1 Real-Time Hybrid Simulations P. Benson Shing University of California, San Diego

2 Better Known as the Pseudodynamic Test Method Early Work: Hakuno et al. (1969) Takanashi et al. (1974) Institute of Industrial Science, University of Tokyo Hybrid: real-time testing; analytical substructuring; distributed testing and simulation; ………. Pseudodynamic: slow rate of loading; dynamic properties simulated numerically

3 Pseudodynamic Test Method Simple concept but requires care to execute.  Precision of displacement control.  Accumulation of experimental errors in numerical computation. Advance to next time step: i = i + 1 Update and Numerical solution of eqs. of motion Test Frame Displacement

Experimental Error Accumulation 4 Main source of systematic experimental errors: time-delay in servo-hydraulic loading apparatus Shing and Mahin (1982)

5 Dermitzakis and Mahin (1985) Substructure Test Methods Advance to next time step: i = i + 1 Update and Numerical solution of eqs. of motion Computer Model Test Frame

Range of Configurations 6

7 Needs for Real-Time Tests Computer Model Test Base Isolation Devices Test Active/ Passive Dampers Computer Model

General Framework for Hybrid Simulation 8 Structural Partitioning

Total Formulation 9

Coupled Subdomain Approach 10 Magonette et al. (1998) Implicit Scheme Explicit Scheme

Dynamic Substructuring I 11

Dynamic Substructuring I 12 Actuator Specimen Shake Table Computational Model Sivaselvan and Reinhorn (2004)

Dynamic Substructuring II 13

Dynamic Substructuring II 14 Actuator Shake Table Computational Model Actual Equipment Tested Horiuchi et al. (2000) Bayer et al. (2005) Bursi et al. (2008)

15  Nakashima et al. (1992, 1999)  Horiuchi et al. (1996)  Tsai et al.  Darby et al. (1999)  Magonette et al. (1998)  Bayer et al. (2000)  Shing et al. (2002)  Wu et al. (2005, 2006) Real-Time Hybrid Test Methods Explicit Integration Schemes Implicit Integration Schemes Implicit-Explicit Coupled Field Analysis

16 Newmark Implicit Method for Time Integration

17 Modified Newton Method

18 Modified Newton Method  Number of iterations varies from time step to time step.  Increment size decreases as solution converges. Convergence is guaranteed as long as is positive definite (Shing and Vannan 1991). Problems for Real-Time Tests:

19 Fixed Number of Iterations with Interpolation Shing et al. (2002)

Response Correction and Update 20 -Method Compatibility Equilibrium

Nonlinear Structure 21

22 System Configuration

23 Real-Time Substructure Test Platform PID Controller Real-Time Processor SCRAMNet Card 2 Analytical Substructure Model Experimental Element/Substructure Target PC –Real-Time Kernel SCRAMNet Card 1 Special Element Data-Acquisition Program Actuators Specimen OpenSEES

24 Issues in a Real-Time Test  Actuator time-lag caused by dynamics of servo-hydraulic system and test structure.  Communication delays among processors.  Accounting for real inertia and damping forces.  Convergence errors in numerical scheme.  Interaction of numerical computation with system dynamics.

25 Phase-Lag Compensation Methods PID with Feedforward Discrete Feedfordward Correction Phase-Lead Compensator

System Model for Test Simulation 26

Physical Test System 27

28 System Transfer Function (Linear System)  Consider dynamics of servo-hydraulic actuators and test structure.  Communication delays.  Error compensation schemes.  Interaction of numerical computation with physical system. Jung and Shing (2006)

29 Implicit Integration Scheme External Force Explicit Prediction Implicit Correction

30 System Block Diagram and Transfer Function

31 Physical Test System

32 Validation with Simulink Model Error Correction:

33 System Performance (PID Only)

34 PID with Feedforward

35 Discrete Feedforward Correction (DFC)

36 Inertia Effect in Real-Time Tests Advance to next time step: i = i + 1 Update and Numerical solution of eqs. of motion Test Frame +

37 Influence of Inertia Force Feedback

38 Actual Test with Inertia Force Removal M t /M = 4.7%

Influence of Support Flexibility 39

40 Nonlinear Structures (2-DOF,  Method) Convergence: has to be positive definite Strain Hardening Strain Softening

Simulation Setup 41

Two-Story Frame 42

Two-DOF Real-Time Tests 43

Two-DOF Real-Time Tests 44

45 Real-Time Substructure Test with a Single Column Actuator Analytical Model in OPENSEES Test Column

46 Real-Time Substructure Test

47 Test of a Zipper Frame Georgia Tech U. At Buffalo UC-Berkeley UC-San Diego/U. of Colorado Florida A&M

48 Test Setup

49 Test Results 80% LA % LA 22

50 Brace Response

51 Brace Damage

52 Future Challenge - Improve Computational Speed Parallel Computing

53 Future Challenge - Develop Mixed Control Strategy Displ. Control Computer Model Test Specimen Force Control Shear Wall

54 Dr. Rae-Young Jung, Former Grad. Student at CU Dr. Zhong Wei, Former Grad. Student at CU Dr. Eric Stauffer, Formerly at Andreas Stavridis, Grad. Student at UCSD Rob Wallen, Thomas Bowen, Contributors Development supported by NSF under NEES Program. Acknowledgments

55 Thank You