Sang-Won Cho* : Ph.D. Student, KAIST Dong-Hyawn Kim: Senior Researcher, KORDI
description
Transcript of Sang-Won Cho* : Ph.D. Student, KAIST Dong-Hyawn Kim: Senior Researcher, KORDI
Sang-Won Cho* : Ph.D. Student, KAISTSang-Won Cho* : Ph.D. Student, KAIST Dong-Hyawn Kim: Senior Researcher, KORDIDong-Hyawn Kim: Senior Researcher, KORDI In-Won Lee: Professor, KAIST In-Won Lee: Professor, KAIST
Neuro-Control of Structures Using CMACNeuro-Control of Structures Using CMAC
APCOM’01APCOM’01
Sydney, AustraliaSydney, Australia
November 20-23, 2001November 20-23, 2001
2 2Structural Dynamics & Vibration Control Lab., KAIST, Korea
CONTENTSCONTENTS
**Cerebellar Model Articulation ControllerCerebellar Model Articulation Controller
IntroductionIntroduction
CMACCMAC** for Vibration Control for Vibration Control
Numerical ExamplesNumerical Examples
ConclusionsConclusions
3 3Structural Dynamics & Vibration Control Lab., KAIST, Korea
mathematical model is not required in mathematical model is not required in designing controllerdesigning controller
- Advantage of neural network for structural control- Advantage of neural network for structural control- Advantage of neural network for structural control- Advantage of neural network for structural control
BackgroundBackground
- Application areas- Application areas- Application areas- Application areascontrol of structures with uncertaintycontrol of structures with uncertaintyor nonlinearityor nonlinearity
- Features of neural network- Features of neural network- Features of neural network- Features of neural networkpromising tool in many fields of engineeringpromising tool in many fields of engineering
Introduction Introduction
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structurestructure
external external loadload
neural neural networknetwork
sensorsensor
responseresponse
- Neural network should be trained before it worksNeural network should be trained before it works
Structural Control Using Neural Network Structural Control Using Neural Network
5 5Structural Dynamics & Vibration Control Lab., KAIST, Korea
Multilayer Neural Network (MLNN)Multilayer Neural Network (MLNN)
control control forceforcecontrol control forceforce
WWijij : weights: weightsWWijij : weights: weights
state ofstate ofstructurestructure
(displacement,(displacement, velocity)velocity)
state ofstate ofstructurestructure
(displacement,(displacement, velocity)velocity)
- Weight should be determined by learning processWeight should be determined by learning process- Training process is too slow to be used for on-line - Training process is too slow to be used for on-line controller controller
input input layerlayer
outputoutputlayerlayer
hiddenhiddenlayerlayer
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• H. M. Chen et al. (1995). H. M. Chen et al. (1995). ASCE J. Comp. in Civil Eng.ASCE J. Comp. in Civil Eng.
• J. Ghaboussi et al. (1995). J. Ghaboussi et al. (1995). ASCE J. Eng. Mech.ASCE J. Eng. Mech.
• K. Nikzad et al. (1996). K. Nikzad et al. (1996). ASCE J. Eng. Mech.ASCE J. Eng. Mech.
• K. Bani-Hani et al. (1998). K. Bani-Hani et al. (1998). ASCE J. Eng. Mech.ASCE J. Eng. Mech.
• J. T. Kim et al. (2000). J. T. Kim et al. (2000). ASCE J. Eng. Mech.ASCE J. Eng. Mech.
Previous StudiesPrevious Studies
- All methods are based on multilayer neural network,All methods are based on multilayer neural network, whose learning speed is too slow whose learning speed is too slow- New neural network with fast learning speed is required !!- New neural network with fast learning speed is required !!
