculated based on a sensitivity matrix

as follows:

1

1

2

2

d0 ... 0

d

d0 ... 0

dδ δ

... ... ... ...

d0 0 ...

d

i

i

i

in

n

MSEED

MSEED

MSEED

=

MSEE D

or MSEEδ δi i=MSEE S D (4-8)

where MSEEiS is the sub-sensitivity matrix of MSEE for the ith mode; and n is the

number of structural elements. Value of each diagonal entry of the above matrix is

calculated by Eq. (4-1).

After the correlative damage vector δD is identified by maximizing the

MDLAC function in Eq. (4-5), the damage extent can be obtained with the scaling

coefficient C calculated by the following expression:

MSEEavg

Δ

[ .δ ]C =

MSEE

S D (4-9)

where MSEEavgS is the average sensitivity matrix obtained from the pre-damaged

sensitivity matrix MSEEuS calculated with modal information at undamaged state, and

the post-damaged sensitivity matrix MSEEdS calculated with modal information at

damaged state. Herein, the undamaged stiffness matrix can be used to calculate

MSEEdS as the damaged stiffness matrix is unknown.

Page 103: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 75

© 2017 Khac-Duy Nguyen Page 75

4.3 SUMMARY OF MSEE CORRELATION DAMAGE IDENTIFICATION METHOD

In summary, the MSEE correlation method incorporates two parameters

which are elemental MSEE and total MSEE. The sensitivity formula for the first

parameter is less accurate due to the assumption that the fractional elemental MSE is

unchanged after damage. Using change in the elemental MSEE is good for

identifying damage location as it directly evaluate the change in stiffness of each

element. However, it potentially generates false positive detection due to the errors

caused by the assumption, especially at low-sensitivity elements. Meanwhile, as the

change in total MSE is calculated without the above assumption, it can be used to

refine the prediction result in which the false positive detection is reduced.

Figure 4-1 illustrates the schematic of the proposed MSEE correlation-based

damage identification method. The procedure is very similar to the one in Fig. 3-1

for GMSEE correlation method. The main difference is that the damage detection

model requires not only types and geometries of the elements but also their material

and section properties. Also, for the MSEE-based damage identification procedure,

both elemental MSEE and total MSEE need to be calculated.

Figure 4-1. Schematic of MSEE correlation-based damage identification method.

Page 104: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 76

© 2017 Khac-Duy Nguyen Page 76

4.4 NUMERICAL VERIFICATION

The 2-D numerical truss model as shown in Fig. 3-2 is used to evaluate the

feasibility of the proposed method. Three damage scenarios shown in Table 3-1 are

considered in this section. Also, the GA optimisation approach is used for searching

optimal solution of the correlative damage vector. The same GA configuration to the

one in Chapter 3 is defined for this verification.

4.4.1 Damage Identification with Noise-free Modal Data

This section will compare the damage identification results by the GMSEE

and the MSEE correlation method using fewer modes. Only the first 4 modes of the

truss model are used in this section. Damage identification results by the MSE,

GMSEE and MSEE correlation methods using the first 4 modes are illustrated in Fig.

4-2. As shown in Fig. 4-2, for all three damage cases, both the MSE and GMSEE

correlation methods are able to identify the actual damaged element with reasonable

accuracy. However, both methods generate some false positive damage

identification. On the other hand, it is shown in Fig. 4-2 that the modified method

using MSEE change vector give better results in which the actual damaged elements

are identified accurately and no false positive damage indication is observed. It is

worth noting that most of the damage extent results for the actual damage elements

by the three methods are comparable. Only damage extent of element 10 in Case 3 is

well overestimated by the GMSEE and MSEE methods compared to the traditional

MSE method but this is expectable as fewer modes are used and both proposed

methods rely on the assumption mentioned in Chapter 3.2.1 (i.e., *ij ijF F ) to simplify

the damage identification problem. From this comparison, the proposed MSEE

correlation method shows its higher capability of identifying damage compared to

the GMSEE correlation method. Compared to the traditional MSE correlation

method, the MSEE method can be considered more accurate regarding false

identification and more practical as it requires much less information for solving the

damage identification problem. However, there is still room for future improvement

Page 105: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 77

© 2017 Khac-Duy Nguyen Page 77

as both GMSEE and MSEE overestimate the damage extent for severe damage when

fewer modes are used.

(a) Case 1: D9 = 20%

(b) Case 2: D4 = 20%, D11 = 30%

(c) Case 3: D7 = 20%, D8 = 25%, D10 = 30%

Figure 4-2. Damage identification results for the 2-D truss model by MSE, GMSEE

and MSEE methods using first 4 modes

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age

Exte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

Actual Damage

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age

Exte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

Actual Damage

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age

Exte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

Actual Damage

Page 106: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 78

© 2017 Khac-Duy Nguyen Page 78

4.4.2 Damage Identification with Measurement Noise

As the lowest noise level did not affect much on performance of the damage

identification methods, this section will evaluate the robustness of the MSEE

correlation method under the high noise levels (i.e., level 2: mode shape noise is 5%,

natural frequency noise is 1%; and level 3: mode shape noise is 7%, natural

frequency noise is 1.25%). Damage results by the MSEE correlation method using

the first 8 modes and the first 4 modes are compared. The same sets of noised modal

data as in Chapter 3 have been used. A similar approach for damage probability

analysis has also been applied. Again, a probability threshold of 60% is used to

decide whether or not an element is damaged.

4.4.2.1 Damage Identification Results using 8 modes

Detection probability results by the MSEE correlation method using the first

8 modes are illustrated in Figs. 4-3 to 4-5. For comparison, results of the MSE and

GMSEE methods are replotted in the same figures. It is shown that all actual

damaged elements are successfully detected by the MSEE method at the high noise

levels. For Case 1, the detection probability level for the actual damaged element

(element 9) is significantly higher than those obtained by the MSE and GMSEE

methods. Also, only the MSEE method is able to detect this damage at the highest

noise level. Other two methods show a probability of the actual damaged element

below the 60%-threshold. For the double damage case (Case 2), although the MSEE

method shows smaller detection probabilities for element 4 in noise level 2 and for

element 11 in noise level 3 compared to those of the MSE method, the differences

between them are not significant. The MSEE method can be considered to have

similar performance to the MSE method for this case. Compared to the original

GMSEE method, the MSEE method has much improved the results. As shown in

Fig. 4-4(b), the detection probabilities of element 4 and 11 have respectively

increased from 63% to 89% and from 68% to 98% by using the MSEE method. For

the third damage case, the MSEE method slightly improves the results of the original

Page 107: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 79

© 2017 Khac-Duy Nguyen Page 79

GMSEE method. Also, results of the MSEE method are comparable with those of the

traditional MSE method. Regarding false positive detection, it is observed that the

detection probabilities of the undamaged elements by the MSEE method do not

exceed the 60%-threshold in all three damage cases. Also, false detection

probabilities by the MSEE method seem to be smaller than those obtained from the

other two methods.

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-3. Detection probability results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 1

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robab

ility

(%

)

MSE Method

GMSEE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robabili

ty (

%)

MSE Method

GMSEE Method

MSEE Method

Page 108: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 80

© 2017 Khac-Duy Nguyen Page 80

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-4. Detection probability results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 2

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

robab

ility

(%

)

MSE Method

GMSEE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robabili

ty (

%)

MSE Method

GMSEE Method

MSEE Method

Page 109: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 81

© 2017 Khac-Duy Nguyen Page 81

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-5. Detection probability results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 3

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

robab

ility

(%

)

MSE Method

GMSEE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robabili

ty (

%)

MSE Method

GMSEE Method

MSEE Method

Page 110: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 82

© 2017 Khac-Duy Nguyen Page 82

Effect of noise on damage quantification is also illustrated in Figs. 4-6 to 4-8.

It is found that the actual damaged elements are more distinguished from the

undamaged ones by using the MSEE method compared to the results obtained by the

MSE and GMSEE methods, especially for Case 1. As shown in Fig. 4-6(b), the

MSEE method still shows a good prediction for the damage at element 9 under noise

level 3, whereas the traditional MSE method even cannot indicate element 9 as

damaged. Table 4-1 shows the errors of damage extents of the actual damaged

elements by the three methods compared to their predictions at the noise-free

condition. As shown in the table, the MSEE method seems to be less affected by

noise than the other two methods. Most of the predictions by the MSEE method

show less errors compared to those obtained from the other two methods. Some

exceptions are observed for element 4 at noise level 2, element 11 at noise level 2,

and element 7 at both noise levels. However, the differences for these cases are not

very noticeable. By taking the average errors for all damage cases, it is shown that

the results by the MSEE method are generally better than those from the MSE and

GMSEE methods.

Page 111: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 83

© 2017 Khac-Duy Nguyen Page 83

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-6. Average damage extent results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 1

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

mag

e E

xte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Avera

ge D

am

age E

xte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

Page 112: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 84

© 2017 Khac-Duy Nguyen Page 84

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-7. Average damage extent results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 2

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

mag

e E

xte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Avera

ge D

am

age E

xte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

Page 113: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 85

© 2017 Khac-Duy Nguyen Page 85

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-8. Average damage extent results by MSE, GMSEE and MSEE correlation

methods under high noise levels using 8 modes: Case 3

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

mag

e E

xte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Avera

ge D

am

age E

xte

nt (%

)

MSE Method

GMSEE Method

MSEE Method

Page 114: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 86

© 2017 Khac-Duy Nguyen Page 86

Table 4-1. Quantification of damage extent prediction error caused by measurement

noise using 8 modes

Damage

scenario

Damaged

elements

MSE Error (%) GMSEE Error (%) MSEE Error (%)

Noise 2 Noise 3 Noise 2 Noise 3 Noise 2 Noise 3

Case 1 9 13.58 19.34 9.34 13.16 7.00 7.60

Case 2 4

11

1.74

6.61

2.48

9.40

2.99

1.06

5.30

10.7

4.60

2.20

2.1

4.1

Case 3

7

8

10

2.20

5.23

7.04

6.50

10.80

13.10

3.05

1.62

11.00

0.10

5.00

14.50

2.60

0.90

9.20

1.8

2.8

12.1

Average error 6.07 10.27 4.84 8.13 4.42 5.08

Noise 2: Frequency noise = 1%, mode shape noise = 5%; Noise 3: Frequency noise = 1.25%, mode shape noise = 7%.

4.4.2.2 Damage Identification Results using 4 modes

Damage detection probability results by the MSEE correlation method using

the first 4 modes are illustrated in Figs. 4-9 to 4-11. For comparison, results of the

traditional MSE correlation method are also plotted in Figs. 4-9 to 4-11. It should be

noted that damage identification by the GMSEE method is not performed since the

method does work very well with fewer modes in noise-free condition (Fig 4.2). It is

showed in Figs. 4-9 to 4.11 that the detection probabilities of the actual damaged

elements by the MSEE method reduce when fewer modes are used. In particular,

damage at element 4 of Case 2 is not detected at noise level 2, and showing slightly

beyond the threshold at noise level 3. However, these results are expected because

the sizes of the numerical and measured MSEE vectors are reduced that leads to

larger influence of noise to the correlation function. Despite the reduction in the

detection probability, most of the damaged elements are well detected. Moreover, the

detection probabilities of undamaged elements do not exceed the probability

threshold in all three damage cases. Compared to the results of the traditional MSE

method, the proposed MSEE method is outperforming in all three damage cases. The

MSEE method gives better detection probabilities for all the damaged elements. As

Page 115: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 87

© 2017 Khac-Duy Nguyen Page 87

shown in Figs. 4-9 and 4-10, the MSE method not only fails to detect the two

damages at element 4 and 11 in Case 2 at noise level 3 but also fails to detect the

single damage of Case 1 at the two noise levels. Also, as shown in Fig. 4-11, false

detection of above 60% is observed at several elements such as elements 11, 15 and

23 at noise level 2, and elements 13 and 14 at noise level 3.

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-9. Detection probability results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 1

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction

Pro

babili

ty (

%)

MSE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robabili

ty (

%)

MSE Method

MSEE Method

Page 116: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 88

© 2017 Khac-Duy Nguyen Page 88

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-10. Detection probability results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 2

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

robab

ility

(%

)

MSE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robabili

ty (

%)

MSE Method

MSEE Method

Page 117: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 89

© 2017 Khac-Duy Nguyen Page 89

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-11. Detection probability results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 3

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

De

tectio

n P

robab

ility

(%

)

MSE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

20

40

60

80

100

Element Number

Dete

ction P

robabili

ty (

%)

MSE Method

MSEE Method

Page 118: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 90

© 2017 Khac-Duy Nguyen Page 90

Damage quantification results are shown in Figs. 4-12 to 4-14. Similar to the

results obtained with 8 modes, the average damage extent results by MSEE method

are more readily compared to the MSE method. The damaged elements are much

more distinguished from the undamaged ones by using the MSEE method. It is also

found that the damage extents of undamaged elements become greater when fewer

modes are used. This is expected as noise effect becomes greater as fewer modes are

used. Table 4-2 shows the errors of damage extents of the actual damaged elements

by the two methods compared to their predictions at the noise-free condition. Similar

to the results with 8 modes, the MSEE method seems to be less affected by noise

than the MSE method. Most of the predictions by the MSEE method show less errors

compared to those obtained from the other two methods. Only one exception is

observed for element 10 at noise level 3 where the error by the MSEE method is little

higher than that of the MSE method. Considering the average errors, the values

obtained by the MSEE method are significantly smaller than those from the MSE

method.

In summary, the improved MSEE correlation method can be considered as a

more robust method compared to the traditional MSE method as well as the original

GMSEE method when modal data is polluted by noise. Although performance of the

improved method reduces when fewer modes are used, it is still able to detect most

of the damage with good accuracy under noise of up to 1.25% in natural frequencies

and 7% in mode shapes.

