2002 Control of a Seismically Excited Cable-Stayed Bridge Employing a Hybrid Control Strategy 2002. 10. 19,

2002 년도 한국전산구조공학회 가을 학술발표회

Control of a Seismically Excited Cable-Stayed Bridge

Employing a Hybrid Control Strategy

2002. 10. 19

박규식 , 한국과학기술원 건설 및 환경공학과 박사과정정형조 , 한국과학기술원 건설 및 환경공학과 연구조교수이종헌 , 경일대학교 토목공학과 교수이인원 , 한국과학기술원 건설 및 환경공학과 교수

Department of Civil and Environmental Engineering, KAISTDepartment of Civil and Environmental Engineering, KAIST 22

Introduction

Benchmark problem statement

Seismic control system using a hybrid control strategy

Numerical simulations

Conclusions

CONTENTS


INTRODUCTION

Many control strategies and devices have been developed and investigated to protect structures against natural hazard.

The 1st generation benchmark control problem for cable-stayed bridges under seismic loads has been developed (Dyke et al., 2000).

The control of very flexible and large structures such as cable-stayed bridges is a unique and challenging problem.


investigate the effectiveness of the hybrid control strategy* for seismic protection of a cable-stayed bridge

Objective of this study:

hybrid control strategy:combination of passive and active control strategies


BENCHMARK PROBLEM STATEMENTBenchmark bridge model

– Under construction in Cape Girardeau, Missouri, USA

– Sixteen STU* devices are employed in the connection between the tower and the deck in the original design.

STUSTU

STU: Shock Transmission Unit


Benchmark bridge model– Under construction in Cape Girardeau, Missouri, USA

– Sixteen STU* devices are employed in the connection between the tower and the deck in the original design.

Two H- shape towersTwo H- shape towers128 128 cablescables

12 12 additional piersadditional piers

STU: Shock Transmission Unit

BENCHMARK PROBLEM STATEMENT


Linear evaluation model- The Illinois approach has a negligible effect on the

dynamics of the cable-stayed portion.

- The stiffness matrix is determined through a nonlinear static analysis corresponding to deformed state of the bridge with dead loads.

- A one dimensional excitation is applied in the longitudinal direction.

- A set of eighteen criteria have been developed to evaluate the capabilities of each control strategy.


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

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

0

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

Mag

nitu

de

PGA: 0.3483gPGA: 0.3483g

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

Acc

eler

atio

n (m

/s2 )

M exico C ity

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

0

1 0 0 0 0

2 0 0 0 0

3 0 0 0 0

4 0 0 0 0

Mag

nitu

de

PGA: 0.1434gPGA: 0.1434g

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

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

0

2 0 0 0 0

4 0 0 0 0

6 0 0 0 0

8 0 0 0 0

Mag

nitu

de

PGA: 0.2648gPGA: 0.2648g


Evaluation criteria

- Peak responses- Peak responses JJ11: Base shear: Base shear

JJ22: Shear at deck level : Shear at deck level

JJ33: Overturning moment: Overturning moment

JJ44: Moment at deck level: Moment at deck level

JJ55: Cable tension: Cable tension

JJ66: Deck dis. at abutment: Deck dis. at abutment- Normed responses- Normed responses JJ77: Base shear: Base shear

JJ88: Shear at deck level: Shear at deck level

JJ99: Overturning moment: Overturning moment

JJ1010: Moment at deck level: Moment at deck level

JJ1111: Cable tension: Cable tension

- Control Strategy (- Control Strategy (JJ1212 – – JJ1818))

JJ1212: Peak force: Peak force

JJ1313: Device stroke: Device stroke

JJ1414: Peak power: Peak power

JJ1515: Total power: Total power

JJ1616: Number of control devices: Number of control devices

JJ1717: Number of sensor: Number of sensor

JJ1818::dim( )c

kx


Passive control devices

SEISMIC CONTROL SYSTEM USINGA HYBRID CONTROL STRATEGY

In this hybrid control strategy, passive control devices have a great role for the effectiveness of control performance.

Lead rubber bearings (LRBs) are used as passive control devices.


The design of LRBs follows a general and recommended procedure provided by Ali and Abdel-Ghaffar 1995.

- The design shear force level for the yielding of the lead plug is taken to be 0.10M.

(M: the part of deck weight carried by bearings)

- The plastic stiffness ratio of the bearings at the bent and

tower is assumed to be 1.0.

