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

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

2

Presentation Outline

Introduction Background and Motivation Experimental Setup Modeling of the System RTHS Comparison HS Efforts Conclusion

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

3

Introduction

Global performance of new systems

Nonlinear response

Options

Shake-table: Scaled Structural Testing

Hybrid Simulation (HS)

Need for Testing

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

4

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.”

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

5

Background

“Development of a Versatile Hybrid Testing System for Seismic Experimentation” by Shao et al. (2012)

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

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

Shake TableRTHS ?6

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

7

Challenges

Accurate modeling of the target structure System Identification

Semi-active controllable nonlinear damper Hard to model rate dependent dynamics Damper-structure interaction

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

8

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

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

9

Phase 1: Numerical Simulation

Test Structure

Base Dimension: 1.84 m by 2.04 m

Story height: 1.2 m

Material: Structural Steel

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

10

MCK Update Method

0 5 10 15-100

-50

0

Floor 1

Ma

gn

itud

e -

dB

0 5 10 15-100

-50

0

Floor 2

Ma

gn

itud

e -

dB

0 5 10 15-100

-50

0

Floor 3

Ma

gn

itud

e -

dB

Frequency - Hz

Experimental Data MCK Update Method

0 20 40 60 80 100 120-20

-10

0

10

20

1s

t Flo

or

- m

m

0 20 40 60 80 100 120-40

-20

0

20

2n

d F

loo

r -

mm

0 20 40 60 80 100 120-40

-20

0

20

40

Time - s

3rd

Flo

or

- m

m

ExperimentSimulation

More details were given in ‘Modeling of Distributed Real-time Hybrid Simulation’ accessible from http://nees.org/resources/6641/Model is awarded by NEES as the best simulation model.

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

11

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

Lord MR damper RD-1005-03

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-300

-200

-100

0

100

200

300

Damper disp (inch)

Dam

per

forc

e (

lbf)

Numerical model for volt = 1.7 V, freq = 2.9Hz

Test data

Simulink model

ODE model

-4 -3 -2 -1 0 1 2 3 4 5-300

-200

-100

0

100

200

300

Damper vel (inch/s)

Dam

per

forc

e (

lbf)

Numerical model for volt = 1.7 V, freq = 2.9Hz

Test data

Simulink model

ODE model

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

12

Phase 2: Shake Table Tests

Location: Harbin Institute of TechnologySize: 3m×4m (shaking direction)Peak acceleration: ±1.33gPeak velocity: ±600 mm/sStroke: ±125 mmMaximum payload: 12tForce capacity: 200kNMaximum overturning moment: 30 t-mFrequency bandwidth: 0 - 30 Hz

Conducted uncontrolled, passive off, passive on and semi-active control cases

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

13

Comparison – Shake Table vs Simulation

64 66 68 70 72 74 76 78 80 82-10

-5

0

5

10

Time-s

Dis

p 3

rd fl

oo

r-m

m

Pure SimulationExperimental Data

69 70 71 72 73 74-10

-5

0

5

10

Time-s

Dis

p 3

rd fl

oo

r-m

m

64 66 68 70 72 74 76 78 80 82-5000

0

5000

Time-s

Acc

3rd

flo

or-

mm

/s2

Pure SimulationExperimental Data

69 70 71 72 73 74-5000

0

5000

Time-s

Acc

3rd

flo

or-

mm

/s2

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

Phase 3: RTHS

MTS loading Frame @ HIT

Clamp for vertical loading

MTS Loading Frame, 2500kN,

Internal LVDT

Load cell, 15kN

Lord MR damper,

2kN

MTS Flex GT ControllerInner Loop Control

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

RTHS Setup

Force

Numerical substruc. Physical substruc.Complete Structure

Damper

Desired Displacement

4

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

RTHS Result: Kobe

0 10 20 30 40 50 60 70 80-15

-10

-5

0

5

10

time (sec)

disp

lace

men

t (m

m)

6 8 10 12 14 16 18-15

-10

-5

0

5

10

time (sec)

disp

lace

men

t (m

m)

Reference

Measured

Due to the limitation of Pump Velocity Limitation, Piston maximum moving speed

50mm/s0 10 20 30 40 50 60 70 80-5

0

5

time (sec)

disp

lace

men

t (m

m)

6 8 10 12 14 16 18-5

0

5

time (sec)

disp

lace

men

t (m

m)

