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Sang-Won Cho* : Ph.D. Student, KAIST Dong-Hyawn Kim: Senior Researcher, KORDI

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

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Sang-Won Cho* : Ph.D. Student, KAIST Dong-Hyawn Kim: Senior Researcher, KORDI

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

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

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

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

  5. Multilayer Neural Network (MLNN) hidden layer input layer output layer control force state of structure (displacement, velocity) Wij: weights • Weight should be determined by learning process- Training process is too slow to be used for on-line controller Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

  8. Proposed Method : Application of 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 output space W1 W2 x   u  Wn Displacement, velocity control signal weights • Learningto determine the weightsis done locally - Due to the locality of learning, the learning time of CMAC could be dramatically reduced Structural Dynamics & Vibration Control Lab., KAIST, Korea

  10. Output Calculation (1) x1 x input layer 1 layer 2 layer 3 layer 4 W11 W12 W13 W14 W21 W22 W23 W24 W31 W32 W33 W34 W41 W42 W43 W44 u = W12+W22+W32+W42 (output) 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 u = W13+W23+W32+W42 (output) • By information-sharing, the required size of memory can be considerably decreased Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

  16. Finallearning rule proposed method (5) Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

  18. 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

  19. Nonlinear Restoring Force (Bilinear hysteresis model, Bouc-Wen, 1981) (7) (8) : linear stiffness : contribution of k0: constants Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

  22. 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

  23. 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

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

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

  26. Linear Cases (=1.0) - Convergence of two neural networks CMAC MLNN ※1 Epoch = 0.005 s × 2000 steps Structural Dynamics & Vibration Control Lab., KAIST, Korea

  27. - Minimum Cost and Epoch 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

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

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

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

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

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

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

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

  35. - Minimum Cost and Epoch 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

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

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

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

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

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

  41. 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

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

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

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

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