A total of 24 LRBs are employed.

- Six LRBs at each deck-tower and deck-bent 1/pier 4 connections


Property Value

ke(N/m) 3.571107

kp(N/m) 3.139106

Dy(cm) 0.765

Qd(kg) 2.540104

Properties of the LRB

ke: Elastic stiffness

kp: Plastic stiffness

Dy: Yield dis. of the lead plug

Qd: Design shear force level for the yielding of

the lead plug

LRBF

rx

1

( , ) (1 )

1

LRB r r e r e y

n n

i r r ry

F x x k x k D y

y A x x y y x yD

0.879, 0.5,

0.5, 1, 1

p

e

i

k

k

A n

where

The Bouc-Wen model is used to simulate the nonlinear dynamics of the LRB.


Active control devices

A total of 24 hydraulic actuator, which are used in the benchmark problem, are employed.

An actuator has a capacity of 1000 kN.

The actuator dynamics are neglected and the actuator is considered to be ideal.

Five accelerometers and four displacement sensors are used for feedback.

An H2/LQG control algorithm is adopted.


Control device and sensor locations

2 2

1

5 accelerometers

8(6) 8(6) 4(6)4(6)

24 hydraulic actuators, 24 LRBs

H2/LQG

Control force

2 2

4 displacement sensors


z: regulated output Q: response weighing matrix

R: control force weighting matrix (I88)

dtEJ

0

uRuzQz1

lim TT

Weighting parameters for active control part

Performance index

where


Step 1. Calculate maximum responses for the candidate weighting parameters as increasing each parameters.

The maximum response approach is used to determine Q.

Responses q

base shears at piers 2 and 3 qbs

shears at deck level at piers 2 and 3 qsd

mom. at base of piers 2 and 3 qom

mom. at deck level at piers 2 and 3 qmd

deck dis. at bent 1 and pier 4 qdd

top dis. at towers 1 and 2 qtd

The selected responses


Step 2. Normalize maximum responses by the results of base structure and plot sum of max. responses.

1 2 3 4 5 6 7 8 9 1 0

S im u la tio n N u m b er

0

2

4

6

8

1 0

1 2

Sum

of

Max

. Res

pons

esB ase sh ea rS h ea r a t d ec k lev e lO v ertu rn in g m o m en tM o m en t a t d ec k lev e lD ec k d isp lacem en tT o p d isp la cem en t

Step 3. Select two parameters which give the smallest sum of max. responses.


Step 4. Calculate maximum responses for the selected two weighting parameters as increasing each parameters simultaneously.

Step 5. Determine the values of the appropriate optimal weighting parameters.


om 4 4 4 4 9 4active om dd

4 4 dd 4 4

, 4 10 , 1 10q

q qq

I 0Q =

0 I

1 2 3 4 5 6 7 8 9 1 0


0

2

4

6

8

1 0

1 2

Sum

of

Max

. Res

pons

es

B ase sh e a rS h e a r a t d e c k le v e lO v e rtu rn in g m o m e n tM o m e n t a t d ec k lev e lD e c k d isp lac em en tT o p d isp la c em en t

min. point

- For active control system


1 2 3 4 5 6 7 8 9 1 0


0

4

8

1 2

1 6

2 0

Sum

of

Max

. Res

pons

es

B ase sh ea rS h ea r a t d eck lev e lO v e rtu rn in g m o m en tM o m en t a t d eck lev e lD eck d isp lacem en tT o p d isp lacem en t

om 4 4 4 4 9 3hybrid om dd

4 4 dd 4 4

, 5 10 , 1 10q

q qq

I 0Q =

0 I

min. point

- For hybrid control system


deck displacementoverturning moment

NUMERICAL SIMULATIONS

Time-history responses


Under the 1940 El Centro earthquake

0 2 0 4 0 6 0 8 0 1 0 0-1 0

-5

0

5

1 0

1 5

Dis

pla

cem

ent(

cm)

