16 th KKCNN Symposium on Civil Engineering Kyungju, Korea, December 8 - 10 , 200 3

16th KKCNN Symposium on Civil EngineeringKyungju, Korea, December 8-10, 2003

Kyu-Sik ParkKyu-Sik Park, Ph. D. Candidate, KAIST, Korea

Hyung-Jo JungHyung-Jo Jung, Assistant Professor, Sejong Univ., Korea

Woo-Hyun YoonWoo-Hyun Yoon, Professor, Kyungwon Univ., Korea

In-Won LeeIn-Won Lee, Professor, KAIST, Korea

Robust Hybrid Seismic IsolationSystem for a Seismically Excited

Cable-Stayed Bridge

Robust Hybrid Seismic IsolationSystem for a Seismically Excited

Cable-Stayed Bridge

Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 22

Introduction

Robust hybrid seismic isolation system

Numerical examples

Conclusions

Contents


Introduction

Hybrid seismic isolation system (HSIS)

A combination of passive and active control devices

• Passive devices: offer some degree of protection in the case of power failure

• Active devices: improve the control performances

However, the robustness of HSIS could be decreased by the

active control devices.

A combination of passive and active control devices

• Passive devices: offer some degree of protection in the case of power failure

• Active devices: improve the control performances

However, the robustness of HSIS could be decreased by the

active control devices.


Objective of this study

Apply robust control algorithms to improve

the controller robustness of HSIS

Apply robust control algorithms to improve

the controller robustness of HSIS


Robust hybrid seismic isolation system (RHSIS)

Control devices

Passive control devices

• Lead rubber bearings (LRBs)

• Design procedure: Ali and Abdel-Ghaffar (1995)

• Bouc-Wen model

Active control devices

• Hydraulic actuators (HAs)

• An actuator capacity has a capacity of 1000 kN.

• The actuator dynamics are neglected.

Passive control devices

• Lead rubber bearings (LRBs)

• Design procedure: Ali and Abdel-Ghaffar (1995)

• Bouc-Wen model

Active control devices

• Hydraulic actuators (HAs)

• An actuator capacity has a capacity of 1000 kN.

• The actuator dynamics are neglected.


Control algorithm

RHSIS I

• Primary control scheme

· Linear quadratic Gaussian (LQG) algorithm

• Secondary control scheme

· On-Off type controller according to LRB’s responses

RHSIS I

• Primary control scheme

· Linear quadratic Gaussian (LQG) algorithm

• Secondary control scheme

· On-Off type controller according to LRB’s responses

HA,HA,

,

0,

i ci

ff

2,LRB ,LRB0.005m or 0.03m/s

otherwise

r ri ix x


Bridge Model

SensorLQGOn-OffHA

LRB

MU

Xey

mysy

HA( )cu

,LRB ,LRB,r rx x

HA / 0uHA / 0f

LRBf

fgx

Block diagram of RHSIS I


RHSIS II

• H2 control algorithm with frequency weighting filters

• Frequency weighting filters

RHSIS II

• H2 control algorithm with frequency weighting filters

• Frequency weighting filters

20

2 2

2

2g g g

gg g g

S sW

s s

0 2.5044

0.3

17 rad/sec

g

g

S

1/ 60 1

1/ 30 1z

sW

s

0.2(1/ 60 1)

1/ 240 1u

sW

s


Bridge Model

SensorH2HA

LRB

MU

X

ey

mysy

,LRB ,LRB,r rx x

HAuHAf

LRBf

fgx

Block diagram of RHSIS II

DMWgkggx

R Wu

WzQzz

v

K

u

uz


RHSIS III

• H control algorithm with frequency weighting filters

RHSIS III

• H control algorithm with frequency weighting filters


Numerical examples

Analysis model

Bridge model

• Bill Emerson Memorial Bridge

· Benchmark control problem (Dyke et al., 2003)

· Under construction in Cape Girardeau, MO, USA

· 16 Shock transmission devices (STDs) are employed between the tower-deck connections.

Bridge model

• Bill Emerson Memorial Bridge

· Benchmark control problem (Dyke et al., 2003)

· Under construction in Cape Girardeau, MO, USA

· 16 Shock transmission devices (STDs) are employed between the tower-deck connections.


