1. Kyu-Sik Park Kyu-Sik Park, Graduate Student, KAIST, Korea Hyung-Jo Jung Hyung-Jo Jung, Research Assistant Professor, KAIST, Korea In-Won Lee In-Won Lee, Professor, KAIST, Korea 7 th U.S. National Conference on Earthquake Engineering Boston, Massachusetts July 21-25, 2002 Hybrid Control Strategy for Seismic Protection of a Benchmark Cable-Stayed Bridge

2. Structural Dynamics & Vibration Control Lab., KAIST, Korea 2 Introduction Seismic control system using hybrid control strategy Numerical simulations Conclusions CONTENTS

3. Structural Dynamics & Vibration Control Lab., KAIST, Korea 3 INTRODUCTION Control Actuator Structure PCD PCD: Passive Control Device HCS: Hybrid Control System HCS

4. Structural Dynamics & Vibration Control Lab., KAIST, Korea 4 investigate the effectiveness of the hybrid control strategy for seismic protection of a cable-stayed bridge Objective of this study:

5. Structural Dynamics & Vibration Control Lab., KAIST, Korea 5 Passive control devices SEISMIC CONTROL SYSTEM USING HYBRID CONTROL STRATEGY In this hybrid control strategy, passive control devices have a great role for the effectiveness of control performance. Lead rubber bearings (LRBs) are used as passive control devices.

6. Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 The design of LRBs follows a general and recommended procedure provided by Ali and Abdel-Ghaffar 1995. - The design shear force level for the yielding of the lead plug is taken to be 0.10M. (M: the part of deck weight carried by bearings) - The plastic stiffness ratio of the bearings at the bent and tower is assumed to be 1.0. A total of 24 LRBs are employed. - Six LRBs at each deck-tower and deck-bent I/Pier IV connections

7. Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 PropertyValue k e (N/m) 3.571  10 7 k p (N/m) 3.139  10 6 D y (cm)0.765 Q d (kg) 2.540  10 4 Properties of the LRB k e : Elastic stiffness k p : Plastic stiffness D y : Yield dis. of the lead plug Q d : Design shear force level for the yielding of the lead plug where The Bouc-Wen model is used to simulate the nonlinear dynamics of LRB.

8. Structural Dynamics & Vibration Control Lab., KAIST, Korea 8 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 H 2 /LQG control algorithm is adopted.

9. Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 Control device and sensor locations 2 2 1 5 accelerometers 8(6) 4(6) 24 hydraulic actuators, 24 LRBs H 2 /LQG Control force 22 4 displacement sensors

10. Structural Dynamics & Vibration Control Lab., KAIST, Korea 10 Q: response weighing matrix R: control force weighting matrix (I 8  8 ) Weighting parameters for active control part Performance index where

11. Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 Step 1. Calculate maximum responses for the candidate weighting parameters as increasing each parameters. The maximum response approach is used to determine Q. Responsesq base shears at piers 2 and 3q bs shears at deck level at piers 2 and 3q sd mom. at base of piers 2 and 3q om mom. at deck level at piers 2 and 3q md deck dis. at bent 1 and pier 4q dd top dis. at towers 1 and 2q td The selected responses

12. Structural Dynamics & Vibration Control Lab., KAIST, Korea 12 Step 2. Normalize maximum responses by the results of base structure and plot sum of max. responses. Step 3. Select two parameters which give the smallest sum of max. responses.

13. Structural Dynamics & Vibration Control Lab., KAIST, Korea 13 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.

14. Structural Dynamics & Vibration Control Lab., KAIST, Korea 14 min. point - For active control system

15. Structural Dynamics & Vibration Control Lab., KAIST, Korea 15 min. point - For hybrid control system

16. Structural Dynamics & Vibration Control Lab., KAIST, Korea 16 deck displacement overturning moment NUMERICAL SIMULATIONS Time-history responses

17. Structural Dynamics & Vibration Control Lab., KAIST, Korea 17 Under the 1940 El Centro earthquake Displacement(cm) Moment(  10 5 N  m)

18. Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 Under the 1985 Mexico City earthquake Displacement(cm) Moment(  10 5 N  m)

19. Structural Dynamics & Vibration Control Lab., KAIST, Korea 19 Under the 1999 Turkey Gebze earthquake Displacement(cm) Moment(  10 5 N  m)

20. Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 (a) El Centro (b) Mexico City (c) Turkey Gebze Restoring force of LRB at pier 2

21. Evaluation criteria PassiveActiveHybrid J 1 : Max. base shear 0.398 0.271 0.264 J 2 : Max. deck shear 1.185 0.790 0.723 J 3 : Max. base moment 0.305 0.254 0.230 J 4 : Max. deck moment 0.608 0.460 0.383 J 5 : Max. cable deviation 0.208 0.147 0.146 J 6 : Max. deck dis. 1.425 1.006 0.746 J 7 : Norm base shear 0.230 0.200 0.198 J 8 : Norm deck shear 1.091 0.716 0.693 J 9 : Norm base moment 0.247 0.201 0.188 J 10 : Norm deck moment 0.713 0.512 0.495 J 11 : Norm cable deviation 2.23e-21.62e-2 1.82e-2 J 12 : Max. control force 1.34e-31.96e-32.64e-3 J 13 : Max. device stroke 0.9360.660 0.490 J 14 : Max. power -4.57e-3 3.32e-3 J 15 : Total power -7.25e-47.10e-4 Evaluation criteria Under the 1940 El Centro earthquake 2.64e-3 LRB: 9.29e-4 HA: 1.96e-3 21 21