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*Cerebellar Model Articulation Controller
Objective and ScopeObjective and Scope
To reduce learning time of controller by applyingTo reduce learning time of controller by applying
CMACCMAC** neural network for structural control neural network for structural control
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CMAC- proposed by J. S. Albus(1975)
- a neural network with fast learning speed
- mainly used for manipulator control
Application of CMAC for Vibration Control
Proposed Method :
9 9Structural Dynamics & Vibration Control Lab., KAIST, Korea
input space output
space
x
memory space
W1
W2
Wn
u
Procedure of CMAC
weights
Displacement,velocity
control signal
- Learning to determine the weights is done locally - Due to the locality of learning, the learning time of CMAC could be dramatically reduced
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Output Calculation (1)Output Calculation (1)
uu = = WW1212+W+W2222+W+W3232+W+W4242
xx
WW1111 W W12 12 WW1313 W W1414
WW2121 W W22 22 WW2323 W W24 24 WW3131 W W32 32 WW3333 W W34 34 WW4141 W W42 42 WW4343 W W44 44
xx11
layer 1layer 1
layer 2layer 2
layer 3layer 3
layer 4layer 4
inputinput
(output)
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Output Calculation (2)Output Calculation (2)
uu = = WW1313+W+W2323+W+W3232+W+W4242
xx
WW1111 W W12 12 WW1313 W W1414
WW2121 W W22 22 WW2323 W W24 24 WW3131 W W32 32 WW3333 W W34 34 WW4141 W W42 42 WW4343 W W44 44
xx11 xx22
layer 1layer 1
layer 2layer 2
layer 3layer 3
layer 4layer 4
inputinput
- By information-sharing, the required size of memory By information-sharing, the required size of memory can be considerably decreased can be considerably decreased
(output)
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CMAC MLNNCMAC MLNN
memory sizememory size large smalllarge small
learning speedlearning speed fast slowfast slow
computing modecomputing mode local globallocal global
General Features of CMAC vs. MLNNGeneral Features of CMAC vs. MLNN
ItemsItems
real-time applicationreal-time application suitablesuitable impossible impossible
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Vibration Control using CMACVibration Control using CMAC
structurestructure
external external loadload
CMACCMACCMACCMAC
learning learning rulerule
sensorsensor
responseresponse
- CMAC should be trained before it worksCMAC should be trained before it works- - Learning rule is required to train CMACLearning rule is required to train CMAC
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Control Criterion Control Criterion
1N
0kk
Tk1k
T1k
f
RuuQzz2
1J (1)(1)
z : cost function: cost function
: state vector: state vector
: control vector: control vector
: relative weighting matrix: relative weighting matrix
: time step: time step
: final time step: final time step
: cost function: cost function
: state vector: state vector
: control vector: control vector
: relative weighting matrix: relative weighting matrix
: time step: time step
: final time step: final time stepk
uQ,R
fN
J
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kTkk
Tkk RuuQzzJ 112
1
: learning rate: learning rate: learning rate: learning rateη
ki,ki,1ki, WWW
(2)(2)
(3)(3)
Learning RuleLearning Rule
i
kki, W
JηW
(4)(4)
-The cost at the The cost at the kkthth step step
-The weight is updated throughThe weight is updated through
-Gradient descent ruleGradient descent rule
-Learning rule is derived by minimizing the cost-Learning rule is derived by minimizing the cost
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(5)(5)
Ru
u
zQzηW T
kk
kT1kki,
1proposedproposedmethodmethodproposedproposedmethodmethod
-FinalFinal learning rulelearning rule
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Numerical ExamplesNumerical Examples
Model StructureModel Structure
AMDAMD
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: Mass matrix: Mass matrix: Damping matrix: Damping matrix: Restoring force : Restoring force : Location vector: Location vector
