Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Reliability analysis of wind-excited structures using domain decomposition method and line sampling

  • Katafygiotis, L.S. (Department of Civil Engineering, Hong Kong University of Science and Technology) ;
  • Wang, Jia (Department of Civil Engineering, Hong Kong University of Science and Technology)
  • Received : 2008.07.04
  • Accepted : 2009.10.28
  • Published : 2009.05.10
⟨ Previous Next ⟩

Abstract

In this paper the problem of calculating the probability that the responses of a wind-excited structure exceed specified thresholds within a given time interval is considered. The failure domain of the problem can be expressed as a union of elementary failure domains whose boundaries are of quadratic form. The Domain Decomposition Method (DDM) is employed, after being appropriately extended, to solve this problem. The probability estimate of the overall failure domain is given by the sum of the probabilities of the elementary failure domains multiplied by a reduction factor accounting for the overlapping degree of the different elementary failure domains. The DDM is extended with the help of Line Sampling (LS), from its original presentation where the boundary of the elementary failure domains are of linear form, to the current case involving quadratic elementary failure domains. An example involving an along-wind excited steel building shows the accuracy and efficiency of the proposed methodology as compared with that obtained using standard Monte Carlo simulations (MCS).

Keywords

Acknowledgement

Supported by : Hong Kong Research Grants Council

References

  1. Au, S.K. and Beck, J.L. (2001), "First excursion probabilities for linear systems by very efficient importance sampling", Probabilist. Eng. Mech., 16(3), 193-207 https://doi.org/10.1016/S0266-8920(01)00002-9
  2. Au, S.K. and Beck, J.L. (2003), "Importance sampling in high dimensions", Struct. Safety, 25(2), 139-163 https://doi.org/10.1016/S0167-4730(02)00047-4
  3. Brigham, E.O. (1988), The Fast Fourier Transform and its Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey
  4. Davenport, A.G. (1961), "The spectrum of horizontal gustiness near the ground in high winds", J. R. Meteorol. Soc., 87, 194-211 https://doi.org/10.1002/qj.49708737208
  5. Davenport, A.G. (1968), "The dependence of wind load upon meteorological parameters", Proceedings of the International Research Seminar on Wind Effects on Buildings and Structures, Toronto
  6. Deodatis, G. (1996), "Simulation of ergodic multivariate stochastic processes", J. Eng. Mech., 122(8), 778-787 https://doi.org/10.1061/(ASCE)0733-9399(1996)122:8(778)
  7. Di Paola, M. and Gullo, I. (2001) "Digital generation of multivariate wind field processes", Probabilist. Eng. Mech., 16, 1-10 https://doi.org/10.1016/S0266-8920(99)00032-6
  8. Grigoriu, M. (2002), Stochastic Calculus: Applications in Science and Engineering, Birkhauser Boston, New York
  9. Jacob, B. (1990), Linear Algebra, W.H. Freeman and Company, New York
  10. Katafygiotis, L.S. and Cheung, S.H. (2006), "Domain decomposition method for calculating the failure probability of linear dynamic systems subjected to Gaussian stochastic loads", J. Eng. Mech., 132(5), 475-486 https://doi.org/10.1061/(ASCE)0733-9399(2006)132:5(475)
  11. Katafygiotis, L.S. and Zuev, K.M. (2008), "Geometric insight to the challenges of solving high-dimensional reliability problems", Probabilist. Eng. Mech., 23(2-3), 208-218 https://doi.org/10.1016/j.probengmech.2007.12.026
  12. Koutsourelakis, P.S., Pradlwarter, H.J. and Schuëller, G.I. (2004), "Reliability of structures in high dimensions, part I: algorithms and applications", Probabilist. Eng. Mech., 19(4), 409-417 https://doi.org/10.1016/j.probengmech.2004.05.001
  13. Melbourne, W.H. (1980), "Comparison of measurements on the CAARC standard tall building model in simulated model wind flows", J. Wind. Eng. Ind. Aerod., 6, 73-88 https://doi.org/10.1016/0167-6105(80)90023-9
  14. Pradlwarter, H.J., Schu$\ddot{e}$ller, G.I., Koutsourelakis, P.S. and Charmpis, D.C. (2007), "Application of line sampling simulation method to reliability benchmark problems", Struct. Safety, 29, 208-221 https://doi.org/10.1016/j.strusafe.2006.07.009
  15. Proppe, C., Pradlwarter, H.J. and Schu$\ddot{e}$ller, G.I. (2003) "Equivalent linearization and Monte Carlo simulations in stochastic dynamics", Probabilist. Eng. Mech., 18(1), 1-15 https://doi.org/10.1016/S0266-8920(02)00037-1
  16. Rubinstein, R.Y. (1981), Simulation and the Monte-Carlo Method, New York: Wiley
  17. Schu$\ddot{e}$ller, G.I., Pradlwarter, H.J. and Koutsourelakis, P.S. (2003), "A comparative study of reliability estimation procedures for high dimensions", 16th ASCE Engineering Mechanics Conference, University of Washington, Seattle
  18. Schu$\ddot{e}$ller, G.I., Pradlwarter, H.J. and Koutsourelakis, P.S. (2004), "A critical appraisal of reliability estimation procedures for high dimensions", Probabilist. Eng. Mech., 19(4), 463-474 https://doi.org/10.1016/j.probengmech.2004.05.004
  19. Schu$\ddot{e}$ller, G.I. and Pradlwarter, H.J. (2007), "Benchmark study on reliability estimation in higher dimensions of structural systems – An overview", Struct. Safety, 29(3), 167-182 https://doi.org/10.1016/j.strusafe.2006.07.010
  20. Shinozuka, M. and Jan, C.M. (1972), "Digital simulation of random processes and its applications", J. Sound Vib., 25(1), 111-128 https://doi.org/10.1016/0022-460X(72)90600-1
  21. Shinozuka, M. and Deodatis, G. (1991), "Simulation of stochastic processes by spectral representation", Appl. Mech. Rev., 44(4), 191-204 https://doi.org/10.1115/1.3119501
  22. Simiu, E. and Scanlan, R.H. (1986), Wind Effects on Structures, John Wiley & Sons, Inc., New York
  23. Yuen, K.V. and Katafygiotis, L.S. (2004), "An efficient simulation method for reliability analysis using simple additive rules of probability", Probabilist. Eng. Mech., 20(1), 109-114 https://doi.org/10.1016/j.probengmech.2004.07.003

