An improved high order moment-based saddlepoint approximation method for reliability analysis

Abstract

Moment-based methods use only statistical moments of random variables for reliability analysis. The cumulative distribution function (CDF) or probability density function (PDF) of a performance function can be constructed from the perspective of the first few statistical moments, and the failure probability can be evaluated accordingly. However, existing moment-based methods may lead to large errors or instability. As such, the present paper focuses on the high order moment method for higher accuracy of reliability estimation by combining the common saddlepoint approximation technique, and an improved high order moment-based saddlepoint approximation (SPA) method for reliability analysis is presented. The approximated cumulant generating function (CGF) and the CDF of the performance function in terms of its first four statistical-moments are constructed. The developed method can be used for reliability evaluation of uncertain structures follow any types of distribution. Several numerical examples are given to demonstrate the efficacy and accuracy of the proposed method. Comparisons of the new method and several existing high order moment methods are also made on the reliability assessment.