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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
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
16
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
18
Development Challenges
• Delay in servo-hydraulic actuators
– How delay affects the simulation:
DisplacementForc
e
Linear Specimen
With Delay
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.
1 1 1
2
,
1 1
1Displacement to actuator
21
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
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.
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
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
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
25
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
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
27.7 8.5kips/in
8.5 3.9
K
50 0 lb
0 25 g
M
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:
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
31
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
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%
1 1 0 0
1 0 1 0
T
33
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
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.
Simulink Diagrams
35
Simulink Diagrams
36
Simulink Diagrams
37
Input file for Matlab: .m file
38
% ***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
39