Verification of Hybrid Simulation
by
Ali. Ozdagli, Wang Xi, Ge Ou, Bo Li, Guoshan Xu
Shirley Dyke, Jian Zhang and Bin Wu
Project funded by
National Science Foundation - CMMI Grant #1011534
National Science Foundation of China – Project #90715036
Purdue University, West Lafayette, IN 47907
•Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: iisl@ecn.purdue.edu
Presentation Outline







Introduction
Background and Motivation
Experimental Setup
Modeling of the System
RTHS Comparison
HS Efforts
Conclusion
2
Purdue University, West Lafayette, IN 47907
•Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: iisl@ecn.purdue.edu
Introduction
Need for Testing

Global performance of new systems

Nonlinear response
Options

Shake-table: Scaled Structural Testing

Hybrid Simulation (HS)
3
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Background
“Comparison of Real-Time Hybrid
Testing with Shake Table Tests for an
MR Damper Controlled Structure” by
Lin et al. (2009)
“The
results show a close correlation
between the shake table tests and the
real-time hybrid simulation.”
“There is clearly a difference
between the hybrid tests and shake
table tests.”
4
Purdue University, West Lafayette, IN 47907
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Background
“Development of a Versatile Hybrid
Testing System for Seismic
Experimentation” by Shao et al. (2012)
5
Purdue University, West Lafayette, IN 47907
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Motivation

How do we know?


RTHS and Numerical Simulations represent the real structural
behavior?
Gain acceptance in community

Compare the RTHS to the real structure responses
Numerical
Simulation
RTHS
Shake Table
6
Purdue University, West Lafayette, IN 47907
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Challenges

Accurate modeling of the target structure


System Identification
Semi-active controllable nonlinear damper


Hard to model rate dependent dynamics
Damper-structure interaction
7
Purdue University, West Lafayette, IN 47907
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Objective

Verification of RTHS methodology using shake table tests on
mid-scale structure
Research Program

