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 School of Mechanical Engineering, Purdue University {amaghare, sdyke, gou,

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

3 Shake Table Testing

Real-time Hybrid Simulation x i+1 R4R4 R3R3 R i+1 Displacements imposed in Real time x2(t)x2(t) x1(t)x1(t) m1m1 m2m2 c2c2 c1c1 k2k2 k1k1 Experimental sub-structure k4k4 k3k3 Numerical integration Numerical sub-structure x4(t)x4(t) x3(t)x3(t) m3m3 m4m4 c4c4 c3c3 k4k4 k3k3 Figures from “Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback” by B. F. Spencer Jr. and Brian M. Phillips x t titi t i+1 xixi x i+1

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

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

RTHS Components

Speedgoat xPC Target System SC6000 Servo-hydraulic Control System Reaction Mounting System + Exp. Substructure

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

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.

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.

Uncertainties in RTHS

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

Evolution of Uncertainties in RTHS

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.

Case Study

Case I Case II

Case Study Results

Case I Case II Low Freq. ErrorHigh Freq. Error

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 and CMMI

23 Thank You!

References  C. Chen, J.M. Ricles, “Tracking error-based servo-hydraulic actuator adaptive compensation for real-time hybrid simulation.” J. Struct. Eng., 136(4),  T. Yang, G. Mosqueda, B. Stojadinovic, “Verification of Hybrid Simulation through On-Line Monitoring of Experimental Errors,” Structures Congress  G. Mosqueda, B. Stojadinovic, and S. A. Mahin, “Implementation and accuracy of continuous hybrid simulation with geographically distributed substructures.” Report UBC/EERC , Earthquake Engineering Research Center, University of California, Berkeley,  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 Taylor and Francis.  K. Takanashi, M. Nakashima, “Japanese activities on on-line testing,” Journal of Engineering Mechanics, ASCE, 113(7): ,  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): ,  G. E. Magonette, P. Negro, “Verification of the pseudodynamic test method,” European Earthquake Engineering, PUB 40-50,  C. R. Thewalt, and S. A. Mahin. Hybrid solutions techniques for generalized pseudodynamic testing. Report UCB/EERC-87/09, EERC, University of California, Berkeley,  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):  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,  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  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,  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,"