,, 2002 2002. 6. 8 Seismic Protection of Benchmark Cable-Stayed Bridge using Hybrid Control...

박규식 , 한국과학기술원 건설환경공학과 , 박사과정정형조 , 한국과학기술원 건설환경공학과 , 연구조교수이종헌 , 경일대학교 토목공학과 , 교수이인원 , 한국과학기술원 건설환경공학과 , 교수

2002 년도 한국강구조학회 학술발표대회

2002. 6. 8

Seismic Protection ofBenchmark Cable-Stayed Bridge

using Hybrid Control Strategy

SDVCL, Dept. of Civil & Environmental Engng., KAIST 2

CONTENTS

Introduction

Benchmark problem statement

Seismic control system using hybrid control strategy

Numerical simulations

Conclusions


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 cable-stayed bridges under seismic loads

Objective of this study:

hybrid control strategy:combination of passive and active control strategies


BENCHMARK PROBLEM STATEMENT

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.

STUSTU

STU: Shock Transmission Unit


BENCHMARK PROBLEM STATEMENT

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


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.

Control design problem- researcher/designer must define the sensor, devices,

algorithms to be used in the proposed 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

PGA: 0.3483gPGA: 0.3483g

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: 0.1434gPGA: 0.1434g

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 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

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: 0.2648gPGA: 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


SEISMIC CONTROL SYSTEM USING HYBRID CONTROL STRATEGY

Passive control devices - in this hybrid control strategy, passive control strategy has 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 (Ali and Abdel-Ghaffar, 1995).

: the asymtotic (or plastic) stiffness ratio of the bearings at the bent and tower are assumed to be 1.0.

: the design shear force level for the yielding of lead plug is taken to be 0.10M. (M: the part of deck weight carried by bearings)

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

0 0( , ) (1 )LRB r r r yF x x k x k D y

11 n n

i r r ry

y A x x y y x yD


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 devices 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


Control design model (reduced-order model)

- formed from the evaluation model and has 30 states

- by forming a balanced realization and condensing out the states with relatively small controllability and observability grammians

- the resulting state space system is

d d d d d g

z z zd d d d g

y y ys d d d d g( )

x

x

x

x A x B u E

z C x D u F

y G C x D u F v

: : State space eq.State space eq.

: Regulated output eq.: Regulated output eq.

: Measured output eq.: Measured output eq.


Weighting parameters for active control part

- performance index

Q: response weighing matrix R: control force weighting matrix (identity matrix)

dtEJ

0

uRuzQz1

lim TT


- the maximum response approach is used to determine Q.

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

Step 2. normalized maximum responses by the results of based structure and plot sum of max. responses.

Step 3. select two parameters which give the smallest 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

es

B 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


1 2 3 4 5 6 7 8 9 10S im u la t io n n u m b e r

4

8

12

Sum

of

max

. res

pons

es

b a se sh ea rsh e a 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 ec k lev e ld e ck d isp lacem e n tto p d isp lac em en t

- the maximum response approach is used to determine Q.

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

Step 2. normalized maximum responses by the results of based structure and plot sum of max. respomses.

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.


- the selected values of appropriate optimal weighting parameters

: for active control strategy

om 4 4 4 4 9 4om dd

4 4 dd 4 4

, 4 10 , 1 10q

q qq

I 0Q =

0 Iom: overturning momentdd: deck dis.

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 hybrid control strategy

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 3om dd

4 4 dd 4 4

, 5 10 , 1 10q

q qq

I 0Q =

0 Iom: overturning momentdd: deck dis.

min.point


NUMERICAL SIMULATIONSSimulation results - time history responses

deck displacementoverturning moment (base moment)

- evaluation criteria


Time history responses under three historical earthquakes

Dis

pla

cem

ent

(cm

)D

isp

lace

men

t (c

m)

Ove

rtu

rnin

g m

omen

t (

Ove

rtu

rnin

g m

omen

t (

101055 k

N k

N·m

)·m

)

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

E l C en tro

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

-4

-2

0

2

4

6

M ex ico C ity

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

-1 0

0

1 0

2 0

3 0

G eb ze

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

-5

0

5

1 0

1 5

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

-1

0

1

2

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

-4

0

4

8

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

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

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


-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

Restoring force of LRB at pier 2

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

-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 under El Centro earthquake

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

2.64e-3

LRB: 9.29e-4

HA: 1.96e-3


Evaluation criteria under Mexico City earthquake


J1. 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


Evaluation criteria under Gebze earthquake


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






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


Maximum evaluation criteria


J1. Max. base shear 0.546 0.507 0.485

J2. Max. deck shear 1.462 1.158 0.936

J3. Max. base moment 0.619 0.448 0.447

J4. Max. deck moment 1.266 0.879 0.672

J5. Max. cable deviation 0.208 0.147 0.146

J6. Max. deck dis. 3.829 1.803 1.663

J7. Norm base shear 0.421 0.376 0.372

J8. Norm deck shear 1.550 0.951 0.917






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

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


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


CONCLUSIONSA hybrid control 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 reliable than the active control method due to the passive control part.


Thank you for your attention!

,, 2002 2002. 6. 8 Seismic Protection of Benchmark Cable-Stayed Bridge using Hybrid Control...

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