Phase 1: Numerical Modeling and Simulation

Phase 2: Shake Table Tests

Phase 3: RTHS Testing
8
Purdue University, West Lafayette, IN 47907
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Phase 1: Numerical Simulation
Test Structure
Base
Dimension: 1.84 m by 2.04 m
Story
height: 1.2 m
Material:
Structural Steel
9
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MCK Update Method
1 Floor - mm
0
st
-50
-100
0
5
10
0
-10
-20
15
0
20
60
40
80
100
120
100
120
2
More detailsFloor
were
given in
20
‘Modeling of Distributed Real-time Hybrid
Simulation’
0
accessible from http://nees.org/resources/6641/
0
-20
Model is awarded by NEES as the-40 best simulation model.
nd
-50
-100
0
5
10
15
0
Floor 3
0
-100
0
5
MCK Update Method
10
Frequency - Hz
rd
-50
Experimental Data
20
40
60
80
40
3 Floor - mm
Magnitude - dB
10
2
Magnitude - dB
20
Floor - mm
Magnitude - dB
Floor 1
15
Experiment
Simulation
20
0
-20
-40
0
20
40
60
Time - s
80
100
120
10
Purdue University, West Lafayette, IN 47907
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MR damper numerical model
alpha_a
alpha_b
c0_a
c0_b
k0
gamma
A
x0
k1
c1_a
c1_b
15.65
57.16
1.00
9.76
11.08
23.44
155.32
0.0
0.009
19.15
139.96
Numerical model for volt = 1.7 V, freq = 2.9Hz
300
Damper force (lbf)
200
100
0
-100
Test data
Simulink model
ODE model
-200
-300
-0.2
-0.15
-0.1
-0.05
0
0.05
Damper disp (inch)
0.1
0.15
0.2
Numerical model for volt = 1.7 V, freq = 2.9Hz
300
Lord MR damper RD-1005-03
Damper force (lbf)
200
100
0
-100
-200
-300
-4
Test data
Simulink model
ODE model
-3
-2
-1
0
1
Damper vel (inch/s)
2
3
4
5
11
Purdue University, West Lafayette, IN 47907
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Phase 2: Shake Table Tests
Location: Harbin Institute of Technology
Size: 3m×4m (shaking direction)
Peak acceleration: ±1.33g
Peak velocity: ±600 mm/s
Stroke: ±125 mm
Maximum payload: 12t
Force capacity: 200kN
Maximum overturning moment: 30 t-m
Frequency bandwidth: 0 - 30 Hz
Conducted uncontrolled, passive off, passive on and semi-active
control cases
12
Purdue University, West Lafayette, IN 47907
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Comparison – Shake Table vs Simulation
5000
5
0
-5
-10
64
66
68
70
72
74
76
78
80
Pure Simulation
Experimental Data
2
Pure Simulation
Experimental Data
Acc 3rd floor-mm/s
Disp 3rd floor-mm
10
0
-5000
64
82
66
68
70
72
74
Time-s
Time-s
78
80
82
2
5000
Acc 3rd floor-mm/s
Disp 3rd floor-mm
10
76
5
0
-5
-10
69
70
71
72
Time-s
73
74
0
-5000
69
70
71
72
73
74
Time-s
13
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Phase 3: RTHS
MTS loading Frame @ HIT
MTS Loading Frame,
2500kN,
Internal LVDT
Load cell,
15kN
MTS Flex GT Controller
Inner Loop Control
Lord MR
damper,
2kN
Clamp for
vertical loading
Purdue University, West Lafayette, IN 47907
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RTHS Setup
Force
Complete Structure
Numerical substruc.
Physical substruc.
Damper
Desired
Displacement
4
Purdue University, West Lafayette, IN 47907
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RTHS Result: Kobe
displacement (mm)
displacement (mm)
5
10
5
0
0
-5
Due to the limitation of Pump Velocity
Limitation, Piston maximum moving speed
20
30
40
50
60
20
30
40
50
60
50mm/s
time (sec)
-10
-5
-15
00
10
10
70
70
80
80
time (sec)
displacement (mm)
displacement (mm)
5
10
Reference
Reference
Measured
Measured
5
0
0
-5
-10
-5
-15
6
6
8
8
10
10
12
12
time (sec)
time (sec)
14
14
16
16
18
18
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displacement
(mm)
displacement (mm)
RTHS Result: Morgan
10
5
5
00
-5
-5
displacement
(mm)
displacement (mm)
-10
0
10
10
20
20
30
30
40
40
time
time(sec)
(sec)
5050
6060
70 70
80 80
10
5
Reference
Reference
Measured
5
Measured
00
-5
-5
-10
6
88
10
10
12
12
time
time(sec)
(sec)
1414
16 16
18 18
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Phase 3: RTHS (Replace pics with IISL Actuator)
Shore Western loading Frame @ IISL
2 kip Actuator
Loading
Frame
High performance
programmable DSP
system plus high
precision servohydraulic motion
control system.
Servo Valve
Lord
MR Damper
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Compensation Performance
2
0.8
Desired Displacement
Measured Displacement
1
Gain (abs)
0.6
-1
0.2
-2
0
5
10
15
20
25
Frequency (Hz)
30
35
40
0
5
10
15
20
25
Frequency (Hz)
30
35
40
0
-0.2
50
Phase (deg)
1st Floor Displacement - cm
0.4
0
-0.4
-0.6
-50
NRMS: 3.62%
-0.8
66
68
70
72
Time - s
74
76
0
78
19
Purdue University, West Lafayette, IN 47907
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Comparison – ST vs RTHS
5000
Experimental Data
RTHS
5
Acc 3rd floor-mm/s2
Disp 3rd floor-mm
10
0
-5
-10
64
66
68
70
72
74
Time-s
76
78
80
66
68
70
72
74
Time-s
76
78
80
82
5000
Acc 3rd floor-mm/s2
Disp 3rd floor-mm
0
-5000
64
82
10
5
0
-5
-10
69
Experimental Data
RTHS
70
71
72
Time-s
73
74
0
-5000
69
70
71
72
Time-s
73
20
74
Purdue University, West Lafayette, IN 47907
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Remarks on RTHS

To verify the RTHS methodology, shake table responses at HIT are
compared to RTHS results at IISL.

