1 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 Aug. 23, 1999.

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

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

4  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.

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

6 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. 2. Neural Networks for Control  Two Neural Networks

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

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

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

10 Controller neural network hidden layer Output layer (2) (3) (4) (5) IiIi ukuk W ji W kj i=1~L j=1~M k=1~N

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

12 (8) (9) (10)where

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

14 (13) (14) where

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

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

17 Parameters Controller neural network

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

epoch < Cost function(J) Minimization of cost function

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

21 (c) Northridge earthquake(untrained)

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

23

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

25 (c) Northridge earthquake(untrained)

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

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