Cited by

  1. A survey on approaches for reliability-based optimization vol.42, pp.5, 2010, https://doi.org/10.1007/s00158-010-0518-6
  2. Robust optimization of a hybrid control system for wind-exposed tall buildings with uncertain mass distribution vol.12, pp.6, 2013, https://doi.org/10.12989/sss.2013.12.6.641
  3. Reliability-based optimal design of linear structures subjected to stochastic excitations vol.47, 2014, https://doi.org/10.1016/j.strusafe.2013.11.002
  4. Robust optimal design of tuned mass dampers for tall buildings with uncertain parameters vol.51, pp.1, 2015, https://doi.org/10.1007/s00158-014-1129-4
  5. Reliability-Based Design Optimization of Uncertain Stochastic Systems: Gradient-Based Scheme vol.138, pp.1, 2012, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000304
  6. An efficient simulation method for the first excursion problem of linear structures subjected to stochastic wind loads vol.166, 2016, https://doi.org/10.1016/j.compstruc.2016.01.007
  7. Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables vol.156, pp.None, 2021, https://doi.org/10.1016/j.ymssp.2021.107616
  8. Efficient Simulation Method for First Passage Problem of Linear Systems Subjected to Non-Gaussian Excitations vol.148, pp.1, 2009, https://doi.org/10.1061/(asce)em.1943-7889.0002047