A new control oriented model updating method is implemented
using mode shapes to derive MCK.



MCK model based on fully identified results
Accurate zero tracking
A new compensation scheme, RIAC is implemented.



High performance even in large noise/signal ratio condition
Flexible to choose loop shaping function
Experimental tuning is easy to perform
21
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Model updating with UKF
m2
c2
kf 2
m1
c1
kf1
Physical BRB
Numerical BRB
r   kd  (1   )kz

n 1
n
z

d

d
z
z


d
z

k , ,  , n, 
r, d
Constrained
Kalman filter
－22－
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Exact
UKF
CUKF
Initial
100
0
-100
100
0
-100
-200
-200
-3
Exact
UKF
CUKF
Initial
200
Restoring force (kN)
Restoring force (kN)
200
-2
-1
0
1
Displacement (mm)
Physical BRB
2
-2
-1
0
1
2
3
Displacement (mm)
Numerical BRB
－23－
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Real-time hybrid test validations
 =30
Physical BRB
 =30
Numerical BRB
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200
200
Restoring force (kN)
300
100
0
-100
-200
-300
-4
Physical BRB
Numerical BRB
-3
-2
-1
0
1
2
3
Initial
300
CUKF
100
0
-100
-200
-300
-4
4
Displacement (mm)
Restoring force (kN)
Restoring force (kN)
300
Physical BRB
Numerical BRB
-3
-2
-1
0
1
2
3
4
Displacement (mm)
UKF
200
100
0
-100
-200
-300
-4
Physical BRB
Numerical BRB
-3
-2
-1
0
1
Displacement (mm)
2
3
4
－25－
Purdue University, West Lafayette, IN 47907
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Finite element based sectional constitutive model
• Section Yield Function
M
fy
N
h
Aw  hw  tw
hw
h
fy
(1  2 )h  h
Af  b  t
（2  1）2 ( N  FaN ) 2 M  FaM
 (s, Fa ) 


,
2
4  1
Ny
MP
N  FaN （4  1） M  FaM
 (s, Fa ) 