Page 119: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 91

© 2017 Khac-Duy Nguyen Page 91

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-12. Average damage extent results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 1

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

mag

e E

xte

nt (%

)

MSE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Avera

ge D

am

age E

xte

nt (%

)

MSE Method

MSEE Method

Page 120: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 92

© 2017 Khac-Duy Nguyen Page 92

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-13. Average damage extent results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 2

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

mag

e E

xte

nt (%

)

MSE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Avera

ge D

am

age E

xte

nt (%

)

MSE Method

MSEE Method

Page 121: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 93

© 2017 Khac-Duy Nguyen Page 93

(a) Noise level 2: frequency noise = 1%, mode shape noise = 5%

(b) Noise level 3: frequency noise = 1.25%, mode shape noise = 7%

Figure 4-14. Average damage extent results by MSE and MSEE correlation methods

under high noise levels using 4 modes: Case 3

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Ave

rage

Da

mag

e E

xte

nt (%

)

MSE Method

MSEE Method

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

Element Number

Avera

ge D

am

age E

xte

nt (%

)

MSE Method

MSEE Method

Page 122: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 94

© 2017 Khac-Duy Nguyen Page 94

Table 4-2. Quantification of damage extent prediction error caused by measurement

noise using 4 modes

Damage

scenario

Damaged

elements

MSE Error (%) MSEE Error (%)

Noise 2 Noise 3 Noise 2 Noise 3

Case 1 9 18.00 18.29 8.30 10.30

Case 2 4

11

18.34

30.82

18.93

31.10

8.90

13.70

6.00

12.30

Case 3

7

8

10

6.20

8.70

15.00

6.10

11.20

14.20

3.00

0.50

13.60

1.50

4.00

15.40

Average error 16.18 16.64 8.00 8.25

Noise 2: Frequency noise = 1%, mode shape noise = 5%; Noise 3: Frequency noise = 1.25%, mode shape noise = 7%.

4.4.3 Damage Identification with Modelling Errors

One difference between the original GMSEE method and MSEE method is

that the MSEE method needs information of stiffness constants of all elements. This

section will evaluate the effect of modelling errors in stiffness constants on the

performance of the MSEE method. Results of the traditional MSE correlation

method are also generated for comparison, as this method also relies on numerical

model.

Elastic modulus of the FE model is assumed consisting of normally

distributed random errors with zero means and specific variances. The elastic

modulus of the errored FE model can be calculated as follows:

(1 )E Ej j jE E = + (4-10)

where jE is the elastic modulus of element j in the errored FE model; jE is elastic

modulus of element j in the correct FE model (or the structure that damage

identification is performed for); E is the error level of the elastic modulus; Ej is a

random number with zero mean and variance of 1. Two error levels are considered in

Page 123: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 95

© 2017 Khac-Duy Nguyen Page 95

this study as 10% and 20%.

Damage identification results using 4 modes with modelling errors are shown

in Figs. 4-15 to 4-17. It is shown that the traditional MSE method is significantly

affected by modelling errors. The quantification accuracy for the actual damaged

elements is much reduced when modelling error increases. Also, false positive errors

become greater when higher modelling error is considered. Compared to the MSE

method, it can be seen that the MSEE method presented in this thesis is less affected

by modelling error. The error in damage quantification for the actual damaged

elements is small even with the modelling error of 20%. Moreover, almost no false

positive errors are generated by the MSEE method.

The results in this section demonstrates that the proposed method is more

practical compared to the traditional MSE method since a correct FE model is not

required. The reason for this is that the traditional MSE method relies not only on

structural information but also on numerical modal parameters, whereas the MSEE

method uses measured modal parameters directly.

Page 124: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 96

© 2017 Khac-Duy Nguyen Page 96

(a) Results of MSE method

(b) Results of MSEE method

Figure 4-15. Damage identification results for the 2-D truss model by MSE and

MSEE methods considering modelling errors: Case 1

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Da

mag

e E

xte

nt (%

)

Modelling Error = 0%

Modelling Error = 10%

Modelling Error = 20%

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt (%

)

Modelling Error = 0%

Modelling Error = 10%

Modelling Error = 20%

Page 125: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 97

© 2017 Khac-Duy Nguyen Page 97

(a) Results of MSE method

(b) Results of MSEE method

Figure 4-16. Damage identification results for the 2-D truss model by MSE and

MSEE methods considering modelling errors: Case 2

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt (%

)

Modelling Error = 0%

Modelling Error = 10%

Modelling Error = 20%

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

Modelling Error = 0%

Modelling Error = 10%

Modelling Error = 20%

Page 126: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 98

© 2017 Khac-Duy Nguyen Page 98

(a) Results of MSE method

(b) Results of MSEE method

Figure 4-17. Damage identification results for the 2-D truss model by MSE and

MSEE methods considering modelling errors: Case 3

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt (%

)

Modelling Error = 0%

Modelling Error = 10%

Modelling Error = 20%

1 3 5 7 9 11 13 15 17 19 21 23 250

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt (%

)

Modelling Error = 0%

Modelling Error = 10%

Modelling Error = 20%

Page 127: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 99

© 2017 Khac-Duy Nguyen Page 99

4.5 EXPERIMENTAL VERIFICATION

The experimental data of the 8-DOF system and the three-story shear

building model is used to experimentally validate the MSEE correlation method. For

the 8-DOF system, its only damage case is considered. For the three-story shear

building, all the six damage states are considered.

Figure 4-18 shows the damage identification results for the 8-DOF system

obtained by using the MSEE correlation method with the first three modes. Similar

to the results obtained from using the GMSEE method, the damaged spring has been

successfully identified and the estimated severity (68.8%) is close to the value

obtained with the GMSEE method (67.8%). Also, no false alarms have been

observed in the damage results predicted by the MSEE method.

Figure 4-18. Damage identification for the 8-DOF system by MSEE method

Figure 4-19 shows the damage probability results obtained by using the

original GMSEE and improved MSEE methods. As shown in Fig. 4-19(c)-(f),

similar results are obtained by both methods for damage states 3-6, showing the

1 2 3 4 5 6 70

20

40

60

80

100

Element Number

Dam

age E

xte

nt (%

)

Page 128: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 100

© 2017 Khac-Duy Nguyen Page 100

detection probabilities of 100% for the actual damaged floors. Regarding the damage

states in the first floor, as shown in Fig. 4-19(a)-(b), the improved method has much

better results compared to the original GMSEE method. For state 1 with 12.5%

damage in the first floor, although both methods show low probability of damage in

the first floor, the MSEE method has greater value (about 70%) compared to the

GMSEE method’s result (about 55%). Also, the detection probability of the first

floor using the MSEE method is greater than the probability threshold (60%). For the

greater damage state in the first floor, as shown in Fig. 4-19(b), results obtained from

the MSEE method shows its outperformance of the original method, indicating

100% of detection probability in the first floor and 0% of detection probability for

other floors.

Average damage extent results of the six damage states are shown in Fig. 4-

20. It is found that the results by the MSEE are quite identical to those obtained with

the GMSEE method, except for state 2 where the MSEE method show better results

in which no damage extents observed at the 2nd and the 3rd floors. Similar to the

results of the GMSEE method, damage extents estimated by the MSEE method

match well to the actual damage extents for the first two states. Results of the MSEE

method for other states also show overestimation by about 10%-30%. It should be

noted again that these errors are understandable for this system considering some

uncertainties associated with the experiment. Regarding the change of damage

extent, the MSEE method was successful to indicate the increasing trend of damage

extent in each floor, similar to what are observed in the results of GMSEE method in

Chapter 3.

Page 129: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 101

© 2017 Khac-Duy Nguyen Page 101

(a) State 2: damage at 1st floor (12.5%) (b) State 3: damage at 1st floor (25%)

(c) State 4: damage at 2nd floor (12.5%) (d) State 5: damage at 2nd floor (25%)

(e) State 6: damage at 3rd floor (12.5%) (f) State 7: damage at 3rd floor (25%)

Figure 4-19. Detection probability results for the shear building by GMSEE and MSEE

methods.

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

GMSEE Method

MSEE Method

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

GMSEE Method

MSEE Method

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

GMSEE Method

MSEE Method

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

GMSEE Method

MSEE Method

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

GMSEE Method

MSEE Method

0 10 20 30 40 50 60 70 80 90 100

Floor 1

Floor 2

Floor 3

Detection Probability (%)

GMSEE Method

MSEE Method

Page 130: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 102

© 2017 Khac-Duy Nguyen Page 102

(a) State 2: damage at 1st floor (12.5%) (b) State 3: damage at 1st floor (25%)

(c) State 4: damage at 2nd floor (12.5%) (d) State 5: damage at 2nd floor (25%)

(e) State 6: damage at 3rd floor (12.5%) (f) State 7: damage at 3rd floor (25%)

Figure 4-20. Average damage extent results for the shear building by GMSEE and

MSEE methods.

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

MSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

MSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

MSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

MSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

MSEE Method

Actual Damage

0 10 20 30 40 50 60 70 80

Floor 1

Floor 2

Floor 3

Average Damage Extent (%)

GMSEE Method

MSEE Method

Actual Damage

Page 131: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 103

© 2017 Khac-Duy Nguyen Page 103

4.6 CONCLUSIONS

The MSEE correlation method which is a modified version of the GMSEE

correlation method was developed for locating damage and estimating damage extent

in structures. The performance of the method was verified through numerical

simulations and laboratory experiments. Results from the numerical study showed

that the MSEE method could predict damage location and damage extent with better

accuracy compared to the GMSEE correlation method when fewer measured modes

are used. False detection is basically reduced with the MSEE method. Also, the

MSEE correlation demonstrated its robustness under noise conditions. Performance

of the MSEE correlation method was better compared to the GMSEE correlation

method with regard to damage detection probability. When fewer modes were used,

performance of the MSEE method reduced but it was still able to detect most of the

damage with good accuracy. In the condition of modelling errors, the results showed

small errors in the damage identification by the MSEE method. Compared to the

traditional MSE method, the MSEE method was much less affected by modelling

errors. By applying the MSEE method to the experimental models, the method also

made improvement in damage identification results compared to the original

GMSEE method.

In summary, the MSEE correlation method improves the damage

identification results compared to the GMSEE method. However, the MSEE requires

information of structural stiffness. Therefore, in the cases where many modes can be

measured and structural stiffness is not accurately measured, the GMSEE correlation

method would be preferred. In the case where only few modes can be measured and

the structural stiffness can be obtained properly, the MSEE correlation method would

be preferred. Compared to the traditional MSE method, the proposed MSEE is more

practical and more robust.

Despite the excellent results obtained from the MSEE method, it is found that

the damage probabilities and damage extents of some undamaged elements become

Page 132: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 4: Modal Strain Energy-Eigenvalue Ratio (MSEE) Correlation Method Page 104

© 2017 Khac-Duy Nguyen Page 104

greater when fewer modes are used. Therefore, it can be expected that false

identification will rise up when dealing with a more complicated structure or with

fewer modes. In the next chapter, an enhanced technique is developed to reduce false

identification caused by measurement noise.

Page 133: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 5: Sensitivity-Weighted Search Space for Correlation-based Damage Identification Page 105

© 2017 Khac-Duy Nguyen Page 105

5Chapter 5: Sensitivity-Weighted Search Space

for Correlation-based Damage Identification

This chapter presents a technique to improve the effectiveness of correlation-

based damage identification methods for large structures where measurement noise

associated with these structures is large. The technique refers sensitivity-weighted

search space which can reduce the fault detection caused by measurement noise. It is

based on the observation that damage identification is only reliable for elements with

high vibration stress. The search technique considers sensitivity of individual

structural element wherein the search space of an element is weighted with its

sensitivity. The developed technique is then tested for the numerical 2D truss model.

5.1 THEORETICAL DEVELOPMENT OF SENSITIVITY-WEIGHTED SEARCH SPACE

As stated in the literature review, the damage identification was found only

reliable for elements with high strain energy since only very small change in modal

parameters will be a result of a very large change in structural stiffness of low-strain-

energy elements. In order to overcome this problem, Wahalathantri et al. (2012)

suggested multiplying the damage results by a modification function as a form of

normalized modal strain energy curve. However, this technique is only suitable for

adjusting a damage location result. It is not suitable to multiply a damage extent

result by this curve as it will affect the true damage extent.

In this study, instead of adjusting the results with a modification function,

adjustment is applied to the search space. Conventionally, search spaces for all

elements are selected to be in a same range (e.g., from 0% to 100%) which represents

the possible range of damage severity for each element. In other words, the high-

sensitivity elements have the same range as the low-sensitivity elements. Therefore,

the conventional range scheme may generate some false detection, especially in the

Page 134: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 5: Sensitivity-Weighted Search Space for Correlation-based Damage Identification Page 106

© 2017 Khac-Duy Nguyen Page 106

conditions of that measurement noise is significant and/or the number of degrees of

freedom is much greater than the number of measured modes.

It is worth noting that the low-sensitivity elements contribute little to the

convergence of the objective function, and therefore, their importance should be

treated differently from high-sensitivity elements in the optimization process.

Considering the distribution of elemental MSE in all modes, a sensitivity-weighted

search space (SWSS) scheme is developed for the optimization-based forward

methods. As the sensitivity of elemental MSEE is in a form of MSE, it can be used to

modify the traditional search space. The range for each element is defined based on

its sensitivity as follows:

mean

meanδ 0;100% .

max( )

j

j

SD

S= (5-1)

where δ jD is the damage extent variable of the jth element, Sjmean is the mean MSEE

sensitivity of the jth element to damage considering all measured modes; max(Smean)

is the maximum value of the mean sensitivities. Using this technique, the importance

of an element is treated unequally with other elements. The elements with high

sensitivity have broader range, while the ones with low sensitivity have narrower

range. The idea behind this scheme is that the high-sensitivity elements are allowed

to vary more flexibly than the low-sensitivity elements; hence, the convergence of

the objective function is more likely affected by the high-sensitivity elements. It is

also worth noting again that the range of the damage extent variable does not

represent the range of the damage. The final damage extent is the product of the best

damage extent vector and a damage coefficient mentioned in Chapter 3 and Chapter

4.

