An Introduction to Hybrid Simulation – Displacement-Controlled Methods

Mehdi Ahmadizadeh, PhDAndrei M Reinhorn, PE, PhD

Initially Prepared: Spring 2007

CIE 616 Fall 2010Experimental Methods in Structural Engineering Prof. Andrei M Reinhorn

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.

Test S tructure

N um erica l M odel

Experim enta l Substructure

Pseudo-Dynamic Testing (Shing, 2008)

8

Test S tructure

N um erica l M odel

Experim enta l Substructure

Pseudo-Dynamic Testing (Shing, 2008)

9

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.

,

1 1

21 1 1

1

1

1

2

n g n n n

n n n n

n n n n n

a mu kd cvm

v v t a a

d d t v t a a

gma cv kd mu

11

Displacement Controlled Hybrid Simulation

• Equation of Motion (for Hybrid Simulation)

• Numerical Solution:– Newmark’s Beta Method:

– Tangential stiffness matrix or iterations?

,

1 1

21 1 1

1

1

1

2

n g n n n n

n n n n

n n n n n

a mu kd r cvm

v v t a a

d d t v t a a

gma cv kd r mu

12

Displacement Controlled Hybrid Simulation

• Typical Block Diagram (Also Called Pseudo-Dynamic Test)

,m md r

cd

Integrator / Simulation

ExperimentAnalysis

Signal Generation

D/A PID Controller

Servo-valve Actuator

Hydraulic Supply

Specimen TransducersA/D

Commands (Desired Values)

Measurements (Achieved Values)

Pseudo-Dynamic Implementation (Pegon, 2008)

13

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

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Development Challenges

• Delay in servo-hydraulic actuators

Time

Dis

pla

cem

en

t

Command

Achieved

Delay

17

Development Challenges

• Delay in servo-hydraulic actuators

– How delay affects the simulation:

DisplacementForc

e

Linear Specimen

Without Delay

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Development Challenges

• Delay in servo-hydraulic actuators

– How delay affects the simulation:

DisplacementForc

e

Linear Specimen

With Delay

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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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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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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.

1 1 1

2

,

1 1

1Displacement to actuator

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Estimated Acceleration for Next Computation

1 Estimated Velocity for Next Computation

n n n n

n

c m c c

c m m cg n n n n

c c c cn n n n

d d t v t a

a mu kd r cvm

v v t a a

0

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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.

21 1 1

1

2n n n nd d t v t a

2

n n n

mn n n n

d d t a

r r k d d

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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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UB Real-Time Hybrid Simulation

SCRAMNet

Data Acquisition and Information Streaming Structural and Seismic Testing Controllers

LAN

UB Hybrid SimulationPhysical Components and Connections

469D

Shake Table 1

Controller

PowerPC

Shake Table 1

GUI

469D

Shake Table 2

Controller

PowerPC

Shake Table 2

GUI

469D

STSController

PowerPC

STS GUI

FlexTest

Controller

PowerPC

FlexTest GUI

Compensator

CompensationController

xPC Target

Compensator

Controller Host

Simulator

Structural Simulator

xPC Target

Structure Simulator

Host

DAQ

SCRAMNet A/D & D/A

Bridge

xPC Target

DAQ Host

Pacific 6000

General Purpose

Data Acquisition

Proprietary OS

Pacific GUI

NTCP Server

NTCP to SCRAMNet

Interface (Distributed

Testing)

Linux

Internet

Real Time Hybrid Simulation Controller

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UB Real-Time Hybrid Simulation

• Essential Components of Displacement-Controlled Hybrid Simulation

Controller

Simulator

SCRAMNet

Host PC

(Running MATLAB Simulink)

TCP/IP

TC

P/I

P SCRAMNet

STS Controller

Actuators

Test SubstructureTransducers

Com

man

ds

Measu

rem

en

ts

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UB Real-Time Hybrid Simulation

• Available test setup

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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

27.7 8.5kips/in

8.5 3.9

K

50 0 lb

0 25 g

M

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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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A Typical Hybrid Simulation

• Test Structure:

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A Typical Hybrid Simulation

• Required information:

– Total number of degrees of freedom: 4– Experimental degrees of freedom: 2

– Numerical stiffness and total mass matrices:

30 12 0 0

12 20 8 0kips/in

0 8 12 4

0 0 4 4

K

8.75 0 0 0

0 6.25 0 0kips/

0 0 3.75 0

0 0 0 1.25

g

M

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A Typical Hybrid Simulation

• Required information:

– Inherent damping ratio: 5%– Numerical damping matrix (in addition to the inherent

damping):

– Influence vector:

0 0 0 0

0 0 0 0kips s/in

0 0 0 0

0 0 0 0

C

8.75

6.25

3.75

1.25

Mι

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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%

1 1 0 0

1 0 1 0

T

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A Typical Hybrid Simulation

• Additional requirements for model-based integration:

– Total number of essential stiffness parameters: 2– Transformation matrix to parameter coordinate system:

1

1 2 2

1/ 0

1/ 1/p

l

l l l

T

11 12

21 22

El

k k

k k

K 1

2

0

0

s

s

P

s2

rx22

s1

rx11

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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.

Simulink Diagrams

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Simulink Diagrams

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Simulink Diagrams

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Input file for Matlab: .m file

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% ***General Information**** NDOF=4; % number of degrees of freedom NACT=2; % number of actuators involved in the simulation NPAR=2; % number of important parameters for formation of stiffness matrix % ***NUMERICAL MODEL**** k1 = 5.543*2; % DOF 1 STORY 1 (two pairs of coupons) k2 = 3.89; % DOF 2 STORY 2 l1=43; l2=46; l=l1+l2; % ***NUMERICAL MODEL DATA*** MT = [7 0 0 0; 0 5 0 0; 0 0 3 0; 0 0 0 1]*1.25/g; % Total mass matrix ME=[0 0 0 0; 0 0.05 0 0; 0 0 0.025 0; 0 0 0 0]/g; % Experimental Mass Matrix K = [30 -12 0 0; -12 20 -8 0; 0 -8 12 -4; 0 0 -4 4]; % Global analytical stiffness KEP = [k1*l1^2 0; 0 k2*l2^2]; % Parameteric experimental stiffness in intrinsic coord. system C=zeros(NDOF,NDOF); % Analytical damping matrix dr=0.05; % Damping ratio forstifness proportional damping L=-MT*ones(NDOF,1); % Influence vector for base motion % COORDINATE SYSTEM TRANSFORMATIONS ***** TDGA=[-1 1 0 0; -1 0 1 0]; % Displacement from global to actuator cs **** FDGA=1; % Displacement scale factor from global to actuator coordinates FFAG=1; % Force scale factor from actuator to global coordinates TDAP=[1/l1 0; -l/l1/l2 1/l2]; % Actuator displacements to parameter cs *** % Simulated experimental model properties Parameters.K1 = k1; % one column Parameters.K2 = k2; % one column Parameters.Uy = 0.20; Parameters.Ep = 0.00; Parameters.Ga = 0.45; Parameters.Be = 0.55; Parameters.N = 1.5; massA=0.025; % Actuator weight (kips) eyd=[Parameters.Uy; Parameters.Uy*3]; % experimental substructure yield displacement

Sequence of Operations

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