8/13/2010. Applied System Identification for Constructed Civil Structures. Outline. 1. Introduction : Definition. 1.Introduction : Objectives

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1 Outline Applied System Identification for Constructed Civil Structures Dionysius Siringoringo Bridge & Structure Lab, Univ of Tokyo July 22, 2010 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 2 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 1Introduction : Objectives Why System Identification for constructed structures? 1 Model Validation of newly constructed structures verify assumptions in design model (eg boundary condition, nonlinear behavior, energy dissipation mechanism/ damping) verify performance of control system (eg 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 1Introduction : 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 (eg 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 (eg pavement effect on bridge response, railway track effect on train comfort measure) 1Introduction : Scopes Global and Local Example of Global Structural Identification : Modal identification of instrumented bridges for global assessment of the structure Yokohama Bay Bridge 1

2 δ= Time (s) peak valley average 8/13/2010 1Introduction : Scopes Global and Local Example of Local Structural Identification : Evaluation of damping on stay cable of cable stayed bridge to asses the effectiveness of cable damper system 2Exp Methods : Classification of Required Data The required data is data collected during experiment and can be classified into: Stonecutters Bridge Cable Hydraulic damper Single mode decay response of the cable : f = 049 Hz 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 Free vibration test of stay cable by pull andrelease test Log (Peak Acc) log(m/s 2 /s) Cable damping (logarithmic decrement : d= 0055) 2Exp Methods : Type of Excitation The excitation can be classified as: 1 Dynamic or static (ie according to whether or not they engage inertial effects) 2 According to controllability, and 3 According to measurability 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) 2Exp Methods : Static Loads Controllable (measurable and un measurable) static loads Relatively 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 2Exp Methods : Dynamic Loads Controllable Measurable 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) 2Exp Methods : Dynamic Loads Controllable Un Measurable 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, dropweight test, Snap back or or step relaxation test Examples: mass exciters, Electro dynamic shakers, instrumented hammer 2

3 Time (s) 8/13/2010 2Exp Methods : Dynamic Loads Controllable Un Measurable Excitation Controllable but unmeasurable dynamic loads Manual excitation : Impact Hammer Test 2Exp Methods : Dynamic Loads Controllable Un Measurable Excitation Manual excitation : Drop Weight Test Giving excitation to a short span bridge by dropping sand bag weight Giving excitation to a short span bridge by impact hammer 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 Example of Free vibration response of the bridge excited by dropped weight Free vibration response of the bridge subjected to impact hammer 2Exp Methods : Dynamic Loads Controllable Un Measurable Excitation Manual excitation : Pull and released test of stay cable 2Exp Methods : Dynamic Loads Controllable Un Measurable Excitation Vehicle excitation/ Controlled Traffic Acceleration (m/s 2 ) Example of free vibration response of a stay cable Example of strain response when a truck passing a bridge Flowchart to obtain damping value of a stay cable Giving excitation to a stay cable by pull and released test Free Vibration Response Raw Data Frequency Response Filtering mode of interest Single mode free vibration response Logarithmic Decrement using envelope of decay response Single mode damping value Example of acceleration response when a truck passing a bridge Vehicle excitation: 1 Response larger than ambient vibration response 2 Stress and acceleration responses can be conducted simultaneously 3 Effect of vehicle bridge interaction should be considered in analysis 2Exp Methods : Dynamic Loads Uncontrollable Measurable Excitation Seismic excitation Transfer 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 2Exp Methods : Dynamic Loads Uncontrollable un measurable Excitation 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 Example : Yokohama Bay Bridge, instrumented cable stayed bridge near Tokyo 3

4 2Exp Methods : Dynamic Loads Uncontrollable un measurable Excitation Example of ambient excitation : wind induced vibration of suspension bridge Tower acceleration response 2Exp Methods : Dynamic Loads Uncontrollable un measurable Excitation Example of ambient excitation : traffic induced vibration of bridge Example of vertical acc and the spectrum of a medium span highway bridge to traffic Treated as stationary random process 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 2Exp Methods : Type of Response Excitation Static : Strain, Deflection Dynamic: Acceleration Relative of absolute displacement Velocity Inclination Strain Stress Water Pressure Structural and environmental temperature Wind Velocity Wind Direction 3 Analysis Methods: Classification 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 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 3 Analysis Methods: Classification Example of Parametric Model Output Error Minimization for system identification using seismic response Theoretical model or structural model is required 3 Analysis Methods: Classification Example of Non Parametric Model State Space System identification using seismic response F = objective function 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 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 4

5 3 Analysis Methods: Types of Model 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 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 Mu&& ( t ) + Cu& ( t ) + Ku ( t ) = Bz ( t ) I A = 0 exp Δt 1 M K M C 1 [ ] [ ] x( k + 1) = A x( k) + B z( k) [ ] y( k) = R x( k) + [ D] z( k) Goal : To Indentify system matrix A in its original form, from which the mass, stiffness and damping matrices can be retrieved 3 Analysis Methods: Types of Model 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 a e aea are analogous a to ege eigensolution sou o of sucua stuctural mass and stiffness Equation of motion in discrete dynamic system, where system matrix A is to be indentified [ ] [ ] x( k + 1) = A x( k) + B z( k) [ ] y( k) = R x( k) + [ D] z( k) Goal : To Indentify system matrix A by solving the Eigenvalue problem and determine the modes 3 Analysis Methods: Types of Model 3 Non Physical Numerical Model Does not have physical relationship with the structure (ie 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 Example : Auto Regressive Moving Average (ARMA) Model where the auto regressive coefficients can be related to modal parameters n n 1 d y( d y( dy( + a 1 a1 a0 y( n n + L n 1 dt dt dt m m 1 d u( d u( du ( = bm + bm 1 + b1 b0u( m L m 1 du du dt 3 Analysis Methods : Domain 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 d( (Schmerr 1982) Eigensystem Realization Algorithm in Frequency Domain (ERA FD) (Juang & Suzuki 1988) Frequency Domain Decomposition (Brincker et al 2001) 28 3 Analysis Methods : Domain 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 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 i lmode Decomposition Hilbert Huang Transform (should be carefully applied since EMD lacks physical meaning of signals)

