1. Structural Dynamics & Vibration Control Lab. 1 모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어 최강민, 한국과학기술원 건설 및 환경공학과 조상원, 한국과학기술원 건설 및 환경공학과 오주원, 한남대학교 토목공학과 이인원, 한국과학기술원 건설 및 환경공학과 2004 년도 한국전산구조공학회 춘계 학술발표회 국민대학교, 서울 2004 년 4 월 10 일

2. Structural Dynamics & Vibration Control Lab. 2 Outline Introduction Proposed Method Numerical Example Conclusions

3. Structural Dynamics & Vibration Control Lab. 3 Introduction Fuzzy theory has been recently proposed for the active structural control of civil engineering systems. The uncertainties of input data from the external loads and structural responses are treated in a much easier way by the fuzzy controller than by classical control theory. If offers a simple and robust structure for the specification of nonlinear control laws.

4. Structural Dynamics & Vibration Control Lab. 4 Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes. Because civil structures has hundred or even thousand DOFs and its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil engineering structure.

5. Structural Dynamics & Vibration Control Lab. 5 Conventional Fuzzy Controller One should determine state variables which are used as inputs of the fuzzy controller. - It is very complicated and difficult for the designer to select state variables used as inputs among a lot of state variables. One should construct the proper fuzzy rule. - Control performance can be varied according to many kinds of fuzzy rules.

6. Structural Dynamics & Vibration Control Lab. 6 Objectives Development of active fuzzy controller on modal coordinates - An active modal-fuzzy control algorithm can be magnified efficiency caused by belonging their’ own advantages together.

7. Structural Dynamics & Vibration Control Lab. 7 Proposed Method Modal Approach Equations of motion for MDOF system Using modal transformation Modal equations (1) (2) (3)

8. Structural Dynamics & Vibration Control Lab. 8 Displacement where State space equation where (4) (5)

9. Structural Dynamics & Vibration Control Lab. 9 Control force Modal approach is desirable for civil engineering structure - Involve hundred or thousand DOFs - Vibration is dominated by the first few modes (6)

10. Structural Dynamics & Vibration Control Lab. 10 Structure Modal Structure Fuzzy controller Force output Active Modal-fuzzy Control System

11. Structural Dynamics & Vibration Control Lab. 11 Modal-fuzzy control system design Input variables Output variables Fuzzification Defuzzification Fuzzy inference Fuzzy inference : membership functions, fuzzy rule Input variables : mode coordinates Output variable : desired control force

12. Structural Dynamics & Vibration Control Lab. 12 Six-Story Building (Jansen and Dyke 2000) Numerical Example

13. Structural Dynamics & Vibration Control Lab. 13 Frequency Response Analysis Under the scaled El Centro earthquake  10 2  10 4 PSD of Displacement PSD of Velocity PSD of Acceleration 1 st Floor 6 th Floor

14. Structural Dynamics & Vibration Control Lab. 14 In frequency analysis, the first mode is dominant. -The responses can be reduced by modal-fuzzy control using the lowest one mode.

15. Structural Dynamics & Vibration Control Lab. 15 Active Modal-fuzzy Controller Design input variables : first mode coordinates output variable : desired control force Fuzzy inference Membership function - A type : triangular shapes (inputs: 5MFs, output: 5MFs) - B type : triangular shapes (inputs: 5MFs, output: 7MFs)  A type : for displacement reduction B type : for acceleration reduction

16. Structural Dynamics & Vibration Control Lab. 16 Fuzzy rule - A type NLNSZEPSPL NLPL PMPSZE NSPLPMPSZENS ZEPMPSZENSNM PS ZENSNMNL PLZENSNMNL - B type NLNSZEPSPL NLPL PS ZE NSPLPS ZENS ZEPS ZENS PS ZENS NL PLZENSNL

17. Structural Dynamics & Vibration Control Lab. 17 - Fuzzy rule surface (A type)

18. Structural Dynamics & Vibration Control Lab. 18 Accel. (m/sec 2 ) Time(sec) Accel. (m/sec 2 ) Kobe (PGA: 0.834g) California (PGA: 0.156g) El Centro (PGA: 0.348g) Input Earthquakes

19. Structural Dynamics & Vibration Control Lab. 19 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

20. Structural Dynamics & Vibration Control Lab. 20 Control Results Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake

21. Structural Dynamics & Vibration Control Lab. 21 Control strategyJ1J1 J2J2 J3J3 J4J4 Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) Active Fuzzy control 0.343 0.548 0.600 0.562 0.635 0.756 1.186 0.601 0.660 0.0178 0.0134 0.0178 Normalized Controlled Maximum Response due to Scaled El Centro Earthquake J1J1 J2J2 J3J3 A type Fuzzy B type

22. Structural Dynamics & Vibration Control Lab. 22 Control strategyJ1J1 J2J2 J3J3 J4J4 Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) Active fuzzy control 0.449 0.729 0.745 0.727 0.762 0.885 1.856 0.842 0.939 0.0178 0.0134 0.0178 High amplitude (the 120% El Centro earthquake) A type Fuzzy B type

23. Structural Dynamics & Vibration Control Lab. 23 Control strategyJ1J1 J2J2 J3J3 J4J4 Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) Active fuzzy control 0.231 0.403 0.473 0.467 0.509 0.640 1.110 0.619 0.531 0.0178 0.0134 0.0178 Low amplitude (the 80% El Centro earthquake) A type Fuzzy B type

24. Structural Dynamics & Vibration Control Lab. 24 Control strategyJ1J1 J2J2 J3J3 J4J4 Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) Active fuzzy control 0.294 0.360 0.430 0.321 0.366 0.402 0.677 0.660 0.614 0.0178 0.0134 0.0178 Scaled Kobe earthquake (1995) A type Fuzzy B type

25. Structural Dynamics & Vibration Control Lab. 25 Control strategyJ1J1 J2J2 J3J3 J4J4 Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) Active fuzzy control 0.175 0.173 0.178 0.485 0.268 0.244 1.144 0.561 0.260 0.0100 0.0070 0.0076 Scaled California earthquake (1994) A type Fuzzy B type

26. Structural Dynamics & Vibration Control Lab. 26 Conclusions A new active modal-fuzzy control strategy for seismic response reduction is proposed. Verification of the proposed method has been investigated according to various amplitudes and frequency components. The performance of the proposed method is comparable to that of conventional method. The proposed method is more convenient and easy to apply to real system