* dong-hyawn kim: graduate student, kaist ju-won oh: professor, hannam university ju-won oh:...

** Dong-Hyawn Kim: Graduate Student, KAIST Dong-Hyawn Kim: Graduate Student, KAIST Ju-Won Oh: Professor, Hannam UniversityJu-Won Oh: Professor, Hannam University In-Won Lee: Professor, KAISTIn-Won Lee: Professor, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST

STRUCTURAL CONTROL USING CMAC NEURAL NETWORK

Nha Trang 2000Nha Trang 2000Nha Trang, Vietnam, Aug. 14-18, 2000Nha Trang, Vietnam, Aug. 14-18, 2000

2 2Structural Dynamics & Vibration Control Lab., KAIST, Korea

1 INTRODUCTION

2 CMAC FOR VIBRATION CONTROL

3 NUMERICAL EXAMPLES

4 CONCLUSIONS

CONTENTS


1 INTRODUCTION1 INTRODUCTION

- mathematical model is not required in

designing controller

• Features of neural network control• Features of neural network control Background

• Application areas• Application areas

- control of structures with uncertainty or nonlinearity


structure

external load

neural networkneural

network

sensor

• Structural control using neural network• Structural control using neural network


• Multilayer neural network (MLNN)• Multilayer neural network (MLNN)

training is too slowtraining is too slow

control forcecontrol force

state ofstructurestate of

structure

weights to be adjustedweights to be adjusted


1) H. M. Chen et al. (1995). ASCE J. Comp. in Civil Eng.

2) J. Ghaboussi et al. (1995). ASCE J. Eng. Mech.

3) K. Nikzad et al. (1996). ASCE J. Eng. Mech.

4) K. Bani-Hani et al. (1998). ASCE J. Eng. Mech.

5) J. T. Kim et al. (2000). ASCE J. Eng. Mech.

Previous studies

- All methods are based on multilayer neural network whose learning speed is too slow- A new neural network with fast learning speed is required


Objective and Scope- apply CMAC* neural network to structural con

trol to reduce learning time.

- compare performance of CMAC with multilayer neural network.

*Cerebellar Model Articulation Controller


Introduction

2 CMAC FOR VIBRATION CONTROL2 CMAC FOR VIBRATION CONTROL

- proposed by J. S. Albus(1975)- a neural network with fast learning speed- mainly used for manipulator control

• CMAC• CMAC


input space output

space

x

memory space

W1

W2

W3

Wn-1

Wn

u

Procedure of CMAC

weight

displacementvelocity

control signal


x2

x1

W13 W14 W15 W16

W9 W10 W11 W12

W5 W6 W7 W8

W1 W2 W3 W4

x1

x2

(quantization mesh)

• Block quantization of input space• Block quantization of input space

W37 W38 W39 W40 W41

W32 W33 W34 W35 W36

W27 W28 W29 W30 W31

W22 W23 W24 W25 W26

W17 W18 W19 W20 W21

(made by shifting left mesh)

block sizeblock size shiftingshifting


x2

x1

W13 W14 W15 W16

W9 W10 W11 W12

W5 W6 W7 W8

W1 W2 W3 W4

x1

x2

1st mesh

• Activation of weights-(1)• Activation of weights-(1)

W37 W38 W39 W40 W41

W32 W33 W34 W35 W36

W27 W28 W29 W30 W31

W22 W23 W24 W25 W26

W17 W18 W19 W20 W21x1*

x2*

x1*

x2*

2nd mesh

input: [x1*, x2

*]T output:[W11 + W34]


x2

x1

W13 W14 W15 W16

W9 W10 W11 W12

W5 W6 W7 W8

W1 W2 W3 W4

x1

x2

• Activation of weights-(2)• Activation of weights-(2)