Page 135: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 5: Sensitivity-Weighted Search Space for Correlation-based Damage Identification Page 107

© 2017 Khac-Duy Nguyen Page 107

5.2 NUMERICAL VERIFICATION

The 2-D truss model shown in Fig.3-2 is used to verify the feasibility of the

proposed search space in correlation-based damage identification. One of the data of

Case 2 under noise level 2 is used for the verification. Also, the MSEE correlation

method using the first 4 modes is used for damage identification. Figure 5-1 shows

the average MSEE sensitivity for all elements of the truss model. It can be seen that

the sensitivities of the elements 13-17 are very low and it is expected that false

detection can be observed at these elements. Using the sensitivity-weighting

technique, the search space is different for each element as shown in Fig. 5-2. The

broadest ranges are applied for elements 1 and 7 and the narrowest ranges are applied

for elements 13-17. The actual damaged elements 4 and 11 have moderate ranges of

[0; 0.37] and [0; 0.23], respectively.

Figure 5-3 shows damage identification results using the conventional search

space and the sensitivity-weighted search space. As shown in Fig. 5-3(a), the MSEE

method gives significant false detection at element 17 when using the conventional

search space. This falsely detected element is found to be one of the low-sensitivity

elements. On the other hand, as shown in Fig. 5-3(b), the MSEE method with the

sensitivity-weighted search space gives more readily results where the predicted

damage extent of element 17 is reduced significantly.

Page 136: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 5: Sensitivity-Weighted Search Space for Correlation-based Damage Identification Page 108

© 2017 Khac-Duy Nguyen Page 108

Figure 5-1. Average MSEE sensitivity of the first 4 modes of the 2-D truss model

Figure 5-2. Sensitivity-weighted search space of all elements of the 2-D truss model

0 5 10 15 20 250

10

20

30

40

Element Number

Avera

ge S

ensitiv

ity

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Element Number

Searc

hin

g r

ange

Page 137: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 5: Sensitivity-Weighted Search Space for Correlation-based Damage Identification Page 109

© 2017 Khac-Duy Nguyen Page 109

(a) using conventional search space

(b) using sensitivity-weighted search space

Figure 5-3. Damage identification results using MSEE method for a noised data in

Case 2 of the 2-D truss model

0 5 10 15 20 250

10

20

30

40

50

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 250

10

20

30

40

50

Element Number

Dam

age E

xte

nt

(%)

Page 138: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 5: Sensitivity-Weighted Search Space for Correlation-based Damage Identification Page 110

© 2017 Khac-Duy Nguyen Page 110

5.3 CONCLUSIONS

An enhanced technique, called sensitivity-weighted search space, was

developed to improve the effectiveness of correlation-based damage identification

methods. The technique was validated for the numerical 2-D truss model. It is found

that the technique can reduce fault detection usually associated with low-sensitivity

elements. In the example of the 2-D truss model, false detection at element 17 with

low-sensitivity was significantly reduced by applying the sensitivity-weighted search

space. In the next chapter, this technique will be applied together with the proposed

correlation methods for damage identification of a much more complicated truss

structure.

Page 139: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 111

© 2017 Khac-Duy Nguyen Page 111

6Chapter 6: Experimental Validation for a

Complex Truss Structure

This chapter presents the validation of the proposed damage identification

methods and enhanced techniques for a laboratory through-truss bridge model with a

large number of degrees of freedom. Firstly, the material properties and dimensions

of the bridge model are described. Also, an FE model of the bridge is presented with

the adjustment in cross section properties to better represent the behaviour of the

experimental model. Secondly, the experimental setup is described regarding sensor

layouts and data acquisition system. Thirdly, modal extraction and modal verification

results are presented. Finally, damage identification results for the bridge model are

presented.

6.1 INTRODUCTION OF LABORATORY THROUGH-TRUSS BRIDGE MODEL

As shown in Fig. 6-1, the steel through-truss bridge model was assembled at

Banyo Pilot Plant Precinct of Queensland University of Technology, as a part of a

previous PhD project on structural health monitoring (Cowled et al. 2015). The

structure is a 3-span cantilever truss bridge model with total length of 8.55m. The

height of the main frame is 1.8m and the width of the bridge is 0.9m. The truss has

20 bays, each of which is 0.45m in length except the bays at two ends with each

length of 0.225m. Detailed dimensions are illustrated in Fig. 6-2. The structure

consists of 198 nodes and 318 members of various cross sectional areas. The main

structural members including chords, webs, struts and beams are made of cold

formed mild steel with square/rectangular hollow sections. Meanwhile, the bracing

members are steel flat bars. Detailed cross section and material properties for all

members are listed in Table 6-1. The members in the two main planes are jointed

using bolt connection and steel gusset plates as shown in Fig. 6-3. The lateral struts

Page 140: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 112

© 2017 Khac-Duy Nguyen Page 112

and beams are also bolted to the gusset plates and the braces are bolted directly to the

struts or beams. M6 bolts were used for most of the joints except at the joints of the

main frames where M8 bolts were used. As healthy condition, the M8 bolts were

fastened to 10Nm and M6 bolts were fastened to 4Nm using a torque wrench. A pin

in slotted hole was set at each far end of the bridge to simulate roller supports. A pin

in fitted hole was set at the bottom of each main frame to simulate hinge support.

Figure 6-1. QUT steel through-truss bridge model

Page 141: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 113

© 2017 Khac-Duy Nguyen Page 113

Figure 6-2. Dimensions of QUT steel through-truss bridge model

(a) chord-chord joint (b) main frame-chord joint (c) brace-beam joint

Figure 6-3 Joint connections at some typical positions

Page 142: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 114

© 2017 Khac-Duy Nguyen Page 114

Table 6-1. Details of structural members of QUT steel through-truss bridge model

Members Section type Dimension

(mm)

Young’s

Modulus

(GPa)

Mass

density

(kg/cm3)

Top and bottom

chords Square hollow 20x20x1.6

200 7.85x103

Diagonals Square hollow 20x20x1.6

Vertical webs (at

supports) Square hollow 30x30x3.0

Webs (others) Square hollow 20x20x1.6

Struts Square hollow 20x20x1.6

Beams Rectangular

hollow 50x25x2.0

Braces Flat bar 20x3.0

6.2 EXPERIMENTAL SETUP

Total 18 accelerometers including 14 PCB393B05 sensors with a nominal

sensitivity of 10V/g and 4 PCB393B04 sensors with a nominal sensitivity of 1V/g

were used to measure vibration response of one plane of the bridge model. The first

14 accelerometers labelled from S1 to S14 are PCB393B05 type and the rest labelled

from S15 to S18 are PCB393B04 type. A chassis NI cDAQ-9172 embedded with

five DSA modules NI-9234 with 4 channels for each was used to capture the signals

from the accelerometers. In order to achieve precise synchronization across different

modules, programming was made using LabVIEW to ensure that all the DSA

modules share one time base source (Nguyen et al. 2014).

Due to the above sensor shortage, a roving test method was designed to

capture the response of most of the DOFs in the examined plane of the truss model.

As shown in Fig. 6-4, six (6) sensor layouts were designed in which 17 sensors were

roved along the truss length and one sensor was used as the reference (i.e., sensor

S2). As modal strain energy of each element is calculated from the mode shape of 4

DOFs at its ends, redundant DOFs were measured for some important elements as

Page 143: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 115

© 2017 Khac-Duy Nguyen Page 115

shown in Fig. 6-4(f) to reduce the uncertainty associated with the roving test. The

structure was excited by a hammer at the joint next to the mid span joint (i.e., the

joint of the 9th and 10th bays). The impact location was covered with a thick rubber

patch to minimize nonlinear interaction between the hammer and the structure. It

should be noted that roving sensors might change the mass of the system in different

layouts. However, as the damage identification methods use the change in modal

parameters before and after damage, the inaccuracy in modal estimation caused this

effect can be considered to induce small error. The sampling rate was set as 2048Hz

and the duration of measurement for each layout was set as 2 minutes. Totally,

vibration responses of 88 DOFs over 100 DOFs of the truss plane were measured.

Later, modal features of the unmeasured 12 DOFs have been estimated from the

measured ones using linear interpolation method. Figure 6-5 shows all the measured

DOFs of the truss bridge model. Figure 6-6 shows the sensor installation at some

typical locations. As an example, time-history acceleration measures of some

locations of the first layout are illustrated in Fig. 6-7. It is worth noting that the

number of elements to be examined in this research is 99 which is one of the largest

numbers of elements that have been considered so far. The elements are numbered

from 1 to 99 as shown in Fig. 6-8.

(a) Layout 1

Figure 6-4. Sensor layouts for vibration measurement of the QUT through-truss

bridge model

Page 144: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 116

© 2017 Khac-Duy Nguyen Page 116

(b) Layout 2

(c) Layout 3

(d) Layout 4

(e) Layout 5

(f) Layout 6

Figure 6-4. Sensor layouts for vibration measurement of the QUT through-truss

bridge model

Page 145: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 117

© 2017 Khac-Duy Nguyen Page 117

Figure 6-5. Measured DOFs for the QUT through-truss bridge model

(a) at joint of 2 inclined-top chords (b) at joint of inclined chord-horizontal

chord

(c) at top of a main frame (d) at joint of bottom chords

Figure 6-6 Sensors at some typical joints of the QUT through-truss bridge model

Page 146: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 118

© 2017 Khac-Duy Nguyen Page 118

(a) Reference channel S2 (z-direction)

(b) Channel S10 (z-direction)

(c) Channel S11 (x-direction)

Figure 6-7 Representative acceleration time-series of layout 1 of the QUT through-

truss bridge model

0 20 40 60 80 100 120-0.1

-0.05

0

0.05

0.1

Time (sec)

Accele

ration A

mplit

ude (

g)

0 20 40 60 80 100 120-0.1

-0.05

0

0.05

0.1

Time (sec)

Accele

ration A

mplit

ude (

g)

0 20 40 60 80 100 120-0.1

-0.05

0

0.05

0.1

Time (sec)

Accele

ration A

mplit

ude (

g)

Page 147: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 119

© 2017 Khac-Duy Nguyen Page 119

(a) Left half of the truss plane

(b) Right half of the truss plane

Figure 6-8. Element numbering for the examined truss plane of the QUT through-

truss bridge model

6.3 MODAL EXTRACTION AND VERIFICATION

6.3.1 Modal Extraction

The modal analysis software package ARTeMIS Extractor Pro version 5.3

developed by Structural Vibration Solution A/S was used to process vibration data

from the truss structure. The frequency domain decomposition (FDD) method

embedded in ARTeMIS was used to extract modal information such as natural

frequencies and mode shapes. For signal processing, the signals were resampled to

Page 148: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 120

© 2017 Khac-Duy Nguyen Page 120

512 Hz that gives the new frequency range of interest to be 256 Hz. The number of

frequency point was set as 2048 that gives the frequency resolution to be 0.125 Hz. It

should be noted only the values from 0 to about the first half of the frequency range

are considered as they are more reliable for mode shape estimation. It is also worth

noting that the frequency resolution can be finer by increasing the number of

frequency point. However, this will make the singular value decomposition (SVD)

diagrams very noisy and it is very hard to pick the modes.

Figure 6-9 shows the SVD diagrams for the vibration data of all the test

layouts in the intact condition. Natural frequencies of the truss plane can be

identified from the peaks of the first SVD diagram and corresponding mode shapes

can be estimated. As shown in Fig. 6-9, there are many peaks, but not all of them can

be used for damage identification. Some peaks represent local modes due to local

vibration of individual elements. Some peaks are not stable due to the nonlinearity of

the structure or due to the uncertainties of the roving test (such as the reference

sensor is close to nodal point of these modes). In order to select appropriate modes

for damage identification, the following criteria are applied: 1) the mode must have

low complexity that represents for a true mode; 2) the mode must have a good

repeatability in modal strain energy for different data sets in a same structural

condition; and 3) the mode must represent global behaviour of the structure.

For the first criterion, the modes with complexity lower than 20 are selected.

For the second criterion, the modal assurance criteria of modal strain energy

(MACMSE) are calculated for the selected modes due to the first criterion, and then the

modes with MAC value greater than 95% are selected. The equation of MACMSE is as

follows:

( )

( )( )

2

,1 ,2

,1 ,1 ,2 ,2

( )

T

i i

MSE T T

i i i i

MAC i =MSE MSE

MSE MSE MSE MSE (6-1)

where ,1iMSE is the first data set of the ith MSE data of the structure, and ,2iMSE is

Page 149: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 121

© 2017 Khac-Duy Nguyen Page 121

the second data set of the ith MSE data of the structure. For the third criterion, we

consider a good MSE distribution must contain a good number of high MSE values.

The quality of the MSE distribution can be evaluated by the ratio of number of MSE

values greater than the mean value over the total number of MSE values, as follows:

100%MSE

np

N

= (6-2)

where nis the number of MSE values being greater than the mean value of MSE

distribution and N is the number of MSE values (e.g., N = 99 for this case study). In

this study, the modes with at least 20% of MSE values greater than the mean value

(i.e., MSEp 20%) are selected. It is worth nothing that this criterion was set as a

result of trade-off between the number of modes and the quality of the MSE

distribution.

