Sang-Won Cho* : Ph.D. Student, KAIST Sang-Won Cho* : Ph.D. Student, KAIST Dong-Hyawn Kim: Senior Researcher, KORDI Dong-Hyawn Kim: Senior Researcher, KORDI In-Won Lee: Professor, KAIST In-Won Lee: Professor, KAIST Neuro-Control of Structures Using CMAC APCOM’01 Sydney, Australia November 20-23, 2001

1 Structural Dynamics & Vibration Control Lab., KAIST, Korea CONTENTS * Cerebellar Model Articulation Controller Introduction Introduction CMAC * for Vibration Control CMAC * for Vibration Control Numerical Examples Numerical Examples Conclusions Conclusions

2 Structural Dynamics & Vibration Control Lab., KAIST, Korea mathematical model is not required in designing controller - Advantage of neural network for structural control Background Background - Application areas control of structures with uncertainty or nonlinearity - Features of neural network promising tool in many fields of engineering Introduction Introduction

3 Structural Dynamics & Vibration Control Lab., KAIST, Korea structure external load neural network sensor response - Neural network should be trained before it works Structural Control Using Neural Network Structural Control Using Neural Network

4 Structural Dynamics & Vibration Control Lab., KAIST, Korea Multilayer Neural Network (MLNN) Multilayer Neural Network (MLNN) controlforce W ij : weights state of structure(displacement, velocity) velocity) - Weight should be determined by learning process - Training process is too slow to be used for on-line controller inputlayeroutputlayer hiddenlayer

5 Structural Dynamics & Vibration Control Lab., KAIST, Korea H. M. Chen et al. (1995). ASCE J. Comp. in Civil Eng.H. M. Chen et al. (1995). ASCE J. Comp. in Civil Eng. J. Ghaboussi et al. (1995). ASCE J. Eng. Mech.J. Ghaboussi et al. (1995). ASCE J. Eng. Mech. K. Nikzad et al. (1996). ASCE J. Eng. Mech.K. Nikzad et al. (1996). ASCE J. Eng. Mech. K. Bani-Hani et al. (1998). ASCE J. Eng. Mech.K. Bani-Hani et al. (1998). ASCE J. Eng. Mech. J. T. Kim et al. (2000). ASCE J. Eng. Mech.J. T. Kim et al. (2000). ASCE J. Eng. Mech. Previous Studies Previous Studies - All methods are based on multilayer neural network, whose learning speed is too slow - New neural network with fast learning speed is required !!

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

7 Structural Dynamics & Vibration Control Lab., KAIST, Korea CMAC -proposed by J. S. Albus(1975) -a neural network with fast learning speed -mainly used for manipulator control Application of CMAC for Vibration Control Proposed Method :

8 Structural Dynamics & Vibration Control Lab., KAIST, Korea input space output space x  memory space W1W1 W2W2 WnWn   u u Procedure of CMAC weights Displacement, velocity control signal - Learning to determine the weights is done locally - Due to the locality of learning, the learning time of CMAC could be dramatically reduced

9 Structural Dynamics & Vibration Control Lab., KAIST, Korea Output Calculation (1) Output Calculation (1) u = W 12 +W 22 +W 32 +W 42 u = W 12 +W 22 +W 32 +W 42 x W 11 W 12 W 13 W 14 W 11 W 12 W 13 W 14 W 21 W 22 W 23 W 24 W 21 W 22 W 23 W 24 W 31 W 32 W 33 W 34 W 31 W 32 W 33 W 34 W 41 W 42 W 43 W 44 W 41 W 42 W 43 W 44 x1x1x1x1 layer 1 layer 2 layer 3 layer 4 input (output)

10 Structural Dynamics & Vibration Control Lab., KAIST, Korea Output Calculation (2) Output Calculation (2) u = W 13 +W 23 +W 32 +W 42 u = W 13 +W 23 +W 32 +W 42 x W 11 W 12 W 13 W 14 W 11 W 12 W 13 W 14 W 21 W 22 W 23 W 24 W 21 W 22 W 23 W 24 W 31 W 32 W 33 W 34 W 31 W 32 W 33 W 34 W 41 W 42 W 43 W 44 W 41 W 42 W 43 W 44 x 1 x 2 layer 1 layer 2 layer 3 layer 4 input - By information-sharing, the required size of memory can be considerably decreased (output)

11 Structural Dynamics & Vibration Control Lab., KAIST, Korea CMAC MLNN memory size large small learning speed fast slow computing mode local global General Features of CMAC vs. MLNN General Features of CMAC vs. MLNN Items real-time application suitable impossible

