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Hybrid Simulation with On-line Updating of Numerical Model based on Measured Experimental Behavior M.J. Hashemi, Armin Masroor, and Gilberto Mosqueda University at Buffalo International Mini-Workshop on Hybrid Simulation Harbin Institute of Technology May 18, 2012

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Acknowledgements Research funding – NSF: CAREER Award CMMI-0748111 – NEESR CMMI-0936633 (PI Eduardo Miranda, Stanford) – NSF Award CMS 0402490 for shared use access of nees@buffalo Collaborators – Eduardo Miranda, Helmut Krawinkler, Stanford University – Dimitrios Lignos, McGill University – Ricardo Medina, University of New Hampshire

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Introduction In hybrid simulation, it is often assumed that a reliable model of numerical substructure exists – Nonlinear behavior can be distributed throughout structural model During a hybrid simulation, experimental data is gathered from experimental structural components – other similar components may be present throughout numerical structure Objective: Use on-line measurements of experimental substructure to update numerical models of similar components (Elnashai et al. 2008) – Could experience similar stress/strain demands – Could experience very different demands, but likely at lower amplitudes (Test component experiencing largest demands)

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Introduction

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Algorithm Numerical Substructure may contain models to be updated Auxiliary model of experiment to calibrate model parameters Other tasks focus on when and what to update

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Online Updating Challenges Experimental Issues: 1.The on-line identification process should instantaneously and automatically track the critical characteristics of the system and their variations as time proceeds, without requiring any major action by the researcher during the test. 2.Measurement data are usually contaminated by errors (noise) that can substantially influence the accuracy of the identification result. 3.In online schemes, it is difficult to manipulate the input–output data as can be done for offline applications.

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Online Updating Issues Numerical Issues: 1.Lack of understanding of nonlinear structural behavior and selection of models/parameters for numerical simulation. 2.For effective on-line identification schemes, it is necessary to develop a reasonable non-linear model that is able to provide a good representation of the system behavior. 3. Problems related to under- and over-parameterization exists that can be overcome by setting boundaries on the parameters. 4.Independent of the system to be identified, online identification algorithm must be adaptable to capture parameter changes as time progresses (ex., if a fracture occurs). 5.Parameters should converge smoothly and rapidly to the proper parameter values.

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Hysteretic Model Modified Bouc-Wen Model: 1.Baber and Noori (1985) extension of the Bouc-Wen model to include degrading behavior. 2.Has been used by several researchers for simulating and identifying hysteretic system response 3.Model is high nonlinear and has nine control parameters including stiffness and strength degradation.

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Parameter Identification System Identification - The parameters of a system model is sought given the excitation and output In this application, the system excitation and output are only known to the current simulation time Early identification of some parameters is difficult – cannot calibrate yield force until structure actually yields Example: Extracting Initial Stiffness, Yield Force and Post Elastic Stiffness Ratio From Experimental Response

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Parameter Identification Objective: Find the best-fit parameters to minimize the error function E defined as: Note: Auxiliary Numerical Model and Experimental Model have identical deformation demands

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Parameter Identification Techniques Downhill Simplex : 1.The Downhill Simplex method is a multidimensional optimization method which uses geometric relationships to aid in finding function minimums 2.The Simplex method is not sensitive to small measurement noise and does not tend to divergence Unscented Kalman Filter: 1.UKF is a recursive algorithm for estimating the optimal state of a nonlinear system from noise-corrupted data 2.To identify the unknown parameters of a system, these parameters should be added to the states of the system to be estimated using experimental substructure response.