: displacement vector: displacement vector: ground acceleration: ground acceleration: control force: control force
(6)(6) gxMLu)xF(x,xCxM 1
C
x
Equation of MotionEquation of Motion
M
F
L
ugx
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dyk)(xk)x(f 00 1
)yxyyxx(d
ypp 11
p,,,
k
0 : linear stiffness : linear stiffness
: contribution of : contribution of kk00
: constants: constants
Nonlinear Restoring Force Nonlinear Restoring Force (Bilinear hysteresis model, Bouc-Wen, 1981)(Bilinear hysteresis model, Bouc-Wen, 1981)
(7)(7)
(8)(8)
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-0 .10 -0.05 0.00 0.05 0.10D isplacem ent (m )
-4 .0
-2.0
0.0
2.0
4.0R
esto
ring
forc
e (N
)
-0 .10 -0.05 0.00 0.05 0.10D isplacem ent (m )
-4 .0
-2.0
0.0
2.0
4.0
Res
torin
g fo
rce
(N)
-0 .10 -0.05 0.00 0.05 0.10D isplacem ent (m )
-4 .0
-2.0
0.0
2.0
4.0
Res
torin
g fo
rce
(N)
-0 .10 -0.05 0.00 0.05 0.10D isplacem ent (m )
-4 .0
-2.0
0.0
2.0
4.0
Res
torin
g fo
rce
(N)
Effect of Effect of Parameters :Parameters :
3.0
6.0 600 k
400 k
39,5.05,5.01,04.0
0
kp
d
6.0,5.05,5.01,04.0
p
d
39,5.05,5.01,04.0
0
kp
d
6.0,5.05,5.01,04.0
p
d
0, k
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mass
pump
Active Mass Driver (AMD)
piston
The dynamic of pump and piston are consideredin the simulation
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mass : 200 kg (story)mass : 200 kg (story)stiffness : 2.25stiffness : 2.25101055 N/m (inter-story) N/m (inter-story)damping ratios : 0.6, 0.7, 0.3% (modal)damping ratios : 0.6, 0.7, 0.3% (modal)
mass : 18 kg (3% of building total mass)mass : 18 kg (3% of building total mass)stiffness : 3.71stiffness : 3.71101033 N/m N/mdamping ratio : 8.65%damping ratio : 8.65%
StructureStructure
AMDAMD
ParametersParameters
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CMAC StructureCMAC Structure
input: 2 (disp., vel. of 3rd floor)input: 2 (disp., vel. of 3rd floor)
output: 1 (control signal)output: 1 (control signal)
no. of divisions: 3 per variableno. of divisions: 3 per variable
no. of layers: 200no. of layers: 200
no. of weights: 1800no. of weights: 1800
input: 2 (disp., vel. of 3rd floor)input: 2 (disp., vel. of 3rd floor)
output: 1 (control signal)output: 1 (control signal)
no. of divisions: 3 per variableno. of divisions: 3 per variable
no. of layers: 200no. of layers: 200
no. of weights: 1800no. of weights: 1800
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integration time: 0.25 msintegration time: 0.25 ms
sampling time: 5.0 mssampling time: 5.0 ms
delay time: 0.5 msdelay time: 0.5 ms
Simulation Parameters Simulation Parameters
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Case StudiesCase Studies
earthquake simulation earthquake simulation El Centro trainEl Centro trainEl Centro controlEl Centro controlNorthridge controlNorthridge controlKern County controlKern County control
El Centro trainEl Centro trainEl Centro control El Centro control Northridge controlNorthridge controlKern County controlKern County control
modelmodel
linearlinear
nonlinearnonlinear
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0 100 200 300 400 500Epoch
0.0
0.1
0.2
0.3
Cos
t fun
ctio
n
Linear Cases (Linear Cases (=1.0)=1.0)
※ ※1 E1 Epoch = 0.005 s poch = 0.005 s ×× 2000 steps 2000 steps ※ ※1 E1 Epoch = 0.005 s poch = 0.005 s ×× 2000 steps 2000 steps
CMACCMAC
MLNNMLNN
- Convergence of two neural networks- Convergence of two neural networks- Convergence of two neural networks- Convergence of two neural networks
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- Minimum Cost and Epoch - Minimum Cost and Epoch - Minimum Cost and Epoch - Minimum Cost and Epoch
MLNN MLNN
CMACCMAC
MLNN MLNN
CMACCMAC1.94 1.94 10 10-2 -2 6565 ((1.091.09) () (0.150.15))1.94 1.94 10 10-2 -2 6565 ((1.091.09) () (0.150.15))
1.77 1.77 10 10-2 -2 412 412 ((1.001.00) () (1.001.00) ) 1.77 1.77 10 10-2 -2 412 412 ((1.001.00) () (1.001.00) )
JJmin min epochepochJJmin min epochepochneuralneuralnetworknetworkneuralneuralnetworknetwork
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- - El Centro EEl Centro Earthquake (3arthquake (3rdrd floor) floor)- - El Centro EEl Centro Earthquake (3arthquake (3rdrd floor) floor)
