Applied System Identification for Constructed Civil Structures
Dionysius Siringoringo, Ph.DBridge & Structure Lab, Univ. of Tokyo
July 22, 2010
Series of lecture on Asia-Pacific Summer School on Smart Structures and Control
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Outline
• Introduction- Definition
- Objectives - Scope
• Experimental Methods- Classification
- Type of Excitation - Type of Response
• Analysis Methods- Classification : Parametric vs Non-parametric
- Type of Model : Structural vs Modal vs Non-Physical Numerical Model - Domain: Time vs Frequency vs Cross Time-Frequency
• Uncertainties
• Examples of Application
• Discussions and Closure
1. Introduction : Definition
• A process to develop or improve mathematical representation of a structural system using experimentally obtained structural response(s).
• Mathematical representation of a structural system: Mass, Stiffness, Damping, Flexibility, Connectivity
• Experimentally obtained structural response : vibrations, static response/deflection, strain response etc.
• System identification is a broad term, when ‘system’ refers to structural system, the term structural identification is commonly used.
Why System Identification for constructed structures ?
1. Model Validation of newly constructed structures- verify assumptions in design model (e.g. boundary condition, nonlinear behavior, energy dissipation mechanism/ damping)- verify performance of control system (e.g. base-isolation, Tuned Mass Damper, etc)
2. Model Updating- obtain FEM calibrated structural model- adjust structural parameters after retrofit or modification
3. Structural/Condition Assessment and Health Monitoring- detect structural changes possibly due to defect or damage- recognize environment/loading influence or pattern on the structure
1.Introduction : Objectives
Why System Identification for constructed structures ?
4. Earthquake Engineering- performance of structure during earthquake- post-earthquake structural assessment
5. Wind Engineering- verification/comparison with wind tunnel results - aerodynamic performance (e.g. aerodynamic damping of long-span bridges)
6. Soil-Structure Interaction- characterize and quantify parameter of surrounding soil medium
7. Traffic-structure Interaction- characterize structural response due to certain type of vehicle/train
- detect changes in structure-vehicle interaction medium (e.g. pavement effect on bridge response, railway track effect on train comfort measure)
1.Introduction : Objectives
Example of Global Structural Identification : Modal identification of instrumented bridges for global assessment of the structure
Yokohama Bay Bridge
1.Introduction : Scopes – Global and Local
Free-vibration test of stay cable by pull-and-release test.
80 100 120 140 160 180 200 220-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
=0.055487
Time (s)
Lo
g (
Pe
ak
Acc
) lo
g(m
/s2 /s)
Log of Envelopes of Filtered Acceleration-Cable119SDATA15-Channel1-Mode1]
peakvalleyaverage
Cable Hydraulic damper
Example of Local Structural Identification : Evaluation of damping on stay cable of cable-stayed bridge to asses the effectiveness of cable damper system.
Stonecutters Bridge
Single mode decay response of the cable : f = 0.49 Hz
Cable damping (logarithmic decrement : d= 0.055)
1.Introduction : Scopes – Global and Local
The required data is data collected during experiment and can be classified into:
• Excitation : measurements made of disturbance forces, pressure, impact, stress applied to the structure.
• Response: measurements made of the reactions of the structures to the applied disturbance, such as, deflection, displacement, velocity, acceleration, strain etc.
2.Exp Methods : Classification of Required Data
The excitation can be classified as: 1. Dynamic or static (i.e. according to whether or not they engage
inertial effects) 2. According to controllability, and3. According to measurability
4. Controllable (measurable and un-measurable) static loads5. Uncontrollable (measurable and un-measurable) static loads6. Controllable (measurable and un-measurable) dynamic loads 7. Uncontrollable measurable dynamic loads 8. Uncontrollable un-measurable dynamic input (ambient
dynamic excitation)
2.Exp Methods : Type of Excitation
Controllable (measurable and un-measurable) static loadsRelatively rare for full-scale experiments on real structures because of the scale of the load required to generate a measurable effect.
Common example is proof testing of bridges often involving use of heavy vehicles, either stationary or moving
Uncontrollable (measurable and un-measurable) static loads
Generally include elements of dynamic load and response monitoring, particularly in the case of traffic and wind which generate quasi-static and dynamic response.
2.Exp Methods : Static Loads
• Forced vibration test (FVT)Transfer functions or frequency response functions (FRFs) scale input (forcing) to output (response) via either mass or stiffness so can both be identified, along with high quality information about dissipative effects (mathematically realised as viscous damping)
Examples: mass exciters, Electro-dynamic shakers , instrumented hammer
2.Exp Methods : Dynamic Loads – Controllable Measurable
• Manual excitationImpulse response functions (IRF) or free-vibration response. Neither mass nor stiffness can be identified. Modal frequency and damping can be estimated quite accurately.
