Purdue University, West Lafayette, IN 47907 Phone: (765) 494-7434 Fax: (765) 494-0539 E-mail:...

Purdue University, West Lafayette, IN 47907 •Phone: (765) 494-7434 •Fax: (765) 494-0539 •E-mail: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

• 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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

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: iisl@ecn.purdue.edu

Thank you!