0 5 10 15 20-0.10-0.050.000.050.10
0 5 10 15 20-1.00-0.500.000.501.00
Dis
plac
emen
t (m
) D
ispl
acem
ent (
m)
Time (sec)Time (sec)
Vel
ocity
(m/s
ec)
Vel
ocity
(m/s
ec)
w/o controlw/o controlw/ control w/ control ( CMAC )( CMAC )
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0 5 10 15 20-20.0-10.0
0.010.020.0
- El Centro E- El Centro Earthquake (3arthquake (3rdrd floor) - continued floor) - continued- El Centro E- El Centro Earthquake (3arthquake (3rdrd floor) - continued floor) - continuedA
ccel
erat
ion
(m
/sec
Acc
eler
atio
n (
m/s
ec22 )
)
Time (sec)Time (sec)
w/o controlw/o controlw/ control w/ control ( CMAC )( CMAC )
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Dis
plac
emen
t (m
) D
ispl
acem
ent (
m)
0 5 10 15 20-0.10-0.050.000.050.10
Time (sec)Time (sec)
0 5 10 15 20-1.00-0.500.000.501.00
Vel
ocity
(m/s
ec)
Vel
ocity
(m/s
ec)
- - Northridge ENorthridge Earthquake (3arthquake (3rdrd floor) floor)- - Northridge ENorthridge Earthquake (3arthquake (3rdrd floor) floor)
w/o controlw/o controlw/ control w/ control ( CMAC )( CMAC )
31 31Structural Dynamics & Vibration Control Lab., KAIST, Korea
0 5 10 15 20-20.0-10.0
0.010.020.0
Acc
eler
atio
n (
m/s
ecA
ccel
erat
ion
(m
/sec
22 ) )
Time (sec)Time (sec)
- - Northridge ENorthridge Earthquake (3arthquake (3rdrd floor) - continued floor) - continued- - Northridge ENorthridge Earthquake (3arthquake (3rdrd floor) - continued floor) - continued
w/o controlw/o controlw/ control w/ control ( CMAC )( CMAC )
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Time (sec)Time (sec)
0 5 10 15 20-0.10-0.050.000.050.10
Dis
plac
emen
t (m
) D
ispl
acem
ent (
m)
0 5 10 15 20-1.00-0.500.000.501.00
Vel
ocity
(m/s
ec)
Vel
ocity
(m/s
ec)
- - Kern County EKern County Earthquake (3arthquake (3rdrd floor) floor)- - Kern County EKern County Earthquake (3arthquake (3rdrd floor) floor)
w/o controlw/o controlw/ control w/ control ( CMAC )( CMAC )
33 33Structural Dynamics & Vibration Control Lab., KAIST, Korea
0 5 10 15 20-20.0-10.0
0.010.020.0
Acc
eler
atio
n (
m/s
ecA
ccel
erat
ion
(m
/sec
22 ) )
w/o controlw/o controlw/ control w/ control ( CMAC )( CMAC )
Time (sec)Time (sec)
- - Kern County Earthquake Kern County Earthquake (3(3rdrd floor) - continued floor) - continued- - Kern County Earthquake Kern County Earthquake (3(3rdrd floor) - continued floor) - continued
34 34Structural Dynamics & Vibration Control Lab., KAIST, Korea
0 100 200 300 400 500Epoch
0.0
0.1
0.2
0.3
Cos
t fun
ctio
n
CMACCMAC
MLNNMLNN
Nonlinear Cases (Nonlinear Cases (=0.5)=0.5)
- Convergence of two neural networks- Convergence of two neural networks- Convergence of two neural networks- Convergence of two neural networks
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MLNN MLNN
CMACCMAC
MLNN MLNN
CMACCMAC 2.02 2.02 10 10-2 -2 3434 ((1.061.06) () (0.080.08))2.02 2.02 10 10-2 -2 3434 ((1.061.06) () (0.080.08))
1.91 1.91 10 10-2 -2 427 427 ((1.001.00) () (1.001.00) ) 1.91 1.91 10 10-2 -2 427 427 ((1.001.00) () (1.001.00) )
JJmin min epochepochJJmin min epochepochneuralneuralnetworknetworkneuralneuralnetworknetwork
- Minimum Cost and Epoch - Minimum Cost and Epoch - Minimum Cost and Epoch - Minimum Cost and Epoch
36 36Structural Dynamics & Vibration Control Lab., KAIST, Korea
- - El Centro EEl Centro Earthquake (1arthquake (1stst floor) floor)- - El Centro EEl Centro Earthquake (1arthquake (1stst floor) floor)
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
w/o controlw/o control w/ control ( CMAC )w/ control ( CMAC )
5.05,5.01,01.0
p
d
5.05,5.01,01.0
p
d
37 37Structural Dynamics & Vibration Control Lab., KAIST, Korea
w/o controlw/o control
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
- - Northridge EaNorthridge Earthquake (1rthquake (1stst floor) floor)- - Northridge EaNorthridge Earthquake (1rthquake (1stst floor) floor)
5.05,5.01,01.0
p
d
5.05,5.01,01.0
p
d
w/ control ( CMAC )w/ control ( CMAC )
38 38Structural Dynamics & Vibration Control Lab., KAIST, Korea
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
Res
