An Introduction to Hybrid Simulation – Displacement-Controlled Methods

1. CIE 616 Fall 2010 Experimental Methods in Structural Engineering Prof. Andrei M Reinhorn An Introduction to Hybrid Simulation – Displacement-Controlled Methods Mehdi Ahmadizadeh, PhD Andrei M Reinhorn, PE, PhD Initially Prepared: Spring 2007

2. Presentation Outline • Structural Test Methods and Hybrid Simulation • Displacement-Controlled Hybrid Simulation • Development Challenges • Hybrid Simulation System at SEESL • A Typical Hybrid Simulation • Simulation Models

3. Structural Seismic Test Methods • Shake Table Tests • The most realistic experimentation of structural systems for seismic events.

4. Structural Seismic Test Methods • Shake Table Tests • Limitations: • Limited capacity of shaking tables • Scaling requirements and resulting unrealistic gravitational loads  It is generally accepted that shake table tests provide an understanding of overall performance of structures subjected to seismic events.

5. Structural Seismic Test Methods • Quasi-Static Tests • Generally used for evaluation of lateral resistance of structural elements.

6. Structural Seismic Test Methods • Quasi-Static Tests • Limitations: • Unable to capture rate-dependent properties of structural components • Slow application of loads may result in stress relaxation and creep, even in rate-independent specimens  The results of quasi-static tests generally have limited dynamic interpretation.

7. Structural Seismic Test Methods • Hybrid Simulation – Pseudo-Dynamic • A parallel numerical and experimental simulation.

8. Pseudo-Dynamic Testing (Shing, 2008)

9. Pseudo-Dynamic Testing (Shing, 2008)

10. Displacement Controlled Hybrid Simulation • Equation of Motion (SDF): • Numerical Solution: • A time-stepping method, such as Newmark’s Beta: • For solution in implicit form, tangential stiffness matrix is needed, or iterations should be used.

11. Displacement Controlled Hybrid Simulation • Equation of Motion (for Hybrid Simulation) • Numerical Solution: • Newmark’s Beta Method: • Tangential stiffness matrix or iterations?

12. Displacement Controlled Hybrid Simulation • Typical Block Diagram (Also Called Pseudo-Dynamic Test) Commands (Desired Values) Analysis Experiment Signal Generation D/A PID Controller Hydraulic Supply Integrator / Simulation Specimen Transducers Servo-valve Actuator A/D Measurements (Achieved Values)

13. Pseudo-Dynamic Implementation (Pegon, 2008)

14. Structural Seismic Test Methods • Hybrid Simulation • Advantages: • Lower cost than shake table tests (construction, moving mass) • Less scaling and size requirements • Able to capture rate-dependent properties of experimental substructure • Provides better understanding of component behavior • Limitations • Inertia and rate-dependent terms are artificial • The number and quality of boundary conditions • Unrealistic gravitational loads

15. Development Challenges • Error Sources • Analytical: • Discretization of structural system in time and space, and simplifications such as lumped-mass models • Errors of the utilized integration methods • Experimental • Measurement contaminations • For example, noise in measurements may lead to excitation of high-frequency modes; if not, it will certainly affect the accuracy • Actuator tracking errors • The most important error source in hybrid simulation – the achieved displacement almost never equals the desired displacement

16. Development Challenges • Delay in servo-hydraulic actuators Command Achieved Displacement Delay Time

17. Development Challenges • Delay in servo-hydraulic actuators • How delay affects the simulation: Force Linear Specimen Without Delay Displacement

18. Development Challenges • Delay in servo-hydraulic actuators • How delay affects the simulation: Force Linear Specimen With Delay Displacement

19. Development Challenges • Delay in servo-hydraulic actuators • How to compensate delay: • First, measure the delay amount (in order of a few milliseconds) • Extrapolate displacements: send a command ahead of desired displacement to the actuator • Or modify forces: extrapolate force measurements, or seek the desired displacements in the force and displacement measurements

20. Development Challenges • In hybrid simulations experimental substructures are involved • Iterations should be avoided, as they may damage the experimental substructures, • A complete tangent stiffness matrix of the experimental substructure may be difficult to establish due to contaminated or insufficient measurements. • As a result, most integration procedures are either explicit, or use initial stiffness matrix approximations, whose applications are limited.

21. Development Challenges • Use explicit Newmark’s Beta method , • Apply displacement, measure restoring force, update acceleration and velocity vectors. Explicit methods are conditionally stable, and have stringent time step requirements for stiff systems and systems containing high-frequency modes.

22. Development Challenges • Or use initial linear stiffness matrix instead of its tangent stiffness, • Apply explicit displacement: • Measure the restoring force and find velocity and acceleration, while updating displacement and measured force vectors:  This is only an approximation. The accuracy may not be sufficient for highly nonlinear systems.

23. Development Challenges • Or use an iterative scheme only in numerical substructure, • Or find a way for global iterations without damage to the experimental setup, • Or use “non-physical” iterations on the measurements, • Or develop a fast method for finding tangential stiffness matrix during the simulation.

24. UB Real-Time Hybrid Simulation

25. SCRAMNet SCRAMNet UB Real-Time Hybrid Simulation • Essential Components of Displacement-Controlled Hybrid Simulation TCP/IP Host PC (Running MATLAB Simulink) Simulator Controller Measurements TCP/IP Commands STS Controller Actuators Transducers Test Substructure

26. UB Real-Time Hybrid Simulation • Available test setup

27. UB Real-Time Hybrid Simulation • Test Setup Properties: • Degrees of Freedom: up to 2 • Actuators: ± 3.0 inches, ± 5.0 kips • Experimental stiffness matrix can be altered by using different number of coupons. With two pairs in the first story and one pair in the second story: • Experimental mass is very small: • The rate-dependency of specimens is negligible

28. UB Real-Time Hybrid Simulation • Fundamental periods of 0.4 s and above have been tested to work fine with the available equipment; a fundamental period of 0.6 s and above is recommended to minimize the noise in the measurements. • If time scaling is acceptable, virtually any natural period can be tested. • Available procedures allow for linear numerical system and linear transformations only.

29. A Typical Hybrid Simulation • Test Structure:

30. A Typical Hybrid Simulation • Required information: • Total number of degrees of freedom: 4 • Experimental degrees of freedom: 2 • Numerical stiffness and total mass matrices:

31. A Typical Hybrid Simulation • Required information: • Inherent damping ratio: 5% • Numerical damping matrix (in addition to the inherent damping): • Influence vector:

32. A Typical Hybrid Simulation • Required information: • Transformation matrix for displacement (from global to actuator local coordinate system): • Displacement factor in actuator coordinate system: 1 • Measured force factor: 1 • Ground motion: 1940 El Centro, 200%

33. A Typical Hybrid Simulation • Additional requirements for model-based integration: • Total number of essential stiffness parameters: 2 • Transformation matrix to parameter coordinate system:

34. Detailed Description of Simulation Models • Simulation and control models are prepared in MATLAB Simulink environment on Host PC. • The models are then ‘downloaded’ to real time computers running MATLAB xPC kernel. • After simulation, the results are ‘uploaded’ to Host PC for observation and analysis.

35. Simulink Diagrams

36. Simulink Diagrams

37. Simulink Diagrams

38. Input file for Matlab: .m file

39. Sequence of Operations