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Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Investigation of the Effect of Transfer System Delay on Real-time Hybrid Simulation
Amin Maghareh and Shirley J. DykePurdue University
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
In order to reduce impacts of dynamic loading on civil structures/infrastructures, we need more experimental capabilities in evaluating structural performances in a suitable and cost-effective manner1.
EarthquakeTsunami
Wind1- NEES. (2010). Vision 2020: An Open Space Technology Workshop on the Future of Earthquake Engineering (Vol. 20). Retrieved
from https://nees.org/resources/1637/download/Vision_2020__Final_Report.pdf
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
E-Defense Earthquake Shake Table (World's Largest Earthquake Shake Table Test in Japan)
Shake Table Testing
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Shake Table Testing
In seismic evaluation of civil structures using shake table testing …1. A researcher needs only to know the capacity/capabilities of the table2. There is usually no stability concern, and the results are highly reliable
However, 3. Very few shake tables in the world are capable of testing full-scale large
civil structures4. Shake table testing is often limited to prototypes, limited in payload,
and/or prohibitively expensive
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Hybrid simulation (HS) is a cost-effective experimental technique to evaluate the dynamic performance of large civil structures.
Real-time hybrid simulation (RTHS) provides the most advanced experimental technique to evaluate the performance of rate-dependent civil structures in laboratories1, 2.
1- NEES. (2010). Vision 2020: An Open Space Technology Workshop on the Future of Earthquake Engineering (Vol. 20). Retrieved from https://nees.org/resources/1637/download/Vision_2020__Final_Report.pdf
2 - NSF. (2007). Issues and Research Needs in Simulation Development. September, Chicago, IL, USA.
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Real-time Hybrid Simulation (RTHS)
Transfer System in RTHS
Time Delay and Time Lag in RTHS
An RTHS Model
Numerical and Experimental Examples
Outline
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
What is RTHS? Real-time hybrid simulation is a cyber-physical technique of partitioning a structure into physical and numerical substructures to study the dynamic performance of complex engineering structures under dynamic loading
Why RTHS? It would facilitate low-cost and broader evaluation of new structural components and systems
Components: • Cyber Components
Real-time Control SystemVisualization and Control Dashboard
• Physical Components Reaction Mounting System Sensing and Actuation System
Real-time Hybrid Simulation
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
xi+1
R4
R3 Ri+1
Displacements imposed in Real
time
gx
x2(t)
x1(t)m1
m2
c2
c1
k2
k1
Physical sub-structure
k4
k3
Numerical integration
Numerical sub-structure
x4(t)
x3(t)m3
m4
c4
c3
k4
k3
Numerical s
ub-
structu
re
Figures from “Real-Time Hybrid Simulation with Model-Based Multi-Metric Feedback” by B. F. Spencer Jr. and Brian M. Phillips
1111 iiii FRxCxM x
tti ti+1
xi xi+1
Real-time Hybrid Simulation
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Communication Delay: To implement RTHS, there is a continuous exchange of information between the cyber and physical components. In RTHS, communication delays vary from almost negligible for an RTHS using a single processor (no network) to more than a hundred milliseconds for geographically distributed testing. Computational Delay: In RTHS, integration schemes are implemented to solve the discretized governing equation of the numerical substructure.
ZOH Converted Signal
Approximate Signal
Signal without DA Conversion
Time Delay in RTHS
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
• In RTHS, the interface interaction between the substructures is enforced by a transfer system which includes servo-hydraulic actuator(s) and/or shake table.
• The transfer system should be designed and controlled to ensure that all the interface boundary conditions are satisfied in real time.
Time Lag in RTHS
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Transfer System
G (s )= 2.382 ×109
s4+485.5 s3+1.317 × 105 s2+3.182 ×107 s+2.382 ×109
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Pure Time Delay:
Linear System Dynamics:
Transfer System
0 20 40 60 80 100
-20
0
20
(rad/sec)
dB
Actuator DynamicsPure Time Delay ( = 13 msec.)
0 20 40 60 80 100-1.5
-1
-0.5
0
(rad/sec)
Pha
se (
rad)
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
RTHS Model
Reference System:
RTHS Model (Neutral Delay Differential Equation):
Reference StructureNumerical Substructure
Physical SubstructureMeasurement Noise
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
RTHS Model
X (t )=A0 X (t )+∑i=1
m
A i X (t − τ i )+ [ B N ] [ Xg (t)
w (t ) ]
-200 -150 -100 -50 0 50 100 150 2000
1
2
3
4
5
6
7x 104
Acceleration Noise (cm/s2)
n
Acceleration of 4th Story // No. of Samples = 409600
= 0.69 cm/s2
= 41.17 cm/s2 = 0.042g
1994 Northridge
1995 Kobe
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
SDOF RTHS
F fb
)(tx
)(txm)(tx
Numerical Substructure Experimental Substructure
Reference StructureX g( t)
X (t)
)(tx
)(txm)(tx
Numerical Substructure Experimental Substructure
Reference Structure
M nCn
Kn
X g( t)
M P
CP
K P
Transfer System
Num. Substructure
Phy. Substructure
X RTHS (t)Reference Structure
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Experimental Results
0 10 20 30 40 50 60
-0.2
-0.1
0
0.1
0.2
0.3
time (sec)
Dis
p (c
m)
=0.75 =0.82 =0.75
Pure Simulation w/ DelayRTHS, NRMSE = 0.9%
12.5 13 13.5 14 14.5-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
20.5 21 21.5 22 22.5 23 23.5 24
-0.1
-0.05
0
0.05
0.1
38.5 39 39.5 40 40.5 41 41.5
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Stability of a SDOF RTHS
α Factor β Factor γ Factor
Case I [0,1] 0.4 0.9
Case II 0.9 0.6 [0,1]
Case III [0,1] 0.6 0.1
Case IV 0.1 0.4 [0,1]
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Performance of a SDOF RTHS
γ = 0.964 Rad.