Examples: Impact hammer, people jump, drop weight test, Snap-back or or step relaxation test
2.Exp Methods : Dynamic Loads – Controllable Un-Measurable
Controllable but unmeasurable dynamic loads • Manual excitation : Impact Hammer Test
2.Exp Methods : Dynamic Loads – Controllable Un-Measurable Excitation
Giving excitation to a short span bridge by impact hammer
Free vibration response of the bridge subjected to impact hammer
Manual excitation : Drop Weight Test
2.Exp Methods : Dynamic Loads – Controllable Un-Measurable Excitation
Giving excitation to a short span bridge by dropping sand bag weight
Example of Free vibration response of the bridge excited by dropped weight
Note: while drop weight test is effective in exciting the free-vibration response of the structure, additional damping is expected as the dropped weight tends to increase the damping.
80 100 120 140 160 180 200 220-1.5
-1
-0.5
0
0.5
1
1.5
Time (s)
Acce
lera
tio
n (
m/s
2 )
Manual excitation : Pull-and-released test of stay cable
2.Exp Methods : Dynamic Loads – Controllable Un-Measurable Excitation
Giving excitation to a stay cable by pull-and released test
Example of free vibration response of a stay cable
Free-Vibration ResponseRaw Data Frequency Response
Filtering mode of interest
Single-mode free-vibration response
Logarithmic Decrement using envelope of decay response
Single-mode damping value
Flowchart to obtain damping value of a stay cable
Vehicle excitation/ Controlled Traffic
2.Exp Methods : Dynamic Loads – Controllable Un-Measurable Excitation
Vehicle excitation:1. Response larger than ambient vibration
response.2. Stress and acceleration responses can
be conducted simultaneously3. Effect of vehicle-bridge interaction
should be considered in analysis.
Example of strain response when a truck passing a bridge
Example of acceleration response when a truck passing a bridge
Seismic excitationTransfer functions or frequency response functions (FRFs) between seismic input (base excitation) to output (structure response) . Structural properties, modal properties and modal participation factor can be estimated.
Example: instrumented bridges and buildings in Japan and California US.
2.Exp Methods : Dynamic Loads – Uncontrollable Measurable Excitation
Example : Yokohama-Bay Bridge, instrumented cable-stayed bridge near Tokyo
Ambient excitation : wind, traffic, and unmeasured micro-tremor.Correlations between response are used to estimate modal properties. Mode-shapes unscaled. Treated as stochastic system identification.
Example: periodic ambient vibration measurement and instrumented bridges and buildings.
2.Exp Methods : Dynamic Loads – Uncontrollable un-measurable Excitation
Example of ambient excitation : wind-induced vibration of suspension bridge.
2.Exp Methods : Dynamic Loads – Uncontrollable un-measurable Excitation
Tower acceleration response
Treated as stationary random process.
Example of ambient excitation : traffic-induced vibration of bridge.
2.Exp Methods : Dynamic Loads – Uncontrollable un-measurable Excitation
Bridge response subjected to open traffic usually treated as stationary random process, since the input is unknown. Effect of vehicle mass is usually neglected. However, in case of short span bridge, the effect of vehicle mass may not be negligible and influence the identified bridge frequency.
Example of vertical acc and the spectrum of a medium span highway bridge to traffic.
Static : Strain, Deflection
Dynamic:• Acceleration• Relative of absolute displacement• Velocity• Inclination• Strain• Stress• Water Pressure• Structural and environmental temperature• Wind Velocity• Wind Direction
2.Exp Methods : Type of Response Excitation
Parametric and Non-parametric Models
Parametric ModelStructural model and initial estimate of model parameters are known a priori. Measured responses are fitted to obtain the best estimate of model parameters.
Non-Parametric ModelModel structure is not specified a priori. Structural responses are used to obtain model parameters by means of dynamical system and quantities such as cross/auto-correlations, transfer function/frequency response function.
3. Analysis Methods: Classification
Example of Parametric ModelOutput-Error Minimization for system identification using seismic response.
Example : comparison between recorded response and computed response of a bridge deck subjected to seismic excitation
Minimize the difference between the measured modal parameters and model generated modal parameters by updating parameters of the model iteratively
3. Analysis Methods: Classification
Theoretical model or structural model is required
F = objective function
Example of Non-Parametric ModelState-Space System identification using seismic response.
3. Analysis Methods: Classification
By modeling the input-output relationship of seismic-induced vibration using state-space model and realization of observability matrix, system matrices A, B, R and D can be obtained and modal parameters are realized.
