Structural Engineering and Mechanics

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Nonlinear stochastic optimal control strategy of hysteretic structures

  • Li, Jie (School of Civil Engineering, Tongji University) ;
  • Peng, Yong-Bo (Shanghai Insititute of Disaster Prevention and Relief, Tongji University) ;
  • Chen, Jian-Bing (School of Civil Engineering, Tongji University)
  • Received : 2009.09.26
  • Accepted : 2010.11.24
  • Published : 2011.04.10
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Abstract

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

Keywords

References

  1. Amini, F. and Tavassoli, M.R. (2005), "Optimal structural active control force, number and placement of controllers", Eng. Struct., 27, 1306-1316. https://doi.org/10.1016/j.engstruct.2005.01.006
  2. Anderson, B.D.O. and Moore, J. (1990), Optimal Control: Linear Quadratic Methods, Prentice-Hall International Editions.
  3. Baber, T.T. and Wen, Y.K. (1981), "Random vibration of hysteretic degrading systems", J. Eng. Mech. Div., 107(6), 1069-1087.
  4. Baber, T.T. and Noori, M.N. (1985), "Random vibration of degrading, pinching systems", J. Eng. Mech., 111(8), 1010-1027. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:8(1010)
  5. Bernstein, D.S. (1993), "Nonquadratic cost and nonlinear feedback control", Int. J. Robust Nonlin., 3, 211-229. https://doi.org/10.1002/rnc.4590030303
  6. Bouc, R. (1967), "Forced vibration of mechanical system with hysteresis", Proceedings of the Fourth Conference on Nonlinear Oscillations, Prague, Czechoslovakia.
  7. Chen, G.P., Malik, O.P., Qin, Y.H. and Xu, G.Y. (1992), "Optimization technique for the design of a linear optimal power system stabilizer", IEEE T. Energy Conver., 7(3), 453-459. https://doi.org/10.1109/60.148566
  8. Chen, J.B. and Li, J. (2005), "Dynamic response and reliability analysis of nonlinear stochastic structures", Probabilist. Eng. Mech., 20(1), 33-44. https://doi.org/10.1016/j.probengmech.2004.05.006
  9. Chen, J.B. and Li, J. (2008), "Strategy for selecting representative points via tangent spheres in the probability density evolution method", Int. J. Numer. Meth. Eng., 74(13), 1988-2014. https://doi.org/10.1002/nme.2246
  10. Chen, J.B., Liu, W.Q., Peng, Y.B. and Li, J. (2007), "Stochastic seismic response and reliability analysis of baseisolated structures", J. Earthq. Eng., 11(6), 903-924. https://doi.org/10.1080/13632460701242757
  11. Chung, J. and Lee, J.M. (1994), "A new family of explicit time integration methods for linear and nonlinear structural dynamics", Int. J. Numer. Meth. Eng., 37, 3961-3976. https://doi.org/10.1002/nme.1620372303
  12. Clough, R.W. and Johnson, S.B. (1966), "Effects of stiffness degradation on earthquake ductility requirements", Proceedings of the 2nd Japan National Earthquake Engineering Conference, Tokyo, Japan.
  13. Clough, R.W. and Penzien, J. (1993), Dynamics of Structures, 2nd Edition, McGraw-Hill, New York.
  14. Eldred, M.S., Adams, B.M., Gay, D.M., Swiler, L.P., Haskell, K., Bohnhoff, W.J., Eddy, J.P., Hart, W.E., Watson, J.P., Griffin, J.D., Hough, P.D., Kolda, T.G., Williams, P.J. and Martinez-Canales, M.L. (2007), DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis (Version 4.1+ User's Manual). Sandia National Laboratories, SAND 2006-6337.
  15. Foliente, G.C. (1995), "Hysteresis modeling of wood joints and structural systems", J. Struct. Eng., 121(6), 1013-1022. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:6(1013)
  16. Iwan, W.D. (1961), The Dynamics Response of Bilinear Hysteretic System, California: California Institute of Technology.
  17. Li, J. and Ai, X.Q. (2006), "Study on random model of earthquake ground motion based on physical process", Earthq. Eng. Eng. Vib., 26(5), 21-26. (in Chinese)
  18. Li, J. and Chen, J.B. (2009), Stochastic Dynamics of Structures, John Wiley & Sons.
  19. Li, J., Peng, Y.B. and Chen, J.B. (2010a), "A physical approach to structural stochastic optimal controls", Probabilist. Eng. Mech., 25, 127-141. https://doi.org/10.1016/j.probengmech.2009.08.006
  20. Li, J., Peng, Y.B. and Chen, J.B. (2010b), "Probabilistic criteria of structural stochastic optimal controls", Probabilist. Eng. Mech., 26(2), 240-253.
  21. Ma, F., Zhang, H., Bochstedte, A., Foliente, G.C. and Paevere, P. (2004), "Parameter analysis of the differential model of hysteresis", J. Appl. Mech., 71, 342-349. https://doi.org/10.1115/1.1668082
  22. Masri, S.F., Bekey, G.A. and Caughey, T.K. (1981) "On-linear control of nonlinear flexible structures", J. Appl. Mech., 49, 871-884.
  23. Peng, Y.B., Ghanem, R. and Li, J. (2010), "Generalized optimal control policy for stochastic optimal control of structures", Struct. Control Hlth Mon. (revised and under review).
  24. Shefer, M. and Breakwell, J.V. (1987), "Estimation and control with cubic nonlinearities", J. Optimiz. Theory App., 53, 1-7. https://doi.org/10.1007/BF00938812
  25. Suhardjo, J., Spencer, J.B.F. and Sain, M.K. (1992), "Nonlinear optimal control of a duffing system", Int. J. Nonlin. Mech., 27(2), 157-172. https://doi.org/10.1016/0020-7462(92)90078-L
  26. Wen, Y.K. (1976), "Method for random vibration of hysteretic systems", J. Eng. Mech. Div., 102(2), 249-263.
  27. Yang, J.N., Agrawal, A.K. and Chen, S. (1996), "Optimal polynomial control for seismically excited non-linear and hysteretic structures", Earthq. Eng. Struct. D., 25, 1211-1230. https://doi.org/10.1002/(SICI)1096-9845(199611)25:11<1211::AID-EQE609>3.0.CO;2-3
  28. Yang, J.N., Akbarpour, A. and Ghaemmaghami, P. (1988), "Optimal control of nonlinear flexible structures", Technical Report NCEER-88-0002, National Center for Earthquake Engineering Research.
  29. Yang, J.N., Li, Z., Danielians, A. and Liu, S.C. (1992), "Hybrid control of nonlinear and hysteretic systems I", J. Eng. Mech., 118(7), 1423-1440. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:7(1423)
  30. Yang, J.N., Li, Z. and Vongchavalitkul, S. (1994), "Stochastic hybrid control of hysteretic structures", Probabilist. Eng. Mech., 9(1-2), 125-133. https://doi.org/10.1016/0266-8920(94)90036-1
  31. Yao, J.T.P. (1972), "Concept of structural control", J. Struct. Div., 98(7), 1567-1574.
  32. Zhu, W.Q., Ying, Z.G., Ni, Y.Q. and Ko, J.M. (2000), "Optimal nonlinear stochastic control of hysteretic systems", J. Eng. Mech., 126(10), 1027-1032. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:10(1027)

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