sang-won cho* : ph.d. student, kaist sang-won cho* : ph.d. student, kaist dong-hyawn kim: senior...

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


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


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


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


• 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 !!


*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


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 :


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


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)


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)


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


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


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


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


(5)(5)

Ru

u

zQzηW T

kk

kT1kki,

1proposedproposedmethodmethodproposedproposedmethodmethod

-FinalFinal learning rulelearning rule


Numerical ExamplesNumerical Examples

Model StructureModel Structure

AMDAMD


: 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


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)


-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


mass

pump

Active Mass Driver (AMD)

piston

The dynamic of pump and piston are consideredin the simulation


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


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


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


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


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


- 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


- - 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 )


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 )

)




Dis

plac

emen

t (m

) D

ispl

acem

ent (

m)

0 5 10 15 20-0.10-0.050.000.050.10


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)



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 ) )


- - Northridge ENorthridge Earthquake (3arthquake (3rdrd floor) - continued floor) - continued- - Northridge ENorthridge Earthquake (3arthquake (3rdrd floor) - continued floor) - continued




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)



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 ) )



- - Kern County Earthquake Kern County Earthquake (3(3rdrd floor) - continued floor) - continued- - Kern County Earthquake Kern County Earthquake (3(3rdrd floor) - continued floor) - continued


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


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


- - 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


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 )


-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 )


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



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


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


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


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


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.


Thank you for your attention.Thank you for your attention.Thank you for your attention.Thank you for your attention.

sang-won cho* : ph.d. student, kaist sang-won cho* : ph.d. student, kaist dong-hyawn kim: senior...

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