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Amin Maghareh, Shirley J. Dyke, Ge Ou , and Yili Qian

Investigation of Uncertainties Associated with Actuation Modeling Error and Sensor Noise on Real Time Hybrid Simulation Performance. Amin Maghareh, Shirley J. Dyke, Ge Ou , and Yili Qian School of Civil Engineering , Purdue University

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Amin Maghareh, Shirley J. Dyke, Ge Ou , and Yili Qian

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  1. Investigation of Uncertainties Associated with Actuation Modeling Error and Sensor Noise on Real Time Hybrid Simulation Performance Amin Maghareh, Shirley J. Dyke, GeOu, and YiliQian School of Civil Engineering, Purdue University School of Mechanical Engineering, Purdue University {amaghare, sdyke, gou, qian26}@purdue.edu

  2. Real-time Hybrid Simulation Objective: Reduce impacts of dynamic loading on infrastructures Earthquake Tsunami Wind

  3. Shake Table Testing

  4. Real-time Hybrid Simulation m4 m2 x4(t) x2(t) c2 c4 k4 m3 m1 x1(t) x3(t) k4 k2 c3 c1 k3 k1 k3 x xi xi+1 ti ti+1 t R4 Numerical integration Ri+1 xi+1 R3 Displacements imposed in Real time Numerical sub-structure Numerical sub-structure Experimental sub-structure Figures from “Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback” by B. F. Spencer Jr. and Brian M. Phillips

  5. Outline • Real-time Hybrid Simulation (RTHS) • RTHS Components • Uncertainties in RTHS • Numerical uncertainties • Experimental uncertainties • Actuation Misidentification and Sensor Noise • Evolution of Uncertainties in RTHS • Case study • Conclusions

  6. RTHS • What is RTHS? Real-time hybrid simulation is a cyber-physical technique of partitioning a structure into physical and numerical substructures to study the dynamic performance of complex engineering structures under dynamic loading • Why RTHS? It would facilitate low-cost and broader evaluation of new structural components and systems • Components: • Cyber Components • Distributed Real-time Control System • Visualization and Control Dashboard • Physical Components • Reaction Mounting System • Sensing and Actuation System

  7. RTHS Components

  8. RTHS Components SC6000 Servo-hydraulic Control System SpeedgoatxPC Target System Reaction Mounting System + Exp. Substructure

  9. Uncertainties in Real-time Hybrid Simulation • Uncertainties are classified into two subcategories: • Numerical uncertainties • Structural Modeling Idealization • Numerical Integration Scheme • Experimental uncertainties

  10. Numerical uncertainties • Structural Modeling Idealization • Structural modeling idealization leads to losing some dynamics of the prototype structure. • Modeling idealization error in hybrid simulation refers to discretization of the continuous equation of motion of a structural model which is just an approximate representation of the dynamics of the structure. • However, it should be noted that there is always a trade-off between accuracy of the model and feasibility of the number of degrees of freedom controllable with available actuators. • Numerical Integration Scheme • To solve the idealized equation of motion, approximate numerical integration schemes are utilized. • Based on what scheme is utilized and how fine time steps are, stability and accuracy of the numerical method adopted for a hybrid simulation is determined.

  11. Experimental uncertainties • Random noise generated by the force and displacement measurement instrumentations can be challenging since these can excite spurious lightly-damped modes of the RTHS system. • Depending upon what the frequency bandwidth of interest is, and the level of nonlinearity of actuators, developing tracking error in RTHS is inevitable. • Moreover computation time delay, communication time delay, and actuator lag are other sources of experimental uncertainty.

  12. Uncertainties in RTHS

  13. Actuation Misidentification and Sensor Noise Ideal Case RTHS with Actuator Misidentification and Measurement Noise

  14. Evolution of Uncertainties in RTHS Displ. Measurement Noise Force Measurement Noise Where • Excitation of the spurious modes by the input acceleration • Excitation of the spurious modes by measurement noises • Excitation of the actual modes of the system by measurement noises

  15. Important Points • The poles of the closed-loop system are associated with the eigenvalues of , the actual system, and the eigenvalues of which are slightly different. • Since the compensator is designed based on the dynamics of , and not , the overall RTHS error system ends up having some closely separated poles and zeros (imperfect cancellation) causing some spurious lightly-damped poles. • These lightly damped poles play a significant role in the propagation of error in the system. • Depending upon whether these spurious poles are at low frequency or high frequency, they will be dominantly excited by either ground acceleration input or measurement noise signals, respectively.

