Aug 23 1999 Artificial Neural Networks for Structural
- Slides: 27
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
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), 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 5
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). 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) 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 9
• 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
(8) (9) where (10) 12
• Learning rule: weights of hidden-input layer (11) (12) 13
(13) where (14) 14
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
• Parameters • Controller neural network 17
• 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 0. 5 0. 0 0 10 20 30 40 50 epoch 19
• Control results (a) El Centro earthquake(trained) (b) California earthquake(untrained) 20
(c) Northridge earthquake(untrained) 21
Control of Nonlinear Structure • Equation of motion (18) (19) (20) • Parameters 22
23
• Control results-1 (a) El Centro earthquake(trained) (b) California earthquake(untrained) 24
(c) Northridge earthquake(untrained) 25
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. • Not only linear but nonlinear structure is controlled successfully. 27
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