1

Real-Time Hybrid Simulations

P. Benson ShingUniversity of California, San Diego

2

Better Known as the Pseudodynamic Test Method

Early Work:Hakuno et al. (1969)Takanashi et al. (1974)

Institute of Industrial Science, University of Tokyo

Hybrid: real-time testing; analytical substructuring; distributed testing and simulation; ……….

Pseudodynamic: slow rate of loading; dynamic properties simulated numerically

3

Pseudodynamic Test Method

Simple concept but requires care to execute. Precision of displacement control. Accumulation of experimental errors in numerical computation.

Advance to nexttime step: i = i + 1

Update and

Numerical solutionof eqs. of motion

-i i giirMa Cv Ma

ir

gia

id

ir

Test FrameDisplacement

Experimental Error Accumulation

4

Main source of systematic experimental errors:time-delay in servo-hydraulic loading apparatus

Shing and Mahin (1982)

5

Dermitzakis and Mahin (1985)

Substructure Test Methods

Advance to nexttime step: i = i + 1

Update and

Numerical solutionof eqs. of motion

-i i i gi Ma Cv r Mba

gia ir

Computer Model

Test Frame

Range of Configurations

6

Slow Fast Real Time

Discontinuous/Continuous

Local Laboratories

Geographically Distributed

7

Needs for Real-Time TestsComputer Model Test

Base IsolationDevices

TestActive/PassiveDampers

Computer Model

General Framework for Hybrid Simulation

8

S Ma Cv r f

( ) ( )A A E EAS

ES M C v r rM a C f

Structural Partitioning

,

,

E ES S B

AA

B

EE

EB

S

0 f

f f f

f

r r

r

A AAA AB

A A A ABA BB BE

A AEB EE

M M 0

M M M M

0 M M

0 0

0E E E EBB BE

A

IEEB

B

E

EEE

M M M r

M

0

0 aM

a

a a

Total Formulation

9

EA A AS M a C v r r f

E E E ES r M a C v r

Whole Frame Analytical Model Physical Substructure

4AM

3AM

2AM

1AM 1

EM

2EM 2d 2

Er

1d 1r

2d

3d

4d

,2A

Sr

,3Sr

,4Sr

+ =

Coupled Subdomain Approach

10

12 2 3 3 2 ,2 2 2

3 3 3 3 4 4 3 ,3 3

4 4 4 4 4 ,4 4

0 0 0

0 0 0

0 0 0 0

A A A A A IS

A A A A AS

A A AS

M a C C v r f f

M a C C C C v r f

M a C C v r f

1 1 11 1 2 22

2 2 2 22 2

1

22

00

0 E

A A A A

E IA A A

a v fM C C C

a v f fM C C

r

r

Physical Substructure

1EM

2EM 2d 2

Er

1d 1r

22AM

1AM

2If

Magonette et al. (1998)

Analytical Model

4AM

3AM

12AM 2d

3d

4d

,2A

Sr

,3Sr

,4Sr

2If

Implicit Scheme

Explicit Scheme

Dynamic Substructuring I

11

2 3 2 ,2 2

3 3 3 4 4 3 ,3 3

4

2

2

4 4 4 24 ,4 4

0 0 0 0 0

ˆ ˆ0 0 0 0

ˆ ˆ0 0 0 0

A A tt

t

A IS

A A A A AS

A A AS

tA

M C v r f

M a C C C v r M

M a C C v r M

a

a

a

Analytical Model

4AM

3AM

2AM 2d

3d

4d

,2A

Sr

,3Sr

,4Sr

2If 2

ta

Physical Substructure

1EM

2EM

2If 2

ta

ga

Dynamic Substructuring I

12

Actuator

Actuator

Specimen

Shake Table

Computational Model

Sivaselvan and Reinhorn (2004)

Dynamic Substructuring II

13

,11 1 11 1 2 2

,22 2 222 2 2

00

0

AA A A AS gA AA A A

S gI

ra v M aM C C C

ra v M aC C fM

2AM

2d

1d

,2A

Sr

,1Sr

2If

Physical Substructure

3EM

2EM

1AM

ga

4EM

2td 2

If

Dynamic Substructuring II

14

Actuator

Shake Table

Computational Model

SD

Smart-UPS

6 2 0

www.apcc.com

Actual Equipment Tested

ga

Horiuchi et al. (2000)Bayer et al. (2005)Bursi et al. (2008)