142.7 m 350.6 m 142.7 m

gx

Schematic of the Bill Emerson Memorial Bridge


142.7 m 350.6 m 142.7 m

gx

Configuration of sensors

: Accelerometer

: Displacement sensor


142.7 m 350.6 m 142.7 m

gx

Configuration of control devices (HAs+LRBs)

2+3

2+3 4+3

4+3

4+3

4+3

2+3

2+3


0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-3

-2

-1

0

1

2

3

4

Acc

eler

atio

n (m

/s2 )

El C entro

PGA: 0.348gPGA: 0.348g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

7

8

Pow

er S

pect

ral D

ensi

ty

Historical earthquake excitations Historical earthquake excitations


0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-3

-2

-1

0

1

2

3

4

Acc

eler

atio

n (m

/s2 )

El C entro

PGA: 0.348gPGA: 0.348g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

7

8

Pow

er S

pect

ral D

ensi

ty0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

T im e (se c )

-2

-1

0

1

2

Acc

eler

atio

n (m

/s2 )

M exico C ity

PGA: 0.143gPGA: 0.143g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

Pow

er S

pect

ral D

ensi

ty



0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-3

-2

-1

0

1

2

3

4

Acc

eler

atio

n (m

/s2 )

El C entro

PGA: 0.348gPGA: 0.348g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

7

8

Pow

er S

pect

ral D

ensi

ty0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

T im e (se c )

-2

-1

0

1

2

Acc

eler

atio

n (m

/s2 )

M exico C ity

PGA: 0.143gPGA: 0.143g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

Pow

er S

pect

ral D

ensi

ty

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0T im e (se c )

-2

-1

0

1

2

3

Acc

eler

atio

n (m

/s2 )

G ebze

PGA: 0.265gPGA: 0.265g

0 1 2 3 4 5 6 7 8 9 1 0F re q u e n c y (H z )

0

1

2

3

4

5

6

7

8

9

Pow

er S

pect

ral D

ensi

ty



• J1/J7 : Peak/Normed base shear

• J2/J8 : Peak/Normed shear at deck level

• J3/J9 : Peak/Normed overturning moment

• J4/J10 : Peak/Normed moment at deck level

• J5/J11 : Peak/Normed cable tension deviation

• J6: Peak Deck dis. at abutment

• J1/J7 : Peak/Normed base shear

• J2/J8 : Peak/Normed shear at deck level

• J3/J9 : Peak/Normed overturning moment

• J4/J10 : Peak/Normed moment at deck level

• J5/J11 : Peak/Normed cable tension deviation

• J6: Peak Deck dis. at abutment

Evaluation criteria Evaluation criteria


Analysis results

Control performances Control performances

Displacement under El Centro earthquake

(a) Uncontrolled (b) RHSIS III


Cable tension under El Centro earthquake



Shear force under El Centro earthquake



Evaluation criteria CHSIS* RHSIS I RHSIS II RHSIS III

J1. Max. base shear 0.4854 0.4607 0.5319 0.4930

J2. Max. deck shear 0.9214 0.9250 0.9607 0.8997

J3. Max. base moment 0.4427 0.4395 0.5057 0.4519

J4. Max. deck moment 0.6558 0.6546 0.6441 0.5617

J5. Max. cable deviation 0.1433 0.1428 0.1252 0.1437

J6. Max. deck dis. 1.5532 1.5598 1.0652 1.1863

J7. Norm base shear 0.3770 0.3762 0.3929 0.3581

J8. Norm deck shear 0.8986 0.9035 0.7868 0.9035

J9. Norm base moment 0.3375 0.3378 0.3590 0.3216

J10. Norm deck moment 0.7277 0.7503 0.5404 0.7338

J11. Norm cable deviation 1.707e-3 1.678e-3 1.275e-2 1.741e-2

• Maximum evaluation criteria for all three earthquakes • Maximum evaluation criteria for all three earthquakes

*Conventional HSIS (HSIS with LQG)


