# An Introduction to Hybrid Simulation – Displacement-Controlled Methods

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An Introduction to Hybrid Simulation – Displacement-Controlled Methods
CIE 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

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

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

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.

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

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.

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

Pseudo-Dynamic Testing (Shing, 2008)

Pseudo-Dynamic Testing (Shing, 2008)

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.

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

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)

Pseudo-Dynamic Implementation (Pegon, 2008)

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

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

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

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

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

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

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.

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.

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.

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.

UB Real-Time Hybrid Simulation

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

UB Real-Time Hybrid Simulation
Available test setup

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

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.

A Typical Hybrid Simulation
Test Structure:

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

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

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%

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

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.