22. Under the 1985 Mexico City earthquake Evaluation criteria PassiveActiveHybrid J 1. Max. base shear 0.546 0.507 0.485 J 2. Max. deck shear 1.110 0.910 0.927 J 3. Max. base moment 0.619 0.448 0.447 J 4. Max. deck moment 0.447 0.415 0.352 J 5. Max. cable deviation 4.88e-2 4.50e-2 4.61e-2 J 6. Max. deck dis. 2.020 1.666 1.080 J 7. Norm base shear 0.421 0.376 0.372 J 8. Norm deck shear 0.963 0.770 0.732 J 9. Norm base moment 0.399 0.356 0.334 J 10. Norm deck moment 0.654 0.691 0.525 J 11. Norm cable deviation 5.18e-3 6.27e-3 6.34e-3 J 12. Max. control force 7.76e-4 1.22e-31.96e-3 J 13. Max. device stroke 1.017 0.839 0.547 J 14. Max. power -2.62e-3 1.10e-3 J 15. Total power -3.49e-41.97e-4 1.96e-3 LRB: 6.43e-4 HA: 7.56e-4 22 22

23. Evaluation criteria PassiveActiveHybrid J 1. Max. base shear 0.423 0.414 0.379 J 2. Max. deck shear 1.462 1.158 0.936 J 3. Max. base moment 0.501 0.342 0.285 J 4. Max. deck moment 1.266 0.879 0.672 J 5. Max. cable deviation 0.160 9.01e-2 9.53e-2 J 6. Max. deck dis. 3.829 1.803 1.663 J 7. Norm base shear 0.334 0.295 0.277 J 8. Norm deck shear 1.550 0.951 0.917 J 9. Norm base moment 0.482 0.351 0.324 J 10. Norm deck moment 1.443 0.762 0.780 J 11. Norm cable deviation 1.71e-2 8.90e-3 1.04e-2 J 12. Max. control force 2.16e-3 1.96e-32.46e-3 J 13. Max. device stroke 2.100 0.989 0.912 J 14. Max. power -9.33e-3 6.67e-3 J 15. Total power -8.80e-48.49e-4 2.46e-3 LRB: 1.22e-3 HA: 1.78e-3 Under the 1999 Turkey Gebze earthquake 23 23

24. Structural Dynamics & Vibration Control Lab., KAIST, Korea 24 Maximum evaluation criteria Evaluation Criteria Values Evaluation criteria J 1. Max. base shear J 2. Max. deck shear J 3. Max. base moment J 4. Max. deck moment J 5. Max. cable deviation J 6. Max. deck dis. J 7. Norm base shear J 8. Norm deck shear J 9. Norm base moment J 10. Norm deck moment J 11. Norm cable deviation J 12. Max. control force J 13. Max. device stroke

25. Structural Dynamics & Vibration Control Lab., KAIST, Korea 25 EarthquakeMax.ActiveHybrid 1940 El Centro NS Force(kN)1000 Stroke(m)0.09820.0728 Vel. (m/s)0.54990.5323 1985 Mexico City Force(kN)622.23385.31 Stroke(m)0.04050.0263 Vel. (m/s)0.23740.2043 1990 Gebze NS Force(kN)1000909.03 Stroke(m)0.12970.1196 Vel. (m/s)0.41570.4223 Actuator requirement constraints Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec Actuator requirements

26. Structural Dynamics & Vibration Control Lab., KAIST, Korea 26 Evaluation criteria J 1. Max. base shear J 2. Max. deck shear J 3. Max. base moment J 4. Max. deck moment J 5. Max. cable deviation J 6. Max. deck dis. J 7. Norm base shear J 8. Norm deck shear J 9. Norm base moment J 10. Norm deck moment J 11. Norm cable deviation Evaluation Criteria Variations (%) Maximum variations for  7% perturbation of K

27. Structural Dynamics & Vibration Control Lab., KAIST, Korea 27 A hybrid 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 the active control design. The proposed hybrid control design is more reliable than the fully active control method due to the passive control part. CONCLUSIONS

28. Structural Dynamics & Vibration Control Lab., KAIST, Korea 28 The proposed hybrid control strategy can be effectively used to seismically excited cable- stayed bridge. More researches on increasing the robustness and performance of the hybrid control system are in progress.

29. Structural Dynamics & Vibration Control Lab., KAIST, Korea 29 Acknowledgments This research is funded by the National Research Laboratory Grant (No.: 2000-N-NL-01-C-251) in Korea. Thank you for your attention!