,
Ny
2(2  1)
Mp
N
1

N y 2  1
N
1

N y 2  1
•Section Restoring Force Model (RFM)
s  k se  e
When  (s, Fa ) 1, Section- elastic
When  (s, Fa ) 1 , Section- plastic
s  k se  (e  e p )
1   T
 ( )  k se  e
where e 
H s s
p
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Numerical example
• Identification results
2050
Yield Axial Force [kN]
2000
1950
1900
True Value
Indtified Value
1850
1800
1750
1700
0
5
10
15
20
25
30
215
210
205
True Value
Indentified Value
200
195
190
185
0
35
0.031
5
10
Time [sec]
25
30
35
0.028
0.026
0.025
0.024
10
0
-10
-20
-30
2
3
Time(s)
4
5
6
5
10
15
20
3000
25
30
Back internal force
Internal force path
Correlation curve
2000
Before updating
100
50
0
-50
After updating
1000
0
After Updating and Kinematic
-1000
-100
-150
1
0
Time [sec]
Axial Force[kN]
20
True Value
Indentified Value
0.027
150
Bending Moment(kN.m)
Horizontal Disp(mm)
20
0.029
200
TR-Response
WO-Update
WI-Update
30
-40
0
15
0.03
Time [sec]
• Model updating results
40
Kinematic hardening coefficient [1]
Plastic Bending Moment [kN.m]
220
-200
-0.03
-0.02
-0.01
0
0.01
Section Curvature(1/m)
TR-Resp
WO-Update
WI-Update
0.02
0.03
-2000
-3000
-300
-200
-100
0
100
200
300
Bending Moment[kN.m]
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Experiment plan
• Test scheme
• Test setup and three cases of HS
Traditional HS (Linear/Nonlinear)
FE Model updating by HS
Distributed Hybrid Simulation
Purdue University, West Lafayette, IN 47907
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Delay over-prediction
Delay compensation based on over-prediction
①Calculate di+1
②Predict with c
③Load with prediction
④Find force measurement
Delay Compensation:
Compensated Delay > System Delay
Purdue University, West Lafayette, IN 47907
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Implicit algorithms for RTHS
Limitations:
1. Iteration
2. Intensive computation
3. Time delay
Fixed Number of Iterations with Interpolation (Shing et al)
Equivalent Force Control Method (Wu et al)
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New implicit algorithm based on over-prediction
(1)
Over-prediction
dp
(2)
Interpolation
(4)
Process 2
FEQ ,i 1
+
Iterative calculation
dc
Actuator
(3)
KN
K PD
r
d
d ik1
Optimal force
Process 1
ui (ai , vi , d i )
ui1(ai1,vi1, di1)
Measured Measured
Force
Disp
RN (dik1 )
K PD dik1
REk ,i 1
++ +
1、Modified Newton’s Method applied results in good iteration performance.
2、System delay is compensated for based on over-prediction method.
－31－
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 Single time step
validation
-5
5
k3/2
m3
m2
0.5
1.5
0.5
1
Shing方法
0.5
k3/2
0
2
4
6
迭代步
8
10
0
2
ke
 10 seconds
X: 426
Y: 0.001369
Shing方法
6
计算步
8
0
10
2
0.5
4
6
迭代步
8
10
-4
x 10
x 10
X: 105
Y: 0.0001493
X: 465
Y: 0.002562
2
1
1.5
EFCM
1
1
0.5
0.5
新方法
0
0
500
积分步
Shing
EFCM
500
积分步
新方法
1000
11
0.005
10
-0.005
-0.015
0
5
10
15
时间 (s)
20
25
30
100
9
8
7
-0.01
500
积分步
x 10
0.01
0
0
0
-3
参考解
位移 (m)
位移 (m)
0
0
1000
0.015
 Delay
comptn
error
2.5
耗时(s)
k1/2
k2/2
4
-3
x 10
耗时(s)
m1
新方法
1
2
1
x 10
EFCM
-3
k2/2
1.5
耗时(s)
k4/2
x 10
2.5
k5/2
耗时(s)
k4/2
m4
3
1.5
耗时(s)
k5/2
-5
-5
x 10
耗时(s)
 Test
Shing
EFCM
新方法
参考解
－32－
6
27.4
27.5
27.6
时间
(s)
Purdue University, West Lafayette, IN 47907
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Trans-pacific test between UCB and HIT
2
MX  CX  R ( X)  MBX g
Conducted in HIT, CHINA
Physical model of structural
resistance
Performed in UCB, USA
PLATEFORM: OpenFresco Express
M  0.04
K  1.8
C =  K
 =0.02
C
1.0m
LEGEND
Analytical model of structural
energy dissipation and inertia
M
K
Y
Ug
1
X
33
Purdue University, West Lafayette, IN 47907
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HIT,CHINA
UCB, USA
Data available @ http://peer.berkeley.edu/~aschell/DHS%20with%20HIT/
Purdue University, West Lafayette, IN 47907
•Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: iisl@ecn.purdue.edu
Acknowledgements

National Science Foundation - CMMI Grant #1011534

National Science Foundation of China – Project #90715036

HIT Lab
Steve Mahin & Andreas Schellenberg @ UCB
Tao Wang @ IEM


Project data will be available @ NEES.org #1076
35
Purdue University, West Lafayette, IN 47907
•Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: iisl@ecn.purdue.edu
China-US collaborative project on hybrid simulation
Bin Wu, Professor
Harbin Institute of Technology
Yurong Guo, Professor
Hunan University
Shirley Dyke, Professor
Purdue University
Tao Wang , Assoc Professor
Institute of Eng. Mechanics
Jian Zhang , Associate Professor
UCLA
Purdue University, West Lafayette, IN 47907
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THANK YOU!
37
Purdue University, West Lafayette, IN 47907
•Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: iisl@ecn.purdue.edu