Figure 6-9 SVD diagram and the identified natural frequencies for the QUT through-

truss bridge model

Page 150: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 122

© 2017 Khac-Duy Nguyen Page 122

Table 6-2 show the summary of modal characteristics of all the peaks selected

from the SVD diagram. It can be seen that only three modes (i.e., 15.375 Hz, 30.25

Hz and 58.75 Hz) satisfy all the three criteria above. These modes are respectively

marked as mode 1, mode 2 and mode 3 in the SVD diagram of Fig. 6-9. Figure 6-10

shows an example of modal strain energy of an unselected mode that does not satisfy

the repeatability and Fig. 6-11 shows an example for an unselected mode that does

not satisfy the global behaviour requirement. Figure 6-12 to 6-14 show modal strain

energies of the three selected modes (modes 1-3). It is obvious that these modes have

good repeatability and represent global behaviour. Figure 6-15 shows the mode

shapes associated with the identified modes. These modes can be in-plane bending

modes or torsional modes (with consideration of the other truss plane). In the later

section, an FE model will provide better understandings for these modes.

Page 151: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 123

© 2017 Khac-Duy Nguyen Page 123

Table 6-2. Summary of mode selection for the QUT through-truss bridge model

Peak

frequency (Hz)

Complexity

(%)

Satisfactory of

low

complexity

Satisfactory of

repeatability

Satisfactory of

global behaviour

4.875 75.985 No - -

7.000 12.930 Yes No (0.42*) -

15.375 0.435 Yes Yes (0.99) Yes (22.20%**)

20.375 48.186 No - -

24.625 94.755 No - -

28.000 27.787 No - -

30.25 12.255 Yes Yes (0.98) Yes (24.24%)

32.375 46.763 No - -

34.625 28.484 No - -

38.875 83.598 No - -

45.375 38.959 No - -

49.875 93.862 No - -

52.125 56.000 No - -

53.750 34.909 No - -

58.750 12.628 Yes Yes (0.98) Yes (30.30%)

62.125 6.852 Yes Yes (1.00) No (15.15%)

64.250 13.685 Yes No (0.92) -

66.000 59.591 No - -

68.75 10.027 Yes Yes (0.99) No (18.18%)

75.125 59.760 No - -

77.625 27.000 No - -

81.500 87.996 No - -

90.625 70.432 No - -

96.125 65.088 No - -

98.625 64.536 No - -

102.125 58.582 No - -

105.625 57.229 No - -

110.750 45.934 No - -

*value in the parentheses represents MACMSE

**value in the parentheses represents MSEp

Page 152: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 124

© 2017 Khac-Duy Nguyen Page 124

Figure 6-10 Modal strain energy of the unselected mode at 7Hz from two different data

sets

Figure 6-11 Modal strain energy of the unselected mode at 62.125Hz

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12x 10

4

Element Number

Modal S

train

Energ

y

Set 1

Set 2

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10x 10

5

Element Number

Modal S

train

Energ

y

Page 153: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 125

© 2017 Khac-Duy Nguyen Page 125

Figure 6-12 Modal strain energy for the first selected mode (15.375Hz) from 2 different

data sets

Figure 6-13 Modal strain energy for the second selected mode (30.25Hz) from 2

different data sets

0 10 20 30 40 50 60 70 80 90 1000

2000

4000

6000

8000

10000

12000

14000

Element Number

Modal S

train

Energ

y

Set 1

Set 2

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8x 10

4

Element Number

Modal S

train

Energ

y

Set 1

Set 2

Page 154: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 126

© 2017 Khac-Duy Nguyen Page 126

Figure 6-14 Modal strain energy for the third selected mode (58.75Hz) from 2 different

data sets

(a) Mode 1: 15.375 Hz

(b) Mode 2: 30.25 Hz

(c) Mode 3: 58.75 Hz

Figure 6-15 Experimental mode shapes identified by FDD method

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2x 10

5

Element Number

Modal S

train

Energ

y

Set 1

Set 2

Page 155: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 127

© 2017 Khac-Duy Nguyen Page 127

6.3.2 Modal Verification

In order to validate the identified experimental modes, a finite element (FE)

model of the bridge was established using SAP2000 software package as shown in

Fig. 6-16. The main structural members including chords, webs and diagonals are

modelled as in-plane truss element, which allows in-plane rotation but constraints

out-of-plane rotation. The struts, beams and braces are modelled as normal truss

element which allows rotations in any plane. The left inner supports are modelled as

pins and the right inner supports are modelled as rollers. For the outer supports, they

are supposed to be rollers but it is observed from the experimental model that these

supports do not link very well to the superstructure. This is also evidenced from their

large displacements showed in the experimental mode shapes (Fig. 6-15). Therefore,

the outer supports are modelled as vertical springs with the same stiffness constant of

80 kN/m obtained from a trial and error process.

Figure 6-16 FE model of the QUT through-truss bridge model

Page 156: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 128

© 2017 Khac-Duy Nguyen Page 128

As the main members are jointed at the gusset plates, their stiffness can be

reduced or increased. In order to calculate their true stiffness, two detailed FE models

of a bottom chord are established and compared. Details of these models are shown

in Fig. 6-17. The first model considers a half bar member fixed at one end.

Meanwhile, the second model considers a system of a gusset and a half bar member

which already exclude the length of the gusset. A same axial resultant force (i.e.,

200N in this study) is put at the end of the truss element in each model and axial

deformation is calculated for each FE model. It is found that the end deformation in

the first model (i.e., 1.803E-3 mm) is about 60% of that in the second model (i.e.,

3.04E-3 mm). That means the gusset make the overall axial stiffness of the truss

member reduce by about 60% (if it is considered fixed). Taking into account this

effect and by considering that bolt connection at the gusset also reduces the overall

axial stiffness of the member, the axial stiffness of the main members in the FE

model of the QUT through-truss bridge structure is nominally reduced by 50%

compared to the as-built stiffness.

(a) FE model considering only the truss

bar

(b) FE model considering truss bar and

gusset plate

Figure 6-17. Comparison of two FE models of a bottom chord for refining member’s

axial stiffness

Page 157: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 129

© 2017 Khac-Duy Nguyen Page 129

Using the refined FE model, three identical modes can be obtained from the

FE model of the truss structure as shown in Fig. 6-18. It can be found that these

numerical modes match quite well with the modes extracted from the experimental

data. The first two modes represent in-plane bending behaviour and the third mode

represents torsional behaviour. As shown in the fourth column of Table 6-3,

differences in the natural frequencies between the experimental model and FE model

are very small, up to only 2%. However, as shown in the fifth column of Table 6-3,

mode shapes of the FE model have low correlation with those of the experimental

model, especially for mode 2. This may be due to the difference in structural

properties of individual elements between the FE model and the experimental model.

For the damage identification methods that heavily rely on FE model (e.g., MSE

correlation method), this FE model may need more refinement or updating in local

(elemental) level. Despite that, the above comparison demonstrates that the three

identified experimental modes are feasible modes and can be used for damage

identification of the proposed methods.

Page 158: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 130

© 2017 Khac-Duy Nguyen Page 130

(a) Mode 1: 15.185 Hz (1st bending mode)

(b) Mode 2: 30.854 Hz (2nd bending mode)

(c) Mode 3: 59.480 Hz (1st torsional mode)

Figure 6-18. Three identical modes obtained from the FE model of the QUT through-

truss bridge structure

Table 6-3. Comparison of natural frequencies obtained from experimental model and

FE model of the QUT through-truss bridge structure

Mode order Natural frequency (Hz) Freq.

Difference (%) MAC

FEM Experiment

1 15.185 15.375 1.24 0.653

2 30.854 30.250 2.00 0.304

3 59.480 58.750 1.24 0.598

Page 159: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 131

© 2017 Khac-Duy Nguyen Page 131

6.4 DAMAGE IDENTIFICATION FOR QUT THROUGH-TRUSS BRIDGE MODEL

Several damage scenarios were designed for the QUT through-truss bridge

model to examine the performance of the proposed correlation damage identification

methods and the enhanced optimisation technique. It is well known that bolt loose is

one of the popular damage types in truss structures. Stiffness of the whole element is

dependent on not only the truss bar but also the joint stiffness. Figure 6-18 shows a

physical model of a truss member, consisting of stiffness of the truss bar and stiffness

of the joints. The joint stiffness represents the tangential contact stiffness of the

bolts, and this value is proportional to contact pressure caused by bolt torque (Kartal

et al. 2011). The equivalent stiffness of the member can be expressed as follows:

joint-1 joint-2

1 1 1 1

e bark k k k= + + (6-3)

where joint-1k and

joint-2k refer to the joint stiffness values at each end of the truss bar;

bark is the axial stiffness of the bar itself. When all bolts are fully fastened (

joint-1 joint-2k k= = ), the equivalent stiffness of the member is equal to bark . When

some bolts are partially loosened, the equivalent stiffness will reduce. When all bolts

are fully loosened (joint-1 0k = or

joint-2 0k = ), the equivalent stiffness become vanish

or the member is totally failed. It is worth noting that the stiffness of the joint is also

affected by many other factors such as surface roughness, elasticities and contact

area; and these factors are hard to be controlled. Therefore, in this study, only the

existence of damage and the increasing trend of damage are considered.

Figure 6-19. Spring-in-series model of bolted truss element

Page 160: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 132

© 2017 Khac-Duy Nguyen Page 132

Various bolt loose scenarios are examined in this study, as summarized in

Table 6-4. In Test 1, the damage identification methods are validated for their

capability of identifying a single damage (i.e., element 10) with different severity

levels. Meanwhile, in Test 2, their performance on identifying a multiple damage

case (i.e., elements 7 and 67) is verified. Figure 6-20 illustrates the positions of the

damaged elements considered in these tests. Table 6-5 summarizes the natural

frequencies of the truss bridge model for the two undamaged states and three

damaged states. It can be seen that the changes in natural frequencies are not very

noticeable. For the first test, only the first natural frequency slightly reduced after all

the bolts of element 10 were loosened to hand tightening. For the second test, only

slight change is observed in the natural frequency of mode 2. These small changes in

natural frequencies are reasonable considering the structure is very large and the

contribution of each individual member on the overall behaviour of the structure is

very small. To clarify this point, a damage of 20% in element 10 (similar to state 1-1)

is simulated in the FE model. The changes in the first three numerical frequencies are

very small of about 0.033 Hz (0.22%), 0.042 Hz (0.14%) and 0.048 Hz (0.09%),

respectively. These changes are even much smaller than the frequency resolution

(0.125) in the experimental study.

Table 6-4. Damage scenarios for the QUT through-truss bridge structure

Test State Description

Test 1

State 1-0 Undamaged

State 1-1 Damage at #10: bolts at one end loosen to hand tightening

State 1-2 Damage at #10: bolts at two ends loosen to hand tightening

Test 2

State 2-0 Undamaged: all bolts refastened

State 2-1 Damage at #7 and #67: bolts at two ends loosen to hand

tightening

Page 161: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 133

© 2017 Khac-Duy Nguyen Page 133

(a) State 1-1 and state 1-2

(b) State 2-1

Figure 6-20. Illustration of damaged elements on the QUT through-truss bridge

model

Table 6-5. Natural frequencies of the QUT through-truss bridge structure at

undamaged and damaged states

Test State Natural frequency (Hz)

Mode 1 Mode 2 Mode 3

Test 1

State 1-0 15.375 30.250 58.750

State 1-1 15.375 30.250 58.750

State 1-2 15.250 30.250 58.750

Test 2 State 2-0 15.250 30.250 58.750

State 2-1 15.250 30.125 58.750

Figure 6-21 shows the search space for each element based on the sensitivity-

weighting technique described Chapter 5. Only some elements have wide ranges

with upper bound of over 0.5, such as elements 10, 20 and 69. A good number of

elements have medium ranges with the upper bound varying from 0.1 to 0.5, such as

elements 6, 36 and 65. And many elements have very narrow ranges with the upper

bound of under 0.1, such as elements 2, 3 and 11. For the location of the elements,

Page 162: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 134

© 2017 Khac-Duy Nguyen Page 134

please refer to Fig. 6-8. The GA solver parameters are set as follows: the number of

variables is 99 corresponding to the total number of truss elements of the examined

plane, the range of the variables is [-1; -1E-10], the population size is 500 as of about

five times of the number of the dimension (i.e., 99), the crossover fraction rate and

the convergence tolerance are respectively set as 0.5 and 1E-10 as similar to the

values selected in Chapter 3. The adaptive feasible mutation function is used to

generate mutated individuals.

Figure 6-21. Sensitivity-weighted search space of all elements of the examined plane

of the QUT through-truss bridge model

6.4.1 Damage Identification using GMSEE Method

Damage identification results by the GMSEE correlation method are

illustrated in Fig. 6-22 to 6-24. It is important to set a damage threshold for decision

making of damage. In a previous study by Park et al. (2013), they chose 5% as a

damage threshold for damage identification of a simple 5-story shear building.

Considering the much larger number of elements and higher uncertainties expected

with the roving test, a threshold of 10% is used in this study for decision making

about the damaged elements. It is worth nothing that a threshold of 10% represents a

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Element Number

Searc

hin

g r

ange

Page 163: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 135

© 2017 Khac-Duy Nguyen Page 135

safety level of 90% where an element with 90% stiffness remaining is still

considered as undamaged. As shown in Fig. 6-22, the GMSEE method is successful

to predict the actual damaged element of state 1-1 (i.e., element 10). It is also shown

that the damage extents of all undamaged elements are below the damage threshold.

For the case of higher damage severity (state 1-2), as shown in Fig. 6-23, the

GMSEE method successfully identify the damaged element at 10 and also

successfully show the increasing trend in the damage severity of this element. It is

also obvious that the method falsely detects elements 8 and 99 as damage although

their damage extents are only lightly beyond the threshold. As these elements are

close to the actual damaged element (i.e, element 10), the induced damage might

change the orientation and/or force distribution of these elements. Therefore, for

maintenance, it is recommended to fix not only the element with high possibility of

damage but also its adjacent elements if their damage extents are beyond the

threshold. As shown in Fig. 6-24, the GMSEE method gives a good prediction for the

multiple damage case (state 2-1) in which the two damaged elements (i.e., elements 7

and 67) are well predicted and no significant false detection is observed.