15

Nakashima et al. (1992, 1999) Horiuchi et al. (1996) Tsai et al. Darby et al. (1999) Magonette et al. (1998) Bayer et al. (2000) Shing et al. (2002) Wu et al. (2005, 2006)

Real-Time Hybrid Test Methods

Explicit IntegrationSchemes

Implicit IntegrationSchemes

Implicit-Explicit CoupledField Analysis

16

Newmark Implicit Method for Time Integration

1 1 , 1 1 1A A A E

i i S i i i M a C v r r f

21 1 1i i it d d a

1 1 1i i it v v a

17

* ( ) ( )1 1

k ki i K d R

1

( 1) ( ) ( )1 1i

k k ki i

d d d

Modified Newton Method

*0 02

A E A E

A Et

t

M M C CK K K

( ) ( ) ( ) ( )1 1 1 1 , 1 1 1

k k A A k E ki i i i S i i i R M d d C v r r f

18

Modified Newton Method

Number of iterations varies from time step to time step. Increment size decreases as solution converges.

Convergence is guaranteed as long as

is positive definite (Shing and Vannan 1991).

Problems for Real-Time Tests:

2

A E A E

A ES S

t

t

M M C CK K K

19

Fixed Number of Iterations with InterpolationShing et al. (2002)

Response Correction and Update

20

11 1 , 1

, 1

1 1 ( )

( ) 1

A A A Ai i i S i

AS i i i

Ei

Ei

M a C v C v

r

r

f

r

r f

( ) ( )1 1

k d ki i d d

( ) * ( ) ( )1 1 1 1

E m k E d k m ki i i i r r K d d

-Method

Compatibility

Equilibrium

Nonlinear Structure

21

0 5 10 15 20 25 30-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Time (sec)

Dis

pla

cem

en

t (in

ch)

CDM t = 0.001

RTI t = 0.01, N =10

RTI t = 0.01, N =50

-1 -0.5 0 0.5 1 1.5 2 2.5 3-30

-20

-10

0

10

20

30

Disp. (inch)

Fo

rce

(ki

ps)

5.42 5.43 5.44-900

-800

-700

-600

-500

-400

-300

-200

-100

0

Time (sec)

Re

sid

ua

l Fo

rce

Err

or

(kip

s)

CDM t = 0.001

RTI t = 0.01, N =10

RTI t = 0.01, N =50

RTI t = 0.01, N =10

RTI t = 0.01, N =50

22

System Configuration

NEES@Colorado

23

Real-Time Substructure Test Platform

dEr

PID Controller

Real-Time Processor

SCRAMNet Card 2

Analytical Substructure Model

ExperimentalElement/Substructure

Target PC –Real-Time Kernel

SCRAMNet Card 1

Special Element

Data-AcquisitionProgram

Actuators

Specimen

OpenSEES

24

Issues in a Real-Time Test

Actuator time-lag caused by dynamics of servo-hydraulic system and test structure.

Communication delays among processors.

Accounting for real inertia and damping forces.

Convergence errors in numerical scheme.

Interaction of numerical computation with system dynamics.

25

Phase-Lag Compensation Methods

( )( ) ( ) ( ) ( ) ( )c

PID ff p i d ff p

de t di t i t k e t k e t dt k k d t

dt dt

( ) ( ) ( 1) ( 1)1 1

c k k c n m ni i DFC i id d k d d

PID with Feedforward

Discrete Feedfordward Correction

Phase-Lead Compensator

d

d d

1( )

1

T sPLC s

T s

System Model for Test Simulation

26

force

Physical test system

Responses update

Iteration with interpolation

Displacement and restoring force,

2se

Delay(2 ms)

1ˆ

id

f

,

,i i

i i

d v

a r

1ˆ

id

m m1 1,i id r

ECd1id

c1id

cp, 1id

m m1 1,i id r

1ˆ

id

1 1

1 1

,

,i i

i i

d v

a r

Error compensation

Explicit part

Converged responses,

m m1 1,i id r

1 1 1 1, , ,i i i id v a r ( Outer loop)

( Inner loop )

Physical Test System

27

Controller

e PID

Servo-valve and hydraulic actuator

md

-+

displacement response

cpd

ppk A

ffk

Δ pressure feedback

Feed-forward loop

+

+i

d

dt

Test specimen

mr

-

se

Delay

mr

Physical testing system

28

System Transfer Function (Linear System)

Consider dynamics of servo-hydraulic actuators and test structure.

