Aug 23 1999 Artificial Neural Networks for Structural

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Aug. 23, 1999. Artificial Neural Networks for Structural Vibration Control Ju-Tae Kim: Graduate Student,

Aug. 23, 1999. Artificial Neural Networks for Structural Vibration Control Ju-Tae Kim: Graduate Student, KAIST, Korea Ju-Won Oh: Professor, Hannam University, Korea In-Won Lee: Professor, KAIST, Korea 1

CONTENTS 1. Introduction 2. Neural Networks for Control 3. Numerical Examples 4. Conclusions 2

CONTENTS 1. Introduction 2. Neural Networks for Control 3. Numerical Examples 4. Conclusions 2

1. Introduction Conventional Control vs. ANN Control Model based conventional control Response based ANN

1. Introduction Conventional Control vs. ANN Control Model based conventional control Response based ANN control Mathematical model required not required Parametric uncertainty impossible/hard simple/easy Parametric variation impossible/hard simple/easy 3

 Previous Works on ANN Control in CE H. M. Chen et al. (1995),

Previous Works on ANN Control in CE H. M. Chen et al. (1995), J. Ghaboussi et al. (1995) - pioneering research in civil engineering K. Nikzad (1996) - delay compensation K. Bani-Hani et al. (1998) - nonlinear structural control Condition : desired response is to be pre-determined. 4

 Scope • Training rule of controller neural network • SDOF linear/nonlinear structural control

Scope • Training rule of controller neural network • SDOF linear/nonlinear structural control 5

2. Neural Networks for Control Two Neural Networks • Emulator neural network - trained

2. Neural Networks for Control Two Neural Networks • Emulator neural network - trained to imitate responses of unknown structures. - used for training of controller neural network. • Controller neural network - trained to make control force. - used for controller. 6

 Previous Studies Weights of controller neural network(W) are updated to minimize error function(E).

Previous Studies Weights of controller neural network(W) are updated to minimize error function(E). Emulator (ANN) Minimize error(E) Controller (ANN) U Load Z-1 Structure E=D-X X+ _ D (desired response) 7

 Proposed Method Weights of controller neural network(W) are updated to minimize cost function(J)

Proposed Method Weights of controller neural network(W) are updated to minimize cost function(J) instead of error function(E). Emulator (ANN) Minimize cost(J) Controller (ANN) U Structure X Load Z-1 8

 • Cost function (1) : response, control force vector where : weighting matrices

• Cost function (1) : response, control force vector where : weighting matrices 9

 • Controller neural network Wji Wkj Ii uk k=1~N i=1~L j=1~M hidden layer

• Controller neural network Wji Wkj Ii uk k=1~N i=1~L j=1~M hidden layer (2) (3) Output layer (4) (5) 10

 • Learning rule: weights of output-hidden layer (6) (7) 11

• Learning rule: weights of output-hidden layer (6) (7) 11

(8) (9) where (10) 12

(8) (9) where (10) 12

 • Learning rule: weights of hidden-input layer (11) (12) 13

• Learning rule: weights of hidden-input layer (11) (12) 13

(13) where (14) 14

(13) where (14) 14

3. Numerical Examples Control of Linear Structure • Equation of motion (15) : mass

3. Numerical Examples Control of Linear Structure • Equation of motion (15) : mass : damping : stiffness : displacement : ground acceleration : control force 15

 • State-space form (16) Let , then (17) 16

• State-space form (16) Let , then (17) 16

 • Parameters • Controller neural network 17

• Parameters • Controller neural network 17

 • Ground accelerations( ) TRAINED (a) El Centro earthquake(1940) UNTRAINED (b) California earthquake(1952)

• Ground accelerations( ) TRAINED (a) El Centro earthquake(1940) UNTRAINED (b) California earthquake(1952) UNTRAINED (c) Northridge earthquake(1994) 18

Cost function(J) • Minimization of cost function 2. 0 < 1. 5 1. 0

Cost function(J) • Minimization of cost function 2. 0 < 1. 5 1. 0 0. 5 0. 0 0 10 20 30 40 50 epoch 19

 • Control results (a) El Centro earthquake(trained) (b) California earthquake(untrained) 20

• Control results (a) El Centro earthquake(trained) (b) California earthquake(untrained) 20

(c) Northridge earthquake(untrained) 21

(c) Northridge earthquake(untrained) 21

 Control of Nonlinear Structure • Equation of motion (18) (19) (20) • Parameters

Control of Nonlinear Structure • Equation of motion (18) (19) (20) • Parameters 22

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 • Control results-1 (a) El Centro earthquake(trained) (b) California earthquake(untrained) 24

• Control results-1 (a) El Centro earthquake(trained) (b) California earthquake(untrained) 24

(c) Northridge earthquake(untrained) 25

(c) Northridge earthquake(untrained) 25

controlled uncontrolled • Control results-2 (a) El Centro earthquake (b) California earthquake (c) Northridge

controlled uncontrolled • Control results-2 (a) El Centro earthquake (b) California earthquake (c) Northridge earthquake 26

4. Conclusions • Training rule of neural network for optimal control is proposed. •

4. Conclusions • Training rule of neural network for optimal control is proposed. • Not only linear but nonlinear structure is controlled successfully. 27