Cheng Chen Ph.D., Assistant Professor School of Engineering San Francisco State University Probabilistic Reliability Analysis of Real-Time Hybrid Simulation Results for Seismic Hazard Mitigation Quake Summit, Boston, MA, 2012

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

3 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

4 Servo-Hydraulic Actuators Critical to maintain the boundary conditions between substructures! Maximum tracking error mm (35% of command maximum)! Command Maximum: 50 mm Frequency Content: 0 ~ 5 Hz TestCompensation  es MTE (mm) 1-1 Inverse compensation Existing AIC New AIC12.4 Delay compensation methods can reduce, but can NOT eliminate actuator tracking error for real-time structural tests!

5 Reliable Experimental Results? How will the tracking errors affect the accuracy of simulated structure response? How will researchers assess the accuracy of simulated response when the true structural response is not available? How do we assess the reliability of real-time hybrid simulation results without knowing the true responses?

6 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

7 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;

8 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.

9 Structural Nonlinearity (β=1.0) Linear elastic case

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

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

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

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

14 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.

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

16 Ground Motions for Analysis EarthquakeStationComponentMagnitude (M w )Distance (km)PGA (g) Northridge24303 LA - Hollywood Stor FFHOL360.AT Santa Barbara283 Santa Barbara CourthouseSBA222.AT El Centro117 El Centro Array #9IELC270.AT Chi CHY006CHY006N.AT Duzce DZC270.AT San Fernando279 Pacoima DamPCD254.AT KocaeliYarimcaYPT330.AT Tabas9101 TabasTABTR.AT :::::: Chi TCU068TCU068-N.AT Northridge24436 Tarzana, Cedar HillTAR090.AT El Alamo117 El Centro Array #9ELC270.AT Hollister1028 Hollister City HallB-HCH271.AT Parkfield1013 Cholame #2C02065.AT Palm Springs5224 Anza - Red MountainARM360.AT Oroville1544 Medical CenterC-OMC336.AT Imperial Valley5028 El Centro Array #7H-E07230.AT A total of fifty ground motion from PEER Strong Motion Data Base

17 Delay for Target Accuracy 5%

18 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

19 Tracking Indicator (TI) Mercan and Ricles 2010  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.

20 Application of Proposed Approach Perform real-time hybrid simulation compare

21 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),

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

23 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%

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

25 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 application to experimental results.

26 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.

27 Thanks for your attention! Questions?