Premium
Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables
Author(s) -
Ji Jian,
Kodikara Jayantha K.
Publication year - 2015
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2380
Subject(s) - limit (mathematics) , gaussian , mathematics , reliability (semiconductor) , transformation (genetics) , limit state design , random variable , algorithm , space (punctuation) , state space , mathematical optimization , simple (philosophy) , computer science , mathematical analysis , statistics , engineering , power (physics) , biochemistry , physics , chemistry , structural engineering , epistemology , philosophy , quantum mechanics , gene , operating system
Summary In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u‐space), the reliability analysis that is simply realized in the original space (x‐space, non‐Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first‐order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x‐space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non‐Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed‐form solution. With the aid of numerical differentiation analysis in x‐space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright © 2015 John Wiley & Sons, Ltd.