Communication delays.

Error compensation schemes.

Interaction of numerical computation with physical system.

Jung and Shing (2006)

29

Implicit Integration Scheme

1d F EP ICid d d d

( )( ) ( )F EF sd s f s

( )( ) ( )EP mEP sd s d s

( )( ) ( )IC mIC sd s d s

External Force

Explicit Prediction

Implicit Correction

30

2

( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

m

s

d s EF s EC s P sRTPD s

f s e IC s EC s P s EP s EC s P s

System Block Diagram and Transfer Function

31

Physical Test System

32

Validation with Simulink Model

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 21

2

3

4

5

6

7

8

9

Frequency (Hz)

Am

p. F

act

or

D

kp = 1

kp = 5

Transfer Function, K = Kt

Simulink Model, K = Kt

Transfer Function, K = Kt * 1.1

Simulink Model, K = Kt * 1.1

( 1) ( 1) ( 1)1 1 1 1

m n d n m ni i ini i i

r r K d d

Error Correction:

33

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 21

2

3

4

5

6

7

8

9

Frequency (Hz)

Am

p. F

act

or

D

70 75 80 85 90 95 100 105 110 115 1200

0.01

0.02

0.03

0.04

0.05

Frequency (Hz)

Am

p. F

act

or

D

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-50

0

50

100

150

200

250

Frequency (Hz)

Ph

ase

An

gle

(d

eg

ree

s)

Analytical Sol.

kp = 1

kp = 3

kp = 5

kp = 7

kp = 7, kp

= -0.0002

Analytical Sol.

kp = 1

kp = 3

kp = 5

kp = 7

kp = 7, kp

= -0.0002

Analytical Sol.

kp = 1

kp = 3

kp = 5

kp = 7

kp = 7, kp

= -0.0002

System Performance (PID Only)

34

PID with Feedforward

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 21

2

3

4

5

6

7

8

9

Frequency (Hz)

Am

p. F

act

or

D

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

150

200

250

Frequency (Hz)

Ph

ase

An

gle

(d

eg

ree

s)

Analytical Sol.

kff = 0

kff = 0.04

kff = 0, k

p = 5

Analytical Sol.

kff = 0

kff = 0.04

kff = 0, k

p = 5

35

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 21

2

3

4

5

6

7

8

9

10

Frequency (Hz)

Am

p. F

acto

r D

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

150

200

250

Frequency (Hz)

Pha

se A

ngle

(deg

rees

)Analytical Sol.k

DFC = 0

kDFC

= 0.5

kDFC

= 1

kDFC

= 0, kP = 5

Analytical Sol.k

DFC = 0

kDFC

= 0.5

kDFC

= 1

kDFC

= 0, kP = 5

Discrete Feedforward Correction (DFC)

36

Inertia Effect in Real-Time Tests

Advance to nexttime step: i = i + 1

Update and

Numerical solutionof eqs. of motion

-A Ai i giirM a C v Ma

,S ir

gia

id

ir

Test Frame

tM a+

37

0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6

7

8

9

Frequency (Hz)

Am

p.

Fa

cto

r D

0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

120

140

160

180

200

Frequency (Hz)

Ph

as

e A

ng

le (

de

gre

es

)

Analytical Sol.

Mt = M * 0.1

Mt = M * 0.4

Mt = M * 0.7

Mt = M * 1.0

Analytical Sol.

Mt = M * 0.1

Mt = M * 0.4

Mt = M * 0.7

Mt = M * 1.0

Influence of Inertia Force Feedback

38

Actual Test with Inertia Force Removal

0 5 10 15 20 25 30-1

-0.5

0

0.5

1

1.5

Time (sec)

Dis

pla

ce

me

nt (in

ch

)

CDM t = 0.001 Without Inertia Force Correction With Inertia Force Correction

1.5 2 2.5 3 3.5 4-1

-0.5

0

0.5

1

1.5

Time (sec)

Dis

plac

emen

t (in

ch)

CDM t = 0.001 Without Inertia Force Correction With Inertia Force Correction

Mt/M = 4.7%

Influence of Support Flexibility

39

0.5 1 1.5 2 2.50

1

2

3

4

5

6

7

8

9

Frequency (Hz)

Amp.