W37 W38 W39 W40 W41

W32 W33 W34 W35 W36

W27 W28 W29 W30 W31

W22 W23 W24 W25 W26

W17 W18 W19 W20 W21x1^

x2^

x1^

x2^

input: [ , ]Tx1^ x2

^ output:[W11 + W30]

x2*

x1*x1

*

x2*

1st mesh 2nd mesh


Weights [W11, W34] [W11, W30] Weights [W11, W34] [W11, W30]

no. of meshes: 2 no. of meshes: 2

3411 WW Output Output

• Summary• Summary

no. of weights: 41 no. of weights: 41

no. of division: 4, 5/variable no. of division: 4, 5/variable

Input [x1*, x2

*]T Input [x1*, x2

*]T x1^ x2

^[ , ]T[ , ]T

3011 WW


CMAC MLNN

memory size Large Small

learning speed Fast Slow

computing mode Local Global

• CMAC vs. MLNN• CMAC vs. MLNN

items

real-time application Feasible Impossible


Vibration Control using CMAC

structure

external load

CMACCMAC

learning rule

sensor


• Control criterion: cost function• Control criterion: cost function

1

0112

1 fN

kk

Tkk

TkJ RuuQzz (1)

fNk

RQuz,, : state, control vector

: relative weighting matrix: time step: final time step

: state, control vector: relative weighting matrix: time step: final time step


kTkk

TkkJ RuuQzz 112

1

: learning rate: learning rate

kikiki WWW ,,1,

(2)

(3)

(5)

Ru

u

zQz T

kk

kTkkiW

11,

• Learning rule• Learning rule

i

kki W

JW

, (4)


3. NUMERICAL EXAMPLES3. NUMERICAL EXAMPLES

Model structure

Three-story building with Active Mass DriverThree-story building with Active Mass Driver


: Mass matrix: Damping matrix: Restoring force : Location vector

: displacement vector: ground acceleration: control force

(6) gxLf 1M)xK(x,xCxM

L

K

C

M

f

xgx

• Equation of motion• Equation of motion


dykxkxk 00 )1()(

)(1 1 pp

yxyyxxd

y

0k : linear stiffness

: contribution of k0

• Nonlinear restoring force (Bouc-Wen, 1981)• Nonlinear restoring force (Bouc-Wen, 1981)

(7)

(8)


mass

pump

• Active Mass Driver (AMD)• Active Mass Driver (AMD)

piston


mass : 200kg (story)stiffness : 2.25105 N/m(inter-story)damping : 0.6, 0.7, 0.3% (modal)

mass : 18kg (3% of building mass)stiffness : 3.71103 N/mdamper : 8.65%

Structure

AMD

• Parameters• Parameters


CMAC structure

input: 2 (disp., vel. of 3rd floor)

output: 1 (control signal)

no. of division: 3/variable

no. of meshes: 200

no. of weights: 1800

input: 2 (disp., vel. of 3rd floor)

output: 1 (control signal)

no. of division: 3/variable

no. of meshes: 200

no. of weights: 1800


integration time: 0.25msec

sampling time: 5.0msec

delay time: 0.5msec

Simulation


• Learning during El Centro earthquake (linear case)• Learning during El Centro earthquake (linear case)

※1 Epoch = 0.005sec × 2000 steps ※1 Epoch = 0.005sec × 2000 steps

CMAC

MLNN

0 100 200 300 400 500Epoch

0.0

0.1

0.2

0.3

Cos

t fun

ctio

n


• Minimum costs • Minimum costs

neural network Jmin (ratio) neural network Jmin (ratio)

MLNN 1.77 10-2 (1.00) MLNN 1.77 10-2 (1.00)

CMAC 1.94 10-2 (1.09) CMAC 1.94 10-2 (1.09)

• Epochs• Epochs

neural network epoch (ratio)neural network epoch (ratio)

MLNN 478 (1.00) MLNN 478 (1.00)

CMAC 65 (0.14) CMAC 65 (0.14)


Dis

plac

emen

t (m

)

w/o controlw/ control

0 5 10 15 20-0.10-0.050.000.050.10

Time (sec)

• Northridge earthquake (3rd floor)• Northridge earthquake (3rd floor)

0 5 10 15 20-1.00-0.500.000.501.00

Vel

ocity

(m/s

ec)


0 5 10 15 20-20.0-10.0

0.010.020.0

Acc

eler

atio

n (

m/s

ec2 )


Time (sec)

• Northridge earthquake (3rd floor) - continued• Northridge earthquake (3rd floor) - continued


• Kern County earthquake (3rd floor)• Kern County earthquake (3rd floor)

Time (sec)

0 5 10 15 20-0.10-0.050.000.050.10

Dis

plac

emen

t (m

)