As summary, the GMSEE method is successful to detect all the simulated

damage for the QUT through-truss bridge model with a large number of elements.

Despite some false detection in state 1-2, the GMSEE method can still be considered

as a reliable method as the number of falsely detected elements is accounted for only

2% of the total number of the elements.

Page 164: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 136

© 2017 Khac-Duy Nguyen Page 136

Figure 6-22. Damage identification results for state 1-1 using GMSEE method with

sensitivity-weighted search space

Figure 6-23. Damage identification results for state 1-2 using GMSEE method with

sensitivity-weighted search space

Figure 6-24. Damage identification results for state 2-1 using GMSEE method with

sensitivity-weighted search space

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

Page 165: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 137

© 2017 Khac-Duy Nguyen Page 137

For comparison, the results obtained by the GMSEE method with

conventional search space are shown in Figs. 6-25 to 6-27. For the single damage

cases (states 1-1 and 1-2), the GMSEE method is still able to detect the actual

damaged element 10. However, it generates a lot of false elements, especially when

the damage severity increases. Also, some of the false elements have the same degree

of damage extents with the actual damaged element. For the multiple damage case

(state 2-1), the actual damaged elements 7 and 67 can be detected but again false

detection is observed at many other elements and some of them have similar damage

extent as the actual ones.

Figure 6-25. Damage identification results for state 1-1 using GMSEE with

conventional search space

Figure 6-26. Damage identification results for state 1-2 using GMSEE with

conventional search space

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

Page 166: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 138

© 2017 Khac-Duy Nguyen Page 138

Figure 6-27. Damage identification results for state 2-1 using GMSEE method with

conventional search space

6.4.2 Damage Identification using MSEE Method

Damage identification results by the MSEE correlation method are illustrated

in Fig. 6-28 to 6-30. The threshold of 10% is also used for decision making about the

damaged elements. As shown in Figs. 6-28 and 6-29, the MSEE method is successful

to predict the actual damaged element of states 1-1 and 1-2 (i.e., element 10). Similar

to the results from the GMSEE method, the MSEE method successfully recognizes

the increasing trend in the damage severity of the actual damaged element.

Regarding false detection, it is found that the MSEE method generates less false

detection. The damage results look more distinguished between the damaged element

and undamaged elements, and only element 99 is falsely detected by the threshold

when larger damage is considered (i.e., state 1-2). For the multiple damage case

(state 2-1), the two actual damaged elements (i.e., elements 7 and 67) are

successfully predicted by the MSEE method with no significant false detection, as

shown in Fig. 6-30. It is again found that the damaged elements are more

distinguished from undamaged elements compared to the one obtained from the

GMSEE method.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

Page 167: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 139

© 2017 Khac-Duy Nguyen Page 139

Figure 6-28. Damage identification results for state 1-1 using MSEE method with

sensitivity-weighted search space

Figure 6-29. Damage identification results for state 1-2 using MSEE method with

sensitivity-weighted search space

Figure 6-30. Damage identification results for state 2-1 using MSEE method with

sensitivity-weighted search space

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

70

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

Page 168: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 140

© 2017 Khac-Duy Nguyen Page 140

Table 6-6 summarizes the prediction results obtained by the both methods.

Compared to the GMSEE method, damage extents predicted by the MSEE method

are higher for all cases. Also, the MSEE method show better prediction regarding

false detection. For state 1-2, only one falsely detected element is found by the

MSEE method, compared to two by the GMSEE method. Also, for state 1-2, the

results obtained by the MSEE method are more distinguished between the actual

damaged element (i.e., element 10 with 61.3%) and the falsely detected element (i.e.,

element 99 with 15.2%).

Table 6-6. Summary of damage identification results for the QUT through-truss

bridge model (with the use of sensitivity-weighted search space)

State Actual damaged

elements

Predicted damaged elements

GMSEE method MSEE method

1-1 10 (left bolts loosen) 10 (18.5%*) 10 (26.3%*)

1-2 10 (all bolts loosen) 8 (11.6%), 10 (51%),

99 (17%)

10 (61.3%), 99 (15.2%)

2-1 7, 67 (all bolts loosen) 7 (22%), 67 (18.4%) 7 (27.1%), 67 (21.4%)

*Values in parentheses indicate predicted damage extent (%)

For comparison, the results obtained by the MSEE method with conventional

search space are shown in Figs. 6-31 to 6-33. For the single damage cases (states 1-1

and 1-2), the MSEE method is successful to identify the actual damaged element 10.

Although false detection is observed in some elements, the MSEE method with

conventional search space give significantly less false elements compared to the

GMSEE method. For the multiple damage case (state 2-1), the MSEE method still

can detect the actual damaged elements 7 and 67 but generates many false elements.

Page 169: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 141

© 2017 Khac-Duy Nguyen Page 141

Figure 6-31. Damage identification results for state 1-1 using MSEE method with

conventional search space

Figure 6-32. Damage identification results for state 1-2 using MSEE method with

conventional search space

Figure 6-33 Damage identification results for state 2-1 using MSEE method with

conventional search space

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

70

Element Number

Dam

age E

xte

nt

(%)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 1000

10

20

30

40

50

60

Element Number

Dam

age E

xte

nt

(%)

Page 170: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 142

© 2017 Khac-Duy Nguyen Page 142

Damage identification results for the three damage states using the same

optimisation settings, but conducted by the traditional MSE correlation method, are

plotted in Figs. 6-34 and 6-35. The results in Fig. 6-34 are obtained by using only 3

experimental modes whereas the results in Fig. 6-35 are obtained with the additional

use of 100 numerical modes from the FE model. For more detail about the calculation

of MSE sensitivity, please refer Eq. 3-4. As shown in the figures, the method fails to

detect the actual damaged elements in all three states either with additional numerical

modes or not. As shown in Fig. 3-3, there are a significant number of false errors when

only 3 experimental modes are used, and therefore, it is impossible to point out the

actual damaged elements. The results by using additional 100 numerical modes are

more readily with significantly fewer false errors (Fig. 3-4). However, the prediction

misses all the actual damaged elements in all three damage states. Therefore, the direct

comparison to the results conducted by the GMSEE and MSEE methods indicates

noteworthy improvements of the proposed methods.

(a) State 1-1 (b) State 1-2

(c) State 2-1

Figure 6-34 Damage results by traditional MSE method using 3 experimental modes

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Element Number

Da

ma

ge

Exte

nt (%

)

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Element Number

Da

ma

ge

Exte

nt (%

)

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Element Number

Da

ma

ge

Exte

nt (%

)

Page 171: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 143

© 2017 Khac-Duy Nguyen Page 143

(a) State 1-1 (b) State 1-2

(c) State 2-1

Figure 6-35 Damage identification results by traditional MSE method using 3

experimental modes together with 100 numerical modes.

6.5 CONCLUSIONS

This chapter presented the vibration tests on the QUT through-truss bridge

model and the verification results of the two proposed correlation methods, GMSEE

and MSEE developed in Chapter 3 and 4 respectively, along with the enhanced

technique, sensitivity-weighted search space developed in Chapter 5.

A roving strategy with six layouts was designed to capture the modal

response of one plane of the bridge model. Three modes were successfully extracted

from the acquired acceleration signals. The FE model was fine-tuned considering the

stiffness reduction of the main elements caused by the gusset plates. Then the

identified experimental modes were successfully verified with the modes obtained

from the FE model. The difference in natural frequencies between the experimental

model and the FE model is very small, up to 1.1%.

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Element Number

Da

ma

ge

Exte

nt (%

)

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Element Number

Da

ma

ge

Exte

nt (%

)

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Element Number

Da

ma

ge

Exte

nt (%

)

Page 172: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 144

© 2017 Khac-Duy Nguyen Page 144

Several damage scenarios were simulated by loosening the bolts connecting

the elements and the gusset plates. The first two damage cases (states 1-1 and 1-2)

refer a single damage at element 10 with different damage extent levels by the

increase of the number of loosened bolts. The third damage case (state 2-1) refers a

multiple damage case in which elements 7 and 67 were damaged. It was found that

the natural frequencies did not change very much after damage was induced. This is

explainable as the structure is very large, and therefore, the contribution of each

element in the global behaviour of the structure is very small.

Damage identification by the GMSEE and MSEE correlation methods

incorporating with the sensitivity-weighting technique was performed. It was found

that both methods successfully detected the actual damaged elements in all the three

damage states. Also, both methods generated small rates of false detection which

were about 2% and 1% by the GMSEE and MSEE methods, respectively. The MSEE

method showed slightly clearer prediction in which damaged elements were more

distinguished from the undamaged elements.

For state 1-2 where damage at element 10 was severe, both methods showed

false detection at element 99 along with the accurate prediction at element 10. It is

noted that the falsely detected element 99 is adjacent to the actual damaged element

10. From this observation, it is recommended to check all the elements within the

region of the identified damaged element as the damage at an element may affect the

orientation of its adjacent members and/or the force distribution to them.

Besides, results obtained from the experiment demonstrated the advantage of

using the sensitivity-weighted search space for modal correlation methods.

Significant false detection was reduced by adopting the technique, especially for the

GMSEE method.

It can be also concluded that both methods developed in this study have better

performance compared to the traditional MSE correlation method for complicated

Page 173: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 145

© 2017 Khac-Duy Nguyen Page 145

experimental structures where measurement noise and modelling error can be

significant. It was shown that the traditional method failed to detect any damage of

the QUT through truss bridge model.

Page 174: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 6: Experimental Validation for a Complex Truss Structure Page 146

© 2017 Khac-Duy Nguyen Page 146

Page 175: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 147

© 2017 Khac-Duy Nguyen Page 147

7Chapter 7: Experimental Validation for a

Real Bridge

This chapter presents the validation of the proposed damage identification

methods and enhanced techniques for a real bridge, the I-40 Bridge over Rio Grande

in Albuquerque, NM, USA. The experimental setup is first described and modal

properties are presented. Then damage identification results by the GMSEE and

MSEE correlation methods are presented.

7.1 EXPERIMENT DESCRIPTION AND MODAL PROPERTIES

As shown in Fig. 7-1, the I-40 Bridge is a slab-on-girder bridge constructed

in the early 1960s. It consists of three continuous spans with a total length of 129 m.

Damage identification experiments on the bridge were conducted by the LANL in

1993, as described in Farrar et al. (1994). A series of forced vibration tests was

performed, using a hydraulic shaker to generate a dynamic force onto the bridge.

Acceleration responses of the bridge were measured at 26 locations distributed along

two plate girders as shown in Fig. 7-2. Four levels of damage were introduced at the

mid-point of the middle span of the north plate girder by cutting the girder. The first

damage case E-1 consisted of a 61 cm long, 0.95 cm side cut through the web

centered at the mid-height of the web. The second case E-2 extends the initial cut to

the bottom of the web. The third case E-3 consisted of the cut in damage E-2 and an

additional halfway cut in the bottom flange from either side. In the last case E-4, the

flange was cut completely through. Details of the damage scenarios are shown in

Fig. 7-3. More details about the experiment can be found in Farrar et al. (1994).

Natural frequencies and modal assurance criterion (MAC) values of the first

six modes before and after the damage episodes are listed in Tables 7-1 and 7-2,

respectively. It is clearly seen that natural frequencies decrease a little for the third

Page 176: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 148

© 2017 Khac-Duy Nguyen Page 148

damage case (E-3) and drop significantly for the last case (E-4). On the other hand,

they are found to increase for the first and the second cuts (E-1 and E-2). This can be

explained as the change in structural properties due to changing environmental

conditions is more significant than the ones caused by these low-level damages.

Also, as shown in Table 7-2, it is found that mode shapes for the fourth damage case

(E-4) significantly change. For other damage cases, very little changes in mode

shapes are observed, except the fifth mode shape. As mode shapes are generally little

affected by environmental changes, this implies the first three damage cases caused

very small effects on dynamic characteristics of the bridge. Note that the large

changes in the fifth mode shape are basically due to measurement errors rather than

due to damage because the location of damage is right at the nodal point of this

mode shape. Based on the above observations, only the two most severe damage

cases (E-3 and E-4) are considered for the verification of the GMSEE and MSEE

correlation methods. Also, only the first two measured modes are used for the

damage identification as it was reported that the higher modes of this experiment are

not reliable (Farrar et al. 1994).

Figure 7-1. I-40 Bridge over Rio Grande in Albuquerque, NM, USA (Farrar et al.

1994)

Page 177: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 149

© 2017 Khac-Duy Nguyen Page 149

Figure 7-2. Sensor layout and location of damage (Farrar et al. 1994)

E-1 E-2 E-3 E-4

Figure 7-3. Four damage levels: cuts at the middle span of on the north plate girder

(Farrar et al. 1994)

Table 7-1. Natural frequencies of the I-40 Bridge

Case Mode number

1 2 3 4 5 6

Undamaged 2.48 2.95 3.49 4.08 4.17 4.64

E-1 2.51

(1.25)

2.99

(1.22)

3.57

(2.08)

4.12

(1.07)

4.21

(0.99)

4.69

(1.20)

E-2 2.52

(1.67)

2.99

(1.40)

3.51

(0.56)

4.10

(0.43)

4.20

(0.69)

4.66

(0.60)

E-3 2.46

(-0.71)

2.94

(-0.26)

3.48

(-0.40)

4.04

(-0.98)

4.14

(-0.69)

4.59

(-0.99)

E-4 2.27

(-8.45)

2.83

(-3.90)

3.49

(-0.19)

3.99

(-2.15)

4.15

(-0.47)

4.52

(-2.41)

*Values in parentheses indicate relative change (%) in natural frequency with

respect to the undamaged case.

