모달변위를 이용한 지진하중을 받는 구조물의 능동 신경망제어 2004 년도 한국전산구조공학회 춘계 학술발표회 국민대학교 2004 년 4 월 10 일 이헌재, 한국과학기술원 건설및환경공학과 박사과정 정형조, 세종대학교 토목환경공학과 조교수 이종헌, 경일대학교 토목공학과 교수 이인원, 한국과학기술원 건설 및 환경공학과 교수

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

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

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

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

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

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

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

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

10 10 Structural Dynamics & Vibration Control Lab., KAIST, Korea 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

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

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

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

14 14 Structural Dynamics & Vibration Control Lab., KAIST, Korea 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 (1) 3(2)(6) 4(3)(7)(10) 5(4)(8)(11)(13) 6(5)(9)(12)(14)(15)

15 15 Structural Dynamics & Vibration Control Lab., KAIST, Korea Procedure of numerical analysis Training El Centro earthquake ( 0 ~ 8 sec ) Accel. (m/sec 2 ) Time(sec) Accel. (m/sec 2 ) Kobe (PGA: 0.834g) Verification El Centro earthquake California earthquake Kobe earthquake California (PGA: 0.156g) El Centro (PGA: 0.348g)

16 16 Structural Dynamics & Vibration Control Lab., KAIST, Korea 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) Evaluation Criteria

17 17 Structural Dynamics & Vibration Control Lab., KAIST, Korea Results of the conventional neuro-controller S 3SS 4SFF 5SFFF 6SSFFF 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.

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

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

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

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

22 22 Structural Dynamics & Vibration Control Lab., KAIST, Korea Results of the proposed neuro-controller J1J1 J2J2 J3J3 J4J Total consuming time for training proposed neuro- controller is 12 hours. Evaluation criteria of the proposed neuro-controller

23 23 Structural Dynamics & Vibration Control Lab., KAIST, Korea Comparison in Evaluation criteria Control Strategy J1J1 J2J2 J3J3 J4J4 NC(active) MNC(active) El Centrol earthquake Time(sec) Displacement (cm) Displacement of the 6 th floor under El Centro earthquake

24 24 Structural Dynamics & Vibration Control Lab., KAIST, Korea Verifications Control Strategy J1J1 J2J2 J3J3 J4J4 NC(active) MNC(active) California earthquake Time(sec) Displacement (cm) Displacement of the 6 th floor under California earthquake

25 25 Structural Dynamics & Vibration Control Lab., KAIST, Korea Control Strategy J1J1 J2J2 J3J3 J4J4 NC(active) MNC(active) Kobe earthquake Time(sec) Displacement (cm) Displacement of the 6 th floor under Kobe earthquake

26 26 Structural Dynamics & Vibration Control Lab., KAIST, Korea 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 !

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