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The Asian-Pacific Symposium on Structural Reliability and its Applications Seoul, Korea, August 18-20, 2004 Kyu-Sik Park Kyu-Sik Park, Ph. D. Candidate,

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Presentation on theme: "The Asian-Pacific Symposium on Structural Reliability and its Applications Seoul, Korea, August 18-20, 2004 Kyu-Sik Park Kyu-Sik Park, Ph. D. Candidate,"— Presentation transcript:

1 The Asian-Pacific Symposium on Structural Reliability and its Applications Seoul, Korea, August 18-20, 2004 Kyu-Sik Park Kyu-Sik Park, Ph. D. Candidate, KAIST, Korea Hyung-Jo Jung Hyung-Jo Jung, Assistant Professor, Sejong Univ., Korea Woon-Hak Kim Woon-Hak Kim, Professor, Hankyong Nat. Univ., Korea In-Won Lee In-Won Lee, Professor, KAIST, Korea Robust Hybrid Control of a Seismically Excited Cable-Stayed Bridge

2 Structural Dynamics & Vibration Control Lab., KAIST, Korea 2 Introduction Robust hybrid control system Numerical examples Conclusions Contents

3 Structural Dynamics & Vibration Control Lab., KAIST, Korea 3 Introduction Hybrid control system (HCS)  A combination of passive and active control devices Passive devices: offer some degree of protection in the case of power failure Active devices: improve the control performances  However, the robustness of HCS could be decreased by the active control devices.

4 Structural Dynamics & Vibration Control Lab., KAIST, Korea 4 Objective of this study Apply robust control algorithms to improve the controller robustness of HCS

5 Structural Dynamics & Vibration Control Lab., KAIST, Korea 5 Robust hybrid control system (RHCS) Control devices  Passive control devices Lead rubber bearings (LRBs) Design procedure: Ali and Abdel-Ghaffar (1995) Bouc-Wen model  Active control devices Hydraulic actuators (HAs) An actuator has a capacity of 1000 kN. The actuator dynamics are neglected.

6 Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 Control algorithm  RHCS I Primary control scheme · Linear quadratic Gaussian (LQG) algorithm Secondary control scheme · On-off type controller according to LRB’s responses

7 Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 Bridge Model Sensor LQG On-Off HA LRB MUX Block diagram of RHCS I

8 Structural Dynamics & Vibration Control Lab., KAIST, Korea 8  RHCS II H 2 control algorithm with frequency weighting filters Frequency weighting filters

9 Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 Bridge Model Sensor H2H2 HA LRB MUX Block diagram of RHCS II DM WgWg kgkg R WuWu WzWz Q K

10 Structural Dynamics & Vibration Control Lab., KAIST, Korea 10  RHCS III H  control algorithm with frequency weighting filters

11 Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 Numerical examples Analysis model  Bridge model Bill Emerson Memorial Bridge · Benchmark control problem (Dyke et al., 2003) · Located in Cape Girardeau, MO, USA · 16 shock transmission devices (STDs) are employed between the tower-deck connections.

12 Structural Dynamics & Vibration Control Lab., KAIST, Korea 12 142.7 m350.6 m 142.7 m Schematic of the Bill Emerson Memorial Bridge

13 Structural Dynamics & Vibration Control Lab., KAIST, Korea 13 142.7 m350.6 m 142.7 m Configuration of sensors : Accelerometer : Displacement sensor

14 Structural Dynamics & Vibration Control Lab., KAIST, Korea 14 142.7 m350.6 m 142.7 m Configuration of control devices (HAs+LRBs) 2+3 4+3 2+3

15 Structural Dynamics & Vibration Control Lab., KAIST, Korea 15 PGA: 0.348g  Historical earthquake excitations

16 Structural Dynamics & Vibration Control Lab., KAIST, Korea 16 PGA: 0.348g PGA: 0.143g  Historical earthquake excitations

17 Structural Dynamics & Vibration Control Lab., KAIST, Korea 17 PGA: 0.348g PGA: 0.143g PGA: 0.265g  Historical earthquake excitations

18 Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 J 1 /J 7 : Peak/Normed base shear J 2 /J 8 : Peak/Normed shear at deck level J 3 /J 9 : Peak/Normed overturning moment J 4 /J 10 : Peak/Normed moment at deck level J 5 /J 11 : Peak/Normed cable tension deviation J 6 : Peak Deck dis. at abutment  Evaluation criteria

19 Structural Dynamics & Vibration Control Lab., KAIST, Korea 19 Analysis results  Control performances Displacement under El Centro earthquake (a) Uncontrolled(b) RHCS III

20 Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 Cable tension under El Centro earthquake (a) Uncontrolled(b) RHCS III

21 Structural Dynamics & Vibration Control Lab., KAIST, Korea 21 Shear force under El Centro earthquake (a) Uncontrolled(b) RHCS III

