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2002 Control of a Seismically Excited Cable-Stayed Bridge Employing a Hybrid Control Strategy ,

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Department of Civil and Environmental Engineering, KAIST 2 Introduction Benchmark problem statement Seismic control system using a hybrid control strategy Numerical simulations Conclusions CONTENTS

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

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Department of Civil and Environmental Engineering, KAIST 4 investigate the effectiveness of the hybrid control strategy * for seismic protection of a cable-stayed bridge Objective of this study: hybrid control strategy: combination of passive and active control strategies

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Department of Civil and Environmental Engineering, KAIST 5 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

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Department of Civil and Environmental Engineering, KAIST 6 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. Two H- shape towers 128 cables 12 additional piers STU: Shock Transmission Unit BENCHMARK PROBLEM STATEMENT

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Department of Civil and Environmental Engineering, KAIST 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.

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Department of Civil and Environmental Engineering, KAIST 8 Historical earthquake excitations PGA: g PGA: g PGA: g

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Department of Civil and Environmental Engineering, KAIST 9 Evaluation criteria - Peak responses J 1 : Base shear J 1 : Base shear J 2 : Shear at deck level J 2 : Shear at deck level J 3 : Overturning moment J 3 : Overturning moment J 4 : Moment at deck level J 4 : Moment at deck level J 5 : Cable tension J 5 : Cable tension J 6 : Deck dis. at abutment J 6 : Deck dis. at abutment - Normed responses J 7 : Base shear J 7 : Base shear J 8 : Shear at deck level J 8 : Shear at deck level J 9 : Overturning moment J 9 : Overturning moment J 10 : Moment at deck level J 10 : Moment at deck level J 11 : Cable tension J 11 : Cable tension - Control Strategy (J 12 – J 18 ) J 12 : Peak force J 12 : Peak force J 13 : Device stroke J 13 : Device stroke J 14 : Peak power J 14 : Peak power J 15 : Total power J 15 : Total power J 16 : Number of control devices J 16 : Number of control devices J 17 : Number of sensor J 17 : Number of sensor J 18 : J 18 :

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Department of Civil and Environmental Engineering, KAIST 10 Passive control devices SEISMIC CONTROL SYSTEM USING A 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.

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Department of Civil and Environmental Engineering, KAIST 11 The design of LRBs follows a general and recommended procedure provided by Ali and Abdel-Ghaffar 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 1/pier 4 connections

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Department of Civil and Environmental Engineering, KAIST 12 PropertyValue k e (N/m) k p (N/m) D y (cm)0.765 Q d (kg) 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 the LRB.

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Department of Civil and Environmental Engineering, KAIST 13 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.

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Department of Civil and Environmental Engineering, KAIST 14 Control device and sensor locations accelerometers 8(6) 4(6) 24 hydraulic actuators, 24 LRBs H 2 /LQG Control force 22 4 displacement sensors

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Department of Civil and Environmental Engineering, KAIST 15 z: regulated output Q: response weighing matrix R: control force weighting matrix (I 8 8 ) Weighting parameters for active control part Performance index where

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Department of Civil and Environmental Engineering, KAIST 16 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

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Department of Civil and Environmental Engineering, KAIST 17 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.

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Department of Civil and Environmental Engineering, KAIST 18 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.

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Department of Civil and Environmental Engineering, KAIST 19 min. point - For active control system

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Department of Civil and Environmental Engineering, KAIST 20 min. point - For hybrid control system

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Department of Civil and Environmental Engineering, KAIST 21 deck displacement overturning moment NUMERICAL SIMULATIONS Time-history responses

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Department of Civil and Environmental Engineering, KAIST 22 Under the 1940 El Centro earthquake Displacement(cm) Moment( 10 5 N m)

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Department of Civil and Environmental Engineering, KAIST 23 Under the 1985 Mexico City earthquake Displacement(cm) Moment( 10 5 N m)

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Department of Civil and Environmental Engineering, KAIST 24 Under the 1999 Turkey Gebze earthquake Displacement(cm) Moment( 10 5 N m)

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Department of Civil and Environmental Engineering, KAIST 25 (a) El Centro (b) Mexico City (c) Turkey Gebze Restoring force of LRB at pier 2

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Evaluation criteria PassiveActiveHybrid 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 2.23e-21.62e e-2 J 12 : Max. control force 1.34e-31.96e-32.64e-3 J 13 : Max. device stroke J 14 : Max. power -4.57e e-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

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Under the 1985 Mexico City earthquake Evaluation criteria PassiveActiveHybrid 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 4.88e e e-2 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 5.18e e e-3 J 12. Max. control force 7.76e e-31.96e-3 J 13. Max. device stroke J 14. Max. power -2.62e e-3 J 15. Total power -3.49e-41.97e e-3 LRB: 6.43e-4 HA: 7.56e

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Evaluation criteria PassiveActiveHybrid 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 e e-2 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 1.71e e e-2 J 12. Max. control force 2.16e e-32.46e-3 J 13. Max. device stroke J 14. Max. power -9.33e e-3 J 15. Total power -8.80e-48.49e e-3 LRB: 1.22e-3 HA: 1.78e-3 Under the 1999 Turkey Gebze earthquake 28 28

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Department of Civil and Environmental Engineering, KAIST 29 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

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Department of Civil and Environmental Engineering, KAIST 30 EarthquakeMax.ActiveHybrid 1940 El Centro NS Force(kN)1000 Stroke(m) Vel. (m/s) Mexico City Force(kN) Stroke(m) Vel. (m/s) Gebze NS Force(kN) Stroke(m) Vel. (m/s) Actuator requirement constraints Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec Actuator requirements

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Department of Civil and Environmental Engineering, KAIST 31 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

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Department of Civil and Environmental Engineering, KAIST 32 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 active control design. The proposed hybrid control design is more robust for stiffness matrix perturbation than the active control with a -synthesis method due to the passive control part. CONCLUSIONS

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Department of Civil and Environmental Engineering, KAIST 33 The proposed hybrid control strategy could 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.

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Department of Civil and Environmental Engineering, KAIST 34 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!

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