Maximum Entropy Method-Based Reliability Analysis With Correlated Input Variables via Hybrid Dimension-Reduction Method

Abstract

The estimation of the statistical moments is widely involved in the industrial application, whose accuracy affects the reliability analysis result considerably. In this study, a novel hybrid dimension-reduction method based on the Nataf transformation is proposed to calculate the statistical moments of the performance function with correlated input variables. Nataf transformation is intrinsically the Gaussian copula, which is commonly used to transform the correlated input variables into independent ones. To calculate the numerical integration of the univariate component function in the proposed method, a normalized moment-based quadrature rule is employed. According to the statistical moments obtained by the proposed method, the probability density function of the performance function can be recovered accurately via maximum entropy method. Six examples are tested to illustrate the accuracy and efficiency of the proposed method, compared with that of Monte Carlo simulation, the conventional univariate dimension-reduction method, and the bivariate dimension-reduction method. It is confirmed that the proposed method achieves a good tradeoff between accuracy and efficiency for structural reliability analysis with correlated input variables.