applied system identification for constructed civil …on stay cable of cable‐stayed bridge to...

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Applied System Identification for Constructed Civil Structures

Dionysius Siringoringo

Bridge & Structure Lab, Univ. of Tokyo

July 22, 2010

Outline

• Introduction‐ Definition‐ Objectives‐ Scope

• Experimental Methods‐ Classification ‐ Type of Excitation‐ Type of Response yp p

• 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 Closure2

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)

1.Introduction : Objectives

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

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

1.Introduction : Objectives

‐ 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)

Example of Global Structural Identification : Modal identification of instrumented bridges for global assessment of the structure

1.Introduction : Scopes – Global and Local

Yokohama Bay Bridge

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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

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

δ=0.055487

Time (s)

Log

(Pea

k A

cc) l

og(m

/s2 /

s)

peakvalleyaverage

Stonecutters Bridge

Single mode decay response of the cable : f = 0.49 Hz

Cable damping (logarithmic decrement : d= 0.055)

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.

2.Exp Methods : Classification of Required Data

• Response: measurements made of the reactions of the structures to the applied disturbance, such as, deflection, displacement, velocity, acceleration, strain etc.

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, and

3. According to measurability

2.Exp Methods : Type of Excitation

1. Controllable (measurable and un‐measurable) static loads

2. Uncontrollable (measurable and un‐measurable) static loads

3. Controllable (measurable and un‐measurable) dynamic loads

4. Uncontrollable measurable dynamic loads

5. Uncontrollable un‐measurable dynamic input (ambient dynamic 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

2.Exp Methods : Static Loads

Uncontrollable (measurable and un‐measurable) static loads

Generally include elements of dynamic load and response monitoring, particularly in the case of traffic and windwhich generate quasi‐static and dynamic response.

• 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

2.Exp Methods : Dynamic Loads – Controllable Measurable

damping)

Examples: mass exciters, Electro‐dynamic shakers , instrumented hammer

• Manual excitation

Impulse 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

2.Exp Methods : Dynamic Loads – Controllable Un‐Measurable

Examples: Impact hammer, people jump, drop weight test, Snap‐back or or step relaxation test

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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


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

tion

(m/s2 )

Manual excitation : Pull‐and‐released test of stay cable


Example of free vibration response of a stay cable

Giving excitation to a stay cable by pull‐and released test

Free‐Vibration ResponseRaw Data

Frequency Response

Filtering mode of interest

Single‐mode free‐vibrationresponse

Logarithmic Decrement using envelope of decay response

Single‐mode damping value

Flowchart to obtain damping value of a stay cable

Vehicle excitation/ Controlled Traffic


Example of strain response when a truck passing a bridge

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 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.

2.Exp Methods : Dynamic Loads – Uncontrollable un‐measurable Excitation

Example: periodic ambient vibration measurement and instrumented bridges and buildings.

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Example of ambient excitation : wind‐induced vibration of suspension bridge.


Tower acceleration response

Treated as stationary random process.

Example of ambient excitation : traffic‐induced vibration of bridge.


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

2.Exp Methods : Type of Response Excitation

• Inclination

• Strain

• Stress

• Water Pressure

• Structural and environmental temperature

• Wind Velocity

• Wind Direction

Parametric and Non‐parametric Models

Parametric Model

Structural model and initial estimate of model parameters are known a priori. Measured responses are fitted to obtain the best estimate of model parameters.

3. Analysis Methods: Classification

Non‐Parametric Model

Model 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.

Example of Parametric ModelOutput‐Error Minimization for system identification using seismic response.


Theoretical model or structural model is required

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

F = objective function

Example of Non‐Parametric Model

State‐Space System identification using seismic response.


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.

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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 Δ⎥

⎦

⎤⎢⎣

⎡−−

= −− 11

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


oda pa a e e s a e a a ogous o e ge so u o o s uc u a assand stiffness.

[ ] [ ]( 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


• Some can be converted to modal model form.

)()()()(

)()()()(

011

1

1

011

1

1

tubdt

tdubdu

tudbdu

tudb

tyadt

tdyadt

tydadt

tyd

m

m

mm

m

m

n

n

nn

n

−++=

−++

−

−

−

−

−

−

L

L

Example : Auto Regressive Moving Average (ARMA) Model where the auto regressive coefficients can be related to modal parameters

1. Frequency Domain

• Peak Picking Method• Transfer Function / Frequency Response Function/ Impulse

Response Function.• Average Normalized Power Spectrum Density (ANPSD)

l l h d ( h

3. Analysis Methods : Domain

• Complex Exponential Frequency Domain Method (Schmerr1982)

• Eigensystem Realization Algorithm in Frequency Domain (ERA‐FD) (Juang & Suzuki 1988)

• Frequency Domain Decomposition (Brincker et al. 2001)

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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.


