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Multicut high dimensional model representation for reliability analysis

  • Chowdhury, Rajib (School of Engineering, Swansea University) ;
  • Rao, B.N. (Structural Engineering Division, Department of Civil Engineering, Indian Institute of Technology Madras)
  • Received : 2010.07.27
  • Accepted : 2011.03.09
  • Published : 2011.06.10

Abstract

This paper presents a novel method for predicting the failure probability of structural or mechanical systems subjected to random loads and material properties involving multiple design points. The method involves Multicut High Dimensional Model Representation (Multicut-HDMR) technique in conjunction with moving least squares to approximate the original implicit limit state/performance function with an explicit function. Depending on the order chosen sometimes truncated Cut-HDMR expansion is unable to approximate the original implicit limit state/performance function when multiple design points exist on the limit state/performance function or when the problem domain is large. Multicut-HDMR addresses this problem by using multiple reference points to improve accuracy of the approximate limit state/performance function. Numerical examples show the accuracy and efficiency of the proposed approach in estimating the failure probability.

References

  1. Adhikari, S. (2004), "Reliability analysis using parabolic failure surface approximation", J. Eng. Mech.-ASCE, 130(12), 1407-1427. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:12(1407)
  2. Adhikari, S. (2005), "Asymptotic distribution method for structural reliability analysis in high dimensions", P. Roy. Soc. London, Series-A, 461(2062), 3141-3158. https://doi.org/10.1098/rspa.2005.1504
  3. Alis, O.F. and Rabitz, H. (2001), "Efficient implementation of high dimensional model representations", J. Math. Chem., 29(2), 127-142. https://doi.org/10.1023/A:1010979129659
  4. Arora, J.S. (2004), Introduction to Optimum Design, Second Edition, Elsevier Academic Press, San Diego, CA.
  5. Au, S.K. and Beck, J.L. (2001), "Estimation of small failure probabilities in high dimensions by subset simulation", Prob. Eng. Mech., 16(4), 263-277. https://doi.org/10.1016/S0266-8920(01)00019-4
  6. Breitung, K. (1984), "Asymptotic approximations for multinormal integrals", J. Eng. Mech.-ASCE, 110(3), 357-366. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:3(357)
  7. Chowdhury, R. and Rao, B.N. (2009), "Assessment of high dimensional model representation techniques for reliability analysis", Prob. Eng. Mech., 24(1), 100-115. https://doi.org/10.1016/j.probengmech.2008.02.001
  8. Chowdhury, R., Rao, B.N. and Prasad, A.M. (2008), "High dimensional model representation for piece wise continuous function approximation", Comm. Numer. Meth. Eng., 24(12), 1587-1609.
  9. Computers and Structures Inc. (2004), CSI Analysis Reference Manual.
  10. Der Kiureghian, A. and Dakessian, T. (1998), "Multiple design points in first and second-order reliability", Struct. Saf., 20(1), 37-49. https://doi.org/10.1016/S0167-4730(97)00026-X
  11. Gavin, H.P. and Yau, S.C. (2008), "High-order limit state functions in the response surface method for structural reliability analysis", Struct. Saf., 30(2), 162-179. https://doi.org/10.1016/j.strusafe.2006.10.003
  12. Gupta, S. and Manohar, C.S. (2004), "An improved response surface method for the determination of failure probability and importance measures", Struct. Saf., 26(2), 123-139. https://doi.org/10.1016/S0167-4730(03)00021-3
  13. Impollonia, N. and Sofi, A. (2003), "A response surface approach for the static analysis of stochastic structures with geometrical nonlinearities", Comp. Meth. Appl. Mech. Eng., 192(37-38), 4109-4129. https://doi.org/10.1016/S0045-7825(03)00379-7
  14. Kaymaz, I. and McMahon, C.A. (2005), "A response surface method based on weighted regression for structural reliability analysis", Prob. Eng. Mech., 20(1), 11-17. https://doi.org/10.1016/j.probengmech.2004.05.005
  15. Lancaster, P. and Salkauskas, K. (1986), Curve and Surface Fitting: An Introduction, Academic Press, London.
  16. Li, G., Rosenthal, C. and Rabitz, H. (2001a), "High dimensional model representations", J. Phys. Chem. A, 105, 7765-7777. https://doi.org/10.1021/jp010450t
  17. Li, G., Wang, S.W. and Rabitz, H. (2001b), "High dimensional model representations generated from low dimensional data samples-I. mp-Cut-HDMR", J. Math. Chem., 30(1), 1-30. https://doi.org/10.1023/A:1013172329778
  18. Liu, P.L. and Der Kiureghian, A. (1991), "Finite element reliability of geometrically nonlinear uncertain structures", J. Eng. Mech.-ASCE, 117(8), 1806-1825. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:8(1806)
  19. Melchers, R.E. (1989), "Importance sampling in structural systems", Struct. Saf., 6(1), 3-10. https://doi.org/10.1016/0167-4730(89)90003-9
  20. Rackwitz, R. (2001), "Reliability analysis-a review and some perspectives", Struct. Saf., 23(4), 365-395. https://doi.org/10.1016/S0167-4730(02)00009-7
  21. Nair, P.B. and Keane, A.J. (2002), "Stochastic reduced basis methods", AIAA J., 40(8), 1653-1664. https://doi.org/10.2514/2.1837
  22. Rubinstein, R.Y. (1981), Simulation and the Monte Carlo Method, Wiley, New York.
  23. Schueller, G.I., Pradlwarter, H.W. and Koutsourelakis, P.S. (2004), "A critical appraisal of reliability estimation procedures for high dimensions", Prob. Eng. Mech., 19(4), 463-474. https://doi.org/10.1016/j.probengmech.2004.05.004
  24. Sobol, I.M. (2003), "Theorems and examples on high dimensional model representations", Rel. Eng. Sys. Saf., 79(2), 187-193. https://doi.org/10.1016/S0951-8320(02)00229-6
  25. Tunga, M.A. and Demiralp, M. (2004), "A factorized high dimensional model representation on the partitioned random discrete data", Appl. Numer. Anal. Comp Math., 1(1), 231-241. https://doi.org/10.1002/anac.200310020
  26. Tunga, M.A. and Demiralp, M. (2005), "A factorized high dimensional model representation on the nods of a finite hyperprismatic regular grid", Appl. Math. Comp., 164, 865-883. https://doi.org/10.1016/j.amc.2004.06.056
  27. Yaman, I. and Demiralp, M. (2009), "A new rational approximation technique based on transformational high dimensional model representation", Numer. Algo., 52(3), 1017-1398.
  28. Yonezawa, M., Okuda, S. and Kobayashi, H. (2009), "Structural reliability estimation based on quasi ideal importance sampling simulation", Struct. Eng. Mech., 32(1), 55-69. https://doi.org/10.12989/sem.2009.32.1.055

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