Structural Engineering and Mechanics

  • 제38권1호
  • /
  • Pages.125-140
  • /
  • 2011
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Low-discrepancy sampling for structural reliability sensitivity analysis

  • Cao, Zhenggang (School of Civil Engineering, Harbin Institute of Technology) ;
  • Dai, Hongzhe (School of Civil Engineering, Harbin Institute of Technology) ;
  • Wang, Wei (School of Civil Engineering, Harbin Institute of Technology)
  • 투고 : 2009.09.14
  • 심사 : 2010.12.15
  • 발행 : 2011.04.10
⟨ 이전 논문 다음 논문 ⟩

초록

This study presents an innovative method to estimate the reliability sensitivity based on the low-discrepancy sampling which is a new technique for structural reliability analysis. Two advantages are contributed to the method: one is that, by developing a general importance sampling procedure for reliability sensitivity analysis, the partial derivative of the failure probability with respect to the distribution parameter can be directly obtained with typically insignificant additional computations on the basis of structural reliability analysis; and the other is that, by combining various low-discrepancy sequences with the above importance sampling procedure, the proposed method is far more efficient than that based on the classical Monte Carlo method in estimating reliability sensitivity, especially for problems of small failure probability or problems that require a large number of costly finite element analyses. Examples involving both numerical and structural problems illustrate the application and effectiveness of the method developed, which indicate that the proposed method can provide accurate and computationally efficient estimates of reliability sensitivity.

