1. VIBRATION CONTROL OF STRUCTURE USING CMAC
ICSSD 2000
VIBRATION CONTROL OF STRUCTURE USING CMAC
* Dong-Hyawn Kim: Postdoctoral Researcher, KAIST
Kyu-Hong Shim: Postdoctoral Researcher, KAIST
In-Won Lee: Professor, KAIST
Jong-Heon Lee: Professor, Kyungil University

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 output space x   u W1 W2
 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
W W W W14
W W W W24
W W W W34
W W W W44
output W12+W22+W32+W42
Structural Dynamics & Vibration Control Lab., KAIST, Korea

11. Output calculation (2) x1 x2 input x layer 1 layer 2 layer 3 layer 4
W W W W14
W W W W24
W W W W34
W W W 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
real-time application
Feasible Impossible
Structural Dynamics & Vibration Control Lab., KAIST, Korea

13. Vibration Control using CMAC
learning
rule
external load
structure
response
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 proposed method (2) (3) (4) : learning rate (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 k : 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 AMD
mass : kg (story) stiffness : 105 N/m (inter-story) damping ratios : 0.6, 0.7, 0.3% (modal)
AMD
mass : kg (3% of building total mass) stiffness : 103 N/m damping ratio : %
Structural Dynamics & Vibration Control Lab., KAIST, Korea

22. CMAC structure input: 2 (disp., vel. of 3rd floor)
output: (control signal)
no. of divisions: 3 per variable
no. of layers:
no. of weights:
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

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

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

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

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

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

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

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

34. Training results Jmin epoch neural network MLNN 1.91  10-2 427 CMAC
1.91 
(1.00) (1.00)
2.02 
(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. 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

39. 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

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
(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)
linear nonlinear
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. Thank you for your attention.
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

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

49. Emulator minutes ~ hours
Evaluation time
Method Time
Emulator minutes ~ hours
Proposed m sampling time
Structural Dynamics & Vibration Control Lab., KAIST, Korea

50. Convergence of learning rule
Structural Dynamics & Vibration Control Lab., KAIST, Korea

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