Browse > Article
http://dx.doi.org/10.12989/sem.2011.38.5.651

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)
Publication Information
Structural Engineering and Mechanics / v.38, no.5, 2011 , pp. 651-674 More about this Journal
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.
Keywords
structural reliability; weight function; high dimensional model representation; multiple design points; failure probability;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 Yaman, I. and Demiralp, M. (2009), "A new rational approximation technique based on transformational high dimensional model representation", Numer. Algo., 52(3), 1017-1398.
2 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.   DOI
3 Adhikari, S. (2004), "Reliability analysis using parabolic failure surface approximation", J. Eng. Mech.-ASCE, 130(12), 1407-1427.   DOI   ScienceOn
4 Adhikari, S. (2005), "Asymptotic distribution method for structural reliability analysis in high dimensions", P. Roy. Soc. London, Series-A, 461(2062), 3141-3158.   DOI   ScienceOn
5 Breitung, K. (1984), "Asymptotic approximations for multinormal integrals", J. Eng. Mech.-ASCE, 110(3), 357-366.   DOI   ScienceOn
6 Alis, O.F. and Rabitz, H. (2001), "Efficient implementation of high dimensional model representations", J. Math. Chem., 29(2), 127-142.   DOI   ScienceOn
7 Arora, J.S. (2004), Introduction to Optimum Design, Second Edition, Elsevier Academic Press, San Diego, CA.
8 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.   DOI   ScienceOn
9 Chowdhury, R. and Rao, B.N. (2009), "Assessment of high dimensional model representation techniques for reliability analysis", Prob. Eng. Mech., 24(1), 100-115.   DOI   ScienceOn
10 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.
11 Computers and Structures Inc. (2004), CSI Analysis Reference Manual.
12 Der Kiureghian, A. and Dakessian, T. (1998), "Multiple design points in first and second-order reliability", Struct. Saf., 20(1), 37-49.   DOI   ScienceOn
13 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.   DOI   ScienceOn
14 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.   DOI   ScienceOn
15 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.   DOI   ScienceOn
16 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.   DOI   ScienceOn
17 Liu, P.L. and Der Kiureghian, A. (1991), "Finite element reliability of geometrically nonlinear uncertain structures", J. Eng. Mech.-ASCE, 117(8), 1806-1825.   DOI
18 Lancaster, P. and Salkauskas, K. (1986), Curve and Surface Fitting: An Introduction, Academic Press, London.
19 Li, G., Rosenthal, C. and Rabitz, H. (2001a), "High dimensional model representations", J. Phys. Chem. A, 105, 7765-7777.   DOI   ScienceOn
20 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.   DOI   ScienceOn
21 Melchers, R.E. (1989), "Importance sampling in structural systems", Struct. Saf., 6(1), 3-10.   DOI   ScienceOn
22 Rackwitz, R. (2001), "Reliability analysis-a review and some perspectives", Struct. Saf., 23(4), 365-395.   DOI   ScienceOn
23 Nair, P.B. and Keane, A.J. (2002), "Stochastic reduced basis methods", AIAA J., 40(8), 1653-1664.   DOI   ScienceOn
24 Rubinstein, R.Y. (1981), Simulation and the Monte Carlo Method, Wiley, New York.
25 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.   DOI   ScienceOn
26 Sobol, I.M. (2003), "Theorems and examples on high dimensional model representations", Rel. Eng. Sys. Saf., 79(2), 187-193.   DOI   ScienceOn
27 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.   DOI   ScienceOn
28 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.   DOI   ScienceOn