키워드

참고문헌

  1. Au, S.K. (2005), "Reliability-based design sensitivity by efficient simulation", Comput. Struct., 83, 1048-1061. https://doi.org/10.1016/j.compstruc.2004.11.015
  2. Bjerager, P. and Krenk, S. (1989), "Parametric sensitivity in first order reliability analysis", J. Eng. Mech., 115, 1577-1582. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:7(1577)
  3. Bucher, C. (2009), "Asymptotic sampling for high-dimensional reliability analysis", Probabilist. Eng. Mech., 24, 504-510. https://doi.org/10.1016/j.probengmech.2009.03.002
  4. Dai, H.Z. and Wang, W. (2009), "Application of low-discrepancy sampling method in structural reliability analysis", Struct. Saf., 31, 55-64. https://doi.org/10.1016/j.strusafe.2008.03.001
  5. Ditlevsen, O. and Madsen, H.O. (1996), Structural Reliability Methods, John Wiley & Sons, Chichester.
  6. Du, X. and Chen, W. (2002), "Efficient uncertainty analysis methods for multidisciplinary robust design", AIAA J., 40, 545-552. https://doi.org/10.2514/2.1681
  7. Enevoldsen, I. and Sorensen, J.D. (1994), "Reliability-based optimization in structural engineering", Struct. Saf., 15, 169-196. https://doi.org/10.1016/0167-4730(94)90039-6
  8. Engelund, S. and Rackwitz, R. (1993), "A benchmark study on importance sampling techniques in structural reliability", Struct. Saf., 12, 255-276. https://doi.org/10.1016/0167-4730(93)90056-7
  9. Fang, K.T. and Wang, Y. (1994), Number-theoretic Methods in Statistics, Chapman & Hall, London.
  10. Helton, J.C., Johnson, J.D., Sallaberry, C.J. and Storlie, C.B. (2006), "Survey of sampling-based methods for uncertainty and sensitivity analysis", Reliab. Eng. Syst. Saf., 91, 1175-1209. https://doi.org/10.1016/j.ress.2005.11.017
  11. Hua, L.K. and Wang, Y. (1981), Applications of Number Theory to Numerical Analysis, Springer/Science Press, Berlin/Beijing.
  12. Kang, S.C., Koh, H.M. and Choo, J.F. (2010), "An efficient response surface method using moving least squares approximation for structural reliability analysis", Probabilist. Eng. Mech., 25, 365-371. https://doi.org/10.1016/j.probengmech.2010.04.002
  13. Karamchandani, A. and Cornell, C.A. (1992), "Sensitivity estimation within first and second order reliability methods", Struct. Saf., 11, 95-107. https://doi.org/10.1016/0167-4730(92)90002-5
  14. Kim, S.H. and Na, S.W. (1997), "Response surface method using vector projected sampling points", Struct. Saf., 19, 3-19. https://doi.org/10.1016/S0167-4730(96)00037-9
  15. L'Ecuyer, P. and Perron, G. (1994), "On the convergence rates of IPA and FDC derivative estimators", Oper. Res., 42, 643-656. https://doi.org/10.1287/opre.42.4.643
  16. Lu, Z.Z., Song, S.F., Yue, Z.F. and Wang, J. (2008), "Reliability sensitivity method by line sampling", Struct. Saf., 30, 517-532. https://doi.org/10.1016/j.strusafe.2007.10.001
  17. Melchers, R.E. (1999), Structural Reliability Analysis and Prediction, second edition, John Wiley & Sons, Chichester.
  18. Melchers, R.E. and Ahammed, M. (2004), "A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability", Comput. Struct., 82, 55-61. https://doi.org/10.1016/j.compstruc.2003.08.003
  19. Nie, J.S. and Ellingwood, B.R. (2004), "A new directional simulation method for system reliability. $Part\;^2$: application of deterministic point sets", Probabilist. Eng. Mech., 19, 425-436. https://doi.org/10.1016/j.probengmech.2004.03.004
  20. Niederreiter, H. (1992), Random Number Generation and Quasi-monte Carlo Methods, SIAM, Philadelphia.
  21. Rahman, S. and Wei, D. (2006), "A univariate approximation at most probable point for higher-order reliability analysis", Int. J. Solids Struct., 43, 2820-2839. https://doi.org/10.1016/j.ijsolstr.2005.05.053
  22. Shinoda, M. (2007), "Quasi-Monte Carlo simulation with low-discrepancy sequence for reinforced soil slopes", J. Geotech. Geoenviron., 133, 393-404. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:4(393)
  23. Song, S.F., Lu, Z.Z. and Qiao, H.W. (2009), "Subset simulation for structural reliability sensitivity analysis", Reliab. Eng. Syst. Saf., 94, 658-665. https://doi.org/10.1016/j.ress.2008.07.006
  24. Sues, H.R. and Cesare, M.R. (2005), "System reliability and sensitivity factors via the MPPSS method", Probabilist. Eng. Mech., 20, 148-157. https://doi.org/10.1016/j.probengmech.2005.02.001
  25. Wu, Y.T. (1994), "Computational methods for efficient structural reliability and reliability sensitivity analysis", AIAA J., 32, 1717-1723. https://doi.org/10.2514/3.12164
  26. Wu, Y.T. and Mohanty, S. (2006), "Variable screening and ranking using sampling-based sensitivity measures", Reliab. Eng. Syst. Saf., 91, 634-647. https://doi.org/10.1016/j.ress.2005.05.004
  27. Zhao, Y.G. and Ang, A.HS. (2003), "System reliability assessment by method of moments", J. Struct. Eng., 129, 1341-1349. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1341)

피인용 문헌

  1. An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method vol.47, 2017, https://doi.org/10.1016/j.cnsns.2016.11.021
  2. Probabilistic sensitivity analysis of suspension bridges to near-fault ground motion vol.15, pp.1, 2013, https://doi.org/10.12989/scs.2013.15.1.15
  3. An adaptive directional importance sampling method for structural reliability analysis vol.70, 2018, https://doi.org/10.1016/j.strusafe.2017.07.006
  4. A new adaptive importance sampling Monte Carlo method for structural reliability vol.17, pp.1, 2013, https://doi.org/10.1007/s12205-013-1779-6
  5. A robust approximation method for nonlinear cases of structural reliability analysis vol.133, 2017, https://doi.org/10.1016/j.ijmecsci.2017.08.038
  6. A new effective approach for computation of reliability index in nonlinear problems of reliability analysis vol.60, 2018, https://doi.org/10.1016/j.cnsns.2018.01.016
  7. Locating design point in structural reliability analysis by introduction of a control parameter and moving limited regions vol.126, 2017, https://doi.org/10.1016/j.ijmecsci.2017.04.003
  8. An efficient reliability analysis strategy for low failure probability problems vol.78, pp.2, 2021, https://doi.org/10.12989/sem.2021.78.2.209