Fac

tor

D

Mr=M

t* 8, K

r=K

t* 8, f

r=f

t * 1

Mr=M

t* 8, K

r=K

t* 32, f

r=f

t * 2

Mr=M

t* 8, K

r=K

t* 128, f

r=f

t * 4

Mr=M

t* 32, K

r=K

t* 128, f

r=f

t * 2

Rigid Support

40

Nonlinear Structures (2-DOF, Method)

2(1 )

t

s

MK KConvergence: has to be positive definite

0 5 10 15 20 25 30-0.6

-0.3

0

0.3

0.6

Time (sec)

Dis

pla

cem

en

t (in

ch)

CDM t = 0.001PIDPID + DFCPID + PLCPID + FFRTI w/o Actuator

0 5 10 15 20 25 30-1.2

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Time (sec)

Dis

pla

cem

en

t (in

ch)

CDM t = 0.001PIDPID + DFCPID + PLCPID + FFRTI w/o Actuator

Strain Hardening

Strain Softening

Simulation Setup

41

Controller PC

Digital controller andData-acquisition System

Servo-hydraulic actuators and test structure

Rae-Young jung

Rae-Young jung

Rae

-Yo

ung

jung

Rae-Y

oung

jun

g

cd

,m md ri

SCRAMNet

Valve command, Sensors feedback

,m md r

Host-target pair 1

Real-timeTarget PC

Host PC

Host-target pair 2

Real-timeTarget PC

Host PC

SCRAMNet

Switch

Two-Story Frame

42

Two-DOF Real-Time Tests

43

Two-DOF Real-Time Tests

44

0 5 10 15 20 25 30-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (sec)

Dis

pla

cem

en

t (in

ch)

CDM t = 0.001 PID PID + DFC PID + PLC PID + FF

3.5 4 4.5 5 5.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (sec)

Dis

pla

ce

me

nt (in

ch

)

CDM t = 0.001 PID PID + DFC PID + PLC PID + FF

45

Real-Time Substructure Test with a Single Column

Actuator

Analytical Model in OPENSEES

Test Column

46

Real-Time Substructure Test

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14

Time (sec)

Dis

pla

ce

me

nt

(in

)

FHT Test Pure Simulation

47

Test of a Zipper Frame

Georgia TechU. At BuffaloUC-BerkeleyUC-San Diego/U. of ColoradoFlorida A&M

48

Test Setup

49

Test Results

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6 7 8 9

Time [sec]

Dis

plac

emen

t [in

]Analysis

Hybrid Test

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

0 1 2 3 4 5 6 7 8 9

Time [sec]

Dis

plac

emen

t [in

]

Analysis

Hybrid TestBrace

Rupture

80% LA 22

200% LA 22

50

Brace Response

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-40

-30

-20

-10

0

10

20

30

40

50

60

Axial Displacement [in]

Axi

al F

orc

e [k

ips]

Hybrid Test

Numerical Model

Brace Rupture

(a) Brace 1

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5-50

-40

-30

-20

-10

0

10

20

30

40

50

60

Axial Displacement [in]

(b) Brace 2

Brace Rupture

51

Brace Damage

52

Future Challenge - Improve Computational Speed

* ( ) ( ) 1 1

1 1

ˆns ns

s k s kee e n e n

s sA A

K d R

*2ˆeeK1( )

1k

e nR 2( ) 1k

e nR*1ˆeeK *ˆ ns

eeK ( ) 1

ns ke nR

Parallel Computing

53

Future Challenge - Develop Mixed Control Strategy

Displ. Control

Computer ModelTest Specimen

Force Control

ShearWall

54

Dr. Rae-Young Jung, Former Grad. Student at CU

Dr. Zhong Wei, Former Grad. Student at CU

Dr. Eric Stauffer, Formerly at NEES@Colorado

Andreas Stavridis, Grad. Student at UCSD

Rob Wallen, NEES@Coloarda

Thomas Bowen, NEES@Colorado

Contributors

Development supported by NSF under NEES Program.

Acknowledgments

55

Thank You