Polyreference Complex Exponential Method (PRCE) (Vold et al. 1982)

• Eigensystem Realization Algorithm (ERA) (Juang & Pappa 1985)

• Stochastic Subspace Identification (Overschee & De Moor 1991)

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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

E i i l M d D iti Hilb t H T f


• Empirical Mode Decomposition – Hilbert Huang Transform(should be carefully applied since EMD lacks physical meaning of signals)

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Direct Method

When the IRF/FRF is available, they can be use as input directly to system identification method.

Indirect Method

3. Analysis Methods : Direct and Indirect Method Time Domain

When 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.

Raw Data NEXT ERA

Randec ITD

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3. Analysis Methods : Checklist

Types of Inputs and Outputs System Identification Method

Controllable dynamic loadsMeasured 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 ResponseSnap‐back, or step relaxation Impulse Response Function/ Free‐vibration ResponseSwinging bell to excite a cathedral tower Impulse Response Function/ Free‐vibration Response

Uncontrollable dynamic loadsMeasured Input(s)

seismic excitation (Single Input) Transfer function, SISO or SIMOseismic multiple excitation (Multiple Input) Transfer function matrix, MIMO

Uncontrollable dynamic loadsUnmeasured Input(s)

ambient vibration test (operational modal analysis) Stationary broadband assumption

wind excitation Output Cross‐correlation traffic excitation Covariance‐Driven System Identificationmicrotremor 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?

4. Uncertainties

1. Error propagation analysis using perturbation method2. Monte Carlo Simulation3. Bootstrap Method

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4. Uncertainties : Error propagation analysis using perturbation

Correlation Matrix Of Input‐Output

[Ryy], [Ryu], [Ruu]

Input [Up]

Output [Yp]

Information Matrix [Rhh]

Singular Value Decomposition

Up(ε) = Up(0) + εΔUp

Yp(ε) = Yp(0) + εΔYp

Ryy(ε) = Ryy(0) + εΔRyy

Ryu(ε) = Ryu(0) + εΔRyu

Ruu(ε) = Ruu(0) + εΔRuu

Correlation Matrix :Information Matrix

Rhh(ε) = Rhh(0) + εΔRhh

Realization of System

Singular Value Decomposition

Example of error propagation in System Realization using Information Matrix

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Realization of Modal Parameters

ω, ζ, ϕ

Realization of System Matrix [A]

Realization of System Matrix

A(ε) = A(0) + εΔA

Realization of Modal Parameters

ω(ε) = ω(0) + εΔω

ζ(ε) = ζ(0) + εΔζ

φ(ε) = φ(0) + εΔφ

Objectives:

To define and quantify the error on the modal parameters as the effect of input and output noise

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

CCF1, CCF2, CCF3,…CCFN

Randomly selected

Randomly selected Ensemble 1 (M component)

CCF1, CCF5, CCF3,…CCFMCompute CCF average

Ensemble 2 (M component)


ERA

ERA

ω1, ξ1,φ1

ω2, ξ2,φ2

CCF : Cross‐correlation function

Randomly selected Ensemble P (M component)


.

.

.

ERA

ωp, ξp,φp

.

.

.

Estimate mean value and95% Confidence bound

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4. Uncertainties : Bootstrap Analysis

Distribution of modal parameters and their mean values and confidence level can be obtained

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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‐box

Tower material : Steel box (welded)

Completed : 1998

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Using NEXT ‐ERA Modal Parameters

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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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A data driven identification method was applied considering multiple input excitation and multiple responses (MIMO System)

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With dense instrumentation and good quality of seismic records we identify bridge modal parameters until high order

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Observation of the performance of seismic isolation devices using 1st longitudinal mode (Siringoringo & Fujino 2008 )


(b) Typical Mixed Slip‐Stick Mode (Earthquake 1995‐07‐03 )

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(a) Typical slip‐slip Mode (Earthquake 1990‐02‐20)

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.

Q & S

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)

Q & SQuestions and Sharing?

• Dionysius Siringoringo

[email protected]‐tokyo.ac.jp

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applied system identification for constructed civil …on stay cable of cable‐stayed bridge to...

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