torin
g fo
rce
(kN
)
- - Kern County EKern County Earthquake (1arthquake (1stst floor) floor)- - Kern County EKern County Earthquake (1arthquake (1stst floor) floor)
w/o controlw/o control
5.05,5.01,01.0
p
d
5.05,5.01,01.0
p
d
w/ control ( CMAC )w/ control ( CMAC )
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0 5 10 15 20-0.04
-0.02
0.00
0.02
0.04
0 5 10 15 20-0.04
-0.02
0.00
0.02
0.04
0 5 10 15 20-0.04
-0.02
0.00
0.02
0.04
Comparison of Control Results (linear, 3rd floor) Comparison of Control Results (linear, 3rd floor)
El Centro El Centro El Centro El Centro
NorthridgeNorthridge NorthridgeNorthridge
Kern CountyKern County Kern CountyKern County
Dis
plac
emen
t (m
) D
ispl
acem
ent (
m)
MLNNMLNNCMACCMAC
Time (sec)Time (sec)
40 40Structural Dynamics & Vibration Control Lab., KAIST, Korea
Comparison of Control Results (nonlinear, 3rd floor) Comparison of Control Results (nonlinear, 3rd floor)
El Centro El Centro El Centro El Centro
NorthridgeNorthridge NorthridgeNorthridge
Kern CountyKern County Kern CountyKern County
Dis
plac
emen
t (m
) D
ispl
acem
ent (
m)
MLNNMLNNCMACCMAC
Time (sec)Time (sec)
0 5 10 15 20-0.04
-0.02
0.00
0.02
0.04
0 5 10 15 20-0.04
-0.02
0.00
0.02
0.04
0 5 10 15 20-0.04
-0.02
0.00
0.02
0.04
41 41Structural Dynamics & Vibration Control Lab., KAIST, Korea
Maximum Responses of 3rd floor (cm)Maximum Responses of 3rd floor (cm)
linearlinear
nonlinearnonlinear
5.01 2.06 1.65 5.01 2.06 1.65 (3.04) (1.24) (1.00) (3.04) (1.24) (1.00)
6.15 2.14 1.38 6.15 2.14 1.38 (4.46) (1.55) (1.00) (4.46) (1.55) (1.00)
3.42 0.97 0.72 3.42 0.97 0.72 (4.75) (1.35) (1.00) (4.75) (1.35) (1.00)
3.48 2.54 2.34 3.48 2.54 2.34 (1.49) (1.09) (1.00) (1.49) (1.09) (1.00)
3.94 2.20 1.63 3.94 2.20 1.63 (2.42) (1.35) (1.00) (2.42) (1.35) (1.00)
2.68 0.97 0.80 2.68 0.97 0.80 (3.35) (1.21) (1.00)(3.35) (1.21) (1.00)
Earthquake w/o controlEarthquake w/o controlw/ controlw/ control
CMAC MLNNCMAC MLNN
El Centro El Centro
Northridge Northridge
Kern County Kern County
El Centro El Centro
Northridge Northridge
Kern CountyKern County
42 42Structural Dynamics & Vibration Control Lab., KAIST, Korea
ConclusionsConclusions• CMAC is applied to structural control.CMAC is applied to structural control.
• Both CMAC and MLNN reduce the dynamicBoth CMAC and MLNN reduce the dynamic responses.responses.
CMAC : CMAC : 59~759~71% 27~64% 1% 27~64%
MLNN : 67~79% 33~70%MLNN : 67~79% 33~70%
• Learning speed of CMAC is much faster thanLearning speed of CMAC is much faster than that of MLNN.that of MLNN. 15% for linear, 8% for nonlinear15% for linear, 8% for nonlinear
• Response controlled by CMAC is larger than Response controlled by CMAC is larger than that by MLNN.that by MLNN.
155% for linear, 135% for nonlinear155% for linear, 135% for nonlinear
• CMAC is applied to structural control.CMAC is applied to structural control.
• Both CMAC and MLNN reduce the dynamicBoth CMAC and MLNN reduce the dynamic responses.responses.
CMAC : CMAC : 59~759~71% 27~64% 1% 27~64%
MLNN : 67~79% 33~70%MLNN : 67~79% 33~70%
• Learning speed of CMAC is much faster thanLearning speed of CMAC is much faster than that of MLNN.that of MLNN. 15% for linear, 8% for nonlinear15% for linear, 8% for nonlinear
• Response controlled by CMAC is larger than Response controlled by CMAC is larger than that by MLNN.that by MLNN.
155% for linear, 135% for nonlinear155% for linear, 135% for nonlinear
for linearfor linearfor linearfor linear for nonlinearfor nonlinearfor nonlinearfor nonlinear
43 43Structural Dynamics & Vibration Control Lab., KAIST, Korea
Future WorkFuture WorkFuture WorkFuture Work
• Further reduction of response controlled by CMAC Further reduction of response controlled by CMAC
with fast learning speed.with fast learning speed.
• Further reduction of response controlled by CMAC Further reduction of response controlled by CMAC
with fast learning speed.with fast learning speed.
44 44Structural Dynamics & Vibration Control Lab., KAIST, Korea
Thank you for your attention.Thank you for your attention.Thank you for your attention.Thank you for your attention.