Evaluation criteria CHSIS* RHSIS I RHSIS II RHSIS III

J1. Max. base shear 0.4854 0.4607 0.5319 0.4930

J2. Max. deck shear 0.9214 0.9250 0.9607 0.8997

J3. Max. base moment 0.4427 0.4395 0.5057 0.4519

J4. Max. deck moment 0.6558 0.6546 0.6441 0.5617

J5. Max. cable deviation 0.1433 0.1428 0.1252 0.1437

J6. Max. deck dis. 1.5532 1.5598 1.0652 1.1863

J7. Norm base shear 0.3770 0.3762 0.3929 0.3581

J8. Norm deck shear 0.8986 0.9035 0.7868 0.9035

J9. Norm base moment 0.3375 0.3378 0.3590 0.3216

J10. Norm deck moment 0.7277 0.7503 0.5404 0.7338

J11. Norm cable deviation 1.707e-3 1.678e-3 1.275e-2 1.741e-2

• Maximum evaluation criteria for all three earthquakes • Maximum evaluation criteria for all three earthquakes

*Conventional HSIS (HSIS with LQG)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11

Evaluation Criteria

Val

ues

CHSIS*RHSIS IRHSIS IIRHSIS III


Controller robustness

• The dynamic characteristic of as-built bridge is not

identical to the numerical model.

• To verify the applicability of RHSIS, the controller

robustness is investigated to perturbation of stiffness

parameter.

Controller robustness

• The dynamic characteristic of as-built bridge is not

identical to the numerical model.

• To verify the applicability of RHSIS, the controller

robustness is investigated to perturbation of stiffness

parameter.

pert (1 ) K K

where

pertKK

: nominal stiffness matrix: perturbed stiffness matrix: perturbation amount (5% ~ 30 %)


• Maximum variations of evaluation criteria for all three earthquakes (%, 5% perturbation)• Maximum variations of evaluation criteria for all three earthquakes (%, 5% perturbation)

Evaluation criteria RHSIS I RHSIS II RHSIS III

J1. Max. base shear 14.24 9.20 6.88

J2. Max. deck shear 17.78 4.42 13.49

J3. Max. base moment 16.74 4.93 5.26

J4. Max. deck moment 6.09 6.21 5.49

J5. Max. cable deviation 13.62 13.96 14.51

J6. Max. deck dis. 4.61 1.48 2.70

J7. Norm base shear 6.73 6.12 5.70

J8. Norm deck shear 8.09 4.93 6.44

J9. Norm base moment 6.33 5.54 5.91

J10. Norm deck moment 8.54 7.56 10.86

J11. Norm cable deviation 16.84 13.78 17.29


• Maximum variations of evaluation criteria for all three earthquakes (%, 20% perturbation)• Maximum variations of evaluation criteria for all three earthquakes (%, 20% perturbation)

Evaluation criteria RHSIS II RHSIS III

J1. Max. base shear 36.51 33.02

J2. Max. deck shear 22.93 34.32

J3. Max. base moment 33.08 30.67

J4. Max. deck moment 34.48 40.71

J5. Max. cable deviation 50.07 33.27

J6. Max. deck dis. 5.02 8.06

J7. Norm base shear 31.78 30.19

J8. Norm deck shear 39.33 35.96

J9. Norm base moment 29.70 28.99

J10. Norm deck moment 45.34 32.40

J11. Norm cable deviation 72.35 52.74


0

20

40

60

80

5 10 15 20 25 30

Stiffness perturbation (±, %)

Max

. var

iati

on (

%)

RHSIS I

RHSIS IIRHSIS III

Max. variation of evaluation criteria for variations of stiffness perturbation


Conclusions

Hybrid seismic isolation system with robust control algorithms

Has excellent robustness for stiffness perturbation without loss of control performances

• RHSIS I obtains robustness only for 5% stiffness perturbations.

• RHSIS III has more larger acting region of controller

than RHSIS II.

Has excellent robustness for stiffness perturbation without loss of control performances

• RHSIS I obtains robustness only for 5% stiffness perturbations.

• RHSIS III has more larger acting region of controller

than RHSIS II. Robust hybrid seismic isolation system could effectively

be used to seismically excited cable-stayed bridge.


This research is supported by the National Research Laboratory (NRL) program from the Ministry of Science of Technology (MOST) and the Grant for Pre-Doctoral Students from the Korea Research Foundation (KRF) in Korea.

Thank you for your attention!

Acknowledgements

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16 th KKCNN Symposium on Civil Engineering Kyungju, Korea, December 8 - 10 , 200 3

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