* Dong-Hyawn Kim: Graduate Student, KAIST Ju-Won Oh: Professor, Hannam University Ju-Won Oh: Professor, Hannam University In-Won Lee: Professor, KAIST In-Won Lee: Professor, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST Kyu-Hong Shim: Postdoctoral Researcher, KAIST STRUCTURAL CONTROL USING CMAC NEURAL NETWORK Nha Trang 2000 Nha Trang, Vietnam, Aug , 2000

1 Structural Dynamics & Vibration Control Lab., KAIST, Korea 1 INTRODUCTION 2 CMAC FOR VIBRATION CONTROL 3 NUMERICAL EXAMPLES 4 CONCLUSIONS CONTENTS

2 Structural Dynamics & Vibration Control Lab., KAIST, Korea 1 INTRODUCTION - mathematical model is not required in designing controller Features of neural network control Background Application areas - control of structures with uncertainty or nonlinearity

3 Structural Dynamics & Vibration Control Lab., KAIST, Korea structure external load neural network sensor Structural control using neural network

4 Structural Dynamics & Vibration Control Lab., KAIST, Korea Multilayer neural network (MLNN) training is too slow control force state of structure weights to be adjusted

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

6 Structural Dynamics & Vibration Control Lab., KAIST, Korea Objective and Scope - apply CMAC * neural network to structural control to reduce learning time. - compare performance of CMAC with multilayer neural network. * Cerebellar Model Articulation Controller

7 Structural Dynamics & Vibration Control Lab., KAIST, Korea Introduction 2 CMAC FOR VIBRATION CONTROL - proposed by J. S. Albus(1975) - a neural network with fast learning speed - mainly used for manipulator control CMAC

8 Structural Dynamics & Vibration Control Lab., KAIST, Korea input space output space x  memory space W1W1 W2W2 W3W3 W n-1 WnWn   u u Procedure of CMAC weight displacement velocity control signal

9 Structural Dynamics & Vibration Control Lab., KAIST, Korea x2x2 x1x1 W 13 W 14 W 15 W 16 W 9 W 10 W 11 W 12 W 5 W 6 W 7 W 8 W 1 W 2 W 3 W 4 x1x1 x2x2 (quantization mesh) Block quantization of input space W 37 W 38 W 39 W 40 W 41 W 32 W 33 W 34 W 35 W 36 W 27 W 28 W 29 W 30 W 31 W 22 W 23 W 24 W 25 W 26 W 17 W 18 W 19 W 20 W 21 (made by shifting left mesh) block size shifting

10 Structural Dynamics & Vibration Control Lab., KAIST, Korea x2x2 x1x1 W 13 W 14 W 15 W 16 W 9 W 10 W 11 W 12 W 5 W 6 W 7 W 8 W 1 W 2 W 3 W 4 x1x1 x2x2 1st mesh Activation of weights-(1) W 37 W 38 W 39 W 40 W 41 W 32 W 33 W 34 W 35 W 36 W 27 W 28 W 29 W 30 W 31 W 22 W 23 W 24 W 25 W 26 W 17 W 18 W 19 W 20 W 21 x1*x1* x2*x2* x1*x1* x2*x2* 2nd mesh input: [x 1 *, x 2 * ] T output:[ W 11 + W 34 ]

11 Structural Dynamics & Vibration Control Lab., KAIST, Korea x2x2 x1x1 W 13 W 14 W 15 W 16 W 9 W 10 W 11 W 12 W 5 W 6 W 7 W 8 W 1 W 2 W 3 W 4 x1x1 x2x2 Activation of weights-(2) W 37 W 38 W 39 W 40 W 41 W 32 W 33 W 34 W 35 W 36 W 27 W 28 W 29 W 30 W 31 W 22 W 23 W 24 W 25 W 26 W 17 W 18 W 19 W 20 W 21 x1x1 ^ x2x2 ^ x1x1 ^ x2x2 ^ input: [, ] T x1x1 ^ x2x2 ^ output:[ W 11 + W 30 ] x2*x2* x1*x1* x1*x1* x2*x2* 1st mesh2nd mesh

12 Structural Dynamics & Vibration Control Lab., KAIST, Korea Weights [W 11, W 34 ] [W 11, W 30 ] no. of meshes: 2 Output Summary no. of weights: 41 no. of division: 4, 5/variable Input [x 1 *, x 2 * ] T x1x1 ^ x2x2 ^ [, ] T

13 Structural Dynamics & Vibration Control Lab., KAIST, Korea CMAC MLNN memory size Large Small learning speed Fast Slow computing mode Local Global CMAC vs. MLNN items real-time applicationFeasible Impossible

14 Structural Dynamics & Vibration Control Lab., KAIST, Korea Vibration Control using CMAC structure external load CMAC learning rule sensor

15 Structural Dynamics & Vibration Control Lab., KAIST, Korea Control criterion: cost function (1) : state, control vector : relative weighting matrix : time step : final time step