12 Structural Dynamics & Vibration Control Lab., KAIST, Korea Vibration Control using CMAC Vibration Control using CMAC structure external load CMAC learningrule sensor response - CMAC should be trained before it works - Learning rule is required to train CMAC

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

14 Structural Dynamics & Vibration Control Lab., KAIST, Korea : learning rate (2) (3) Learning Rule Learning Rule (4) -The cost at the k th step -The weight is updated through -Gradient descent rule -Learning rule is derived by minimizing the cost

15 Structural Dynamics & Vibration Control Lab., KAIST, Korea (5) proposedmethod -Final learning rule

16 Structural Dynamics & Vibration Control Lab., KAIST, Korea Numerical Examples Numerical Examples Model Structure Model Structure AMD

17 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 Equation of Motion

18 Structural Dynamics & Vibration Control Lab., KAIST, Korea : linear stiffness : contribution of k 0 : constants Nonlinear Restoring Force Nonlinear Restoring Force (Bilinear hysteresis model, Bouc-Wen, 1981) (Bilinear hysteresis model, Bouc-Wen, 1981) (7) (8)

19 Structural Dynamics & Vibration Control Lab., KAIST, Korea Effect of Parameters : Effect of Parameters :

20 Structural Dynamics & Vibration Control Lab., KAIST, Korea mass pump Active Mass Driver (AMD) piston The dynamic of pump and piston are considered in the simulation

21 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 Parameters

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

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

24 Structural Dynamics & Vibration Control Lab., KAIST, Korea Case Studies 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 modellinearnonlinear

25 Structural Dynamics & Vibration Control Lab., KAIST, Korea Linear Cases (  =1.0) Linear Cases (  =1.0) ※ 1 Epoch = s × 2000 steps ※ 1 Epoch = s × 2000 steps CMACMLNN - Convergence of two neural networks

26 Structural Dynamics & Vibration Control Lab., KAIST, Korea - Minimum Cost and Epoch MLNNCMAC 1.94  (1.09) (0.15) (1.09) (0.15) 1.77   (1.00) (1.00) (1.00) (1.00) J min epoch neuralnetwork

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

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

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

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

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

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

33 Structural Dynamics & Vibration Control Lab., KAIST, Korea CMACMLNN Nonlinear Cases (  =0.5) Nonlinear Cases (  =0.5) - Convergence of two neural networks

34 Structural Dynamics & Vibration Control Lab., KAIST, Korea MLNNCMAC 2.02  (1.06) (0.08) (1.06) (0.08) 1.91   (1.00) (1.00) (1.00) (1.00) J min epoch neuralnetwork - Minimum Cost and Epoch

35 Structural Dynamics & Vibration Control Lab., KAIST, Korea - El Centro Earthquake (1 st floor) w/o control w/ control ( CMAC )

36 Structural Dynamics & Vibration Control Lab., KAIST, Korea w/o control - Northridge Earthquake (1 st floor) w/ control ( CMAC )

37 Structural Dynamics & Vibration Control Lab., KAIST, Korea - Kern County Earthquake (1 st floor) w/o control w/ control ( CMAC )

38 Structural Dynamics & Vibration Control Lab., KAIST, Korea Comparison of Control Results (linear, 3rd floor) Comparison of Control Results (linear, 3rd floor) El Centro El Centro Northridge Kern County Displacement (m) MLNNCMAC Time (sec)

39 Structural Dynamics & Vibration Control Lab., KAIST, Korea Comparison of Control Results (nonlinear, 3rd floor) Comparison of Control Results (nonlinear, 3rd floor) El Centro El Centro Northridge Kern County Displacement (m) MLNNCMAC Time (sec)

40 Structural Dynamics & Vibration Control Lab., KAIST, Korea Maximum Responses of 3rd floor (cm) Maximum Responses of 3rd 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) (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 Earthquake w/o control w/ control CMAC MLNN CMAC MLNN El Centro Northridge Kern County El Centro Northridge Kern County

41 Structural Dynamics & Vibration Control Lab., KAIST, Korea Conclusions Conclusions CMAC is applied to structural control. CMAC is applied to structural control. Both CMAC and MLNN reduce the dynamic Both CMAC and MLNN reduce the dynamic responses. responses. CMAC : 59~71% 27~64% CMAC : 59~71% 27~64% MLNN : 67~79% 33~70% MLNN : 67~79% 33~70% Learning speed of CMAC is much faster than Learning speed of CMAC is much faster than that of MLNN. that of MLNN. 15% for linear, 8% for nonlinear 15% for linear, 8% for nonlinear Response controlled by CMAC is larger than Response controlled by CMAC is larger than that by MLNN. that by MLNN. 155% for linear, 135% for nonlinear 155% for linear, 135% for nonlinear for linear for nonlinear

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

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