Cheng Chen, Ph.D. Assistant Professor San Francisco State University Interpreting Reliability of...

Cheng Chen, Ph.D.

Assistant Professor San Francisco State University

Interpreting Reliability of Real-Time Hybrid Simulation Results from Actuator Tracking Errors

International Workshop on Hybrid SimulationHarbin Institute of Technology, 2012

2

Presentation Overview

Background

Need for Reliability Analysis

Proposed Probabilistic Approach for Reliability Analysis

Application to Experimental Results

Summary and Conclusion

Future Work

3

EQ Experimental Techniques

Courtesy of NEES@UCSD Shake Table at E-Defense

W12x40

BRB100

BRB100

10’

18’

6’

9’

7’-6

”7

’-6”

7’-6

”

W12x40

8’-11”BRB80BRB80

W12x40

BRB60

BRB30

8’-11”

W8

x67(

C1

)

W8

x67(

C1

)

W12x40

BRB60

BRB30

W12x40

9’-1”

Courtesy of Fahnstock et al. Courtesy of Fahnstock et al. Courtesy of NEES@UCSD

4

Real-Time Hybrid Simulation

d a m p e rs

d a m p e rs

d a m p e rs

d a m p e rs

4 @ 9.15m = 36.6m

4.5

7m

3.9

6m

Analytical substructure

Floor 1 damper

N

RTMDActuator

Dampers

North A-Frame

SouthA-Frame

RollerBearings

Actuator Support

Loading Stub

NN

RTMDActuator

Dampers

North A-Frame

SouthA-Frame

RollerBearings

Actuator Support

Loading Stub

Experimental substructure 2

Floor 2 damper

N

RTMDActuator

Dampers

North A-Frame

SouthA-Frame

RollerBearings

Actuator Support

Loading Stub

NN

RTMDActuator

Dampers

North A-Frame

SouthA-Frame

RollerBearings

Actuator Support

Loading Stub

Experimental substructure 1

5


Background





Future Work

6

Role of Hydraulic Actuators

• Apply desired responses to experimental specimens in a real-time manner;

• Measure the restoring forces of the experimental substructures and feed back to the integration algorithm;

Critical to maintain the boundary conditions between substructures!

Courtesy of Lehigh RTMD

Block Diagram for Real-Time Hybrid Simulation

ExcitationForce

IntegrationAlgorithm

ServoController

HydraulicActuator

Analytical Substructure(MRF: FE Program)

Experimental Substructure(Damper 1: Lab)

Experimental Substructure(Damper 2: Lab)

RampGenerator

7

Actuator Delay and Tracking Error

Maximum tracking error 16.90 mm (35% of command maximum)!

Command Maximum: 50 mm

Frequency Content: 0 ~ 5 Hz

8

Actuator Delay Compensation

•Linear Acceleration Compensation (Horiuchi et al. 2001)

•Feedforward Compensation (Jung et al. 2007)

•Dual Compensation (Chen and Ricles 2009; Lin et al.

2012)

•Minimal Control Synthesis (MCS) (Stoten et al. 2005)

•Adaptive Inverse Control (AIC) (Chen and Ricles 2010)

•Improved Adaptive Inverse Control (IAIC) (Chen and Ricles

2012)

•Other researches other include Wallace et al. [2007];

Ahmadizadeh et al. (2008)

Delay compensation methods can reduce, but can NOT eliminate actuator tracking

error for real-time structural tests!

Test Compensation aesMTE (mm)

RMS (%)

Max TI (mm2)

Max EE (kN-m)

1-1 Inverse compensation 1 16.9 24.1 1.38E4 21.5

1-2 Existing AIC 1 4.9 3.4 1.26E2 13.1

1-3 New AIC 1 2.4 2.1 1.08E2 2.4

9

Questions to be answered?How will the tracking errors affect the accuracy of simulated structure response?

Will this difference between simulated and true responses be acceptable for researches?

How will researchers assess the accuracy of simulated response in replicating the true structural response when the latter is not available?

10

Reliable Experimental Results?

How reliably did the real-time hybrid simulation results replicate the true structural response under earthquakes?

How do we assess the reliability of real-time hybrid simulation results without knowing the true responses?