Mom

ent(

105 N

m)

max

max

max

max

STU =6.95cm

Passive =11.83cm

Active =9.58cm

Hybrid =6.77cm

6max

5max

5max

5max

STU =1.02 10 Nm

Passive =2.82 10 Nm

Active =2.48 10 Nm

Hybrid =2.01 10 Nm

0 2 0 4 0 6 0 8 0 1 0 0-1 5

-1 0

-5

0

5

1 0

1 5

U n co n tro lled (S T U )P ass iv eA c tiv eH y b rid


Under the 1985 Mexico City earthquakeD

isp

lace

men

t(cm

)M

omen

t(

105 N

m) 0 2 0 4 0 6 0 8 0 1 0 0

-6

-4

-2

0

2

4

6

U n co n tro lled (S T U )P ass iv eA c tiv eH y b rid

0 2 0 4 0 6 0 8 0 1 0 0-2

-1

0

1

2

max

max

max

max

STU =1.37cm

Passive =4.68cm

Active =3.79cm

Hybrid =2.66cm

5max

5max

4max

4max

STU =1.98 10 Nm

Passive =1.13 10 Nm

Active =8.89 10 Nm

Hybrid =8.23 10 Nm


Under the 1999 Turkey Gebze earthquakeD

isp

lace

men

t(cm

)M

omen

t(

105 N

m) 0 2 0 4 0 6 0 8 0 1 0 0

-2 0

-1 0

0

1 0

2 0

3 0

U n co tro lled (S T U )P ass iv eA c tiv eH y b rid

0 2 0 4 0 6 0 8 0 1 0 0-8

-4

0

4

8

max

max

max

max

STU =4.87cm

Passive =26.57cm

Active =13.09cm

Hybrid =11.45cm

5max

5max

5max

5max

STU =6.98 10 Nm

Passive =3.50 10 Nm

Active =2.39 10 Nm

Hybrid =1.90 10 Nm


(a) El Centro (b) Mexico City (c) Turkey Gebze

Restoring force of LRB at pier 2

-1 5 -1 0 -5 0 5 1 0 1 5D e fo rm a tio n (c m )

-8 0 0

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

Res

tori

ng f

orce

(kN

)

P a ss iv e C o n tro lH y b rid C o n tro l

- 6 - 4 - 2 0 2 4 6D e fo rm a tio n (c m )

-4 0 0

-2 0 0

0

2 0 0

4 0 0

-3 0 -2 0 -1 0 0 1 0 2 0 3 0D e fo rm a tio n (c m )

-1 2 0 0

-8 0 0

-4 0 0

0

4 0 0

8 0 0

1 2 0 0

-1 5 -1 0 -5 0 5 1 0 1 5D e fo rm a tio n (c m )

-8 0 0

-6 0 0

-4 0 0

-2 0 0

0

2 0 0

4 0 0

6 0 0

8 0 0

Res

tori

ng f

orce

(kN

)

P a ss iv e C o n tro lH y b rid C o n tro l

- 6 - 4 - 2 0 2 4 6D e fo rm a tio n (c m )

-4 0 0

-2 0 0

0

2 0 0

4 0 0

-3 0 -2 0 -1 0 0 1 0 2 0 3 0D e fo rm a tio n (c m )

-1 2 0 0

-8 0 0

-4 0 0

0

4 0 0

8 0 0

1 2 0 0

Evaluation criteria Passive Active Hybrid

J1: Max. base shear 0.398 0.271 0.264

J2: Max. deck shear 1.185 0.790 0.723

J3: Max. base moment 0.305 0.254 0.230

J4: Max. deck moment 0.608 0.460 0.383

J5: Max. cable deviation 0.208 0.147 0.146

J6: Max. deck dis. 1.425 1.006 0.746

J7: Norm base shear 0.230 0.200 0.198

J8: Norm deck shear 1.091 0.716 0.693

J9: Norm base moment 0.247 0.201 0.188

J10: Norm deck moment 0.713 0.512 0.495

J11: Norm cable deviation 2.23e-2 1.62e-2 1.82e-2

J12: Max. control force 1.34e-3 1.96e-3 2.64e-3

J13: Max. device stroke 0.936 0.660 0.490

J14: Max. power - 4.57e-3 3.32e-3

J15: Total power - 7.25e-4 7.10e-4

Evaluation criteria

Under the 1940 El Centro earthquake

2.64e-3

LRB: 9.29e-4

HA: 1.96e-3

2626

Under the 1985 Mexico City earthquakeEvaluation criteria Passive Active HybridJ1. Max. base shear 0.546 0.507 0.485

