1. Cheng Chen, Ph.D. Assistant Professor San Francisco State University Interpreting Reliability of Real- Time Hybrid Simulation Results from Actuator Tracking Errors International Workshop on Hybrid Simulation Harbin Institute of Technology, 2012

2. 2 Presentation Overview  Background  Need for Reliability Analysis  Proposed Probabilistic Approach for Reliability Analysis  Application to Experimental Results  Summary and Conclusion  Future Work

3. 3 EQ Experimental Techniques Courtesy of NEES@UCSD Shake Table at E-Defense Courtesy of Fahnstock et al. Courtesy of NEES@UCSD

4. 4 Real-Time Hybrid Simulation Analytical substructure Floor 1 damper N RTMD Actuator Dampers North A-Frame South A-Frame Roller Bearings Actuator Support Loading Stub NN RTMD Actuator Dampers North A-Frame South A-Frame Roller Bearings Actuator Support Loading Stub Experimental substructure 2 Floor 2 damper N RTMD Actuator Dampers North A-Frame South A-Frame Roller Bearings Actuator Support Loading Stub NN RTMD Actuator Dampers North A-Frame South A-Frame Roller Bearings Actuator Support Loading Stub Experimental substructure 1

5. 5 Presentation Overview  Background  Need for Reliability Analysis  Proposed Probabilistic Approach for Reliability Analysis  Application to Experimental Results  Summary and Conclusion  Future Work

6. 6 Role of Hydraulic Actuators Apply desired responses to experimental specimens in a real-time manner; Measure the restoring forces of the experimental substructures and feed back to the integration algorithm; Critical to maintain the boundary conditions between substructures! Courtesy of Lehigh RTMD Block Diagram for Real-Time Hybrid Simulation Excitation Force Integration Algorithm Servo Controller Hydraulic Actuator Analytical Substructure (MRF: FE Program) Experimental Substructure (Damper 1: Lab) Experimental Substructure (Damper 2: Lab) Ramp Generator

7. 7 Actuator Delay and Tracking Error Maximum tracking error 16.90 mm (35% of command maximum)! Command Maximum: 50 mm Frequency Content: 0 ~ 5 Hz

8. 8 Actuator Delay Compensation Linear Acceleration Compensation (Horiuchi et al. 2001) Feedforward Compensation (Jung et al. 2007) Dual Compensation (Chen and Ricles 2009; Lin et al. 2012) Minimal Control Synthesis (MCS) (Stoten et al. 2005) Adaptive Inverse Control (AIC) (Chen and Ricles 2010) Improved Adaptive Inverse Control (IAIC) (Chen and Ricles 2012) Other researches other include Wallace et al. [2007]; Ahmadizadeh et al. (2008) Delay compensation methods can reduce, but can NOT eliminate actuator tracking error for real-time structural tests! TestCompensation  es MTE (mm) RMS (%) Max TI (mm 2 ) Max EE (kN-m) 1-1 Inverse compensation 116.924.11.38E421.5 1-2Existing AIC14.93.41.26E213.1 1-3New AIC12.42.11.08E22.4

9. 9 Questions to be answered? How will the tracking errors affect the accuracy of simulated structure response? Will this difference between simulated and true responses be acceptable for researches? How will researchers assess the accuracy of simulated response in replicating the true structural response when the latter is not available?

10. 10 Reliable Experimental Results? How reliably did the real-time hybrid simulation results replicate the true structural response under earthquakes? How do we assess the reliability of real-time hybrid simulation results without knowing the true responses? A successful real-time hybrid simulation requires that the effect of actuator delay not only be compensated throughout the simulation but also be assessed after the simulation!

11. 11 Tracking Indicator (TI) Tracking Indicator (Mercan and Ricles 2010) TestCompen. MTE (mm) RMS (%) Max TI (mm 2 ) 1-1IC16.924.11.38E4 1-2AIC4.93.41.26E2 1-3IAIC2.42.11.08E2 Positive TI

12. 12 Needs for Reliability Assessment  TI provides a useful tool to compare performances of different actuator control techniques.  Link between TI and simulation accuracy is missing making it difficult to apply for reliability assessment.  TI is response history dependent and vary for simulations with various ground motion inputs and different intensities.

13. 13 Presentation Overview  Background  Need for Reliability Analysis  Proposed Probabilistic Approach for Reliability Analysis  Application to Experimental Results  Summary and Conclusion  Future Work

14. 14 RTHS of SDOF Structures Exact solution can be easily computed and used for validating the proposed approach Similar equations have been analyzed by researchers for the effect of actuator delay on the stability of real-time hybrid simulations

15. 15 Simulated Responses w/ Delay SDOF Structure: m=503.4 tons; f=0.77 Hz;  =2% β=1.0; 1940 El Centro earthquake recorded at Canoga Park station;

16. 16 Factors to be considered Structural Nonlinearity Different Ground Motion Inputs Ground Motion Intensity Structural Damping Stiffness Ratio between substructures Accuracy of simulated response is evaluated through comparison with true response using the ratio between maximum difference and maximum response (MAX); and the RMS of response difference.

