An Efficient High-Order-Moment-Based Reliability Method Combining the Maximum Likelihood Point and Cubic Normal Transformation

Abstract

Moment-based methods can measure the safety degrees of mechanical systems affected by unavoidable uncertainties, utilizing only the statistical moments of random variables for reliability analysis. For the conventional derivation of the first four statistical moments based on the second-order Taylor expansion series evaluated at the most likelihood point (MLP), skewness and kurtosis involve the higher fourth raw moments of random variables and thus are unfavorable for engineering applications. This paper develops new computing formulae for the first four statistical moments which require only the first four central moments of random variables, and the probability distribution of the performance function is approximated using cubic normal transformation. Several numerical examples are given to demonstrate the accuracy of the proposed methods. Comparisons of the two proposed approaches and the maximum entropy method (ME) are also made regarding reliability assessment.