cheng chen ph.d., assistant professor school of engineering san francisco state university...

Cheng Chen

Ph.D., Assistant Professor School of Engineering

San Francisco State University

Probabilistic Reliability Analysis of Real-Time Hybrid Simulation

Results for Seismic Hazard Mitigation

Quake Summit, Boston, MA, 2012

2

Presentation Overview

Background

Need for Reliability Analysis

Proposed Probabilistic Approach for Reliability Analysis

Application to Experimental Results

Summary and Conclusion

3

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

4

Servo-Hydraulic Actuators

Critical to maintain the boundary conditions between substructures!

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

Command Maximum: 50 mm

Frequency Content: 0 ~ 5 Hz

Test Compensation aesMTE (mm)

1-1 Inverse compensation 1 16.9

1-2 Existing AIC 1 4.9

1-3 New AIC 1 2.4

Delay compensation methods can reduce, but

can NOT eliminate actuator tracking error for real-time

structural tests!

5

Reliable Experimental Results?

How will the tracking errors affect the accuracy of simulated structure response?

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

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

6

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

7

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;

8

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.

9

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

10

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

11

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%


12

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 (%

)



13

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

14

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.

15

EQ Response Analysis

Courtesy of Chopra (2001)

ASCE-7-10

16

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

17

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%

18

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

19

Tracking Indicator (TI)

Mercan and Ricles 2010

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.

20

Application of Proposed ApproachPerform real-time hybrid simulation

compare

21

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.

22

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

23

Reliability Assessment

Test 1: inverse compensationwith αes=15

P.E.=50%

Test 2: AIC with αes=15

P.E.=50%

P.E.=15%

24

Reliability Assessment

Test 3: AIC with αes=30

P.E.=5%

25

Summary and Conclusion

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 application to experimental results.

26

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.

27

Thanks for your attention!

Questions?

cheng chen ph.d., assistant professor school of engineering san francisco state university...

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