0 5 10 15 20-1.00-0.500.000.501.00


Vel

ocity

(m/s

ec)


0 5 10 15 20-20.0-10.0

0.010.020.0

Acc

eler

atio

n (

m/s

ec2 )


Time (sec)

• Kern County earthquake (3rd floor) - continued• Kern County earthquake (3rd floor) - continued


5.0

0 100 200 300 400 500Epoch

0.0

0.1

0.2

0.3

Cos

t fun

ctio

n

• Learning during El Centro earthquake (nonlinear case, )• Learning during El Centro earthquake (nonlinear case, )

CMAC

MLNN


• Minimum costs• Minimum costs

neural network Jmin (ratio) neural network Jmin (ratio)

MLNN 1.91 10-2 (1.00) MLNN 1.91 10-2 (1.00)

CMAC 2.02 10-2 (1.06) CMAC 2.02 10-2 (1.06)

• Epochs• Epochs

neural network epoch (ratio)neural network epoch (ratio)

MLNN 484 (1.00) MLNN 484 (1.00)

CMAC 34 (0.07) CMAC 34 (0.07)


w/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

)

w/ control

• Northridge earthquake (1st floor)• Northridge earthquake (1st 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

)

• Kern County earthquake (1st floor)• Kern County earthquake (1st floor)

w/o control w/ control


• Performance comparison (El Centro, 3rd floor)• Performance comparison (El Centro, 3rd floor)

0 5 10 15 20-0.04-0.020.000.020.04

CMAC

MLNN

Dis

plac

emen

t (m

)

Time (sec)


4. CONCLUSIONS4. CONCLUSIONS

• Response controlled by CMAC is almost

same as that by MLNN.

• Learning speed of CMAC is much faster

than that of MLNN.

• Response controlled by CMAC is almost

same as that by MLNN.

• Learning speed of CMAC is much faster

than that of MLNN.


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


utqgg

tqgg

)(1

)(2121

21, gg

u

q

: oil flow rate: control signal: time constant: valve gains

• Pump dynamics• Pump dynamics

(9)


qfa

Vf

a

cxa

rr

lrr

2

: displacement of ram

: area of ram

: compression coefficient

: volume of cylinder

: leakage coefficientl

r

r

c

V

a

x

• Piston dynamics• Piston dynamics

(10)


BuAzz

B

A

u

z : state vector

: control force vector

: system matrix

: control matrix

: state vector

: control force vector

: system matrix

: control matrix)(

)(

)1(

)1(

mn

nn

m

n

(s-1)

• Sensitivity Evaluation• Sensitivity Evaluation

• State equation• State equation


kkk HuGzz 1

sTeAG

(s-2)

(s-3)

(s-4)

sT : sampling time: sampling time

BAH A 1 Ie sT

Hu

z

k

k 1 (s-5)

• Discretized equation using ZOH• Discretized equation using ZOH

• Sensitivity matrix• Sensitivity matrix


kkk HuGzz 1

][0z k

mjijif

ijifkj ~1

)(0

)(1,

u

ik hz 1

initial condition:initial condition:

loading condition:loading condition:

measurement: measurement:

(s-6)

(s-7)

(s-8)

(s-9)

• Computation of H• Computation of H


Method Time Method Time

Emulator minutes ~ hours Emulator minutes ~ hours

Proposed m sampling time Proposed m sampling time

Evaluation timeEvaluation time

mi hhhhH 21 (s-10)


1

1

2

1

1n

i

n

j

eji

ji

ee WW

JJJ

1

0,

fN

k

ekji

eji WW

(c-1)

(c-2)

(c-3)

1

0

fN

kkJJ

1

0

fN

k ji

k

ji W

J

W

J

ji

kekji

W

JW

,

(c-4)

(c-5)

• Convergence of learning rule• Convergence of learning rule


(c-6)

(c-7)

(c-8)

1

1

2

1

21

1

1n

i

n

j

N

k ji

keef

W

JJJ

eee JJJ 1

)0(1

1

2

1

21

1

n

i

n

j

N

k ji

kef

W

JJ

minlim JJ ee

(c-9)

Inserting (3), (4) into (2)

* dong-hyawn kim: graduate student, kaist ju-won oh: professor, hannam university ju-won oh:...

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