1. Structural Model• System is modeled in terms of mass, stiffness, or flexibility, and
damping matrices.• Geometric distribution of mass, stiffness and damping are known • Structural connectivity between degree of freedom is preserved
3. Analysis Methods: Types of Model
( 1) ( ) ( )x k A x k B z k
( ) ( ) [ ] ( )y k R x k D z k
)()()()( tBztKutuCtuM
tCMKM
IA
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0exp
Equation of motion :
System matrix A in state-space form for discrete data:
Equation of motion in discrete dynamic system, where system matrix A is to be indentified
Goal : To Indentify system matrix A in its original form, from which the mass, stiffness and damping matrices can be retrieved.
2. Modal Model• System is defined in modal coordinates describing the vibratory motion of
structures in terms of modal frequency, modal damping and mode shapes (also mode phase angle for complex modes)
• Geometric distribution of mass, stiffness and damping and information on structural connectivity are not preserved.
• Describes the resonant spatial (mode shapes) and temporal of the structure. • Modal parameters are analogous to eigensolution of stuctural mass and
stiffness.
3. Analysis Methods: Types of Model
( 1) ( ) ( )x k A x k B z k
( ) ( ) [ ] ( )y k R x k D z k
Equation of motion in discrete dynamic system, where system matrix A is to be indentified
Goal : To Indentify system matrix A by solving theEigenvalue problem and determine the modes.
3. Non-Physical Numerical Model
• Does not have physical relationship with the structure (i.e. no spatial information, no geometry distribution of mass, stiffness, and damping)
• Simply a parameter curve-fit of the given mathematical model to the measured data.
• Examples : Auto Regressive Moving Average (ARMA) and its variants, Rational Polynomial Model etc.
• Some can be converted to modal model form.
3. Analysis Methods: Types of Model
)()()()(
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tdub
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tudb
du
tudb
tyadt
tdya
dt
tyda
dt
tyd
m
m
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m
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n
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nn
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Example : Auto Regressive Moving Average (ARMA) Model where the auto regressive coefficients can be related to modal parameters
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1. Frequency Domain
• Peak Picking Method• Transfer Function / Frequency Response Function/ Impulse
Response Function.• Average Normalized Power Spectrum Density (ANPSD)• Complex Exponential Frequency Domain Method (Schmerr
1982)• Eigensystem Realization Algorithm in Frequency Domain (ERA-
FD) (Juang & Suzuki 1988)• Frequency Domain Decomposition (Brincker et al. 2001)
3. Analysis Methods : Domain
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2. Time Domain
• Ibrahim Time Domain (ITD) (Ibrahim & Mikulcik 1973)• Least Squared Complex Exponential Method (LSCE) (Brown
1979)• Polyreference Complex Exponential Method (PRCE) (Vold et al.
1982)• Eigensystem Realization Algorithm (ERA) (Juang & Pappa 1985)• Stochastic Subspace Identification (Overschee & De Moor
1991)
3. Analysis Methods : Domain
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3. Cross Time-Frequency Domain Represents frequency evolution as time progresses. Can detect non-linearity and non-stationary signals
• Short Time Fourier Transform (STFT)• Wavelet-based system identification• Empirical Mode Decomposition – Hilbert Huang Transform (should be carefully applied since EMD lacks physical meaning of
signals)
3. Analysis Methods : Domain
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Direct MethodWhen the IRF/FRF is available, they can be use as input directly to system identification method.
Indirect MethodWhen the IRF/FRF is unavailable such as in case of ambient vibration measurement, an additional method is needed to construct synthetic IRF , ex. through cross-correlation (Natural Excitation Technique (NEXT) or through Random Decrement.
3. Analysis Methods : Direct and Indirect Method Time Domain
Raw Data NEXT ERA
Randec ITD
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3. Analysis Methods : Checklist
Types of Inputs and Outputs System Identification Method
Controllable dynamic loads Measured Input(s) Mass exciter and Shaker Transfer Functions (Input-Output SysID)
Instrumented Impact HammerSingle Input Single Output (SISO) or Single Input Multi Output (SIMO) system
Unmeasured Input (s) Manual excitation (people jumping) Impulse Response Function/ Free-vibration Response Snap-back, or step relaxation Impulse Response Function/ Free-vibration Response Swinging bell to excite a cathedral tower Impulse Response Function/ Free-vibration Response Uncontrollable dynamic loads Measured Input(s) seismic excitation (Single Input) Transfer function, SISO or SIMO seismic multiple excitation (Multiple Input) Transfer function matrix, MIMO Uncontrollable dynamic loads Unmeasured Input(s) ambient vibration test (operational modal analysis) Stationary broadband assumption wind excitation Output Cross-correlation traffic excitation Covariance-Driven System Identification microtremor with unmeasured input Data Driven Stochastic Subspace Identification
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Uncertainty is unavoidable in understanding the results of system identification. Modal properties are susceptible to variation even when structural condition remains the same.