16 Structural Dynamics & Vibration Control Lab., KAIST, Korea : learning rate (2) (3) (5) Learning rule (4)

17 Structural Dynamics & Vibration Control Lab., KAIST, Korea 3. NUMERICAL EXAMPLES Model structure Three-story building with Active Mass Driver

18 Structural Dynamics & Vibration Control Lab., KAIST, Korea : Mass matrix : Damping matrix : Restoring force : Location vector : displacement vector : ground acceleration : control force (6) Equation of motion

19 Structural Dynamics & Vibration Control Lab., KAIST, Korea : linear stiffness : contribution of k 0 Nonlinear restoring force (Bouc-Wen, 1981) (7) (8)

20 Structural Dynamics & Vibration Control Lab., KAIST, Korea mass pump Active Mass Driver (AMD) piston

21 Structural Dynamics & Vibration Control Lab., KAIST, Korea mass : 200kg (story) stiffness : 2.25  10 5 N/m(inter-story) damping : 0.6, 0.7, 0.3% (modal) mass : 18kg (3% of building mass) stiffness : 3.71  10 3 N/m damper : 8.65% Structure AMD Parameters

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

23 Structural Dynamics & Vibration Control Lab., KAIST, Korea integration time: 0.25msec sampling time: 5.0msec delay time: 0.5msec Simulation

24 Structural Dynamics & Vibration Control Lab., KAIST, Korea Learning during El Centro earthquake (linear case) ※ 1 Epoch = 0.005sec × 2000 steps CMAC MLNN

25 Structural Dynamics & Vibration Control Lab., KAIST, Korea Minimum costs neural network J min (ratio) MLNN 1.77  (1.00) CMAC 1.94  (1.09) Epochs neural network epoch (ratio) MLNN 478 (1.00) CMAC 65 (0.14)

26 Structural Dynamics & Vibration Control Lab., KAIST, Korea Displacement (m) w/o control w/ control Time (sec) Northridge earthquake (3 rd floor) Velocity(m/sec)

27 Structural Dynamics & Vibration Control Lab., KAIST, Korea Acceleration (m/sec 2 ) w/o control w/ control Time (sec) Northridge earthquake (3 rd floor) - continued

28 Structural Dynamics & Vibration Control Lab., KAIST, Korea Kern County earthquake (3 rd floor) Time (sec) Displacement (m) w/o control w/ control Velocity(m/sec)

29 Structural Dynamics & Vibration Control Lab., KAIST, Korea Acceleration (m/sec 2 ) w/o control w/ control Time (sec) Kern County earthquake (3 rd floor) - continued

30 Structural Dynamics & Vibration Control Lab., KAIST, Korea Learning during El Centro earthquake (nonlinear case, ) CMAC MLNN

31 Structural Dynamics & Vibration Control Lab., KAIST, Korea Minimum costs neural network J min (ratio) MLNN 1.91  (1.00) CMAC 2.02  (1.06) Epochs neural network epoch (ratio) MLNN 484 (1.00) CMAC 34 (0.07)

32 Structural Dynamics & Vibration Control Lab., KAIST, Korea w/o controlw/ control Northridge earthquake (1 st floor)

33 Structural Dynamics & Vibration Control Lab., KAIST, Korea Kern County earthquake (1 st floor) w/o controlw/ control

34 Structural Dynamics & Vibration Control Lab., KAIST, Korea Performance comparison (El Centro, 3 rd floor) CMAC MLNN Displacement (m) Time (sec)

35 Structural Dynamics & Vibration Control Lab., KAIST, Korea 4. CONCLUSIONS Response controlled by CMAC is almost same as that by MLNN. Learning speed of CMAC is much faster than that of MLNN.

36 Structural Dynamics & Vibration Control Lab., KAIST, Korea Thank you for your attention.

37 Structural Dynamics & Vibration Control Lab., KAIST, Korea : oil flow rate : control signal : time constant : valve gains Pump dynamics (9)

38 Structural Dynamics & Vibration Control Lab., KAIST, Korea : displacement of ram : area of ram : compression coefficient : volume of cylinder : leakage coefficient Piston dynamics (10)

39 Structural Dynamics & Vibration Control Lab., KAIST, Korea : state vector : control force vector : system matrix : control matrix (s-1) Sensitivity Evaluation State equation

40 Structural Dynamics & Vibration Control Lab., KAIST, Korea (s-2) (s-3) (s-4) : sampling time (s-5) Discretized equation using ZOH Sensitivity matrix

41 Structural Dynamics & Vibration Control Lab., KAIST, Korea initial condition: loading condition: measurement: (s-6) (s-7) (s-8) (s-9) Computation of H

42 Structural Dynamics & Vibration Control Lab., KAIST, Korea Method Time Emulator minutes ~ hours Proposed m sampling time Evaluation time (s-10)

43 Structural Dynamics & Vibration Control Lab., KAIST, Korea (c-1) (c-2) (c-3) (c-4) (c-5) Convergence of learning rule

44 Structural Dynamics & Vibration Control Lab., KAIST, Korea (c-6) (c-7) (c-8) (c-9) Inserting (3), (4) into (2)