2002. 3. 23 2002년도 한국지진공학회 춘계학술발표회 Hybrid Control Strategy for Seismic Protection of Benchmark Cable-Stayed Bridges 박규식, 한국과학기술원 토목공학과 박사과정 정형조, 한국과학기술원 토목공학과 연구조교수 이종헌, 경일대학교 토목공학과 교수 이인원, 한국과학기술원 토목공학과 교수

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

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).

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

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 STU: Shock Transmission Unit

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. 128 cables Two H- shape towers 12 additional piers STU: Shock Transmission Unit

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.

Historical earthquake excitations PGA: 0.3483g PGA: 0.1434g PGA: 0.2648g

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 - 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: - Normed responses J7: Base shear J8: Shear at deck level J9: Overturning moment J10: Moment at deck level J11: Cable tension

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.

- The design of LRBs follows a general and recommended procedure (Ali and Abdel-Ghaffar, 1995). : The combined plastic or/and elastic stiffness of the bearings at the pier or/and bent are assumed to be 1.15M/m. (M: the part of deck weight carried by bearings) : The elastic stiffness of LRB is assumed to be 10 times the plastic stiffness. : The design shear force level for the yielding of lead plug is taken to be 0.15M. - The equivalent linear model for LRB is used.

Active control devices - A total of 24 hydraulic actuator, which are used in the benchmark problem, are employed. - The actuators have a capacity of 1000 kN. - 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.

24 LRBs, 24 hydraulic actuators Control devices and sensor locations H2/LQG Control force 2 1 5 accelerometers 2 4 displacement sensors 8 4 24 LRBs, 24 hydraulic actuators

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.

Weighting parameters for active control part - performance index Q: Response weighing matrix R: Control force weighting matrix (identity matrix)

- the maximum response approach is used. 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. 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. 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.

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

: for hybrid control strategy unstable controller min.point bs: base shear td: top tower dis.

NUMERICAL SIMULATIONS Simulation results - time history response deck displacement base moment (overturning moment) - evaluation criteria

Time history responses under three historical earthquakes

Displacement (cm) Base moment (105 kN·m)

Evaluation criteria under El Centro earthquake

Evaluation criteria Passive Active Hybrid 0.314 0.271 0.321 0.894 J1. Max. base shear 0.314 0.271 0.321 J2. Max. deck shear 0.894 0.790 0.653 J3. Max. base moment 0.299 0.254 0.309 J4. Max. deck moment 0.443 0.460 0.302 J5. Max. cable deviation 0.170 0.147 0.144 J6. Max. deck dis. 1.184 1.006 0.793 J7. Norm base shear 0.246 0.200 0.237 J8. Norm deck shear 0.728 0.716 0.541 J9. Norm base moment 0.281 0.201 0.244 J10. Norm deck moment 0.391 0.512 0.265 J11. Norm cable deviation 1.31e-2 1.62e-2 1.56e-2 J12. Max. control force 7.82e-3 1.96e-3 4.53e-3 J13. Max. device stroke 0.778 0.660 0.521 J14. Max. power - 4.57e-3 3.76e-3 J15. Total power 7.25e-4 5.96e-4 4.53e-3 LRB: 5.24e-3 HA: 1.96e-3

Evaluation criteria under Mexico City earthquake

Evaluation criteria Passive Active Hybrid 0.578 0.507 0.546 1.025 J1. Max. base shear 0.578 0.507 0.546 J2. Max. deck shear 1.025 0.910 0.773 J3. Max. base moment 0.768 0.448 0.500 J4. Max. deck moment 0.364 0.415 0.259 J5. Max. cable deviation 4.70e-2 4.50e-2 4.20e-2 J6. Max. deck dis. 2.194 1.666 1.342 J7. Norm base shear 0.503 0.376 0.419 J8. Norm deck shear 0.820 0.770 0.632 J9. Norm base moment 0.579 0.356 0.412 J10. Norm deck moment 0.567 0.691 0.370 J11. Norm cable deviation 5.05e-3 6.27e-3 4.84e-3 J12. Max. control force 3.48e-3 1.22e-3 1.96e-3 J13. Max. device stroke 1.105 0.839 0.676 J14. Max. power - 2.62e-3 1.30e-3 J15. Total power 3.49e-4 1.73e-4 1.96e-3 LRB: 2.33e-3 HA: 9.89e-4

Evaluation criteria under Gebze earthquake

Evaluation criteria Passive Active Hybrid 0.425 0.414 0.408 0.963 J1. Max. base shear 0.425 0.414 0.408 J2. Max. deck shear 0.963 1.158 0.665 J3. Max. base moment 0.364 0.342 0.387 J4. Max. deck moment 0.526 0.879 0.420 J5. Max. cable deviation 0.101 9.01e-2 8.15e-2 J6. Max. deck dis. 1.207 1.803 0.880 J7. Norm base shear 0.312 0.295 0.299 J8. Norm deck shear 0.876 0.951 0.669 J9. Norm base moment 0.343 0.351 0.311 J10. Norm deck moment 0.489 0.762 J11. Norm cable deviation 6.46e-3 8.90e-3 6.48e-3 J12. Max. control force 5.97e-3 1.96e-3 2.98e-3 J13. Max. device stroke 1.73e-4 0.989 0.482 J14. Max. power - 9.33e-3 5.38e-3 J15. Total power 8.80e-4 5.07e-4 2.98e-3 LRB: 3.99e-3 HA: 1.96e-3

Maximum evaluation criteria

Evaluation criteria Passive Active Hybrid 0.578 0.507 0.546 1.025 J1. Max. base shear 0.578 0.507 0.546 J2. Max. deck shear 1.025 1.158 0.773 J3. Max. base moment 0.768 0.448 0.500 J4. Max. deck moment 0.526 0.879 0.420 J5. Max. cable deviation 0.170 0.147 0.144 J6. Max. deck dis. 2.194 1.803 1.342 J7. Norm base shear 0.503 0.376 0.419 J8. Norm deck shear 0.876 0.951 0.669 J9. Norm base moment 0.579 0.356 0.412 J10. Norm deck moment 0.567 0.762 0.370 J11. Norm cable deviation 1.31e-2 1.62e-3 1.56e-2 J12. Max. control force 7.82e-3 1.96e-3 4.53e-3 J13. Max. device stroke 1.105 0.989 0.676 J14. Max. power - 9.33e-3 5.38e-3 J15. Total power 8.80e-4 5.96e-3 4.53e-3 LRB: 5.24e-3 HA: 1.96e-3

Actuator requirements Earthquake Max. Active Hybrid 1940 El Centro NS Force(kN) 1000 Stroke(m) 0.0982 0.0774 Vel. (m/s) 0.5499 0.5208 1985 Mexico City 622.23 504.60 0.0405 0.0326 0.2374 0.1665 1990 Gebze NS 0.1297 0.0633 0.4157 0.3142 Actuator requirement constraints Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec

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 quite effective compared to that of the passive control design and slightly better than that of active control design. The proposed hybrid control design is more reliable that the active control method due to the passive control part.

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