A successful real-time hybrid simulation requires that the effect of actuator delay not only be compensated throughout the simulation but also be assessed after the

simulation!

11

Tracking Indicator (TI)

Tracking Indicator (Mercan and Ricles 2010)

Test Compen. MTE (mm)

RMS (%)

Max TI (mm2)

1-1 IC 16.9 24.1 1.38E4

1-2 AIC 4.9 3.4 1.26E2

1-3 IAIC 2.4 2.1 1.08E2

Positive TI

12

Needs for Reliability Assessment

TI provides a useful tool to compare performances of different actuator control techniques.

Link between TI and simulation accuracy is missing making it difficult to apply for reliability assessment.

TI is response history dependent and vary for simulations with various ground motion inputs and different intensities.

13


Background





Future Work

14

RTHS of SDOF Structures

r

c

m

F

x

(a) SDOF Structure

r

r

x

c

m

F

(b) Experimental Substructure (c) Numerical Substructure

r

x

ra

e

e

rae

e

tFtrtrtxctxm ea )()()()(

• Exact solution can be easily computed and used for validating the proposed approach

• Similar equations have been analyzed by researchers for the effect of actuator delay on the stability of real-time hybrid simulations

txktr aa )( txktr e

e )( )/( eae kkk

15

Simulated Responses w/ Delay

0 5 10 15 20 25 30 35 40-0.2

-0.1

0

0.1

0.2

0.3(a)

Time (sec)

Dis

pla

ce

me

nt (m

)

= 0 sec = 0.0025 sec = 0.005 sec = 0.0075 sec

0 5 10 15 20 25 30 35 40-0.2

-0.1

0

0.1

0.2(b)

Time (sec)

Err

or

(m)

0 5 10 15 20 25 30 35 40-0.2

-0.1

0

0.1

0.2

0.3(a)

Time (sec)

Dis

pla

ce

me

nt (m

)

= 0 sec = 0.0025 sec = 0.005 sec = 0.0075 sec

0 5 10 15 20 25 30 35 40-0.2

-0.1

0

0.1

0.2(b)

Time (sec)

Err

or

(m)

SDOF Structure: m=503.4 tons; f=0.77 Hz; =2%β=1.0; 1940 El Centro earthquake recorded at Canoga Park station;

16

Factors to be considered

• Structural Nonlinearity

• Different Ground Motion Inputs

• Ground Motion Intensity

• Structural Damping

• Stiffness Ratio between substructures

Accuracy of simulated response is evaluated through comparison with true response using the ratio

between maximum difference and maximum response (MAX); and the RMS of response difference.

17

Structural Nonlinearity (β=1.0)

0 0.002 0.004 0.006 0.008 0.010

50

100

150

200

250(a)

Time Delay (sec)

Ma

x E

rro

r (%

)

xy = infinity

xy = 100 mm

xy = 50 mm

xy = 10 mm

0 0.002 0.004 0.006 0.008 0.010

50

100

150

200

250(b)

Time Delay (sec)

RM

S E

rro

r (%

)

xy = infinity

xy = 100 mm

xy = 50 mm

xy = 10 mm

Linear elastic case

0 0.002 0.004 0.006 0.008 0.010

50

100

150

200

250(a)

Time Delay (sec)

Ma

x E

rro

r (%

)

xy = infinity

xy = 100 mm

xy = 50 mm

xy = 10 mm

0 0.002 0.004 0.006 0.008 0.010

50

100

150

200

250(b)

Time Delay (sec)

RM

S E

rro

r (%

)

xy = infinity

xy = 100 mm

xy = 50 mm

xy = 10 mm

18

Ground Motion Intensity (β=1.0)

0 2 4 6 8

x 10-3

0

20

40

60

80

100(a)

Ma

x E

rro

r (%

)

PGA = 0.1 gPGA = 0.2 gPGA = 0.5 g

0 2 4 6 8

x 10-3

0

20

40

60

80

100

120

140(b)

RM

S E

rro

r (%

)

PGA = 0.1 gPGA = 0.2 gPGA = 0.5 g

0 2 4 6 8

x 10-3

0

0.5

1

1.5(c)

Time Delay (sec)

Ma

x E

rro

r (%

)