Page 178: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 150

© 2017 Khac-Duy Nguyen Page 150

Table 7-2. MAC values after the introduction of damage

Case Mode number

1 2 3 4 5 6

E-1 0.997 0.999 0.998 0.994 0.976 0.998

E-2 0.995 0.997 1 0.989 0.991 1

E-3 0.998 0.998 0.999 0.990 0.975 0.998

E-4 0.863 0.894 0.997 0.947 0.940 0.969

7.2 DAMAGE IDENTIFICATION USING GMSEE CORRELATION METHOD

A damage detection model is established as an extended experimental model,

consisting of 72 Euler-Bernoulli beam elements with an average length of 3.58 m for

each element. Note that the model does not require the information of material and

cross sectional properties such as elastic modulus and 2nd moment of area. Model of

opened cracks studied by Christides and Barr (1984) is used to estimate stiffness

variation in vicinity of the crack in the I-40 Bridge. The stiffness can be considered

to be linearly reducing from the location of the crack, and the crack effective length

is equal to one and a half of the girder height (Sinha et al. 2002). A shown in Fig. 7-

4, the effective length of the crack of the I-40 Bridge is accounted for 4.845m for the

girder height of 3.23m. The equivalent stiffness reduction of the elements at the crack

can be obtained by averaging the stiffness reduction along the elements, as listed in

Table 7-3. It is clearly shown that only small damage was induced in the first two

crack scenarios, and only the last two crack scenarios made severe damage on the

cracked elements.

Cubic smoothing spline interpolation method is used to generate the refined

experimental mode shapes from the measured values. Herein, the refined mode

shapes are constructed separately for each span considering appropriate boundary

conditions. This is to reduce fitting error associated with high order curves of the

Page 179: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 151

© 2017 Khac-Duy Nguyen Page 151

whole mode shapes. Refined experimental modal curvatures are then estimated from

the refined experimental mode shapes and used to calculate geometric modal strain

energy, based on the Euler-Bernoulli beam theory as follows:

" 2[ ( )] dj

ij ilU x x= (7-1)

where "( )i x is the modal curvature at location x for the ith mode; and jl is the

length of the jth element.

Figure 7-4. Variation in stiffness around the crack

Table 7-3. Equivalent stiffness reduction

Damage case E-1 E-2 E-3 E-4

Stiffness reduction (%) 0.82 7.4 25.6 50

Figures 7-5 and 7-6 show damage identification results for damage cases E-3

and E-4 respectively, using the GMSEE method and sensitivity-weighting technique.

As shown in Fig. 7-5, it is possible to detect the actual damage location for case E-3

around sensor N7. The method also detects a false-positive region in the middle span

of the south girder. However, this false detection is acceptable as two girders are well

connected by a system of concrete deck, stringers and floor beams. It is also found

that the predicted damage extents for the actual damage members and the false ones

are very small, being less than 5%. Although this result is quite far from the induced

Page 180: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 152

© 2017 Khac-Duy Nguyen Page 152

damage (25.6%), it still well represents the little changes in natural frequencies and

mode shapes shown in Tables 7-1 and 7-2. Please note that the crack model shown in

Fig. 7-4 was developed for opened cracks but the crack in case E-3 was not well

opened. Also, the opened part of this crack is more likely representing a crack in

lateral bending mode. A model for this type of crack will need to be studied in future

to better represent its damage effect.

For the most severe damage case (E-4), as shown in Fig. 7-6, the GMSEE

correlation method shows excellent performance by accurately detecting the location

of damage without false alarms. The damage extent is predicted as about 45% which

is very close to the equivalent induced stiffness reduction (i.e., 50%). Compared to

the results obtained from the two popular methods, MSE damage index method and

the modal flexibility method, the proposed method shows similar performance in

locating damage. However, the two existing methods could not provide proper values

of damage extents. Details of the results obtained from these two methods can be

found elsewhere (Farrar and Jauregui, 1996).

For comparison, the results obtained by the GMSEE method with

conventional search space are shown in Figs. 7-7 to 7-8. As shown in Fig. 7-7, ones

are still able to detect the actual damage for case E-3 but there are many more false

locations obtained in the result such as at locations N5, N9, N13 and S5. For the

damage case E-4, the actual damage location can be realized but some false locations

are also observed at N5, N9 and S5 (Fig. 7-8).

Page 181: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 153

© 2017 Khac-Duy Nguyen Page 153

Figure 7-5. Result for damage case E-3 by GMSEE correlation method with

sensitivity-weighted search space

Figure 7-6. Result for damage case E-4 by GMSEE correlation method with

sensitivity-weighted search space

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

2

4

6

8

10

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

2

4

6

8

10

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

20

40

60

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

20

40

60

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

Page 182: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 154

© 2017 Khac-Duy Nguyen Page 154

Figure 7-7. Result for damage case E-3 by GMSEE correlation method with

conventional search space.

Figure 7-8. Result for damage case E-4 by GMSEE correlation method with

conventional search space.

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

2

4

6

8

10

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

2

4

6

8

10

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

20

40

60

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

20

40

60

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

Page 183: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 155

© 2017 Khac-Duy Nguyen Page 155

7.3 DAMAGE IDENTIFICATION USING MSEE CORRELATION METHOD

A similar damage detection model of 72 Euler-Bernoulli beam elements is

used for the MSEE method. Different from the damage detection model of the

GMSEE method, the one of the MSEE method requires the information of material

and cross sectional properties but these can be considered constant for all elements.

The same interpolation strategy as the one of the GMSEE method is used to generate

the refined experimental mode shapes from the measured values. Then refined

experimental modal curvatures are estimated and the modal strain energy is

calculated based on the Euler-Bernoulli beam theory as follows:

" 2[ ( )] d

j

ij ilU k(x) x x= (7-2)

where "( )i x is the modal curvature at location x for the ith mode; jl is the length of

the jth element; and k(x) is the stiffness constant for the element at location x.

Figures 7-9 and 7-10 show damage identification results for damage cases E-

3 and E-4 respectively, using the MSEE method and sensitivity-weighting technique.

As shown in Fig. 7-9, the MSEE method also shown a false-positive region in the

middle span of the south girder, however the region is narrower compared to the one

observed in the results of the GMSEE method. Besides, the damage location is well

located and the predicted region is narrower to the actual damage compared to the

results of the GMSEE method. Similar to the result of GMSEE method, damage

extents estimated by the MSEE method are less than 5%. For the most severe

damage case (E-4), as shown in Fig. 7-10, the MSEE correlation method shows

slightly better performance by more accurately locating the region of the damage.

The damage extent is well predicted as about 48% which is similar to the prediction

of the GMSEE method and close to the induced damage extent. It is worth noting

that, to the best of the candidate’s knowledge, this study is one of a few studies

which are able to give good estimations of damage extents for damage cases E-3 and

E-4. A study by Kim and Stubbs (2003) was also successful in quantifying damage

Page 184: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 156

© 2017 Khac-Duy Nguyen Page 156

for these cases by using frequency change, but they considered the first damage level

(E-1) as the baseline.

For comparison, the results obtained by the MSEE method with conventional

search space are shown in Figs. 7-11 to 7-12. As shown in Fig. 7-11, the MSEE

method is still successful to detect the actual damage location for the case E-3 but

there is one more false location is observed in between N8 and N9. For the most

severe damage case E-4, the actual damage location is well detected by the MSEE

method even the sensitivity-weighting technique is not employed (Fig. 7-12).

Page 185: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 157

© 2017 Khac-Duy Nguyen Page 157

Figure 7-9. Result for damage case E-3 by MSEE correlation method with

sensitivity-weighted search space

Figure 7-10. Result for damage case E-4 by MSEE correlation method with

sensitivity-weighted search space

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

2

4

6

8

10

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

2

4

6

8

10

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

20

40

60

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

20

40

60

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

Page 186: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 158

© 2017 Khac-Duy Nguyen Page 158

Figure 7-11. Result for damage case E-3 by MSEE correlation method with

conventional search space.

Figure 7-12. Result for damage case E-4 by MSEE correlation method with

conventional search space.

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

2

4

6

8

10

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

2

4

6

8

10

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11 N12 N130

20

40

60

Dam

age E

xte

nt

(%)

North Girder

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S130

20

40

60

Sensor Location

Dam

age E

xte

nt

(%)

South Girder

Page 187: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 159

© 2017 Khac-Duy Nguyen Page 159

7.4 CONCLUSIONS

This chapter presented the verification of the two proposed correlation

methods, GMSEE and MSEE along with the sensitivity-weighted search space for a

real bridge, the I-40 Bridge in NM, USA.

The modal data were provided by the SHM research group at LANL, USA.

Modal properties of the first six modes were provided but only the first two modes

were used as the higher modes are not reliable. Also, the two most severe damage

levels, E-3 and E-4, were considered for the verification of the proposed methods.

Damage identification by the GMSEE and MSEE correlation methods were

performed. By integrating the sensitivity-weighting technique, both methods

successfully detected the actual damage location for the two damage scenarios. Also,

both methods generated a false detection at the mid span of the south girder for the

damage case E-3. However, this false detection is acceptable considering two girders

are well connected by a system of concrete deck, stringers and floor beams. Besides,

the MSEE method showed slightly better prediction in both damage cases. The

damage regions were more localized by the MSEE method rather than by the

GMSEE method.

Also, the sensitivity-weighted search space showed its important role in

reducing false-positive detection. When the sensitivity-weighted search space is not

incorporated, performance of both methods generally reduced. The actual damage

location could still be detected but more false locations were observed. It was also

found that the MSEE method performed better than the GMSEE method when using

the conventional search space. This is expected as the GMSEE method generally

requires more reliable modes to give good results.

From the experimental verification results, both GMSEE and MSEE

correlation methods demonstrated their excellent performance in damage

identification for the I-40 Bridge. It can be concluded that results obtained in this

Page 188: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 7: Experimental Validation for a Real Bridge Page 160

© 2017 Khac-Duy Nguyen Page 160

study are more reliable than the previous results obtained by Kim at Stubbs (2003)

where the first damage level (E-1) was used as baseline. In this study, both proposed

methods were able to give good estimations of damage for the last two damage cases

by considering the baseline as the undamaged state. Especially for case E-4, very

accurate predictions were obtained by the GMSEE and MSEE methods.

Page 189: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 161

© 2017 Khac-Duy Nguyen Page 161

8Chapter 8: Conclusions and Future Studies

8.1 SUMMARY AND CONCLUSIONS

The research in this thesis provided a new damage identification strategy

using correlation approach. Two damage identification algorithms using modal strain

energy-eigenvalue ratio (MSEE) were developed. Firstly, a method using a

simplified term of MSEE called geometric modal strain energy-eigenvalue ratio

(GMSEE) was developed. Secondly, a modification of this method was presented

considering use of the full term of MSEE. The modified method is capable for

damage identification with fewer modes compared with the original one although it

requires both material and sectional properties of the structural element. Thirdly, a

sensitivity-weighted search space was proposed to reduce the effect of measurement

noise on the damage identification for low-sensitivity elements. Performance of the

proposed damage identification algorithms and enhanced technique has been

validated with a simple numerical model and some experimental models of various

scales from small to large. The main findings of this thesis can be summarized as

follows:

1. A new damage identification algorithm using geometric modal strain

energy-eigenvalue ratio (GMSEE) has been developed (Chapter 3). The

sensitivity of GMSEE to stiffness reduction in structural elements has

been derived. Damage is identified by optimizing the correlation level

between a measured GMSEE change vector and a numerical one. The

method requires only measured modal parameters (i.e., natural frequency

and mode shape) and geometric information of the structural element.

Comparative studies of the proposed method have been made against the

conventional MSE correlation method on a 2D numerical truss bridge

Page 190: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 162

© 2017 Khac-Duy Nguyen Page 162

model. From the results, the proposed GMSEE correlation method could

predict damage location and damage extent with reasonable accuracy

compared to the MSE correlation method. All damaged elements for

single damage case, double damage case and multiple damage case were

successfully detected by the proposed method. Also, the GMSEE

correlation showed its robustness under noise conditions. Performance of

the proposed method was equivalent with the MSE correlation method

with regard to damage detection probability and false alarm probability.

Moreover, damage quantification results from the proposed method were

found to be less affected by noise than those from the existing method.

The GMSEE method has also been verified for two simple experimental

models, an 8-DOF spring-mass system and a 4-DOF multi-story building.

From the result of the 8-DOF spring-mass system, the GMSEE method

successfully predicted the actual damaged elements with no false

detection. Although the damage extent was not well predicted, it was due

to the uncertainty induced from the change in the friction between the

mass and the spring. For the 4-DOF multi-story building, the GMSEE

method could accurately identify the actual damage location for most of

the examined scenarios. The damage extents were successfully predicted

for some scenarios. Also, the increasing trend of damage severity was

well detected by the GMSEE method.

2. A modification of the initially developed GMSEE correlation method was

presented considering use of the full term of modal strain energy-

eigenvalue ratio (MSEE) (Chapter 4). The sensitivities of elemental

MSEE and total MSEE to structural stiffness reduction have been derived.

A MSEE change vector was constructed including both elemental MSEE

change and total MSEE change. Incorporating the total MSEE change in

Page 191: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 163

© 2017 Khac-Duy Nguyen Page 163

the MSEE change vector can overcome the calculation error caused by the

assumption made for the GMSEE method that is the fractional modal

strain energy is unchanged after damage. However, the modified method

requires not only geometric information of the structural element but also

material and cross sectional properties of the element.

