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
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Introduction
Benchmark problem statement
Seismic control system using a hybrid control strategy
Numerical simulations
Conclusions
CONTENTS
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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.
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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
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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
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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
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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.
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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
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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
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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.
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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
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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.
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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.
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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
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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
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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
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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.
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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.
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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
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 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
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1 2 3 4 5 6 7 8 9 1 0
S im u la tio n N u m b er
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
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deck displacementoverturning moment
NUMERICAL SIMULATIONS
Time-history responses
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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
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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
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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
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(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
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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
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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
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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
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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
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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.
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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!