A novel approach for reliability analysis with correlated variables based on the concepts of entropy and polynomial chaos expansion

Abstract

Correlated random variables are common in industry field. In reliability analysis community, Nataf transformation is considered as a powerful tool for handling correlated random variables, since it only requires the marginal probability distribution functions of input random variables. However, when accurate marginal probability distributions are unavailable, Nataf transformation cannot be used. This paper presents an alternative method for transforming correlated random variables into independent ones based on the maximum entropy principle and the polynomial chaos expansion. The proposed method only requires the first-several statistical moments of input random variables but not the probability distribution functions. Based on the proposed method for handling correlated random variables, the statistical moments of performance functions can be calculated. In order to predict the failure probability, the fractional moment-based maximum entropy method (FM-MEM) is employed due to its accuracy. However, the FM-MEM is sensitive to the initial point of its outer loop and also requires too much CPU time. Thus, an improved version is developed to enhance the performance of the algorithm. To verify the validity of the proposed method, three numerical examples and one engineering example are tested. The results show that the proposed method is a good choice for reliability analysis with correlated random variables, especially when only the statistical moment information of input random variables is available.