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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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 3
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 4
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 5
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 6
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 7
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 8
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 9
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 10
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 11
- 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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 12
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 13
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 14
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 15
Weighting parameters for active control part
- performance index
Q: response weighing matrix R: control force weighting matrix (identity matrix)
dtEJ
0
uRuzQz1
lim TT
SDVCL, Dept. of Civil & Environmental Engng., KAIST 16
- 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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 17
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 18
- 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
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 19
: for hybrid control strategy
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 3om dd
4 4 dd 4 4
, 5 10 , 1 10q
q qq
I 0Q =
0 Iom: overturning momentdd: deck dis.
min.point
SDVCL, Dept. of Civil & Environmental Engng., KAIST 20
NUMERICAL SIMULATIONSSimulation results - time history responses
deck displacementoverturning moment (base moment)
- evaluation criteria
SDVCL, Dept. of Civil & Environmental Engng., KAIST 21
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 23
-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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 24
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 26
Evaluation criteria under Mexico City earthquake
Evaluation criteria Passive Active Hybrid
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 28
Evaluation criteria under Gebze earthquake
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 30
Maximum evaluation criteria
Evaluation criteria Passive Active Hybrid
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
J9. Norm base moment 0.482 0.356 0.334
J10. Norm deck moment 1.443 0.762 0.780
J11. Norm cable deviation 2.23e-2 1.62e-3 1.82e-2
J12. Max. control force 2.16e-3 1.96e-3 2.64e-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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 32
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
SDVCL, Dept. of Civil & Environmental Engng., KAIST 33
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.
SDVCL, Dept. of Civil & Environmental Engng., KAIST 34
Thank you for your attention!