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Structural Model NumericalExperimental One Bay Frame Structure – Element 1: Experimental substructure – Element 2: Numerical substructure similar to Element 1 – Element 3: Spring that varies demands between Element 1 and Element 2

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Experimental Substructure

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One Bay Frame Structural Properties Experimental ControlxPCtarget Values Period (sec)0.5182 Elastic Stiffness (kips/in)5.88 Mass for Each DoF (kips/g)0.04 Integration SchemeNewmark Explicit Integration Time Step (sec)0.005 Ground Motion Time Step (sec)0.02 Simulation Time Step (sec)0.25 El Centro

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Test Protocol Test Series 1:Verification of Parameter Identification Techniques: – Mass 1 and 2 are equivalent and Element 3 is rigid: – Deformation demands in Element 1 and 2 are identical. – Online calibration of the Element 2 using parameter identification techniques, ideally, should produce a hysteresis identical to Element 1. Test Series 2: Implementation in General Condition: Element 3 is flexible, Mass 1 and 2 are different: Deformation demands in Element 1 and 2 different. Although elements may have similar properties, they experience different deformation demands and damage at different times

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Test Series 1 [Identical Deformation Demands] Reference Model: Reference Model: Response of Element 2 is replaced by measured behavior for Element 1 since both have the same demands

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Test Series 1 [Identical Deformation Demands] Calibration of the Experimental Response Calibration:

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Test Series 1 [Identical Deformation Demands] Initial Values For Updating Test Initial Values: No stiffness or strength degradation assigned to the numerical model No updating is implemented

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Test Series 1 [Identical Deformation Demands] Results for updating in real time: Auxiliary model is numerical model in this case Downhill SimplexUnscented Kalman Filter

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Test Series 2 [Different Deformation Demands] Reference Model: Reference Model: Response of Element 2 is Based on the Calibration of Experimental Element Response without degradation

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Test Series 2 [Different Deformation Demands] Updating Tests: Simplex Downhill: Unscented Kalman Filter: Initial values for numerical model parameters used in the Downhill Simplex Method are the same as the calibrated numerical model with no strength and stiffness degradation; these are the Updating Parameters : Initial values for the updating parameters for the UKF Method were chosen the same as the test with “no updating”. Updating Parameters :

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Test Series 2 [Different Deformation Demands] Results: Comparison of Element 2 Hysteresis For Different Tests

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Test Series 2 [Different Deformation Demands] Results: Comparison of Element 2 Forces History for Different Tests

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Test Series 2 [Different Deformation Demands] Results: Comparison of Element 2 (=DOF2) Displacement History For Different Tests

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Test Series 2 [Different Deformation Demands] Parameter Calibration: Note: Initial values for the updating parameters for the UKF Method were obtained from test with “no updating”. Updated Parameter Values In UKF Identification Technique Updating Parameters:

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Test Series 2 [Different Deformation Demands] Parameter Calibration: Updated Parameter Values In UKF Identification Technique

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Test Series 2 [Different Deformation Demands] Parameter Calibration: Updated Parameter Values In UKF Identification Technique

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Test Series 2 [Different Deformation Demands] Results: Updated Parameter Values In UKF Identification Technique

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Test Series 2 [Different Deformation Demands] Parameter Calibration: Updated Parameter Values for Downhill Simplex Technique Note: Initial values for the updating parameters for the Downhill Simplex Method were chosen the same as the calibrated numerical model with “no strength and stiffness degradation”. Updating Parameters:

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Experimental Substructure Numerical Substructure Substructuring Techniques – Techniques to reduce number of actuators for boundary conditions Updating of numerical model

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Conclusion 1.A basic objective is to implement and advance the methodology of hybrid simulation with updating of the numerical substructure model(s) during the test and thereby better predict the response of inelastic structures more accurately. 2.An auxiliary numerical model was implemented to calibrate numerical model parameters. Different optimization techniques were examined to minimize the objective function, defined as the error between numerical and experimental substructure response. Both methods give relatively accurate estimates. 3.Hybrid simulation with updating can be implemented using common software such as OpenSEES and MATLAB®. Algorithms for updating process, time of implementing the updated parameters in numerical model and others can be coded by the researcher and used in the proposed framework. 4.The procedure was implemented here for a simple structural model, with more complex applications expected in the near future

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It follows that and Step 1: Assume system to be described as, where y is the output, u is the input and is the vector of all unknown parameters. Step 2:

It follows that and Step 1: Assume system to be described as, where y is the output, u is the input and is the vector of all unknown parameters. Step 2:

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