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* 김동현 : KAIST 토목공학과 , 박사후연구원 오주원 : 한남대학교 토목환경공학과 , 교수 이규원 : 전북대학교 토목환경공학과 , 교수

토목학회 2000 학술발표회. CMAC 신경망을 이용한 구조물의 진동제어. * 김동현 : KAIST 토목공학과 , 박사후연구원 오주원 : 한남대학교 토목환경공학과 , 교수 이규원 : 전북대학교 토목환경공학과 , 교수 이인원 : KAIST 토목공학과 , 교수. CONTENTS. 1 INTRODUCTION 2 CMAC * FOR VIBRATION CONTROL 3 NUMERICAL EXAMPLES 4 CONCLUSIONS.

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* 김동현 : KAIST 토목공학과 , 박사후연구원 오주원 : 한남대학교 토목환경공학과 , 교수 이규원 : 전북대학교 토목환경공학과 , 교수

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  1. 토목학회 2000 학술발표회 CMAC 신경망을 이용한 구조물의 진동제어 *김동현: KAIST 토목공학과, 박사후연구원 오주원: 한남대학교 토목환경공학과, 교수 이규원: 전북대학교 토목환경공학과, 교수 이인원: KAIST 토목공학과, 교수

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

  3. 1 INTRODUCTION • Background • Features of neural network control • mathematical model is not required in designing controller • Application areas - control of structures with uncertainty or nonlinearity Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

  6. Previous studies 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. - All methods are based on multilayer neural network, whose learning speed is too slow Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  8. 2 CMAC FOR VIBRATION CONTROL • CMAC - proposed by J. S. Albus(1975) - a neural network with fast learning speed - mainly used for manipulator control Structural Dynamics & Vibration Control Lab., KAIST, Korea

  9. Procedure of CMAC memory space input space W1 output space W2 W3 x   u  displacement velocity Wn-1 control signal Wn weights Structural Dynamics & Vibration Control Lab., KAIST, Korea

  10. Output calculation (1) x1 input x layer 1 layer 2 layer 3 layer 4 W11 W12 W13 W14 W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44 output W12+W22+W32+W42 Structural Dynamics & Vibration Control Lab., KAIST, Korea

  11. Output calculation (2) x1x2 input x layer 1 layer 2 layer 3 layer 4 W11 W12 W13 W14 W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44 output W13+W23+W32+W42 Structural Dynamics & Vibration Control Lab., KAIST, Korea

  12. CMAC vs. MLNN items CMAC MLNN memory size Large Small computing mode Local Global learning speed Fast Slow Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

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

  18. Nonlinear restoring force • (Bouc-Wen, 1981) (7) (8) : linear stiffness : contribution of k0: constants Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

  21. Parameters Structure mass : 200 kg (story)stiffness : 2.25105 N/m (inter-story)damping ratios : 0.6, 0.7, 0.3% (modal) AMD mass : 18 kg (3% of building total mass)stiffness : 3.71103 N/mdamping ratio :8.65% Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  23. Simulation integration time: 0.25 mssampling time: 5.0 msdelay time: 0.5 ms Structural Dynamics & Vibration Control Lab., KAIST, Korea

  24. Case studies model linear nonlinear earthquake simulation El Centro trainEl Centro controlNorthridge controlKern County control El Centro trainEl Centro control Northridge controlKern County control Structural Dynamics & Vibration Control Lab., KAIST, Korea

  25. CMAC MLNN • Linear cases (=1.0) • training under El Centro earthquake ※1 Epoch = 0.005 s × 2000 steps Structural Dynamics & Vibration Control Lab., KAIST, Korea

  26. Training results Jmin epoch neural network MLNN CMAC 1.77  10-2 412 (1.00) (1.00) 1.94  10-2 65 (1.09)(0.15) Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  28. w/o control w/ control • El Centro earthquake (3rd floor) - continued Acceleration (m/sec2) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  30. w/o control w/ control • Northridge earthquake (3rd floor) - continued Acceleration (m/sec2) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  32. w/o control w/ control • Kern County earthquake (3rd floor) - continued Acceleration (m/sec2) Time (sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  34. Training results Jmin epoch neural network MLNN CMAC 1.91  10-2 427 (1.00) (1.00) 2.02  10-2 34 (1.06)(0.08) Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

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

  40. Maximum responses of 3rd floor (cm) w/ control CMAC MLNN Earthquake w/o control El Centro Northridge Kern County El Centro Northridge Kern County 5.01 2.06 1.65 (3.04) (1.24) (1.00) 6.15 2.14 1.38 (4.46) (1.55) (1.00) 3.42 0.97 0.72 (4.75) (1.35) (1.00) 3.48 2.54 2.34 (1.49) (1.09) (1.00) 3.94 2.20 1.63 (2.42) (1.35) (1.00) 2.68 0.97 0.80 (3.35) (1.21) (1.00) linearnonlinear Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

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

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

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

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

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

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

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