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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
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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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Structural Seismic Test Methods
• Shake Table Tests
– The most realistic experimentation of structural systems for seismic events.
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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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Structural Seismic Test Methods
• Quasi-Static Tests
– Generally used for evaluation of lateral resistance of structural elements.
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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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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
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Pseudo-Dynamic Testing (Shing, 2008)
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Test S tructure
N um erica l M odel
Experim enta l Substructure
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Pseudo-Dynamic Testing (Shing, 2008)
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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
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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
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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)
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Pseudo-Dynamic Implementation (Pegon, 2008)
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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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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
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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.
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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
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Sequence of Operations
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