* 김동현 : kaist 토목공학과 , 박사후연구원 오주원 : 한남대학교...

** 김동현김동현 : KAIST : KAIST 토목공학과토목공학과 , , 박사후연구원박사후연구원 오주원오주원 : : 한남대학교 토목환경공학과한남대학교 토목환경공학과 , , 교수 교수 이규원이규원 : : 전북대학교 토목환경공학과전북대학교 토목환경공학과 , , 교수교수 이인원이인원 : KAIST : KAIST 토목공학과토목공학과 , , 교수교수

CMAC 신경망을 이용한 구조물의 진동제어

토목학회 토목학회 2000 2000 학술발표회학술발표회

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

1 INTRODUCTION

2 CMAC* FOR VIBRATION CONTROL

3 NUMERICAL EXAMPLES

4 CONCLUSIONS

CONTENTS

*Cerebellar Model Articulation Controller

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

response

• Multilayer Neural Network (MLNN)• Multilayer Neural Network (MLNN)

control forcecontrol force

state ofstructure

(displacement)(velocity)

state ofstructure

(displacement)(velocity)

WijWij

Wij : weightsWij : weights

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

Objective and Scope

- To reduce learning time, we apply CMAC*

neural network for structural control

*Cerebellar Model Articulation Controller

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

input space output

memory space

Procedure of CMAC

weights

displacementvelocity

control signal

• Output calculation (1)• Output calculation (1)

output W12+W22+W32+W42

W11 W12 W13 W14

W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44

layer 1

layer 2

layer 3

layer 4

• Output calculation (2)• Output calculation (2)

output W13+W23+W32+W42

W11 W12 W13 W14

W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44

layer 1

layer 2

layer 3

layer 4

CMAC MLNN

memory size Large Small

learning speed Fast Slow

computing mode Local Global

• CMAC vs. MLNN• CMAC vs. MLNN

Vibration Control using CMAC

structure

external load

CMACCMAC

learning rule

sensor

response

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

Tk1k1k

1J RuuQzzT (1)

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

T1kk 2

1J RuuQzz

: learning rate: learning rateη

ki,ki,1ki, WWW

1kT1kki, ηW

• Learning rule• Learning rule

kki, W

proposedmethodproposedmethod

3. NUMERICAL EXAMPLES3. NUMERICAL EXAMPLES

Model structure

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

: displacement vector: ground acceleration: control force

(6) gxLu 1M)xF(x,xCxM

• Equation of motion• Equation of motion

dykxkxf 00 )1()(

)(1 1 pp

yxyyxxd

: linear stiffness

: contribution of k0

: constants

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

• Effect of parameters

-0 .10 -0.05 0.00 0.05 0.10D isplacem ent (m )

6.0 600 k

395.055.0104.0

6.05.055.0104.0

395.055.0104.0

6.05.055.0104.0

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

piston

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

mass : 18 kg (3% of building total mass)stiffness : 3.71103 N/mdamping ratio : 8.65%

Structure

• Parameters• Parameters

CMAC structure

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

output: 1 (control signal)

no. of divisions: 3 per variable

no. of layers: 200

no. of weights: 1800

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

output: 1 (control signal)

no. of divisions: 3 per variable

no. of layers: 200

no. of weights: 1800

integration time: 0.25 ms

sampling time: 5.0 ms

delay time: 0.5 ms

Simulation

Case studiesearthquake simulation

El Centro trainEl Centro controlNorthridge controlKern County controlEl Centro trainEl Centro control Northridge controlKern County control

linear

nonlinear

• Linear cases (=1.0)• Linear cases (=1.0)

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

0 100 200 300 400 500Epoch

n • training under El Centro earthquake • training under El Centro earthquake

• Training results • Training results

Jmin epochJmin epoch

1.94 10-2 65 (1.09) (0.15)

1.77 10-2 412 (1.00) (1.00)

neuralnetworkneuralnetwork

w/o controlw/ control

• El Centro earthquake (3rd floor)• El Centro earthquake (3rd 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

Time (sec)

0 5 10 15 20-20.0-10.0

0.010.020.0

• El Centro earthquake (3rd floor) - continued• El Centro earthquake (3rd floor) - continuedA

Time (sec)

0 5 10 15 20-0.10-0.050.000.050.10

Time (sec)

0 5 10 15 20-1.00-0.500.000.501.00

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

0 5 10 15 20-20.0-10.0

0.010.020.0

Time (sec)

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

Time (sec)

