* 김동현 : KAIST 토목공학과, 박사후연구원 오주원 : 한남대학교 토목환경공학과, 교수 오주원 : 한남대학교 토목환경공학과, 교수 이규원 : 전북대학교 토목환경공학과, 교수 이규원 : 전북대학교 토목환경공학과, 교수 이인원 : KAIST 토목공학과, 교수 이인원 : KAIST 토목공학과, 교수 CMAC 신경망을 이용한 지진시 구조물의 진동제어 지진공학회 2000 추계학술발표회

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

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 response

4 Structural Dynamics & Vibration Control Lab., KAIST, Korea Multilayer Neural Network (MLNN) control force W ij W ij : weights state of structure (displacement) (velocity)

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

6 Structural Dynamics & Vibration Control Lab., KAIST, Korea * Cerebellar Model Articulation Controller Objective and Scope -To reduce learning time, we apply CMAC * neural network for structural control

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

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 weights displacement velocity control signal

9 Structural Dynamics & Vibration Control Lab., KAIST, Korea Output calculation (1) output W 12 +W 22 +W 32 +W 42 x W 11 W 12 W 13 W 14 W 21 W 22 W 23 W 24 W 31 W 32 W 33 W 34 W 41 W 42 W 43 W 44 x1x1 layer 1 layer 2 layer 3 layer 4 input

10 Structural Dynamics & Vibration Control Lab., KAIST, Korea Output calculation (2) output W 13 +W 23 +W 32 +W 42 x W 11 W 12 W 13 W 14 W 21 W 22 W 23 W 24 W 31 W 32 W 33 W 34 W 41 W 42 W 43 W 44 x 1 x 2 layer 1 layer 2 layer 3 layer 4 input

11 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

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

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

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

15 Structural Dynamics & Vibration Control Lab., KAIST, Korea 3. NUMERICAL EXAMPLES Model structure

16 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

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

18 Structural Dynamics & Vibration Control Lab., KAIST, Korea Effect of parameters

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

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

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

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

23 Structural Dynamics & Vibration Control Lab., KAIST, Korea Case studies earthquake simulation El Centro train El Centro control Northridge control Kern County control El Centro train El Centro control Northridge control Kern County control model linear nonlinear

24 Structural Dynamics & Vibration Control Lab., KAIST, Korea Linear cases (  =1.0) ※ 1 Epoch = s × 2000 steps CMAC MLNN training under El Centro earthquake

25 Structural Dynamics & Vibration Control Lab., KAIST, Korea Training results MLNN CMAC 1.94  (1.09) (0.15) 1.77  (1.00) (1.00) J min epoch neural network

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

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

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

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

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

31 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

32 Structural Dynamics & Vibration Control Lab., KAIST, Korea Learning under El Centro earthquake CMAC MLNN Nonlinear cases (  =0.5)

33 Structural Dynamics & Vibration Control Lab., KAIST, Korea MLNN CMAC 2.02  (1.06) (0.08) 1.91  (1.00) (1.00) Training results J min epoch neural network

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

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

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

37 Structural Dynamics & Vibration Control Lab., KAIST, Korea Comparison of control results (linear, 3 rd floor) El Centro Northridge Kern County Displacement (m) MLNN CMAC Time (sec)

38 Structural Dynamics & Vibration Control Lab., KAIST, Korea Comparison of control results (nonlinear, 3 rd floor) El Centro Northridge Kern County Displacement (m) MLNN CMAC Time (sec)

39 Structural Dynamics & Vibration Control Lab., KAIST, Korea Maximum responses of 3 rd floor (cm) linear nonlinear (3.04) (1.24) (1.00) (4.46) (1.55) (1.00) (4.75) (1.35) (1.00) (1.49) (1.09) (1.00) (2.42) (1.35) (1.00) (3.35) (1.21) (1.00) Earthquake w/o control w/ control CMAC MLNN El Centro Northridge Kern County

40 Structural Dynamics & Vibration Control Lab., KAIST, Korea 4. CONCLUSIONS Learning speed of CMAC is much faster than that of MLNN. Response controlled by CMAC is slightly larger than that by MLNN.

41 Structural Dynamics & Vibration Control Lab., KAIST, Korea Future work Further reduction of response controlled by CMAC with fast learning speed.

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

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

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

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

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

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

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

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

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