the asian-pacific symposium on structural reliability and its applications seoul, korea, august...

The Asian-Pacific Symposium on Structural Reliability and its ApplicationsSeoul, Korea, August 18-20, 2004

Kyu-Sik ParkKyu-Sik Park, Ph. D. Candidate, KAIST, KoreaHyung-Jo JungHyung-Jo Jung, Assistant Professor, Sejong Univ., KoreaWoon-Hak KimWoon-Hak Kim, Professor, Hankyong Nat. Univ., KoreaIn-Won LeeIn-Won Lee, Professor, KAIST, Korea

Robust Hybrid Control ofa Seismically Excited Cable-Stayed Bridge

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

Introduction

Robust hybrid control system Numerical examples

Conclusions

Contents


Introduction Hybrid control system (HCS)

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 HCS could be decreased by the active control devices.


Objective of this study

Apply robust control algorithms to improvethe controller robustness of HCS


Robust hybrid control system (RHCS)

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 has a capacity of 1000 kN. • The actuator dynamics are neglected.


Control algorithm RHCS 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 c

i

ff

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

otherwiser 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 RHCS I


RHCS 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 2.50440.3

17 rad/secg

g

S

1/ 60 11/ 30 1z

sWs

0.2(1/ 60 1)1/ 240 1u

sWs


Bridge Model

SensorH2HA

LRB

MU

X

ey

mysy

,LRB ,LRB,r rx x

HAuHAf

LRBf

fgx

Block diagram of RHCS II

DMWgkggx

R Wu

WzQzz

v

K

u

uz


RHCS 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) · Located 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 10 2 0 3 0 40 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


0 10 2 0 3 0 40 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 10F 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 10 2 0 3 0 40 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 10F 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 ebzePGA: 0.265gPGA: 0.265g

0 1 2 3 4 5 6 7 8 9 10F 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

Evaluation criteria


Analysis results Control performances

Displacement under El Centro earthquake

(a) Uncontrolled (b) RHCS III


Cable tension under El Centro earthquake



Shear force under El Centro earthquake



Evaluation criteria CHCS* RHCS I RHCS II RHCS IIIJ1. Max. base shear 0.4854 0.4607 0.5319 0.4930J2. Max. deck shear 0.9214 0.9250 0.9607 0.8997J3. Max. base moment 0.4427 0.4395 0.5057 0.4519J4. Max. deck moment 0.6558 0.6546 0.6441 0.5617J5. Max. cable deviation 0.1433 0.1428 0.1252 0.1437J6. Max. deck dis. 1.5532 1.5598 1.0652 1.1863J7. Norm base shear 0.3770 0.3762 0.3929 0.3581J8. Norm deck shear 0.8986 0.9035 0.7868 0.9035J9. Norm base moment 0.3375 0.3378 0.3590 0.3216J10. Norm deck moment 0.7277 0.7503 0.5404 0.7338J11. Norm cable deviation 1.707e-3 1.678e-3 1.275e-2 1.741e-2

• Maximum evaluation criteria for all three earthquakes

*Conventional HCS controlled by LQG algorithm


Evaluation criteria CHCS* RHCS I RHCS II RHCS IIIJ1. Max. base shear 0.4854 0.4607 0.5319 0.4930J2. Max. deck shear 0.9214 0.9250 0.9607 0.8997J3. Max. base moment 0.4427 0.4395 0.5057 0.4519J4. Max. deck moment 0.6558 0.6546 0.6441 0.5617J5. Max. cable deviation 0.1433 0.1428 0.1252 0.1437J6. Max. deck dis. 1.5532 1.5598 1.0652 1.1863J7. Norm base shear 0.3770 0.3762 0.3929 0.3581J8. Norm deck shear 0.8986 0.9035 0.7868 0.9035J9. Norm base moment 0.3375 0.3378 0.3590 0.3216J10. Norm deck moment 0.7277 0.7503 0.5404 0.7338J11. Norm cable deviation 1.707e-3 1.678e-3 1.275e-2 1.741e-2

• Maximum evaluation criteria for all three earthquakes

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

CHCS*RHCS IRHCS IIRHCS III

*Conventional HCS controlled by LQG algorithm


Controller robustness • The dynamic characteristic of as-built bridge is not identical to the numerical model. • To verify the applicability of RHCS, the controller robustness is investigated to perturbation of stiffness parameter.

pert (1 ) K K

wherepertK

K

: nominal stiffness matrix: perturbed stiffness matrix: perturbation amount (5% ~ 20 %)


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

Evaluation criteria RHCS I RHCS II RHCS IIIJ1. Max. base shear 14.24 9.20 6.88J2. Max. deck shear 17.78 4.42 13.49J3. Max. base moment 16.74 4.93 5.26J4. Max. deck moment 6.09 6.21 5.49J5. Max. cable deviation 13.62 13.96 14.51J6. Max. deck dis. 4.61 1.48 2.70J7. Norm base shear 6.73 6.12 5.70J8. Norm deck shear 8.09 4.93 6.44J9. Norm base moment 6.33 5.54 5.91J10. Norm deck moment 8.54 7.56 10.86J11. Norm cable deviation 16.84 13.78 17.29


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

Evaluation criteria RHCS II RHCS IIIJ1. Max. base shear 36.51 33.02J2. Max. deck shear 22.93 34.32J3. Max. base moment 33.08 30.67J4. Max. deck moment 34.48 40.71J5. Max. cable deviation 50.07 33.27J6. Max. deck dis. 5.02 8.06J7. Norm base shear 31.78 30.19J8. Norm deck shear 39.33 35.96J9. Norm base moment 29.70 28.99J10. Norm deck moment 45.34 32.40J11. Norm cable deviation 72.35 52.74


0

20

40

60

80

5 10 15 20

Stiffness perturbation (±, %)

Max

. var

iatio

n (%

)

RHCS IRHCS IIRHCS III

Max. variation of evaluation criteria for variations of stiffness perturbation


Conclusions Hybrid control system with robust control algorithms

Has excellent robustness for stiffness perturbation without loss of control performances

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

• RHCS III is more robust than RHCS II.

Robust hybrid control 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

the asian-pacific symposium on structural reliability and its applications seoul, korea, august...

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