22 Structural Dynamics & Vibration Control Lab., KAIST, Korea 22 Evaluation criteria CHCS * RHCS IRHCS IIRHCS III J 1. Max. base shear 0.48540.4607 0.5319 0.4930 J 2. Max. deck shear 0.92140.9250 0.9607 0.8997 J 3. Max. base moment 0.44270.4395 0.5057 0.4519 J 4. Max. deck moment 0.65580.6546 0.6441 0.5617 J 5. Max. cable deviation 0.14330.1428 0.1252 0.1437 J 6. Max. deck dis. 1.55321.5598 1.0652 1.1863 J 7. Norm base shear 0.37700.3762 0.3929 0.3581 J 8. Norm deck shear 0.89860.9035 0.7868 0.9035 J 9. Norm base moment 0.33750.3378 0.3590 0.3216 J 10. Norm deck moment 0.72770.7503 0.5404 0.7338 J 11. Norm cable deviation1.707e-31.678e-31.275e-21.741e-2 Maximum evaluation criteria for all three earthquakes * Conventional HCS controlled by LQG algorithm

23 Structural Dynamics & Vibration Control Lab., KAIST, Korea 23 Evaluation criteria CHCS * RHCS IRHCS IIRHCS III J 1. Max. base shear 0.48540.4607 0.5319 0.4930 J 2. Max. deck shear 0.92140.9250 0.9607 0.8997 J 3. Max. base moment 0.44270.4395 0.5057 0.4519 J 4. Max. deck moment 0.65580.6546 0.6441 0.5617 J 5. Max. cable deviation 0.14330.1428 0.1252 0.1437 J 6. Max. deck dis. 1.55321.5598 1.0652 1.1863 J 7. Norm base shear 0.37700.3762 0.3929 0.3581 J 8. Norm deck shear 0.89860.9035 0.7868 0.9035 J 9. Norm base moment 0.33750.3378 0.3590 0.3216 J 10. Norm deck moment 0.72770.7503 0.5404 0.7338 J 11. Norm cable deviation1.707e-31.678e-31.275e-21.741e-2 Maximum evaluation criteria for all three earthquakes * Conventional HCS controlled by LQG algorithm

24 Structural Dynamics & Vibration Control Lab., KAIST, Korea 24  Controller robustness The dynamic characteristic of as-built bridge is not identical to the numerical model. To verify the applicability of RHCS, the controller robustness is investigated to perturbation of stiffness parameter. where: nominal stiffness matrix : perturbed stiffness matrix : perturbation amount (  5% ~  20 %)

25 Structural Dynamics & Vibration Control Lab., KAIST, Korea 25 Maximum variations of evaluation criteria for all three earthquakes (%,  5% perturbation) Evaluation criteria RHCS IRHCS IIRHCS III J 1. Max. base shear 14.24 9.20 6.88 J 2. Max. deck shear 17.78 4.42 13.49 J 3. Max. base moment 16.74 4.93 5.26 J 4. Max. deck moment 6.09 6.21 5.49 J 5. Max. cable deviation 13.62 13.96 14.51 J 6. Max. deck dis. 4.61 1.48 2.70 J 7. Norm base shear 6.73 6.12 5.70 J 8. Norm deck shear 8.09 4.93 6.44 J 9. Norm base moment 6.33 5.54 5.91 J 10. Norm deck moment 8.54 7.56 10.86 J 11. Norm cable deviation16.8413.7817.29

26 Structural Dynamics & Vibration Control Lab., KAIST, Korea 26 Maximum variations of evaluation criteria for all three earthquakes (%,  20% perturbation) Evaluation criteria RHCS IIRHCS III J 1. Max. base shear36.51 33.02 J 2. Max. deck shear22.93 34.32 J 3. Max. base moment33.08 30.67 J 4. Max. deck moment34.48 40.71 J 5. Max. cable deviation50.07 33.27 J 6. Max. deck dis.5.02 8.06 J 7. Norm base shear31.78 30.19 J 8. Norm deck shear39.33 35.96 J 9. Norm base moment29.70 28.99 J 10. Norm deck moment45.34 32.40 J 11. Norm cable deviation72.3552.74

27 Structural Dynamics & Vibration Control Lab., KAIST, Korea 27 Max. variation of evaluation criteria for variations of stiffness perturbation

28 Structural Dynamics & Vibration Control Lab., KAIST, Korea 28 Conclusions Hybrid control system with robust control algorithms  Has excellent robustness for stiffness perturbation without loss of control performances RHCS I obtains robustness only for  5% stiffness perturbations. RHCS III is more robust than RHCS II.  Robust hybrid control system could effectively be used to seismically excited cable-stayed bridge.

29 Structural Dynamics & Vibration Control Lab., KAIST, Korea 29 This research is supported by the National Research Laboratory (NRL) program from the Ministry of Science of Technology (MOST) and the Grant for Pre-Doctoral Students from the Korea Research Foundation (KRF) in Korea. Thank you for your attention! Acknowledgements

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