1. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Investigation of the Effect of Transfer System Delay on Real-time Hybrid Simulation Amin Maghareh and Shirley J. Dyke Purdue University

2. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu In order to reduce impacts of dynamic loading on civil structures/infrastructures, we need more experimental capabilities in evaluating structural performances in a suitable and cost-effective manner 1. Earthquake Tsunami Wind 1- NEES. (2010). Vision 2020: An Open Space Technology Workshop on the Future of Earthquake Engineering (Vol. 20). Retrieved from https://nees.org/resources/1637/download/Vision_2020__Final_Report.pdf

3. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu E-Defense Earthquake Shake Table (World's Largest Earthquake Shake Table Test in Japan) Shake Table Testing

4. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Shake Table Testing In seismic evaluation of civil structures using shake table testing … 1. A researcher needs only to know the capacity/capabilities of the table 2. There is usually no stability concern, and the results are highly reliable However, 1. Very few shake tables in the world are capable of testing full-scale large civil structures 2. Shake table testing is often limited to prototypes, limited in payload, and/or prohibitively expensive

5. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu  Hybrid simulation (HS) is a cost-effective experimental technique to evaluate the dynamic performance of large civil structures.  Real-time hybrid simulation (RTHS) provides the most advanced experimental technique to evaluate the performance of rate-dependent civil structures in laboratories 1, 2. 1- NEES. (2010). Vision 2020: An Open Space Technology Workshop on the Future of Earthquake Engineering (Vol. 20). Retrieved from https://nees.org/resources/1637/download/Vision_2020__Final_Report.pdf 2 - NSF. (2007). Issues and Research Needs in Simulation Development. September, Chicago, IL, USA.

6. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu  Real-time Hybrid Simulation (RTHS)  Transfer System in RTHS  Time Delay and Time Lag in RTHS  An RTHS Model  Numerical and Experimental Examples Outline

7. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu 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 Real-time Control System Visualization and Control Dashboard Physical Components Reaction Mounting System Sensing and Actuation System Real-time Hybrid Simulation

8. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu 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 Physical 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 Real-time Hybrid Simulation

9. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Communication Delay: To implement RTHS, there is a continuous exchange of information between the cyber and physical components. In RTHS, communication delays vary from almost negligible for an RTHS using a single processor (no network) to more than a hundred milliseconds for geographically distributed testing. Computational Delay: In RTHS, integration schemes are implemented to solve the discretized governing equation of the numerical substructure. ZOH Converted Signal Approximate Signal Signal without DA Conversion Time Delay in RTHS

10. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu In RTHS, the interface interaction between the substructures is enforced by a transfer system which includes servo-hydraulic actuator(s) and/or shake table. The transfer system should be designed and controlled to ensure that all the interface boundary conditions are satisfied in real time. Time Lag in RTHS

11. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Transfer System

12. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Transfer System

13. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu RTHS Model Reference Structure Numerical Substructure Physical Substructure Measurement Noise

14. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu RTHS Model 1994 Northridge 1995 Kobe

15. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu SDOF RTHS Transfer System Num. Substructure Phy. Substructure Reference Structure

16. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Experimental Results

17. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Stability of a SDOF RTHS α Factorβ Factorγ Factor Case I 0.40.9 Case II 0.90.6 Case III 0.60.1 Case IV 0.10.4

18. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Performance of a SDOF RTHS

19. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Simulation Results

20. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu RTHS Model m 1 = m p1 + m n1 c 1 = c p1 + c n1 k 1 = k p1 + k n1 Reference Sys. Physical Sub.

21. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Stability Analysis Instability Mode Critical Frequency (Hz.) Critical Time Delay (msec.) 1 st 1.957.3 2 nd 3.11149.7 3 rd 5.138.0 After conducting stability analysis, the results show that to avoid instability in conducting RTHS with these substructures, the maximum time lag tolerated within the operation range is 7.3 msec.

22. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Modeling Results Response of the Ref. System, RTHS with Transfer System Dynamics, and the DDE Model Subject to 1995 Kobe Ground Acceleration

23. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Experimental Example Phy. Substructure Num. Substructure Reference System Phy. Substructure Num. Substructure

24. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Experimental Results Time Lag at the 1 st Mode (msec.) Time Lag at the 2 nd Mode (msec.) Controller 13.984.02 Controller 25.405.44 Controller 37.407.44 Instability Mode Critical Frequency (Hz.) Critical Time Delay (msec.) 2 nd 4.4510

25. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Experimental Results Input used in this experiment is the 1994 Northridge ground acceleration.

26. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Experimental Results

27. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Concluding Remarks  HS is a cost-effective experimental technique to evaluate the dynamic performance of large civil structures.  RTHS provides the most advanced experimental technique to evaluate the performance of rate-dependent civil structures in laboratories.  In RTHS, time lags and time delays can be classified into three major categories, 1) communication delays, 2) computational delays, and 3) transfer system dynamics.  In this study, we 1. modeled RTHS using a set of neutral delay differential equations 2. showed the fidelity of the proposed model using a SDOF and MDOF RTHS examples 3. Presented the effects of transfer system delay on RTHS results

28. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Acknowledgements This material is based in part upon work supported by the National Science Foundation under Grant Numbers NSF-1136075 and CMMI-1011534.

29. Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail: iisl@ecn.purdue.edu Thank you!