A fourth-order moment based hybrid reliability analysis method integrating high-dimensional model decomposition and Taylor expansion

In uncertain engineering structures involving both random and interval variables, the upper and lower bounds of failure probability serve as critical indicators for evaluating the reliability and safety of the structure. Whether the upper and lower bounds of failure probability can be accurately and efficiently estimated has become a critical factor in addressing such problems. Therefore, this article proposes an efficient random-interval hybrid reliability analysis method. Firstly, this study applies the multiplicative dimension reduction method to approximate the performance function as the product of a series of univariate functions. By leveraging the Taylor series expansion, it enables efficient computation of arbitrary-order moments of the performance function. Secondly, building upon this foundation, this study performs a Taylor expansion of the interval univariate function and proposes an approximation approach for determining the extrema of the high-dimensional function. Furthermore, based on the decomposition of the high-dimensional model, the random-interval hybrid fourth-order moment reliability index is expanded into a univariate quadratic function form. By leveraging the mathematical properties of this function, an efficient solution for the upper and lower bounds of the failure probability is obtained. Finally, the accuracy and efficiency of the proposed method are verified through three numerical examples and one finite element example.