0 5 10 15 20-0.10-0.050.000.050.10

0 5 10 15 20-1.00-0.500.000.501.00

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

0 5 10 15 20-20.0-10.0

0.010.020.0

Time (sec)

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

0 100 200 300 400 500Epoch

n • Learning under El Centro earthquake • Learning under El Centro earthquake

• Nonlinear cases (=0.5)• Nonlinear cases (=0.5)

Jmin epochJmin epoch

2.02 10-2 34 (1.06) (0.08)

1.91 10-2 427 (1.00) (1.00)

• Training results • Training results

neuralnetworkneuralnetwork

• El Centro earthquake (1st floor)• El Centro earthquake (1st floor)

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )

w/o control w/ control

5.05,5.01,01.0

w/o control

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )

w/ control

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

5.05,5.01,01.0

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0D isp lacem ent (cm )

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

w/o control w/ control

5.05,5.01,01.0

0 5 10 15 20-0.04

• Comparison of control results (linear, 3rd floor) • Comparison of control results (linear, 3rd floor)

El Centro El Centro

Northridge Northridge

Kern County Kern County

MLNNCMAC

Time (sec)

• Comparison of control results (nonlinear, 3rd floor) • Comparison of control results (nonlinear, 3rd floor)

El Centro El Centro

Northridge Northridge

Kern County Kern County

MLNNCMAC

Time (sec)

0 5 10 15 20-0.04

• Maximum responses of 3rd floor (cm)• Maximum responses of 3rd floor (cm)

linear

nonlinear

5.01 2.06 1.65 (3.04) (1.24) (1.00)

6.15 2.14 1.38 (4.46) (1.55) (1.00)

3.42 0.97 0.72 (4.75) (1.35) (1.00)

3.48 2.54 2.34 (1.49) (1.09) (1.00)

3.94 2.20 1.63 (2.42) (1.35) (1.00)

2.68 0.97 0.80 (3.35) (1.21) (1.00)

Earthquake w/o controlw/ control

CMAC MLNN

El Centro

Northridge

Kern County

El Centro

Northridge

Kern County

4. CONCLUSIONS4. CONCLUSIONS

• Learning speed of CMAC is much faster

than that of MLNN.

• Response controlled by CMAC is slightly

larger than that by MLNN.

• Learning speed of CMAC is much faster

than that of MLNN.

• Response controlled by CMAC is slightly

larger than that by MLNN.

Future workFuture work

• Further reduction of response controlled

by CMAC with fast learning speed.

• Further reduction of response controlled

by CMAC with fast learning speed.

)(2121

21, gg

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

• Pump dynamics• Pump dynamics

: displacement of ram

: area of ram

: compression coefficient

: volume of cylinder

: leakage coefficientl

• Piston dynamics• Piston dynamics

z : state vector

: control force vector

: system matrix

: control matrix

: state vector

: control force vector

: system matrix

: control matrix)(

• Sensitivity Evaluation• Sensitivity Evaluation

• State equation• State equation

kkk HuGzz 1

sT : sampling time: sampling time

BAH A 1 Ie sT

k 1 (s-5)

• Discretized equation using ZOH• Discretized equation using ZOH

• Sensitivity matrix• Sensitivity matrix

kkk HuGzz 1

][0z k

mjijif

ijifkj ~1

ik hz 1

initial condition:initial condition:

loading condition:loading condition:

measurement: measurement:

• 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)

eji WW

• Convergence of learning rule• Convergence of learning rule

eee JJJ 1

minlim JJ ee

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

* 김동현 : kaist 토목공학과 , 박사후연구원 오주원 : 한남대학교...

Documents

※소개순서 교수 가나다순 교수 세포간...

통섭적 지식인(정지훈 교수)

교수-학습 과정안(수학)

new innovation of urban water infrastructure in korea...

대한교통학회 제74회...

한국하천협회 신임 제4대 임원단 명단 ※...

2018 아주대학교요 - ajou.ac.kr ·...

제일병원 안현경 교수

기독교 학문 할 것인가?...길원평 (부산대...

조홍기 한국과학기술원 토목공학과 석사과정...

문법 교수 학습 방법의 실태와 개선 방안104 2....

캐나다 마더리스크프로그램연수기 - 최준식...

임신과당뇨병 - 김희숙 교수

2011년 원광대학교 토목환경공학과 특성...

정보보호학과 이정수 교수

제일병원 양광문 교수

1. 김효석 교수 프로필

마더세이프라운드 - 국립의료원 이소희 교수

강 영 종 교수 사회환경시스템 (...

한양대학교 박성주 교수