Numerical verification of the proposed MSEE method has been made for

the 2D numerical truss bridge model. From the results, the proposed

MSEE correlation method could predict damage location and damage

extent with better accuracy compared to the GMSEE correlation method

when fewer modes were used. All damaged elements for single damage

case, double damage case and multiple damage case were successfully

detected by the MSEE method with only 4 modes. Meanwhile, the

initially developed GMSEE method showed some false detection when

only 4 modes were used. Also, the MSEE correlation showed its

robustness under noise conditions. The MSEE method showed excellent

results in noise condition when 8 modes were used. Its performance

reduced when fewer modes (i.e., 4 modes) were used but it still could

detect most of the damage with good accuracy. When modelling errors

were introduced, the MSEE method showed significant better

performance compared to the traditional MSE method. There were small

errors in the prediction of damage location and damage extent by the

MSEE method even at modelling error of 20%.

By applying the MSEE method to the experimental models (i.e., 8-DOF

spring-mass system and 4-DOF multi-story building), it also showed the

improvement in damage identification results. For the spring-mass

system, similar results were obtained by the MSEE method compared to

the GMSEE method. For the multi-story building, the MSEE method

Page 192: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 164

© 2017 Khac-Duy Nguyen Page 164

performed better than the GMSEE method in the first two damage states

representing damage in the first floor. The MSEE method gave higher

probability of damage for the actual damaged floor and fewer errors.

3. Improvement has been made for the correlation-based damage

identification method regarding search space of damage variables. The

technique refers sensitivity-weighted search space in which the search

space of an element is weighted with its MSEE sensitivity. The technique

was validated for the numerical 2-D truss model. Results demonstrated

that the technique could significantly reduce fault detection caused by

high noise effect in low-sensitivity elements.

4. The proposed GMSEE and MSEE correlation methods and the enhanced

technique have been validated for the QUT through-truss bridge model.

Due to sensor shortage, a roving strategy with total 6 layouts was

designed to capture the responses of most DOFs of one plane of the truss

bridge model. Three modes were successfully extracted from the acquired

acceleration signals. These modes were well verified with the numerical

mode obtained from a FE model.

Three damage states including two single and one multiple damage cases

have been simulated by loosening the bolts connecting the elements and

the gusset plates. Damage identification by the GMSEE and MSEE

correlation methods incorporating with the sensitivity-weighting

technique was performed. It was found that both methods successfully

detected the actual damaged elements in all the three damage states. Also,

both methods generated small rates of false detection which were up to

about 2% and 1% by the GMSEE and MSEE methods, respectively. The

MSEE method showed slightly clearer prediction in which damaged

elements were more distinguished from the undamaged elements.

Page 193: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 165

© 2017 Khac-Duy Nguyen Page 165

It is also observed that damage in a truss member can lead to slighter

damage on its adjacent members. In the case of severe damage in element

10, both methods showed false detection at element 99 which is adjacent

to the actual damaged element 10. This may be due to the change in the

orientation of element 99 or the force redistribution of this element after

element 10 was damaged. From this observation, it is recommended to

check all the elements within the region of the identified damaged

element in a truss structure.

Besides, results obtained from the experiment demonstrated the advantage

of using the sensitivity-weighted search space for modal correlation

methods. Significant false detection was reduced by adopting the

technique, especially for the GMSEE method.

5. The proposed GMSEE and MSEE correlation methods and the enhanced

technique have also been validated for a real bridge, the I-40 Bridge in

NM, USA. Only modal properties of the first two modes were used due

to their higher reliability compared to the higher order modes. Also, the

two most severe damage levels, E-3 and E-4, were used for the analysis.

Damage identification by the GMSEE and MSEE correlation methods

incorporating with the sensitivity-weighting technique was performed.

Both methods successfully detected the actual damage location for the

two damage scenarios. Also, both methods generated a false detection at

the mid span of the south girder for the damage case E-3 but this is

acceptable as the two girders were well connected by a system of concrete

deck, stringers and floor beams. It was found that the MSEE method

showed slightly better prediction in both damage cases. The damage

regions were more localized by the MSEE method rather than by the

GMSEE method.

Page 194: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 166

© 2017 Khac-Duy Nguyen Page 166

Results also demonstrated the important role of the sensitivity-weighted

search space in reducing false-positive detection. Performance of both

damage identification methods generally reduced when the conventional

search space was used instead of the sensitivity-weighted search space.

The actual damage location could still be detected but more false

locations were observed.

In summary, this research provided an innovative development of correlation-

based damage identification scheme including robust damage identification

algorithms and effective search space technique. The new damage identification

algorithms (i.e., GMSEE- and MSEE-based methods) incorporated with the

enhanced search space technique are capable of detecting the locations of damage

and estimating their damage extents. The methods work reliably for single and

multiple damage scenarios. Generally, the MSEE correlation method gives better

damage identification results compared to the GMSEE method. However, the MSEE

requires information of structural stiffness. Moreover, by employing the sensitivity-

weighted search space, the predictions by the both methods can significantly

improve. Therefore, in the cases where sufficient modes can be measured and

structural information is not reliable, the GMSEE correlation method incorporated

with the sensitivity-weighting technique would be preferred. In the case where only

few modes can be measured and the structural stiffness can be obtained properly, the

MSEE correlation method incorporated with the sensitivity-weighting technique

would be preferred.

Page 195: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 167

© 2017 Khac-Duy Nguyen Page 167

8.2 FUTURE STUDIES

Although the proposed damage identification algorithms and enhanced search

space technique have shown their promise for several illustrative numerical and

experimental examples, there are several issues which need to be addressed to make

them more applicable for practice. Recommendations for future work include the

following:

1. The present study used MDLAC as a basis for estimating the correlation

level between the measured modal vector and numerical one. It would be

beneficial to conduct a comparative study on using different correlation

functions. Then ones can choose appropriate function for their particular

problem.

2. The proposed damage identification methods and enhanced technique

have been verified for several structure types such as spring-mass system,

multi-story building, truss structure and plate-on-girder bridge. There is a

need to extent the study to other types of structures such as plates, frames,

cable-supported bridges, arch bridges.

3. The methodologies developed in this study were derived by considering

damage as stiffness reduction in structural elements. Although it is

popularly used to represent many types of damage, there is a need to

extent this study for real damage types such as crack, corrosion, material

degradation, etc. The information of damage in real forms would help to

evaluate more accurately the impact of the damage on the structure.

4. The study showed some limitations on prediction accuracy especially on

damage extent estimation. The undamaged stiffness matrix was used to

calculate the damaged MSEE sensitivity which could generate some

errors. Therefore, development of a more effective approach for damage

extent estimation is necessary. Besides, more effort should be made on

developing techniques of reducing false-positive identification.

Page 196: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Chapter 8: Conclusions and Future Studies Page 168

© 2017 Khac-Duy Nguyen Page 168

5. In the experimental study for the QUT through truss bridge mode, a

damage threshold of 10% was used for the discrimination of undamaged

and damaged states. The identification of the damage threshold should be

systematically studied in the future. Moreover, there are some issues in

the experimental test that should be carefully examined in the future.

They include effect of mass variation due to sensor roving, and

improvement of frequency resolution. Identification of true stiffness

constants of truss members at various bolt torques is also recommended as

future study.

6. This research only considered damage at some elements in both numerical

and experimental studies. In future, a study on the sensitivity of the

proposed methods to damage at different locations with different extents

should be carried out.

Page 197: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 169

© 2017 Khac-Duy Nguyen Page 169

References

Abdel Wahab, M. M., and De Roeck, G. (1999). Damage detection in bridges using

modal curvatures: application to a real damage scenario. Journal of Sound and

Vibration, 226(2), 217-235.

Adams, R.D., Cawley, P., Pye, C.J. and Stone, B.J. (1978). A vibration technique for

non-destructively assessing the integrity of structures. J. Mech. Eng. Science,

20(2), 93-100.

Aktan, A.E., Lee, K.L., Chuntavan, C. and Aksel, T (1994). Modal testing for

structural identification and condition assessment of constructed facilities.

Proceedings of 12th International Modal Analysis Conference, Honolulu,

Hawaii, 1, 462-468.

Aktan A.E., Catbas F.N., Grimmelsman K.A. and Tsikos C.J (2000). Issues in

infrastructure health monitoring for management. Journal of Engineering

Mechanics (ASCE), 126, 711–724.

An, Y., Jo. H., Spencer Jr, B.F. and Ou, .J (2014). A damage localization method

based on the ‘jerk energy’. Smart Materials and Structures, 23, 1-14.

Balageas, D., Fritzen, C.-P. and Güemes, A. (2006). Structural health monitoring.

John Wiley & Sons Inc.

Bandara, R. P., Chan, T. H. T., and Thambiratnam, D. P. (2014). Frequency response

function based damage identification using principal component analysis and

pattern recognition technique. Engineering Structures, 66, 116-128.

Cawley, P., and Adams, R.D. (1979). The location of defects in structures from

measurements of natural frequencies. Journal of Strain Analysis for

Engineering Design, 14(2), 49-57.

Chan T.H.T. and Thambiratnam D.P. (Editors) (2011). Structural Health Monitoring

in Australia, Nova Science Publisher, New York Inc.

Chen, B., and Nagarajaiah, S. (2007). Flexibility-based structural damage

identification using Gauss-Newton method. Proceedings of SPIE – Sensors and

Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems,

San Diego, USA.

Chou, J. H. and Ghaboussi, J. (2001). Genetic algorithm in structural damage

detection. Computers and Structures, 79, 1335-1353.

Christides, S. and Barr, A.D.S. (1984). One-dimensional theory of Bernoulli–Euler beams.

International Journal of Mechanical Science, 26, 639–648.

Cowled, C.J.L., Thambiratnam, D.P., Chan, T.H.T. and Tan, A.C.C. (2015).

Structural complexity in structural health monitoring: Preliminary experimental

Page 198: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 170

© 2017 Khac-Duy Nguyen Page 170

modal testing and analysis. Proceedings of the 7th World Congress on

Engineering Asset Management (WCEAM 2012), Daejeon, South Korea, 183-

193.

Cross, E.J., Koo, K.Y., Brownjohn, J.M.W. and Worden, K. (2013). Long-term

monitoring and data analysis of the Tamar Bridge. Mechanical Systems and

Signal Processing, 35, 16-34.

Dackermann, U. (2010). Vibration-based damage identification methods for civil

engineering structures using artificial neural networks. PhD Dissertation,

University of Technology Sydney.

Doebling, S. W., Farrar, C. R., and Prime, M. B. (1998). A summary review of

vibration-based damage identification methods. Shock and Vibration Digest,

30(2), 91-105.

Doebling, S.W., Farrar, C.R. and Goodman, R.S. (1997). Effects of measurement

statistics on the detection of damage in the Alamosa Canyon Bridge.

Proceedings of the 15th International Modal Analysis Conference, Orlando,

Florida, USA, 919-929.

Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996). Damage

identification and health monitoring of structural and mechanical systems from

changes in their vibration characteristics: A literature review. Report No. LA-

13070-MS, Los Alamos National Laboratory, Los Alamos, NM.

Duffey, T. A., Doebling, S. W., Farrar, C. R., Baker, W. E. and Rhee, W. H. (2001).

Vibration-based damage identification in structures exhibiting axial and

torsional response. Journal of vibration and acoustics, 123(1), 84-91.

Fan, W., and Qiao, P. (2009). A 2-D continuous wavelet transform of mode shape

data for damage detection of plate structures. International Journal of Solids

and Structures, 46(25–26), 4379-4395.

Fan, W., and Qiao, P. (2010). Vibration-based damage identification methods: a

review and comparative study. Structural Health Monitoring. 10(1), 83-111.

Farrar, C.R., Baker, W.E., Bell, T.M., Cone, K.M., Darling, T.W., Duffey, T.A.,

Eklund, A. and Migliori, A. (1994). Dynamic characteristics and damage

detection in the I-40 bridge over the Rio Grande. Report No. LA-12767-MS,

Los Alamos National Laboratory, Los Alamos, NM.

Farrar, C.R. and Jauregui, D. (1996) Damage detection algorithms applied to

experimental and numerical modal data from the I-40 bridge. Report No.

13074-MS, Los Alamos National Laboratory, NM, USA.

Farrar C.R. and Doebling S.W. (1997). An overview of modal-based damage

identification methods. Proceedings of DAMAS conference, 269-278.

Farrar, C.R., Doebling, S.W., Cornwell, P.J and Straser, E.G. (1997). Variability of

modal parameters measured on the Alamosa Canyon Bridge. Proceedings of

Page 199: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 171

© 2017 Khac-Duy Nguyen Page 171

the 15th International Modal Analysis Conference, Orlando, Florida, USA, 257-

263.

Farrar C.R and Doebling S.W. (1998). Damage detection II: Field applications to

large structures. Report LA-UR-98-1497 , Los Alamos National Laboratory,

Los Alamos, NM.

Figueiredo, E., Park, G., Figueiras, J., Farrar, C. and Worden, K. (2009). Structural

health monitoring algorithm comparisons using standard data sets. Report No.

LA-14393, Los Alamos National Laboratory, Los Alamos, NM.

Friswell M, Penny J and Garvey S. (1997). Parameter subset selection in damage

location. Inverse Problems in Engineering, 5, 189 –215.

Friswell, M., Penny, J., and Garvey, S. (1998). A combined genetic and

eigensensitivity algorithm for the location of damage in structures. Computers

& Structures, 69(5), 547-556.

Geem, Z. W., Kim, J. H., and Loganathan, G. (2001). A new heuristic optimization

algorithm: harmony search. Simulation, 76(2), 60-68.

Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine

Learning. Addison-Wesley Longman Publishing Co., Inc.

Gomes, H. M., and Silva, N. R. S. (2008). Some comparisons for damage detection

on structures using genetic algorithms and modal sensitivity method. Applied

Mathematical Modelling, 32(11), 2216-2232.

Gudmundson, P. (1982). Eigenfrequency changes of structures due to cracks, notches

or other geometrical changes. Journal of Mechanics and Physics of Solids,

30(5), 339-353.

