Novel probabilistic model for searching most probable point in structural reliability analysis

Abstract

The Most Probable Point (MPP) is typically searched by transforming the basic random variables from original to standard normal space in the traditional first order reliability method (FORM). However, the FORM formulation may provide inaccurate MPP for those reliability problems with several local MPPs. The FORM based probabilistic model is a computational method and it may provide inaccuracy and unstable results for complex problems. In this paper, a probabilistic model is proposed to evaluate the MPP using cumulative distribution function (CDF) of basic random variables. The MPP is determined by solving an optimization problem in the original space which maximizes a multiplier function in terms of the CDF of the random variables. The performance of the proposed probabilistic model, usual FORM and first order saddle point approximation method (FOSAM) using SQP optimization solver is demonstrated by several numerical and engineering problems with normal and non-normal variables. The results of the numerical study illustrate that the proposed model provides an efficient approach to obtain the MPP which is simpler and more accurate than the usual FORM and FOSAM; particularly for reliability problems with non-normal random variables.