PGA = 0.1 gPGA = 0.2 gPGA = 0.5 g

0 2 4 6 8

x 10-3

0

0.5

1

1.5

2(d)

Time Delay (sec)

RM

S E

rro

r (%

)

PGA = 0.1 gPGA = 0.2 gPGA = 0.5 g

(a) and (b) for linear elastic structure; (c) and (d) for nonlinear structure

19

Structural Damping (β=1.0)

0 2 4 6 8

x 10-3

0

20

40

60

80

100(a)

Ma

x E

rro

r (%

)

= 5% = 10% = 20%

0 2 4 6 8

x 10-3

0

20

40

60

80

100

120

140(b)

RM

S E

rro

r (%

)

= 5% = 10% = 20%

0 2 4 6 8

x 10-3

0

0.5

1

1.5

2(c)

Time Delay (sec)

Ma

x E

rro

r (%

)

= 5% = 10% = 20%

0 2 4 6 8

x 10-3

0

0.5

1

1.5

2(d)

Time Delay (sec)

RM

S E

rro

r (%

)

= 5% = 10% = 20%


20

Different Ground Motions (β=1.0)

0 2 4 6 8

x 10-3

0

50

100

150(a)

Time Delay (sec)

Ma

x E

rro

r (%

)

KobeChi ChiMendocino

0 2 4 6 8

x 10-3

0

50

100

150

200(b)

Time Delay (sec)

RM

S E

rro

r (%

)


0 2 4 6 8

x 10-3

0

1

2

3

4(c)

Time Delay (sec)

Ma

x E

rro

r (%

)


0 2 4 6 8

x 10-3

0

1

2

3

4(d)

Time Delay (sec)

RM

S E

rro

r (%

)



21

Stiffness Ratio of Substructures

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100(a)

Ma

x E

rro

r (%

)

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

140(b)

RM

S E

rro

r (%

)

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5(c)

Ma

x E

rro

r (%

)

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5(d)

RM

S E

rro

r (%

)

= 0.0025 sec = 0.0050 sec = 0.0075 sec


β

ββ

β

22

Findings from Numerical Analysis

• An actuator delay that leads to simulated response with acceptable accuracy for linear elastic structures will also result in simulated response with acceptable accuracy for corresponding nonlinear structures;

• Different ground motion inputs and different intensities will lead to different accuracy of simulated responses especially for structures with nonlinear behavior.

23

EQ Response Analysis

Courtesy of Chopra (2001)

ASCE-7-10

24

Ground Motions for Analysis

Earthquake Station Component Magnitude (Mw) Distance (km) PGA (g)

Northridge 24303 LA - Hollywood Stor FF HOL360.AT2 6.7 25.5 0.358Santa Barbara 283 Santa Barbara Courthouse SBA222.AT2 6 14 0.203

El Centro 117 El Centro Array #9 IELC270.AT2 7 8.3 0.215Chi Chi CHY006 CHY006N.AT2 7.6 14.93 0.345Duzce Duzce DZC270.AT2 7.1 8.2 0.535

San Fernando 279 Pacoima Dam PCD254.AT2 6.6 2.8 1.16Kocaeli Yarimca YPT330.AT2 7.4 2.6 0.349Tabas 9101 Tabas TABTR.AT2 7.4 3 0.852: : : : : :

Chi Chi TCU068 TCU068-N.AT2 7.6 1.09 0.462Northridge 24436 Tarzana, Cedar Hill TAR090.AT2 6.7 17.5 1.779El Alamo 117 El Centro Array #9 ELC270.AT2 - 130 0.052Hollister 1028 Hollister City Hall B-HCH271.AT2 - 19.6 0.196Parkfield 1013 Cholame #2 C02065.AT2 6.1 0.1 0.476

Palm Springs 5224 Anza - Red Mountain ARM360.AT2 6 45.6 0.129Oroville 1544 Medical Center C-OMC336.AT2 4.4 11.1 0.043

Imperial Valley 5028 El Centro Array #7 H-E07230.AT2 6.5 0.6 0.463

A total of fifty ground motion from PEER Strong Motion Data Base

25

Delay for Target Accuracy

0 2 4 6 8

x 10-3

0

50

100

150(a)