Reference

Measured

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

RTHS Result: Morgan

0 10 20 30 40 50 60 70 80-10

-5

0

5

10

time (sec)

disp

lace

men

t (m

m)

6 8 10 12 14 16 18-10

-5

0

5

10

time (sec)

disp

lace

men

t (m

m)

Reference

Measured

10 20 30 40 50 60 70 80

-5

0

5

time (sec)

disp

lace

men

t (m

m)

8 10 12 14 16 18

-5

0

5

time (sec)

disp

lace

men

t (m

m)

Reference

Measured

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

Phase 3: RTHS (Replace pics with IISL Actuator)

Shore Western loading Frame @ IISL

Servo Valve

High performance programmable DSP system plus high precision servo-hydraulic motion control system.

LordMR Damper

2 kip Actuator Loading Frame

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

19

Compensation Performance

66 68 70 72 74 76 78-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time - s

1st

Flo

or

Dis

pla

cem

en

t - c

m

Desired DisplacementMeasured Displacement

0 5 10 15 20 25 30 35 40-2

-1

0

1

2

Frequency (Hz)

Ga

in (

ab

s)

0 5 10 15 20 25 30 35 40

-50

0

50

Frequency (Hz)

Ph

ase

(d

eg

)

NRMS: 3.62%

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

20

Comparison – ST vs RTHS

64 66 68 70 72 74 76 78 80 82-10

-5

0

5

10

Time-s

Dis

p 3

rd fl

oo

r-m

m

Experimental DataRTHS

69 70 71 72 73 74-10

-5

0

5

10

Time-s

Dis

p 3

rd fl

oo

r-m

m

64 66 68 70 72 74 76 78 80 82-5000

0

5000

Time-s

Acc

3rd

flo

or-

mm

/s2

Experimental DataRTHS

69 70 71 72 73 74-5000

0

5000

Time-s

Acc

3rd

flo

or-

mm

/s2

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

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

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

2fk2c2m

1m

1c

1fk

Numerical BRB

Physical BRB

1

(1 )

-n n

r kd kz

z d d z z d z

, , , ,k n

,r d

Constrained Kalman filter

－ 22－

Model updating with UKF

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

-3 -2 -1 0 1 2

-200

-100

0

100

200

Res

tori

ng fo

rce

(kN

)

Displacement (mm)

Exact UKF CUKF Initial

Physical BRB

－ 23－

-2 -1 0 1 2 3

-200

-100

0

100

200

Res

tori

ng fo

rce

(kN

)Displacement (mm)

Exact UKF CUKF

Initial

Numerical BRB

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

Real-time hybrid test validations

Numerical BRBPhysical BRB

=30 =30

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

-4 -3 -2 -1 0 1 2 3 4-300

-200

-100

0

100

200

300

Res

tori

ng f

orce

(kN

)

Displacement (mm)

Physical BRB Numerical BRB

-4 -3 -2 -1 0 1 2 3 4-300

-200

-100

0

100

200

300

Res

tori

ng fo

rce

(kN

)

Displacement (mm)

Physical BRB Numerical BRB

-4 -3 -2 -1 0 1 2 3 4-300

-200

-100

0

100

200

300

Res

tori

ng fo

rce

(kN

)

Displacement (mm)

Physical BRB Numerical BRB

CUKF Initial

－ 25－

UKF

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

•Section Restoring Force Model (RFM)

Finite element based sectional constitutive model

yf

yf

M N

h hw

fA b t

ww

wA

ht

(12

)h

h

h 22

2

( )2 1 1( , ) ,

4 1 2 1

1 1( , ) ,

2(2 1) 2 1

aMaNa

y P y

aN aMa

y p y

M FN F N

N M N

N F M F N

N M N

s F

s F

（ ）

（4 ）

When , Section- elastic When , Section- plastic

se s k e( , ) 1a s F

( , ) 1a s F ( )pse s k e e1

( )p TseH

e k e

s swhere

• Section Yield Function

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

Numerical example

0 5 10 15 20 25 30 351700

1750

1800

1850

1900

1950

2000

2050

Yie

ld A

xial

For

ce [

kN]

Time [sec]

True ValueIndtified Value

0 5 10 15 20 25 30 35185

190

195

200

205

210

215

220

Pla

stic

Ben

ding

Mom

ent [

kN.m

]

