A new structural reliability analysis method under non-parameterized probability box variables

The probability box (P-box) model is an effective quantification tool that can deal with aleatory and epistemic uncertainties and can generally be categorized into two classes, namely, parameterized P-box and non-parameterized P-box ones. This paper proposes a new structural reliability analysis method with the non-parameterized P-box uncertainty, through which bounds of the failure probability can be obtained efficiently. For the convenience of calculation, the reliability analysis problems are divided into the univariate and multivariate ones. Firstly, structural failure probability bound analysis for the univariate problem is converted into solving two linear programming models by discretizing the cumulative distribution function (CDF) of the P-box variable, which can be solved efficiently by the simplex algorithm. Secondly, an iterative technique is used to decompose the multivariate problem into a series of univariate problems, in which only one non-parameterized P-box's CDF is optimized and the remaining counterparts are fixed. Hence, the failure probability bounds can be obtained by solving a series of linear programming problems. Finally, the effectiveness of the proposed method is demonstrated by investigating three numerical examples.