DOI QR코드

DOI QR Code

Stochastic optimal control of coupled structures

  • Ying, Z.G. (Department of Mechanics, Zhejiang University) ;
  • Ni, Y.Q. (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University) ;
  • Ko, J.M. (Department of Civil and Structural Engineering, The Hong Kong Polytechic University)
  • 투고 : 2002.03.18
  • 심사 : 2003.04.08
  • 발행 : 2003.06.25

초록

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

키워드

참고문헌

  1. Agrawal, A.K. and Yang, J.N. (1996), "Optimal polynomial control of seismically excited linear structures", J. Engrg. Mech., ASCE, 122, 753-761. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:8(753)
  2. Christenson, R.E., Spencer, Jr. B.F. and Johnson, E.A. (1999), "Coupled building control using active and smart damping strategies", Optimization and Control in Civil and Struct. Engrg., Civil-Comp Press, Edinburgh, 187- 195.
  3. Fleming, W.H. and Rishel, R.W. (1975), Deterministic and Stochastic Optimal Control, Springer-Verlag, New York.
  4. Gurley, K., Kareem, A., Bergman, L.A., Johnson, E.A. and Klein, R.E. (1994), "Coupling tall buildings for control of response to wind", Struct. Safety Reliability, Balkema, Rotterdam, 1553-1560.
  5. Iwanami, K., Suzuki, K. and Seto, K. (1996), "Vibration control method for parallel structures connected by damper and spring", JSME Int. J., Series C, 39, 714-720. https://doi.org/10.1299/jsmeb.39.714
  6. Kanai, K. (1957), "Seismic-empirical formula for the seismic characteristics of the ground", Bull. Earthquake Res. Institute, University of Tokyo, Tokyo, 309-325.
  7. Luco, J.E. and De Barros, F.C.P. (1998), "Optimal damping between two adjacent elastic structures", Earthq. Engrg. Struct. Dyn., 27, 649-659. https://doi.org/10.1002/(SICI)1096-9845(199807)27:7<649::AID-EQE748>3.0.CO;2-5
  8. Luco, J.E. and Wong, H.L. (1994), "Control of the seismic response of adjacent structures", Proc. of the 1st World Conf. on Structural Control, Los Angeles, California, 21-30.
  9. Matsumoto, Y., Doi, F. and Seto, K. (1999), "Vibration control of multiple building structures connected with active bridges", Proc. of the 2nd World Conf. on Structural Control, John Wiley & Sons, Chichester, 599-607.
  10. Mitsuta, S. and Seto, K. (1992), "Active vibration control of structures arranged in parallel", Proc. of the 1st Int. Conf. on Motion and Vibration Control, Japan, 146-151.
  11. Ni, Y.Q., Ko, J.M. and Ying, Z.G. (2001), "Random seismic response analysis of adjacent building coupled with non-linear hysteretic dampers", J. Sound Vib., 246, 403-417. https://doi.org/10.1006/jsvi.2001.3679
  12. Seto, K. (1994), "Vibration control method for flexible structures arranged in parallel", Proc. of the 1st World Conf. on Structural Control, Los Angeles, California, 62-71.
  13. Stengel, R.F. (1986), Stochastic Optimal Control: Theory and Application, John Wiley & Sons, New York.
  14. Sugino, S., Sakai, D., Kundu, S. and Seto, K. (1999), "Vibration control of parallel structures connected with passive devices designed by GA", Proc. of the 2nd World Conf. on Structural Control, John Wiley & Sons, Chichester, 329-337.
  15. Tajimi, H. (1960), "A statistics method of determining the maximum response of a building structure during an earthquake", Proc. of the 2nd World Conf. on Earthquake Engineering, Tokyo-Kyoto, 781-798.
  16. Xu, Y.L., He, Q. and Ko J.M. (1999), "Dynamic response of damper-connected adjacent buildings under earthquake excitation", Engrg. Struct., 21, 135-148. https://doi.org/10.1016/S0141-0296(97)00154-5
  17. Yamada, Y., Ikawa, N., Yokoyama, H. and Tachibana, E. (1994), "Active control of structures using the joining member with negative stiffness", Proc. of the 1st World Conf. on Structural Control, Los Angeles, California, 41-49.
  18. Yang, J.N., Agrawal, A.K. and Chen, S. (1996), "Optimal polynomial control for seismically excited non-linear and hysteretic structures", Earthq. Engrg. Struct. Dyn., 25, 1211-1230. https://doi.org/10.1002/(SICI)1096-9845(199611)25:11<1211::AID-EQE609>3.0.CO;2-3
  19. Zhu, W.Q., Huang, Z.L. and Yang, Y.Q. (1997), "Stochastic averaging of quasi-integrable Hamiltonian systems", J. Appl. Mech., ASME, 64, 975-984. https://doi.org/10.1115/1.2789009
  20. Zhu, W.Q. and Lin, Y.K. (1991), "Stochastic averaging of energy envelope", J. Engrg. Mech., ASCE, 117, 1890- 1905. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:8(1890)
  21. Zhu, W.Q. and Ying, Z.G. (1999), "Optimal nonlinear feedback control of quasi-Hamiltonian systems", Sci. China, Series A, 42, 1213-1219. https://doi.org/10.1007/BF02875989
  22. Zhu, W.Q., Ying, Z.G., Ni, Y.Q. and Ko, J.M. (2000), "Optimal nonlinear stochastic control of hysteretic systems", J. Engrg. Mech., ASCE, 126, 1027-1032. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:10(1027)
  23. Zhu, W.Q., Ying, Z.G. and Soong, T.T. (1999), "Optimal nonlinear feedback control of structures under random loading", Stochastic Struct. Dyn., Balkema, Rotterdam, 141-148.
  24. Zhu, W.Q., Ying, Z.G. and Soong, T.T. (2001), "An optimal nonlinear feedback control strategy for randomly excited structural systems", Nonlinear Dyn., 24, 31-51. https://doi.org/10.1023/A:1026527404183
  25. Zhu, W.Q., Ying, Z.G. and Suzuki, Y. (2000), "Optimal nonlinear feedback control of building structures with AMD under non-white random ground acceleration excitation", Adv. Struct. Dyn., Elsevier, 1429-1436.

피인용 문헌

  1. A stochastic optimal time-delay control for nonlinear structural systems vol.31, pp.5, 2009, https://doi.org/10.12989/sem.2009.31.5.621