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,, 2002 2002. 6. 8 Seismic Protection of Benchmark Cable-Stayed Bridge using Hybrid Control Strategy

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 2 CONTENTS Introduction Benchmark problem statement Seismic control system using hybrid control strategy Numerical simulations Conclusions

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SDVCL, Dept. of Civil & Environmental Engng., 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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SDVCL, Dept. of Civil & Environmental Engng., KAIST 4 investigate the effectiveness of the hybrid control strategy for seismic protection of cable-stayed bridges under seismic loads Objective of this study: hybrid control strategy: combination of passive and active control strategies

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SDVCL, Dept. of Civil & Environmental Engng., 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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SDVCL, Dept. of Civil & Environmental Engng., KAIST 6 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. Two H- shape towers 128 cables 12 additional piers STU: Shock Transmission Unit

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SDVCL, Dept. of Civil & Environmental Engng., 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. Control design problem - researcher/designer must define the sensor, devices, algorithms to be used in the proposed control strategy.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 8 Historical earthquake excitations PGA: 0.3483g PGA: 0.1434g PGA: 0.2648g

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SDVCL, Dept. of Civil & Environmental Engng., 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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SDVCL, Dept. of Civil & Environmental Engng., KAIST 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.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 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.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 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 H 2 /LQG control algorithm is adopted.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 13 Control devices 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

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 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.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 15 Weighting parameters for active control part - performance index Q: response weighing matrix R: control force weighting matrix (identity matrix)

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 16 - the maximum response approach is used to determine Q. 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.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 17 - the maximum response approach is used to determine Q. 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.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 18 - the selected values of appropriate optimal weighting parameters : for active control strategy om: overturning moment dd: deck dis. min. point

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 19 : for hybrid control strategy om: overturning moment dd: deck dis. min.point

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 20 NUMERICAL SIMULATIONS Simulation results - time history responses deck displacement overturning moment (base moment) - evaluation criteria

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 21 Time history responses under three historical earthquakes

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Displacement (cm) Overturning moment ( 10 5 kN·m)

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 23 Restoring force of LRB at pier 2 (a) El Centro (b) Mexico City (c) Gebze

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 24 Evaluation criteria under El Centro earthquake

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Evaluation criteria PassiveActiveHybrid J 1 : Max. base shear 0.3980.2710.264 J 2 : Max. deck shear 1.1850.7900.723 J 3 : Max. base moment 0.3050.2540.230 J 4 : Max. deck moment 0.6080.4600.383 J 5 : Max. cable deviation 0.2080.1470.146 J 6 : Max. deck dis. 1.4251.0060.746 J 7 : Norm base shear 0.2300.2000.198 J 8 : Norm deck shear 1.0910.7160.693 J 9 : Norm base moment 0.2470.2010.188 J 10 : Norm deck moment 0.7130.5120.495 J 11 : Norm cable deviation 2.23e-21.62e-21.82e-2 J 12 : Max. control force 1.34e-31.96e-32.64e-3 J 13 : Max. device stroke 0.9360.6600.490 J 14 : Max. power -4.57e-33.32e-3 J 15 : Total power -7.25e-47.10e-4 2.64e-3 LRB: 9.29e-4 HA: 1.96e-3

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 26 Evaluation criteria under Mexico City earthquake

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Evaluation criteria PassiveActiveHybrid J 1. Max. base shear 0.5460.5070.485 J 2. Max. deck shear 1.1100.9100.927 J 3. Max. base moment 0.6190.4480.447 J 4. Max. deck moment 0.4470.4150.352 J 5. Max. cable deviation 4.88e-24.50e-24.61e-2 J 6. Max. deck dis. 2.0201.6661.080 J 7. Norm base shear 0.4210.3760.372 J 8. Norm deck shear 0.9630.7700.732 J 9. Norm base moment 0.3990.3560.334 J 10. Norm deck moment 0.6540.6910.525 J 11. Norm cable deviation 5.18e-36.27e-36.34e-3 J 12. Max. control force 7.76e-41.22e-31.96e-3 J 13. Max. device stroke 1.0170.8390.547 J 14. Max. power -2.62e-31.10e-3 J 15. Total power -3.49e-41.97e-4 1.96e-3 LRB: 6.43e-4 HA: 7.56e-4

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 28 Evaluation criteria under Gebze earthquake

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Evaluation criteria PassiveActiveHybrid J 1. Max. base shear 0.4230.4140.379 J 2. Max. deck shear 1.4621.1580.936 J 3. Max. base moment 0.5010.3420.285 J 4. Max. deck moment 1.2660.8790.672 J 5. Max. cable deviation 0.1609.01e-29.53e-2 J 6. Max. deck dis. 3.8291.8031.663 J 7. Norm base shear 0.3340.2950.277 J 8. Norm deck shear 1.5500.9510.917 J 9. Norm base moment 0.4820.3510.324 J 10. Norm deck moment 1.4430.7620.780 J 11. Norm cable deviation 1.71e-28.90e-31.04e-2 J 12. Max. control force 2.16e-31.96e-32.46e-3 J 13. Max. device stroke 2.1000.9890.912 J 14. Max. power -9.33e-36.67e-3 J 15. Total power -8.80e-48.49e-4 2.46e-3 LRB: 1.22e-3 HA: 1.78e-3

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 30 Maximum evaluation criteria

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Evaluation criteria PassiveActiveHybrid J 1. Max. base shear 0.5460.5070.485 J 2. Max. deck shear 1.4621.1580.936 J 3. Max. base moment 0.6190.4480.447 J 4. Max. deck moment 1.2660.8790.672 J 5. Max. cable deviation 0.2080.1470.146 J 6. Max. deck dis. 3.8291.8031.663 J 7. Norm base shear 0.4210.3760.372 J 8. Norm deck shear 1.5500.9510.917 J 9. Norm base moment 0.4820.3560.334 J 10. Norm deck moment 1.4430.7620.780 J 11. Norm cable deviation 2.23e-21.62e-31.82e-2 J 12. Max. control force 2.16e-31.96e-32.64e-3 J 13. Max. device stroke 2.1000.9890.912 J 14. Max. power -9.33e-36.67e-3 J 15. Total power -8.80e-48.49e-4

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 32 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

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 33 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.

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SDVCL, Dept. of Civil & Environmental Engng., KAIST 34 Thank you for your attention!

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