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

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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

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

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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.

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

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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.

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

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Pseudo-Dynamic Testing (Shing, 2008) 8

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

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11 Displacement Controlled Hybrid Simulation Equation of Motion (for Hybrid Simulation) Numerical Solution: –Newmarks Beta Method: –Tangential stiffness matrix or iterations?

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

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Pseudo-Dynamic Implementation (Pegon, 2008) 13

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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

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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

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

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

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

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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

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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.

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21 Development Challenges Use explicit Newmarks 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.

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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.

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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.

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24 UB Real-Time Hybrid Simulation

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

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26 UB Real-Time Hybrid Simulation Available test setup

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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

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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.

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29 A Typical Hybrid Simulation Test Structure:

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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:

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

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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%

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

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34 Detailed Description of Simulation Models Simulation and control models are prepared in MATLAB Simulink environment on Host PC. MATLAB 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.

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Simulink Diagrams 35

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Simulink Diagrams 36

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Simulink Diagrams 37

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Input file for Matlab:.m file 38

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Sequence of Operations 39

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