How to quantify the confidence of the identified modal properties?
1. Error propagation analysis using perturbation method2. Monte Carlo Simulation3. Bootstrap Method
4. Uncertainties
4. Uncertainties : Error propagation analysis using perturbation
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Correlation Matrix Of Input-Output
[Ryy], [Ryu], [Ruu]
Input [Up]
Output [Yp]
Information Matrix [Rhh]
Realization of Modal Parameters
, , w z j
Realization of System Matrix [A]
Singular Value Decomposition
Up(e) = Up(0) + eDUp
Yp(e) = Yp(0) + eDYp
Ryy(e) = Ryy(0) + eDRyy
Ryu(e) = Ryu(0) + eDRyu
Ruu(e) = Ruu(0) + eDRuu
Correlation Matrix :Information Matrix
Rhh(e) = Rhh(0) + eDRhh
Realization of System Matrix
A(e) = A(0) + eDA
Singular Value Decomposition
Realization of Modal Parameters ( ) = (0) + w e weDw
( ) = (0) + z e zeDz
( ) = (0) + f e f eDf
Objectives:
To define and quantify the error on the modal parameters as the effect of input and output noise
Example of error propagation in System Realization using Information Matrix
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4. Uncertainties : Bootstrap Analysis
Example of investigation of the effect of variability and to estimate the confidence bounds of identified modal parameters by NEXT-ERA
CCF : Cross-correlation function
CCF1, CCF2, CCF3,…CCFN
Randomly selected
Randomly selected Ensemble 1 (M component)
CCF1, CCF5, CCF3,…CCFM
Compute CCF average
Ensemble 2 (M component)
CCF7, CCF2, CCF1,…CCFM
Compute CCF average
Randomly selected Ensemble P (M component)
CCF4, CCF6, CCF2,…CCFM
Compute CCF average
. . .
ERA
ERA
ERA
w1, x1,f1
w2, x2,f2
wp, xp,fp
. . .
Estimate mean value and 95% Confidence bound
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4. Uncertainties : Bootstrap Analysis
Distribution of modal parameters and their mean values and confidence level can be obtained
Modal parameters are considered as stochastic variable that have distribution with certain statistical characteristics . Therefore decision made on structural condition involved statistical confidence.
Examples of bridge 1st frequency statistical distribution on different structural conditions using Bootstrap Method
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5. Examples: Ambient Vibration Measurement of Suspension Bridge
Bridge Type:3-Span Suspension Bridge Simply-supported at the tower
Length: 1,380m
Span: 330-720-330 m
Total Deck Width: 20m
Tower Height : 130 m
Tower width : 21m at base18 m on top
Girder material : Streamlined steel-boxTower material : Steel box (welded) Completed : 1998
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5. Examples: Ambient Vibration Measurement of Suspension Bridge
Using NEXT -ERA Modal Parameters
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5. Examples: Ambient Vibration Measurement of Suspension Bridge
Structural identification : effect of friction force and aerodynamic forces on identified frequency and damping (Nagayama et. al 2005)
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5. Examples: Seismic-Induced System Identification of Cable-Stayed Bridge
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5. Examples: Seismic-Induced System Identification of Cable-Stayed Bridge
A data driven identification method was applied considering multiple input excitation and multiple responses (MIMO System)
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5. Examples: Seismic-Induced System Identification of Cable-Stayed Bridge
With dense instrumentation and good quality of seismic records we identify bridge modal parameters until high order
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(b) Typical Mixed Slip-Stick Mode (Earthquake 1995-07-03 )(a) Typical slip-slip Mode (Earthquake 1990-02-20)
Observation of the performance of seismic isolation devices using 1st longitudinal mode (Siringoringo & Fujino 2008 )
5. Examples: Seismic-Induced System Identification of Cable-Stayed Bridge
From the first longitudinal mode we can observe behavior of Link-Bearing Connection during earthquake.
Different behaviour of Link-Bearing Connection at the end-piers was observed during different level of earthquake excitation.
It was found that the expected slip-slip mode only occurred during large earthquake.
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Q & SQuestions and Sharing?
• Dionysius [email protected]
Suggested Readings Materials:
Theoretical and Experimental Modal Analysis by Maia, Silva, He, Lieven et al.Applied System Identification by Jer Nan JuangMonitoring and Assessment of Structures by GST ArmerThe State of the Art in Structural Identification of Constructed Facilities (ASCE Report 1999)
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