  16. Important Points • Ground acceleration inputs have much higher power in a low frequency bandwidth compared to measurement noise signals. Wavelet Transformation of the 1994 Northridge EQ • If the spurious poles are located in the excitation bandwidth of ground acceleration, the quality of RTHS results will be significantly degraded.

  17. Case Study

  18. Case Study Case I Case II

  19. Case Study Results

  20. Case Study Results High Freq. Error Low Freq. Error Case I Case II

  21. Conclusions • Hybrid simulation is a cyber-physical technique of partitioning a structure into physical and numerical substructures to study and enhance the dynamic performance of complex engineering structures under dynamic loading • It would facilitate low-cost and broader evaluation of new structural components and systems • In this study, evolution of uncertainties sourced from actuation misidentification and sensor noise is formulated. • Better understanding of the evolution of uncertainties in RTHS will help us design the closed-loop more effectively as shown in the case study.

  22. Acknowledgements • This material is based in part upon work supported by the  National Science Foundation under Grant Numbers NSF-1136075 and CMMI-1011534.

  23. Thank You!

  24. References • C. Chen, J.M. Ricles, “Tracking error-based servo-hydraulic actuator adaptive compensation for real-time hybrid simulation.” J. Struct. Eng., 136(4), 2010. • T. Yang, G. Mosqueda, B. Stojadinovic, “Verification of Hybrid Simulation through On-Line Monitoring of Experimental Errors,” Structures Congress 2008. • G. Mosqueda, B. Stojadinovic, and S. A. Mahin, “Implementation and accuracy of continuous hybrid simulation with geographically distributed substructures.” Report UBC/EERC 2005-2, Earthquake Engineering Research Center, University of California, Berkeley, 2005. • G. Mosqueda, T. Y. Yang, B. Stojadinovic, “Assessment of experimental errors in hybrid simulation of seismic structural response,” In Hybrid Simulation: Theory, Implementation and Applications, V.E Saouma and M.V. Sivaselvan, Eds. March 2008. Taylor and Francis. • K. Takanashi, M. Nakashima, “Japanese activities on on-line testing,” Journal of Engineering Mechanics, ASCE, 113(7):1014-1032, 1987. • S. A. Mahin, P. B. Shing, C. R. Thewalt, and R. D. Hanson, “Pseudodynamic test method - Current status and future direction,” Journal of Structural Engineering, ASCE, 115(8):2113-2128, 1989. • G. E. Magonette, P. Negro, “Verification of the pseudodynamic test method,” European Earthquake Engineering, PUB 40-50, 1998. • C. R. Thewalt, and S. A. Mahin. Hybrid solutions techniques for generalized pseudodynamic testing. Report UCB/EERC-87/09, EERC, University of California, Berkeley, 1987. • S. J. Dyke, B. F. Spencer, P. Quast, and M. K. Sain, “The Role of Control-Structure Interaction in Protective System Design,” ASCE Journal of Engineering Mechanics 121, no.2 (1995): 322-338. • A. Maghareh, S. J. Dyke, A. Prakash, G. Bunting, and P. Lindsay, “Evaluating Modeling Choices in the Implementation of Real-time Hybrid Simulation,” Joint Conference of the Engineering Mechanics Institute and the Probabilistic Mechanics and Structural Reliability, Notre Dame, 2012. • X. Gao, N. Castaneda, and S. J. Dyke, “Development and Validation of a Robust Actuator Motion Controller for Real-time Hybrid Testing Applications.” Report IISL-001, Purdue University, December 2011. • B. M. Phillips, B. F. Spencer, “Model-Based Servo-Hydraulic Control for Real-Time Hybrid Simulation,” Newmark Structural Engineering Laboratory Report Series, Urbana, IL: UIUC, 2011. • B. F. Phillips, Y. Chae, Z. Jiang, B. F. Spencer, J. M. Ricles, R. Christenson, S. J. Dyke, A. K. Agrawal, "Real-time Hybrid Simulation Benchmark Study with a Large-Scale MR Damper," http://nees.org/resources/676, 2010

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