6 3 Analysis Methods : Direct and Indirect Method Time Domain 3 Analysis Methods : Checklist Direct Method Types of Inputs and Outputs System Identification Method When the IRF/FRF is available, they can be use as input directly to system identification method Controllable dynamic loads Measured Input(s) Mass exciter and Shaker Instrumented Impact Hammer Transfer Functions (Input Output SysID) Single Input Single Output (SISO) or Single Input Multi Output (SIMO) system Indirect Method 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 31 Unmeasured Input (s) Manual excitation (people jumping) Snap back, or step relaxation Swinging bell to excite a cathedral tower Uncontrollable dynamic loads Measured Input(s) seismic excitation (Single Inpu seismic multiple excitation (Multiple Inpu Uncontrollable dynamic loads Unmeasured Input(s) ambient vibration test (operational modal analysis) wind excitation traffic excitation microtremor with unmeasured input Impulse Response Function/ Free vibration Response Impulse Response Function/ Free vibration Response Impulse Response Function/ Free vibration Response Transfer function, SISO or SIMO Transfer function matrix, MIMO Stationary broadband assumption Output Cross correlation Covariance Driven System Identification Data Driven Stochastic Subspace Identification 32 4 Uncertainties 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 method 2 Monte Carlo Simulation 3 Bootstrap Method 33 4 Uncertainties : Error propagation analysis using perturbation Example of error propagation in System Realization using Information Matrix Input [Up] Correlation Matrix : Correlation Matrix Up(ε) = Up(0) + εδup Ryy(ε) = Ryy(0) + εδryy Of Input Output Ryu(ε) [Ryy], = Ryu(0) [Ryu], + εδryu [Ruu] Yp(ε) = Yp(0) Output + εδyp [Yp] Ruu(ε) = Ruu(0) + εδruu Objectives: To define and quantify the error on the modal parameters as the effect of input and output noise Information Matrix [Rhh] Rhh(ε) = Rhh(0) + εδrhh Singular Value Singular Value Decomposition Decomposition Realization of System Realization of System Matrix Matrix [A] A(ε) = A(0) + εδa Realization of Modal Realization of Modal Parameters Parameters ω(ε) = ω(0) + εδω ω, ζ, ϕ ζ(ε) = ζ(0) + εδζ φ(ε) = φ(0) + εδφ 34 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 4 Uncertainties : Bootstrap Analysis Distribution of modal parameters and their mean values and confidence level can be obtained CCF 1, CCF 2, CCF 3, CCF N Randomly selected Ensemble 1 (M componen CCF 1, CCF 5, CCF 3, CCF M Compute CCF average ERA ω 1, ξ 1,φ 1 Randomly selected Ensemble 2 (M componen ERA ω 2, ξ 2,φ 2 CCF 7, CCF 2, CCF 1, CCF M Compute CCF average Randomly selected Ensemble P (M componen CCF 4, CCF 6, CCF 2, CCF M Compute CCF average ERA ω p, ξ p,φ p Examples of bridge 1 st frequency statistical distribution on different structural conditions using Bootstrap Method CCF : Cross correlation function Estimate mean value and 95% Confidence bound 35 Modal parameters are considered as stochastic variable that have distribution with certain statistical characteristics Therefore decision made on structural condition involved statistical confidence 36 6

7 5 Examples: Ambient Vibration Measurement of Suspension Bridge 5 Examples: Ambient Vibration Measurement of Suspension Bridge Using NEXT ERA Modal Parameters 3 Span Suspension Bridge Bridge Type: Simply supported at the tower Length: 1,380m Span: m Total Deck Width: 20m Tower Height : 130 m Tower width : 21m at base 18 m on top Girder material : Streamlined steel box Tower material : Steel box (welded) Completed : Examples: Ambient Vibration Measurement of Suspension Bridge 5 Examples: Seismic Induced System Identification of Cable Stayed Bridge Structural identification : effect of friction force and aerodynamic forces on identified frequency and damping (Nagayama et al 2005) 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) 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

8 5 Examples: Seismic Induced System Identification of Cable Stayed Bridge Observation of the performance of seismic isolation devices using 1 st longitudinal mode (Siringoringo & Fujino 2008 ) Suggested Readings Materials: Theoretical and Experimental Modal Analysis by Maia, Silva, He, Lieven et al Applied System Identification by Jer Nan Juang Monitoring and Assessment of Structures by GST Armer The State of the Art in Structural Identification of Constructed Facilities (ASCE Report 1999) (a) Typical slip slip Mode (Earthquake ) (b) Typical Mixed Slip Stick Mode (Earthquake ) 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 Q & S Questions and Sharing? Dionysius Siringoringo dion@bridgetu tokyoacjp It was found that the expected slip slip mode only occurred during large earthquake