Hao, H., and Xia, Y. (2002). Vibration-based damage detection of structures by

genetic algorithm. Journal of Computing in Civil Engineering, 16(3), 222-229.

Hosseinzadeh, A. Z., Bagheri, A., Amiri, G. G., and Koo, K.-Y. (2014). A flexibility-

based method via the iterated improved reduction system and the cuckoo

optimization algorithm for damage quantification with limited sensors. Smart

Materials and Structures, 23(4), 045019.

Hou, Z., Noori, M., and Amand, R. S. (2000). Wavelet-based approach for structural

damage detection. Journal of Engineering Mechanics, 126(7), 677-683.

Hu, S.J., Wang, S., and Li, H. (2006). Cross-modal strain energy method for

estimating damage severity. Journal of Engineering Mechanics, 132(4), 429-

437.

Jayawardhana, M., Zhu, X., and Liyanapathirana, R. (2011). An experimental study

on distributed damage detection algorithms for structural health monitoring.

Journal of Physics: Conference Series, 305, 1-11.

Page 200: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 172

© 2017 Khac-Duy Nguyen Page 172

Jayawardhana, M., Zhu, X., and Liyanapathirana, R. (2013). Damage detection of

reinforced concrete structures based on the Wiener filter. Australian Journal of

Structural Engineering, 14(1), 57-69.

Kang, F., Li, J.J. and Xu, Q. (2012). Damage detection based on improved particle

swarm optimization using vibration data. Applied Soft Computing, 12(8), 2329-

2335.

Kartal, M.E., Mulvihill, D.M., Nowel, D. and Hills D.A. (2011). Measurements of

pressure and area dependent tangential contact stiffness between rough

surfaces using digital image correlation. Tribology International, 44, 1188-

1198.

Kennedy, J., and Eberhart, R. (1995). Particle swarm optimization. Proceedings of

IEEE International Conference on Neural Networks, 4(2), 1942-1948.

Kim, J.T. and Stubbs, N. (1995). Model-uncertainty impact and damage detection

accuracy in plate girder. Journal of Structural Engineering, 121(10), 1409-

1417.

Kim, J.T., and Stubbs, N. (2002). Improved damage identification method based on

modal information. Journal of Sound and Vibration, 252(2), 223-238.

Kim, J.T. and Stubbs, N. (2003). Nondestructive crack detection algorithm for full-

scale bridges. Journal of Structural Engineering, 129, 1358-1366.

Kim, J.T., Park, J.H., Yoon, H.S. and Yi, J.H. (2007). Vibration-based damage

detection in beams using genetic algorithm. Smart Structures and Systems,

3(3), 263-280.

Kim, J.T., Ryu, Y.S., Cho, H.M. and Stubbs, N. (2003a). Damage identification in

beam-type structures: frequency-based method vs mode shape-based method.

Eng. Structures, 25, 57-67.

Kim, J.T., Yun, C.B and Yi, J.H. (2003b). Temperature effects on frequency-based

damage detection in plate-girder bridges. KSCE Journal of Civil Engineering,

7(6), 725-733.

Kim, J.T., Park, J.H. and Lee, B.J. (2007). Vibration-based damage monitoring in model plate-

girder bridges under uncertain temperature conditions. Engineering Structures, 29, 1354–

1365.

Ko, J. M., Ni, Y.-Q. and Chan, H.-T. T. (2000). Feasibility of damage detection of

Tsing Ma Bridge using vibration measurements. Proceedings of the SPIE's 5th

Annual International Symposium on Nondestructive Evaluation and Health

Monitoring of Aging Infrastructure, USA.

Ko, J., Wong, C., and Lam, H. (1994). Damage detection in steel framed structures

by vibration measurement approach. Proceedings of the 12th International

Modal Analysis Conference (IMAC), USA, 280-286.

Page 201: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 173

© 2017 Khac-Duy Nguyen Page 173

Koo, K.Y., Sung, S.H. and Jung, H.J. (2010). Damage Quantification of Shear

Buildings Using Deflections Obtained by Modal Flexibility. Smart Materials

and Structures, 20(4), 1-9.

Lee, K. S., and Geem, Z. W. (2005). A new meta-heuristic algorithm for continuous

engineering optimization: harmony search theory and practice. Computer

methods in applied mechanics and engineering, 194(36), 3902-3933.

Lieven, N., and Ewins, D. (1988). Spatial Correlation of Mode Shapes, the

Coordinate Modal Assurance Criterion (COMAC). Proceedings of the 4th

International Modal Analysis Conference (IMAC), USA, 690-695.

Liu, X., Cao, J., Xu, Y., Wu, H., and Liu, Y. (2009). A multi-scale strategy in

wireless sensor networks for structural health monitoring. Proceedings of 5th

International Conference on Intelligent Sensors, Sensor Networks and

Information Processing (ISSNIP), Melbourne, Australia.

MATLAB 2012a (2012). Natick, Massachusetts: The Mathworks Inc.

Messina, A., Jones, I.A. and Williams, E.J. (1996). Damage detection and

localization using natural frequency changes. Proceedings of International

Conference on Identification in Engineering Systems, Swansea, UK.

Messina, A., Williams, E., and Contursi, T. (1998). Structural damage detection by a

sensitivity and statistical-based method. Journal of Sound and Vibration,

216(5), 791-808.

Miguel, L. F. F., Miguel, L. F. F., Kaminski Jr, J., and Riera, J. D. (2012). Damage

detection under ambient vibration by harmony search algorithm. Expert

Systems with Applications, 39(10), 9704-9714.

Ni, Y.Q., Zhou, H. F., Chan, K. C., and Ko, J. M. (2008). Modal Flexibility Analysis

of Cable-Stayed Ting Kau Bridge for Damage Identification. Computer-Aided

Civil and Infrastructure Engineering, 23(3), 223-236.

Ni, Y.Q., Wang, B. S., and Ko, J. M. (2000). Simulation studies of damage location

in Tsing Ma Bridge deck. Proceedings of the SPIE's 5th Annual International

Symposium on Nondestructive Evaluation and Health Monitoring of Aging

Infrastructure, San Diego, USA

Ni, Y.Q., Hua, X.G., Fan, K.Q. and Ko, J.M. (2005). Correlating modal properties with

temperature using long-term monitoring data and support vector machine technique.

Engineering Structures, 27, 1762–1773.

Nguyen T., Chan, T.H.T., and Thambiratnam D.P. (2014). Effects of wireless sensor

network uncertainties on output-only modal analysis employing merged data of

multiple tests. Advances in Structural Engineering, 17(3), 319-329.

Pandey, A. K., and Biswas, M. (1994). Damage Detection in Structures Using

Changes in Flexibility. Journal of Sound and Vibration, 169(1), 3-17.

Page 202: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 174

© 2017 Khac-Duy Nguyen Page 174

Pandey, A.K., Biswas, M., and Samman, M.M. (1991). Damage detection from

changes in curvature mode shapes. Journal of Sound and Vibration, 145(2),

321-332.

Pandey, P.C. and Barai, S.V. (1995). Multilayer perceptron in damage detection of

bridge structures. Computers & Structures, 54(4), 597-608.

Park, J.W., Sim, S.H. and Jung, H.J. (2013). Wireless sensor network for

decentralized damage detection of building structures. Smart Structures and

Systems, 12(3-4), 399-414.

Peeters, B., and De Roeck, G. (2001). One-year monitoring of the Z 24-Bridge:

environmental effects versus damage events. Earthquake engineering &

structural dynamics, 30(2), 149-171.

Rahai, A., Bakhtiari-Nejad, F. and Esfandiari, A. (2007). Damage assessment of

structure using incomplete measured mode shape. Structural Control and

Health Monitoring, 14(5), 808-829.

Ren, W. X. and De Roeck, G. (2002). Structural damage identification using modal

data. I: Simulation verification. Journal of Structural Engineering, 128, 87-95.

Rytter, A. (1993). Vibration based inspection of civil engineering structures. PhD

Dissertation, Aalborg University, Denmark.

Rytter, A. and Kirkegaard, P. H. (1994). Vibration based inspection of a steel mast.

Proceedings of the 12th International Modal Analysis Conference, Honolulu,

Hawaii, 1602-1608.

Salane, H., and Baldwin Jr, J. (1990). Identification of modal properties of bridges.

Journal of Structural Engineering, 116(7), 2008-2021.

Salawu, O.S. (1997). Detection of structural damage through changes in frequency: a

review. Engineering Structures, 19(9), 718-723.

Seyedpoor, S.M. (2012). A two stage method for structural damage detection using a

modal strain energy based index and particle swarm optimization. International

Journal of Non-Linear Mechanics, 47(1), 1-8.

Shi, Z.Y., Law, S.S., and Zhang, L.M. (1998). Structural damage localization from

modal strain energy change. Journal of Sound and Vibration, 218(5), 825-844.

Shi, Z., Law, S., and Zhang, L. M. (2000a). Structural damage detection from modal

strain energy change. Journal of Engineering Mechanics, 126(12), 1216-1223.

Shi, Z.Y., Law, S.S. and Zhang, L.M. (2000b). Damage localization by directly using

incomplete mode shapes. Journal of Engineering Mechanics, 126(6), 656-660.

Sinha, J.K., Friswell, M.I. and Edwards, S. (2002). Simplified models for the

locations of cracks in beam structures using measured vibration data. Journal

of Sound and Vibration, 251, 13-38.

Page 203: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 175

© 2017 Khac-Duy Nguyen Page 175

Shih, H.W. (2009). Damage assessment in structures using vibration characteristics.

PhD Dissertation, Queensland University of Technology.

Sohn, H., and Farrar, C. R. (2001). Damage diagnosis using time series analysis of

vibration signals. Smart Materials and Structures, 10(3), 446-451.

Sohn, H., Czarnecki, J. A., and Farrar, C. R. (2000). Structural health monitoring

using statistical process control. Journal of Structural Engineering, 126(11),

1356-1363.

Stubbs, N. and Osegueda, R. (1990). Global non-destructive damage evaluation in

solids. The International Journal of Analytical and Experimental Modal

Analysis, 5(2), 67-79.

Stubbs, N., Kim, J., and Topole, K. (1992). An efficient and robust algorithm for

damage localization in offshore platforms. Proceedings of ASCE 10th

Structures Congress, New York, USA, 543-546.

Wang, L. and Chan, T.H.T. (2009). Review of vibration-based damage detection and

condition assessment of bridge structures using structural health monitoring.

QUT Conference Proceedings.

Wang, F.L., Chan, T.H.T., Thambiratnam, D.P., Tan, A.C.C. and Cowled, C.J.L.

(2012). Correlation-based damage detection for complicated truss bridges

using multi-layer genetic algorithm. Advances in Structural Engineering,

15(5), 693-706.

Wang, L. (2012). Innovative damage assessment of steel truss bridges using modal

strain energy correlation. PhD Dissertation, Queensland University of

Technology.

West, W. M. (1986). Illustration of the use of modal assurance criterion to detect

structural changes in an Orbiter test specimen. Proceedings of the Air Force

Conference on Aircraft Structural Integrity, Los Angeles, USA, 1-6.

Wu, X., Ghaboussi, J., and Garrett Jr, J. H. (1992). Use of neural networks in

detection of structural damage. Computers & Structures, 42(4), 649-659.

Yang, X.S. and Deb, S. (2009). Cuckoo Search via Levy flights. Proceedings of the

Nature & Biologically Inspired Computing (NaBIC 2009): IEEE Publications,

4, 210-214.

Yi, J.H., Kim, D. and Feng, M.Q. (2009). Periodic seismic performance evaluation of

highway bridges using structural health monitoring system. Structural

Engineering and Mechanics, 31(5), 527-544.

Zadeh, L.A. (1994). Fuzzy logic, neural networks, and soft computing.

Communications of the ACM, 37(3), 77-84.

Zhao, J., & DeWolf, J. T. (1999). Sensitivity study for vibrational parameters used in

damage detection. Journal of Structural Engineering, 125(4), 410-416.

Page 204: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Reference Page 176

© 2017 Khac-Duy Nguyen Page 176

Page 205: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Appendices Page 177

© 2017 Khac-Duy Nguyen Page 177

Appendices

APPENDIX – A: EXAMPLES OF GEOMETRIC QUANTITY OF STIFFNESS MATRIX

Elem

ent ty

pe

Stiffn

ess matrix

G

eom

etric quan

tity o

f stiffness m

atrix

Flex

ural elem

ent

Ax

ial elem

ent

Flex

ural +

axial E

lemen

t

For flex

ural co

mp

onen

t:

For ax

ial com

ponen

t:

Page 206: Khac-Duy Nguyen M.E., B Duy Nguyen.pdf · 2018-05-28 · Khac-Duy Nguyen M.E., B.E A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School

Appendices Page 178

© 2017 Khac-Duy Nguyen Page 178

APPENDIX – B: PUBLICATIONS DERIVED FROM THIS PROJECT

Journal Articles:

Nguyen, K.D., Chan, T.H.T. and Thambiratnam, D.P. (2016). Structural damage

identification based on change in geometric modal strain energy-eigenvalue

ratio. Smart Materials and Systems, 25, 14pp.

Nguyen, K.D., Chan, T.H.T., Thambiratnam, D.P. and Nguyen, A. A new modal

strain energy method for damage identification using a correlation technique

(Under preparation).

Nguyen, K.D., Chan, T.H.T., Thambiratnam, D.P. and Nguyen, A. Damage

identification for a complex truss structure using correlation approach and

sensitivity-weighted search space technique (Under preparation).

Conference papers:

Nguyen, K.D., Chan, T.H.T. and Thambiratnam, D.P. (2015). Correlation-based

damage detection using geometric modal strain energy and natural frequency.

Proceedings of the 7th International Conference on Structural Health

Monitoring of Intelligent Infrastructures (SHMII-7), Turin, Italy (July 2015)