Time [sec]

True ValueIndentified Value

0 5 10 15 20 25 300.024

0.025

0.026

0.027

0.028

0.029

0.03

0.031

Kin

emat

ic h

arde

ning

coe

ffic

ient

[1]

Time [sec]

True ValueIndentified Value

0 1 2 3 4 5 6-40

-30

-20

-10

0

10

20

30

40

Time(s)

Hor

izon

tal D

isp(

mm

)

TR-ResponseWO-UpdateWI-Update

-0.03 -0.02 -0.01 0 0.01 0.02 0.03-200

-150

-100

-50

0

50

100

150

200

Section Curvature(1/m)

Ben

ding

Mom

ent(

kN.m

)

TR-RespWO-UpdateWI-Update

-300 -200 -100 0 100 200 300-3000

-2000

-1000

0

1000

2000

3000

Axi

al F

orce

[kN

]Bending Moment[kN.m]

Back internal forceInternal force pathCorrelation curve

After Updating and Kinematic

After updating

Before updating

• Identification results

• Model updating results

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

• Test setup and three cases of HS

Experiment plan

Traditional HS (Linear/Nonlinear)

FE Model updating by HS

Distributed Hybrid Simulation

• Test scheme

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

Delay Compensation:

Compensated Delay > System Delay

①Calculate di+1

②Predict with c

③Load with prediction

④Find force measure-ment

Delay compensation based on over-prediction

Delay over-prediction

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

Implicit algorithms for RTHS

Fixed Number of Iterations with Interpolation (Shing et al)

Equivalent Force Control Method (Wu et al)

Limitations:

1. Iteration2. Intensive computation3. Time delay

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

－ 31－

New implicit algorithm based on over-prediction

1、Modified Newton’s Method applied results in good iteration performance.

2、 System delay is compensated for based on over-prediction method.

Process 2

Process 1 Over-prediction Interpolation

Iterative calculation

Actuator

Optim

al force

( , , )i i i iu a v d

(1)pd

d

cd(2)

Measured Disp

Measured Force

r+

(4)

1 1 1 1( , , )i i i iu a v d

, 1EQ iF

NK1( )k

N iR d

1kid

PDK 1k

PD iK d , 1kE iR

++ +

(3)

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

－ 32－

5

m4

m3

m2

m1

k5/2

k4/2

k3/2

k2/2

kek1/2

k5/2

k4/2

k3/2

k2/2

2 4 6 8 100

0.5

1

1.5

x 10-5

迭代步

(s)

耗时

Shing方法

2 4 6 8 100

0.5

1

1.5

2

2.5

3x 10

-5

计算步

(s)

耗时

EFCM

2 4 6 8 100

0.5

1

1.5x 10

-5

迭代步

(s)

耗时

新方法

Single time step

0 500 10000

0.5

1

x 10-3

积分步

(s)

耗时

X: 426Y: 0.001369

Shing方法

0 500 10000

0.5

1

1.5

2

2.5x 10

-3

X: 465Y: 0.002562

积分步(s

)耗

时

EFCM

0 500 10000

0.5

1

x 10-4

X: 105Y: 0.0001493

积分步

(s)

耗时

新方法10 seconds

0 5 10 15 20 25 30-0.015

-0.01

-0.005

0

0.005

0.01

0.015

(s)时间

(m

)位

移

Shing EFCM 新方法 参考解

27.4 27.5 27.66

7

8

9

10

11

x 10-3

(s)时间

(m

)位

移

ShingEFCM新方法参考解

Delay comptn error

Test validation

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

33

Trans-pacific test between UCB and HIT

U g

1.0m

1X

Y

M 0.04

K 1.8

C = K

=0.02

K

M ( ) g RMX C XX MBX 2

LEGEND

Analytical model of structural energy dissipation and inertia

Conducted in HIT, CHINA

Physical model of structural resistance

Performed in UCB, USA

PLATEFORM: OpenFresco Express

C

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

UCB, USA

HIT,CHINA

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

35

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

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

Bin Wu, ProfessorHarbin Institute of Technology

Shirley Dyke, ProfessorPurdue University

Jian Zhang , Associate ProfessorUCLA

Yurong Guo, ProfessorHunan University

Tao Wang , Assoc ProfessorInstitute of Eng. Mechanics

China-US collaborative project on hybrid simulation

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

37

THANK YOU!