J2. Max. deck shear 1.110 0.910 0.927

J3. Max. base moment 0.619 0.448 0.447

J4. Max. deck moment 0.447 0.415 0.352

J5. Max. cable deviation 4.88e-2 4.50e-2 4.61e-2

J6. Max. deck dis. 2.020 1.666 1.080

J7. Norm base shear 0.421 0.376 0.372

J8. Norm deck shear 0.963 0.770 0.732

J9. Norm base moment 0.399 0.356 0.334

J10. Norm deck moment 0.654 0.691 0.525

J11. Norm cable deviation 5.18e-3 6.27e-3 6.34e-3

J12. Max. control force 7.76e-4 1.22e-3 1.96e-3

J13. Max. device stroke 1.017 0.839 0.547

J14. Max. power - 2.62e-3 1.10e-3

J15. Total power - 3.49e-4 1.97e-4

1.96e-3

LRB: 6.43e-4

HA: 7.56e-4

2727

Evaluation criteria Passive Active Hybrid

J1. Max. base shear 0.423 0.414 0.379

J2. Max. deck shear 1.462 1.158 0.936

J3. Max. base moment 0.501 0.342 0.285

J4. Max. deck moment 1.266 0.879 0.672

J5. Max. cable deviation 0.160 9.01e-2 9.53e-2

J6. Max. deck dis. 3.829 1.803 1.663

J7. Norm base shear 0.334 0.295 0.277

J8. Norm deck shear 1.550 0.951 0.917

J9. Norm base moment 0.482 0.351 0.324

J10. Norm deck moment 1.443 0.762 0.780

J11. Norm cable deviation 1.71e-2 8.90e-3 1.04e-2

J12. Max. control force 2.16e-3 1.96e-3 2.46e-3

J13. Max. device stroke 2.100 0.989 0.912

J14. Max. power - 9.33e-3 6.67e-3

J15. Total power - 8.80e-4 8.49e-4

2.46e-3

LRB: 1.22e-3

HA: 1.78e-3

Under the 1999 Turkey Gebze earthquake

2828


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11 J12 J13

Passive control

Active control

Hybrid control

Maximum evaluation criteria

Evaluation Criteria

Val

ues

Evaluation criteria

J1. Max. base shear

J2. Max. deck shear

J3. Max. base moment

J4. Max. deck moment

J5. Max. cable deviation

J6. Max. deck dis.

J7. Norm base shear

J8. Norm deck shear

J9. Norm base moment

J10. Norm deck moment

J11. Norm cable deviation

J12. Max. control force

J13. Max. device stroke


Earthquake Max. Active Hybrid

1940El Centro NS

Force(kN) 1000 1000

Stroke(m) 0.0982 0.0728

Vel. (m/s) 0.5499 0.5323

1985Mexico City

Force(kN) 622.23 385.31

Stroke(m) 0.0405 0.0263

Vel. (m/s) 0.2374 0.2043

1990Gebze NS

Force(kN) 1000 909.03

Stroke(m) 0.1297 0.1196

Vel. (m/s) 0.4157 0.4223

Actuator requirement constraints

Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec

Actuator requirements


Evaluation criteria

J1. Max. base shear

J2. Max. deck shear

J3. Max. base moment

J4. Max. deck moment

J5. Max. cable deviation

J6. Max. deck dis.

J7. Norm base shear

J8. Norm deck shear

J9. Norm base moment

J10. Norm deck moment

J11. Norm cable deviation

-60

-50

-40

-30

-20

-10

0

10

20

J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11

mu-synthesis(Turan 2001)

Hybrid control

Evaluation Criteria

Var

iatio

ns (

%)

Maximum variations for 7% perturbation of K


A hybrid control strategy combining passive and active control systems has been proposed for the benchmark bridge problem.

The performance of the proposed hybrid control design is superior to that of the passive control design and slightly better than that of active control design.

The proposed hybrid control design is more robust for stiffness matrix perturbation than the active control with a -synthesis method due to the passive control part.

CONCLUSIONS


The proposed hybrid control strategy could be effectively used to seismically excited cable-stayed bridge.

More researches on increasing the robustness and performance of the hybrid control system are in progress.


Acknowledgments

This research is funded by the National Research Laboratory Grant (No.: 2000-N-NL-01-C-251) in Korea.

Thank you for your attention!

2002 Control of a Seismically Excited Cable-Stayed Bridge Employing a Hybrid Control Strategy 2002. 10. 19,

Documents

deck level j

abutment j

number of control devices

base shear j

cable tension j

overturning moment j

peak power j

peak force j