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박규식 , 한국과학기술원 건설환경공학과, 박사과정 정형조 , 한국과학기술원 건설환경공학과, 연구조교수 이종헌 , 경일대학교 토목공학과, 교수

2002. 6. 8. 2002 년도 한국강구조학회 학술발표대회. Seismic Protection of Benchmark Cable-Stayed Bridge using Hybrid Control Strategy. 박규식 , 한국과학기술원 건설환경공학과, 박사과정 정형조 , 한국과학기술원 건설환경공학과, 연구조교수 이종헌 , 경일대학교 토목공학과, 교수 이인원 , 한국과학기술원 건설환경공학과, 교수. CONTENTS. Introduction Benchmark problem statement

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박규식 , 한국과학기술원 건설환경공학과, 박사과정 정형조 , 한국과학기술원 건설환경공학과, 연구조교수 이종헌 , 경일대학교 토목공학과, 교수

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  1. 2002. 6. 8 2002년도 한국강구조학회 학술발표대회 Seismic Protection of Benchmark Cable-Stayed Bridge using Hybrid Control Strategy 박규식, 한국과학기술원 건설환경공학과, 박사과정 정형조,한국과학기술원 건설환경공학과, 연구조교수 이종헌,경일대학교 토목공학과, 교수 이인원,한국과학기술원 건설환경공학과, 교수

  2. CONTENTS • Introduction • Benchmark problem statement • Seismic control system using hybrid control strategy • Numerical simulations • Conclusions

  3. INTRODUCTION • Many control strategies and devices have been developed and investigated to protect structures against natural hazard. • The control of very flexible and large structures such as cable-stayed bridges is a unique and challenging problem. • The 1st generation benchmark control problem for cable-stayed bridges under seismic loads has been developed (Dyke et al., 2000).

  4. Objective of this study: investigate the effectiveness of the hybrid control strategy for seismic protection of cable-stayed bridges under seismic loads hybrid control strategy: combination of passive and active control strategies

  5. STU BENCHMARK PROBLEM STATEMENT • Benchmark bridge model • under construction in Cape Girardeau, Missouri, USA • sixteen STU* devices are employed in the connection between the tower and the deck in the original design. STU: Shock Transmission Unit

  6. 128 cables 12 additional piers Two H- shape towers BENCHMARK PROBLEM STATEMENT • Benchmark bridge model • under construction in Cape Girardeau, Missouri, USA • sixteen STU* devices are employed in the connection between the tower and the deck in the original design. STU: Shock Transmission Unit

  7. Linear evaluation model - the Illinois approach has a negligible effect on the dynamics of the cable-stayed portion. - the stiffness matrix is determined through a nonlinear static analysis corresponding to deformed state of the bridge with dead loads. - a one dimensional excitation is applied in the longitudinal direction. - a set of eighteen criteria have been developed to evaluate the capabilities of each control strategy. • Control design problem - researcher/designer must define the sensor, devices, algorithms to be used in the proposed control strategy.

  8. PGA: 0.3483g PGA: 0.1434g PGA: 0.2648g • Historical earthquake excitations

  9. - Control strategy (J12 – J18) J12: Peak force J13: Device stroke J14: Peak power J15: Total power J16: Number of control devices J17: Number of sensor J18: • Evaluation criteria - Peak responses J1: Base shear J2: Shear at deck level J3: Overturning moment J4: Moment at deck level J5: Cable tension J6: Deck dis. at abutment - Normed responses J7: Base shear J8: Shear at deck level J9: Overturning moment J10: Moment at deck level J11: Cable tension

  10. SEISMIC CONTROL SYSTEM USING HYBRID CONTROL STRATEGY • Passive control devices - in this hybrid control strategy, passive control strategy has a great role for the effectiveness of control performance. - lead rubber bearings (LRBs) are used as passive control devices.

  11. - the design of LRBs follows a general and recommended procedure (Ali and Abdel-Ghaffar, 1995). : the asymtotic (or plastic) stiffness ratio of the bearings at the bent and tower are assumed to be 1.0. : the design shear force level for the yielding of lead plug is taken to be 0.10M. (M: the part of deck weight carried by bearings) - the Bouc-Wen model is used to simulate the nonlinear dynamics of LRBs.

  12. Active control devices - a total of 24 hydraulic actuator, which are used in the benchmark problem, are employed. - an actuator has a capacity of 1000 kN. - the actuator dynamics are neglected and the actuator is considered to be ideal. - five accelerometers and four displacement sensors are used for feedback. - an H2/LQG control algorithm is adopted.

  13. H2/LQG 2 2 2 2 1 8(6) 4(6) 8(6) 4(6) 5 accelerometers 4 displacement sensors 24 hydraulic actuators, 24 LRBs Control force • Control devices and sensor locations

  14. Control design model (reduced-order model) - formed from the evaluation model and has 30 states - by forming a balanced realization and condensing out the states with relatively small controllability and observability grammians - the resulting state space system is : State space eq. : Regulated output eq. : Measured output eq.

  15. Weighting parameters for active control part - performance index Q: response weighing matrix R: control force weighting matrix (identity matrix)

  16. Step 1. calculate maximum responses for the candidate weighting parameters as increasing each parameters. Step 2. normalized maximum responses by the results of based structure and plot sum of max. responses. Step 3. select two parameters which give the smallest sum of max. responses. - the maximum response approach is used to determine Q.

  17. Step 1. calculate maximum responses for the candidate weighting parameters as increasing each parameters. Step 2. normalized maximum responses by the results of based structure and plot sum of max. respomses. Step 3. select two parameters which give the smallest sum of max. responses. Step 4. calculate maximum responses for the selected two weighting parameters as increasing each parameters simultaneously. Step 5. determine the values of the appropriate optimal weighting parameters. - the maximum response approach is used to determine Q.

  18. min. point om: overturning moment dd: deck dis. - the selected values of appropriate optimal weighting parameters : for active control strategy

  19. min.point om: overturning moment dd: deck dis. : for hybrid control strategy

  20. deck displacement overturning moment (base moment) NUMERICAL SIMULATIONS • Simulation results - time history responses - evaluation criteria

  21. Time history responses under three historical earthquakes

  22. Displacement (cm) Overturning moment (105 kN·m)

  23. (a) El Centro (b) Mexico City (c) Gebze Restoring force of LRB at pier 2

  24. Evaluation criteria under El Centro earthquake

  25. LRB: 9.29e-4 HA: 1.96e-3 2.64e-3

  26. Evaluation criteria under Mexico City earthquake

  27. LRB: 6.43e-4 HA: 7.56e-4 1.96e-3

  28. Evaluation criteria under Gebze earthquake

  29. LRB: 1.22e-3 HA: 1.78e-3 2.46e-3

  30. Maximum evaluation criteria

  31. Actuator requirements Actuator requirement constraints Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec

  32. CONCLUSIONS • A hybrid control control strategy combining passive and active control systems has been proposed for the benchmark bridge problem. • The performance of the proposed hybrid control design is superior to that of the passive control design and slightly better than that of active control design. • The proposed hybrid control design is more reliable than the active control method due to the passive control part.

  33. Thank you for your attention!

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