An Improved Modal Strain Energy Method for Damage...
Transcript of An Improved Modal Strain Energy Method for Damage...
Queensland University of Technology
CRICOS No. 00213J
An Improved Modal Strain Energy
Method for Damage Assessment
Presented By:
Buddhi L. WahalathantriD. P. Thambirathnam
T.H.T. Chan
S. Fawzia
CRICOS No. 00213Ja university for the worldrealR
Presentation Outline
• Introduction
• Theory: Strain Energy based Damage Indices
• Problem Identification
• Improved SE Method
• Results
• Conclusions & Future Work
CRICOS No. 00213Ja university for the worldrealR
Introduction
• Damage Detection
– Vibration Based Damage Identification Techniques
• Modal Strain Energy Method
• SE Method
– Damage Identification & Localization [Ref 6]
– Require first few modes to be measured and used
– False Alarms
– Not detect some damage locations (multiple damage)
– Improved SE Method
CRICOS No. 00213Ja university for the worldrealR
Theory: SE of a Euler Bernoulli Beam
• Strain energy of a Euler-Bernoulli beam: Mode
‘i’, Element ‘j’:
1 2 j N
Node 1 2 3 j j+1 N N+1
Distance 0 aj aj+1 L
CRICOS No. 00213Ja university for the worldrealR
SE based Damage Indices
• β1: Cornwell et al [Ref. 9]
• β2: Park et al [Ref. 10]
CRICOS No. 00213Ja university for the worldrealR
SE based Damage Indices
• β3: Li et al [Ref. 11] & Shih et al [Ref 12]
CRICOS No. 00213Ja university for the worldrealR
Problem Identification
• False Alarms
– At Nodal Points
• Indicates undamaged locations as damage
– Missing information
• Not detecting some damage locations
– Small damage severities
– Multiple damage locations
• Need higher mode addition
CRICOS No. 00213Ja university for the worldrealR
Improved SE Method
• New DI
– Minimise false alarms
– Improve damage detection
– Minimise number of modes
• Improved DI: β4
CRICOS No. 00213Ja university for the worldrealR
Improved SE Method
• Modification Function: MFij
– Using Mode shape curvature values
– Simply supported beam
CRICOS No. 00213Ja university for the worldrealR
Present Study Summarizes……..
• Simply Supported Beam
– Single Damage
• 28 Damage Cases
– 7 Damage Locations: L/8, 9L/56, 3L/16, L/4, 3L/8, 7L/16, L/2
– 4 Damage Severities: 10%, 20%, 30%, 40%
– Multiple Damage Cases (Two Damages):
• 32 Damage Cases
– By varying both Damage Locations and Severities
• Multiple Spans (Two Spans)• 30 Damage Cases
CRICOS No. 00213Ja university for the worldrealR
Method
• Data Analysis
– Data Analysis Software
• MATLAB Environment
• By Developing a Programme
• With GUI
• Supports 3 Types of Input (to date) data
– Experiment Results (extracted mode shape values)
– FEM Results: ABAQUS & SAP 2000
• Simultaneous Analysis with different number of modes
• Ability to address Forward and Inverse Problem
CRICOS No. 00213Ja university for the worldrealR
Results
• Simply Supported Beam
– Single Damage with different;
• Damage Location (DL)
• Damage Severity (DS)
– Multiple Damages
• Case 1: DL1 = L/4, DS1 = 40%, DL2 = L/2, DS2 = 40%
• Case 2: DL1 = L/4, DS1 = 10%, DL2 = L/2, DS2 = 40%
• Two Span Beam
– Damage locations: Mid Spans
CRICOS No. 00213Ja university for the worldrealR
Results: Comparison of DIs
• β1 vs. β4
– Simply supported beam [Ref. 12]
– DL: L/2
0
2.5
5
7.5
10
12.5
15
0 0.7 1.4 2.1 2.8
β1
Distance: x (m)
β1:Mode 3
-2
0
2
4
6
8
10
0 0.7 1.4 2.1 2.8
β4
Distance: x (m)
β4:Mode 3
CRICOS No. 00213Ja university for the worldrealR
Results: Comparison of DIs
• β2 vs. β4
– Simply Supported Beam
– DL1 = L/4, DS1 = 40%, DL2 = L/2, DS2 = 40%
-2
0
2
4
6
8
10
12
0 0.7 1.4 2.1 2.8
β4
Distance: x (m)
β4:Mode 2
0.98
1
1.02
1.04
1.06
1.08
1.1
0 0.7 1.4 2.1 2.8
β2
Distance: x (m)
β2:Mode 2
CRICOS No. 00213Ja university for the worldrealR
Results: Comparison of DIs
• β3 vs. β4
– Simply Supported Beam
– DL1 = L/4, DS1 = 10%, DL2 = L/2, DS2 = 40%
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
0 0.7 1.4 2.1 2.8
β3
Distance: x (m)
β3:Modes 1-5
-1
0
1
2
3
4
5
6
0 0.7 1.4 2.1 2.8
β4
Distance: x (m)
β4:Modes 1-5
CRICOS No. 00213Ja university for the worldrealR
Damage Index: β4
• Two Span Beam
– Damage at middle of each spans
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1.4 2.8 4.2 5.6
β4
Distance: x (m)
β4:Mode 1
-0.2
0
0.2
0.4
0.6
0.8
1
0 1.4 2.8 4.2 5.6
β4
Distance: x (m)
β4:Modes 1, 2 & 3
CRICOS No. 00213Ja university for the worldrealR
Damage Index: β4
• Potential to Damage Quantification
0
2
4
6
8
10
0 0.35 0.7 1.05 1.4
β4
Distance: x (m)
β4:Mode 1
DS=10%
DS=20%
DS=30%
DS=40%
CRICOS No. 00213Ja university for the worldrealR
Damage Index: β4
• Potential to Damage Quantification
0
2
4
6
8
10
0 5 10 15 20 25 30 35 40 45
β4
Damage Severity (DS%)
β4:Mode 1
x=0.4375 m
x=0.525 m
x=0.7 m
x=1.4 m
CRICOS No. 00213Ja university for the worldrealR
Conclusions
• Proposed Damage Index;
– Minimise False Alarms
– Improved damage detection
• Compared to other SE based methods
– Minimise Number of Modes
– Potential to Damage Quantification
CRICOS No. 00213Ja university for the worldrealR
Further Studies
• Improved Results with Noisy Data
– Up to 5% Noise
– Reinforced Concrete Beams
– Load Induced Damage Cases
• Need studies on;
– Damage quantification
Queensland University of Technology
CRICOS No. 00213J
Thank You
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