High-Order Moment Method for Structural Reliability Analysis Including Random Variables with Unknown Distributions

Abstract

The high-order moment methods, being very simple, are widely used for structural reliability analysis. The basic procedure of moment methods includes two steps: firstly, the first few moments of the performance function were determined using the new point estimate method

secondly, the corresponding failure probability can be obtained from the moment-based reliability index. In the new point estimate method, the basic random variables are assumed having known probability distributions to realize the Rosenblatt transformation and its inverse transformation. However, in practical applications, the probability distributions of some random variables maybe unknown, and the probabilistic characteristics of these variables maybe expressed using only statistical moments. This paper aims to investigate the high-order moment methods including random variables with unknown probability distribution based on the fourth-moment transformation technique. Several examples are examined under different conditions to demonstrate the accuracy and efficiency of the present method. Since only the first few moments of the performance functions are used, and it can be conducted even when the probability distributions of the random variables are unknown, structural reliability analysis should become simpler and more convenient using the present method.