ωn3 E [(X REF − X RTHS)
2]
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Simulation Results
0 1000 2000 3000 4000 5000-20
-15
-10
-5
0
5
10
15
20
Dis
pl. (
cm)
t (sec)
BLWN Input (sec) = 1.17 = %1.3 = 0.964
RTHS ResponseREF Response
0 1000 2000 3000 4000 5000-15
-10
-5
0
5
10
15D
ispl
. (cm
)
t (sec)
BLWN Input (sec) = 1.17 = %1.3 = 0.964 = 10.2728
Error Response
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
RTHS Model
m1 = mp1 + mn1
c1 = cp1 + cn1
k1 = kp1 + kn1
Reference Sys.
Physical Sub.
0 5 10 150
0.5
1
1.5
2
Freq. (Hz)
dB
1st Mode 2nd Mode 3rd Mode 4th Mode
0 5 10 15
-10
-5
0
Freq. (Hz)
Pha
se (
deg)
Transfer System DynamicsApproximate Delay
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Stability Analysis
Instability Mode
Critical Frequency (Hz.)
Critical Time Delay (msec.)
1st 1.95 7.3
2nd 3.11 149.7
3rd 5.13 8.0
After conducting stability analysis, the results show that to avoid instability in conducting RTHS with these substructures, the maximum time lag tolerated within the operation range is 7.3 msec.
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Modeling Results
Response of the Ref. System, RTHS with Transfer System Dynamics, and the DDE Model Subject to 1995 Kobe Ground Acceleration
8 10 12 14 16 18 20 22 24 26 28 30-0.2
0
0.2
0.4
time (sec)
Dis
p. (
m)
Displacement of 4th Floor
0 10 20 30 40 50 60
-500
0
500
time (sec)
For
ce (
N)
Feedback Force Normalized RMSE = %0.029051
Restoring Force using Transfer System DynamicsError of the Approximate Model
Ref.RTHS Transfer System DynamicsRTHS System Delay14 14.5 15 15.5 16
-0.1
0
0.1
time (sec)
Dis
p. (
m)
Displacement of 4th Floor
0 10 20 30 40 50 60
-500
0
500
time (sec)
For
ce (
N)
Feedback Force Normalized RMSE = %0.029051
Restoring Force using Transfer System DynamicsError of the Approximate Model
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Experimental Example
Phy. Substructure
Num. Substructure
Reference System
Phy. Substructure
Num. Substructure
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Experimental Results
Time Lag at the 1st Mode (msec.)
Time Lag at the 2nd Mode (msec.)
Controller 1 3.98 4.02
Controller 2 5.40 5.44
Controller 3 7.40 7.44
Instability Mode Critical Frequency (Hz.)
Critical Time Delay (msec.)
2nd 4.45 10
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Experimental Results
1 2 3 4 5 6 7 8 9 10-140
-120
-100
-80
-60
-40
-20
Freq (Hz)
dB
Experimental Results
RTHS with Controller 1RTHS with Controller 2RTHS with Controller 3Reference System (Pure Numerical)
Input used in this experiment is the 1994 Northridge ground acceleration.
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Experimental Results
1 2 3 4 5 6 7 8 9 10-140
-120
-100
-80
-60
-40
-20
Freq (Hz)
dB
Simulation Results t = 1/4096 sec.
= 1 t = 5 t = 10t = 20t = 25t
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Concluding Remarks
HS is a cost-effective experimental technique to evaluate the dynamic performance of large civil structures.
RTHS provides the most advanced experimental technique to evaluate the performance of rate-dependent civil structures in laboratories.
In RTHS, time lags and time delays can be classified into three major categories, 1) communication delays, 2) computational delays, and 3) transfer system dynamics.
In this study, we 1. modeled RTHS using a set of neutral delay differential equations2. showed the fidelity of the proposed model using a SDOF and MDOF
RTHS examples3. Presented the effects of transfer system delay on RTHS results
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Acknowledgements
This material is based in part upon work supported by the National Science Foundation under Grant Numbers NSF-1136075 and CMMI-1011534.
Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: [email protected]
Thank you!