Time Delay (sec)

Ma

x E

rro

r (%

)


0 2 4 6 8

x 10-3

0

50

100

150

200(b)

Time Delay (sec)R

MS

Err

or

(%)


0 2 4 6 8

x 10-3

0

1

2

3

4(c)

Time Delay (sec)

Ma

x E

rro

r (%

)


0 2 4 6 8

x 10-3

0

1

2

3

4(d)

Time Delay (sec)

RM

S E

rro

r (%

)


0 2 4 6 8

x 10-3

0

50

100

150(a)

Time Delay (sec)

Ma

x E

rro

r (%

)


0 2 4 6 8

x 10-3

0

50

100

150

200(b)

Time Delay (sec)

RM

S E

rro

r (%

)


0 2 4 6 8

x 10-3

0

1

2

3

4(c)

Time Delay (sec)

Ma

x E

rro

r (%

)


0 2 4 6 8

x 10-3

0

1

2

3

4(d)

Time Delay (sec)

RM

S E

rro

r (%

)


5%

5%

26

Proposed Probabilistic Approach

Probabilistic Model of Critical Delay for 5% MAX Error of Simulated Response

Probability distribution of delay leading to 5% MAX error

Lognormal distribution

27

Proposed Probabilistic Approach

r

c

m

F

x

(a) SDOF Structure

r

r

x

c

m

F

(b) Experimental Substructure (c) Numerical Substructure

r

x

ra

e

e

rae

e

SDOF structural properties: Mass of 503.4 metric tons; Natural frequency of 0.77 Hz; Inherent damping ζ of 0.02; β=1.0; 1940 El Centro earthquake

recorded at Canoga Park station with PGA of 0.2 g;

P.E.=50%

P.E.=15%

P.E.=5%

Time History of TI based on Delay for Different Probability of Exceedance

28


• Background

• Need for Reliability Analysis

• Probabilistic Approach for Reliability Analysis

• Application to Experimental Results

• Summary and Conclusion

• Future Work

29

SDOF Prototype Structure

Canoga Park EQ

d(t)

PassiveDamper

Analytical Substructure

d(t)=

Experimental Substructure

d(t)

damperactuator

+

Analytical Substructure Properties:• structural mass: m=503.4 ton;• natural frequency: fn=0.77 Hz; • viscous damping ratio:

ζ=0.02;Analytical Substructure modeled using Bouc-Wen model [Wen 1980]

Chen, C., Ricles, J.M., Marullo, T. and Mercan, O. (2009). “Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm.” Earthquake Engineering and Structural Dynamics, 38(1), 23-44.

30

Experimental Setup

N

RTMDActuator

Dampers

North A-Frame

SouthA-Frame

RollerBearings

Actuator Support

Loading Stub

NN

RTMDActuator

Dampers

North A-Frame

SouthA-Frame

RollerBearings

Actuator Support

Loading Stub

Test aes Compensation

1 15 Inverse compensation2 15 Adaptive Inverse Compensation3 29 Adaptive Inverse Compensation

31

Reliability Assessment

Test 1: inverse compensationwith αes=15

P.E.=50%

Test 2: AIC with αes=15

P.E.=50%

P.E.=15%

32

Reliability Assessment

Test 3: AIC with αes=30

P.E.=5%

33


Numerical analysis is conducted to investigate the accuracy of real-time hybrid simulation with actuator delay;

A probabilistic approach using tracking indicator is proposed for reliability assessment of real-time hybrid simulation;

The effectiveness of the proposed method is validated through applying it to experimental results.

34

Future Work

Further develop the probabilistic model for actuator delay corresponding to different accuracy level for SDOF structures;

Extend the proposed approach to real-time hybrid simulations involving multiple servo-hydraulic actuators.

35

Acknowledgement

This study is supported by the Presidential Award of San Francisco State University and the CSU Wang Family Faculty Award.

The presented experimental results were conducted at ATLSS Center of Lehigh University using NEES RTMD equipment;

The MR damper used for the predefined displacement tests was provided by Dr. Richard Christenson at University of Connecticut.

36

Thanks for your attention!

Questions?

Cheng Chen, Ph.D. Assistant Professor San Francisco State University Interpreting Reliability of...

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