17. 17 Structural Nonlinearity (β=1.0) Linear elastic case

18. 18 Ground Motion Intensity (β=1.0) (a) and (b) for linear elastic structure; (c) and (d) for nonlinear structure

19. 19 Structural Damping (β=1.0) (a) and (b) for linear elastic structure; (c) and (d) for nonlinear structure

20. 20 Different Ground Motions (β=1.0) (a) and (b) for linear elastic structure; (c) and (d) for nonlinear structure

21. 21 Stiffness Ratio of Substructures (a) and (b) for linear elastic structure; (c) and (d) for nonlinear structure β β β β

22. 22 Findings from Numerical Analysis An actuator delay that leads to simulated response with acceptable accuracy for linear elastic structures will also result in simulated response with acceptable accuracy for corresponding nonlinear structures; Different ground motion inputs and different intensities will lead to different accuracy of simulated responses especially for structures with nonlinear behavior.

23. 23 EQ Response Analysis Courtesy of Chopra (2001) ASCE-7-10

24. 24 Ground Motions for Analysis EarthquakeStationComponentMagnitude (M w )Distance (km)PGA (g) Northridge24303 LA - Hollywood Stor FFHOL360.AT26.725.50.358 Santa Barbara283 Santa Barbara CourthouseSBA222.AT26140.203 El Centro117 El Centro Array #9IELC270.AT278.30.215 Chi CHY006CHY006N.AT27.614.930.345 Duzce DZC270.AT27.18.20.535 San Fernando279 Pacoima DamPCD254.AT26.62.81.16 KocaeliYarimcaYPT330.AT27.42.60.349 Tabas9101 TabasTABTR.AT27.430.852 :::::: Chi TCU068TCU068-N.AT27.61.090.462 Northridge24436 Tarzana, Cedar HillTAR090.AT26.717.51.779 El Alamo117 El Centro Array #9ELC270.AT2-1300.052 Hollister1028 Hollister City HallB-HCH271.AT2-19.60.196 Parkfield1013 Cholame #2C02065.AT26.10.10.476 Palm Springs5224 Anza - Red MountainARM360.AT2645.60.129 Oroville1544 Medical CenterC-OMC336.AT24.411.10.043 Imperial Valley5028 El Centro Array #7H-E07230.AT26.50.60.463 A total of fifty ground motion from PEER Strong Motion Data Base

25. 25 Delay for Target Accuracy 5%

26. 26 Proposed Probabilistic Approach Probabilistic Model of Critical Delay for 5% MAX Error of Simulated Response Probability distribution of delay leading to 5% MAX error Lognormal distribution

27. 27 Proposed Probabilistic Approach SDOF structural properties:  Mass of 503.4 metric tons;  Natural frequency of 0.77 Hz;  Inherent damping ζ of 0.02;  β=1.0;  1940 El Centro earthquake recorded at Canoga Park station with PGA of 0.2 g; P.E.=50% P.E.=15% P.E.=5% Time History of TI based on Delay for Different Probability of Exceedance

28. 28 Presentation Overview Background Need for Reliability Analysis Probabilistic Approach for Reliability Analysis Application to Experimental Results Summary and Conclusion Future Work

29. 29 SDOF Prototype Structure Canoga Park EQ d(t)PassiveDamper Analytical Substructure d(t) = Experimental Substructure d(t) damper actuator + Analytical Substructure Properties: structural mass: m=503.4 ton; natural frequency: f n =0.77 Hz; viscous damping ratio: ζ =0.02; Analytical Substructure modeled using Bouc-Wen model [Wen 1980] Chen, C., Ricles, J.M., Marullo, T. and Mercan, O. (2009). “Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm.” Earthquake Engineering and Structural Dynamics, 38(1), 23-44.

30. 30 Experimental Setup Test  es Compensation 115Inverse compensation 215Adaptive Inverse Compensation 329Adaptive Inverse Compensation

31. 31 Reliability Assessment Test 1: inverse compensation with α es =15 P.E.=50% Test 2: AIC with α es =15 P.E.=50% P.E.=15%

32. 32 Reliability Assessment Test 3: AIC with α es =30 P.E.=5%

33. 33 Summary and Conclusion  Numerical analysis is conducted to investigate the accuracy of real-time hybrid simulation with actuator delay;  A probabilistic approach using tracking indicator is proposed for reliability assessment of real-time hybrid simulation;  The effectiveness of the proposed method is validated through applying it to experimental results.

34. 34 Future Work  Further develop the probabilistic model for actuator delay corresponding to different accuracy level for SDOF structures;  Extend the proposed approach to real- time hybrid simulations involving multiple servo-hydraulic actuators.

35. 35 Acknowledgement  This study is supported by the Presidential Award of San Francisco State University and the CSU Wang Family Faculty Award.  The presented experimental results were conducted at ATLSS Center of Lehigh University using NEES RTMD equipment;  The MR damper used for the predefined displacement tests was provided by Dr. Richard Christenson at University of Connecticut.

36. 36 Thanks for your attention! Questions?