신경망의 입력으로 모달응답을 이용한 지진하중을 받는 구조물의 능동 신경망제어

1. 2004년도 한국강구조공학회 춘계 학술발표회 단국대학교 서울캠퍼스 2004년 6월 5일 신경망의 입력으로 모달응답을 이용한 지진하중을 받는 구조물의 능동 신경망제어 이헌재, 한국과학기술원 건설 및 환경공학과 박사과정 조상원, 한국과학기술원 건설 및 환경공학과 박사후연구조교수 정형조, 세종대학교 토목환경공학과 조교수 이인원, 한국과학기술원 건설 및 환경공학과 교수

2. Contents • Introduction • Proposed Method • Numerical Example • Conclusions Structural Dynamics & Vibration Control Lab., KAIST, Korea

3. Introduction • Backgrounds • Ghaboussi et al.(1995) and Chen et al.(1995) • Neural network can be successfully applied to the control of large civil structures. • For the training of the network, the responses of a few future steps are predicted by the emulator neural network • One should predetermine the desired structural response for the training of a neuro-controller. Structural Dynamics & Vibration Control Lab., KAIST, Korea

4. Kim et al. (2000,2001) Predetermining the Desired Response New Training Algorithm using Cost Function Kim et al. (2000, 2001) Need of Emulator Neural Network Sensitivity Evaluation Algorithm Problems Solutions • Lee et al. (2003) • Applied Kim’s new neuro-controller to semi-active control using MR damper. Structural Dynamics & Vibration Control Lab., KAIST, Korea

5. Conventional Neuro-Controllers • One should determine which state variables is used as inputs of the neural network. • If the mathematical model’s DOF is large, there are so many combinations of the state variables. • Selecting state variables is very complicated and troublesome task for the designer. Structural Dynamics & Vibration Control Lab., KAIST, Korea

6. Proposed Neuro-Controller • adopts modal states as inputs of the neural network. • The modal states contain the information of the whole structural system’s behavior. • It is proper to use modal states as inputs of the neuro- controller. Structural Dynamics & Vibration Control Lab., KAIST, Korea

7. Conventional neuro-control (Kim et al.) The neuro-controller is trained by minimizing the cost function, . (1) : state vector : control signal : weighting matrices • Selecting state variables is very complicated and troublesome task for the designer. Structural Dynamics & Vibration Control Lab., KAIST, Korea

8. Proposed Method • The proposed neuro-controller is trained by minimizing the new cost function, . (2) : modal state vector : new weighting matrix • Conventional weighting matrix : New weighting matrix .: • It’s very simple, because there is no need to determine which state variable is used as inputs. Structural Dynamics & Vibration Control Lab., KAIST, Korea

9. By applying the gradient decent rule to the cost at k-th step, the update for the weight can be expressed as : training rate Using the chain rule, the partial derivative of Eq. (3) can be rewritten as Structural Dynamics & Vibration Control Lab., KAIST, Korea

10. Let’s define the generalized error as Finally, the weight update can be simply expressed as In Eq. (6), the gain factor, , satisfies The bias is also updated by Structural Dynamics & Vibration Control Lab., KAIST, Korea

11. In the same manner, updates for the weight and bias between input layer and hidden layer can be obtained as Structural Dynamics & Vibration Control Lab., KAIST, Korea

12. Numerical Example • six-story building structure (Dyke et al., 2000) Structural Dynamics & Vibration Control Lab., KAIST, Korea

13. Proposed neural network input output • Neural networks used in the numerical example Conventional neural network output input Structural Dynamics & Vibration Control Lab., KAIST, Korea

14. Initial weightings setup • 100 initial weightings are randomly chosen. • They are applied to both conventional and proposed neuro-controllers. • Combinations of the state variables as the input Structural Dynamics & Vibration Control Lab., KAIST, Korea

15. Procedure of numerical analysis El Centro (PGA: 0.348g) • Training • • El Centro earthquake • ( 0 ~ 8 sec ) Accel. (m/sec2) • Verification • • El Centro earthquake • • California earthquake • • Kobe earthquake California (PGA: 0.156g) Accel. (m/sec2) Kobe (PGA: 0.834g) Accel. (m/sec2) Time(sec) Structural Dynamics & Vibration Control Lab., KAIST, Korea

16. Evaluation Criteria Normalized maximum floor displacement Normalized maximum inter-story drift Normalized peak floor acceleration Maximum control force normalized by the weight of the structure • This evaluation criteria is used in the second generation linear • control problem for buildings (Spencer et al. 1997) Structural Dynamics & Vibration Control Lab., KAIST, Korea

17. Results of the conventional neuro-controller S : Successful training F : Failed training • Each combination takes about 12 hours for training. • Therefore, total consuming time for training conventional neuro-controller is 180 hours. Structural Dynamics & Vibration Control Lab., KAIST, Korea

18. J1 of the neuro-controller which gives the best performance • among the each successful trained neuro-controller S : Successful training F : Failed training Structural Dynamics & Vibration Control Lab., KAIST, Korea

19. J2 of the neuro-controller which gives the best performance • among the each successful trained neuro-controller S : Successful training F : Failed training Structural Dynamics & Vibration Control Lab., KAIST, Korea

20. J3 of the neuro-controller which gives the best performance • among the each successful trained neuro-controller S : Successful training F : Failed training Structural Dynamics & Vibration Control Lab., KAIST, Korea

21. Evaluation criteria of the each combination J1 J2 J3 Structural Dynamics & Vibration Control Lab., KAIST, Korea

22. Results of the proposed neuro-controller • Evaluation criteria of the proposed neuro-controller • Total consuming time for training proposed neuro-controller is 12 hours. Structural Dynamics & Vibration Control Lab., KAIST, Korea

23. Comparison in Evaluation criteria • El Centrol earthquake Displacement (cm) Time(sec) Displacement of the 6th floor under El Centro earthquake Structural Dynamics & Vibration Control Lab., KAIST, Korea

24. Verifications • California earthquake Displacement (cm) Time(sec) Displacement of the 6th floor under California earthquake Structural Dynamics & Vibration Control Lab., KAIST, Korea

25. • Kobe earthquake Displacement (cm) Time(sec) Displacement of the 6th floor under Kobe earthquake Structural Dynamics & Vibration Control Lab., KAIST, Korea

26. Conclusions • A new active neuro-control strategy for seismic reduction using modal states is proposed. • The performance of the proposed method is comparable with that of the conventional method. • The proposed method is more convenient and simple to use in comparison with conventional method. • ( Consuming time for training: 6.7 % lesser ) The proposed active neuro-control technique using modal states could be effectively used for control of seismically excited structures! Structural Dynamics & Vibration Control Lab., KAIST, Korea

27. Sensitivity evaluation algorithm (Kim et al., 2001) State space equation of structure (9) In the discrete-time domain, (10) where represents the sensitivity, . Structural Dynamics & Vibration Control Lab., KAIST, Korea