1. Quake Summit 2012
July 9-12, 2012, Boston
Real-Time Hybrid Simulation Studies of Complex Large-Scale Systems Using Multi-Grid Processing
dampers
Dampers
Yunbyeong Chae
James M. Ricles
Thomas M. Marullo
Stephanie Tong
ATLSS Center
Lehigh University

2. Objectives of Study
Improving the speed of computational time in real-time hybrid simulation (RTHS) for investigation of dynamic response of large-scale structural systems
Implementing RTHS for a large complex structure using multi-grid processing

3. Why Multi-Grid Real-Time Hybrid Simulation?
photo from Maurer Sohne
Difficult (size and $) to conduct shaking table tests for large-scale structural systems
RTHS can be an effective tool to enable the investigation of dynamic response of large-scale structures with rate-dependent devices
Fast computational demand can be resolved using multi-grid processing
From

4. Case Study: 9-Story ASCE Benchmark Structure
Ohtori et al. 2004, ASCE Journal of Engineering Mechanics, 130(4),

5. Structural Design Performance Objective
Limit story drift to 1.5% under the design basis earthquake (DBE) ground motion (satisfying the life safety performance level)
 Use large-scale MR dampers to control the story drift
MCE ground motion: a 2% probability of exceedance in 50 years
DBE ground motion: a 2/3rd intensity of the MCE

6. Large-Scale Magneto-Rheological (MR) Damper by Lord Corporation
Length = 1.47m (58in)
Stroke = ±297mm (±12in)
Weight = 280kg (615lb)
Force capacity = 200kN
at V=0.1m/sec, I=2.5A

7. Deployment of MR Dampers
Performance Objective: to limit story drift to 1.5% under DBE
How many MR dampers?
Where to install dampers?
 Simplified Analysis Procedure

8. Simplified Analysis Procedure
Response prediction method for MDOF structure with MR dampers
(Chae, Y., Ph.D. Dissertation, Lehigh University, 2011)
Calculate representative loss factor of MR damper
Assume x0 and set
Determine maximum damper displacements
Calculate equivalent damping ratio using lateral force energy method
Calculate equivalent stiffness of MR dampers
Perform response spectrum analysis with effective stiffness and equivalent damping ratio
Update effective stiffness of structural system
Update x0 using modal combination rules (SRSS, CQC, etc.) No
Update modal frequency and modal vector
Check x0 convergence
Yes
Calculate damper force from the Hershel-Bulkley quasi-static MR damper model

9. (based on Simplified Analysis Procedure, Chae 2011)
Deployment of MR dampers
(based on Simplified Analysis Procedure, Chae 2011)
Number of MR dampers
1 damper
2 dampers
5 dampers
10 dampers
MR damper

10. + Schematic of Real-Time Hybrid Simulation Structure with MR dampers
Analytical substructure +
Experimental substructure(s)
Actuators
1st story MR damper
2nd story MR damper

11. Real-Time Hybrid Simulation
Structural analysis program: HybridFEM, a MATLAB-based nonlinear finite element analysis program (nonlinear fiber elements, panel zone elements, strength deterioration elements, geometric nonlinearities, etc.; Karavasilis et al. 2009)
Integration algorithm: CR integration method, a unconditionally stable and explicit time integration algorithm (Chen and Ricles 2008, JEM)
Integration time step: Δt=5/512 sec (≅0.01 sec)
Actuator delay compensation method: Inverse Compensation (Chen and Ricles 2010, JSE)
Hybrid simulation platform: Mathwork’s xPC Target
Semi-active control of MR dampers: Linear Quadratic Regulator (LQR) 11

12. Multi-Grid Real-Time Hybrid Simulation
2 xPCs used
xPC1
xPC1: Intel Core 2 Duo (2.66GHz CPU), 2GB RAM; runs at 512Hz (1/512sec)
Ground
motion
Update accelerations from equations of motion
Update displacements/ velocities
Integration
algorithm
Structural
response
Experimental substructure restoring forces +
xPC2
xPC2: Intel Pentium 4 (2.4GHz CPU), 1GB RAM; runs at 102.4Hz (5/512sec)
Analytical restoring forces 12

13. Analytical Substructure: 9-Story Building
(using HybridFEM)
Beams and columns are modeled using a distributed plasticity displacement-based beam-column element (nonlinear fiber element)
Bi-linear material model
Gravity frames modeled as a lean-on column with a geometric stiffness to account for P-Δ effect
Lean-on
column
Number of degrees-of-freedom: 508
Number of nonlinear fiber elements: 357

14. Maxwell Nonlinear Slider (MNS) Model –
Modeling of MR Dampers in Analytical Substructure
Maxwell Nonlinear Slider (MNS) Model –
(Chae et al. 2012, EESD)
Pre- and post-yield behaviors are described independently by the Maxwell element and the nonlinear slider, respectively, making it easy to identify model parameters
Non-Newtonian fluid property is effectively accounted for by the nonlinear slider utilizing the Hershel-Bulkley visco-plasticity
Suitable for a discretized frame work with moderate time steps

15. - MR dampers in the 1st and 2nd stories -
Experimental Substructure
- MR dampers in the 1st and 2nd stories -
2nd story
MR damper
1st story
1700kN
actuator
Current driver
Load cell

16. Input Ground Motion
1994 Northridge earthquake recorded at Beverley Hills station (009 component)
Scaled to DBE level with scale factor of 1.17
Unscaled ground motion

17. Results of Multi-Grid RTHS
Multi-grid RTHS Video

18. Story drifts for 9-story building with MR dampers
Results of Multi-Grid RTHS
Story drifts for 9-story building with MR dampers
Performance objective (1.5% story drift)
Performance objective (1.5% story drift)
Performance objective (1.5% story drift)

19. Story drifts for 9-story building without MR dampers
1st story
2nd story
3rd story
1.5% story drift
1.5% story drift

20. - Comparison of displacements between RTHS and numerical simulation -
Validation of Multi-Grid RTHS
- Comparison of displacements between RTHS and numerical simulation -
9th floor
5th floor
3rd floor
1st floor

21. Comparison of Normalized TET
Task Execution Time (TET): the amount of time needed to complete a single step during real-time hybrid simulation
With Two xPCs
xPC1 only
xPC1
xPC2
Maximum TET (TETmax, sec)
0.0009
0.0048
0.0016
Running time step (δt, sec)
1/512 (=0.0019)
5/512 (=0.0098)

22. Summary and Conclusions
Real-time hybrid simulation for a large-scale structure with large complexity has been conducted successfully using multi-grid processing procedure
The use of multiple xPCs enables the computations to be completed over a shorter duration, which may not be achieved with the conventional implementation of the RTHS method (i.e., using a single xPC)
Multi-grid real-time hybrid simulation enables the investigation of dynamic response of a large complex structural system under earthquake ground motions

23. Acknowledgements
This study is based upon work supported by grants from the Pennsylvania Department of Community and Economic Development through the Pennsylvania Infrastructure Technology Alliance, and by the National Science Foundation under Award No. CMS NEES Consortium Operation, and NEES REU Program. We would like to thank Lord Corporation and Professor Richard Christenson for their generous support of this research by providing the MR dampers. 23

24. Thank you 24