An Adaptive Mixture of Normal-Inverse Gaussian Distributions for Structural Reliability Analysis

Recovering the probability distribution of the limit state function is an effective method of structural reliability analysis, in which it still is challenging to balance the precision and computational efforts. This paper proposes an adaptive mixture of normal-inverse Gaussian distributions which exhibits high flexibility to deal with this issue. First, the mixture distributions with two components were revisited briefly, and the limitations are pointed out. Then the proposed mixture distribution was established. According to the limit condition, one or two components are employed in the proposed mixture distribution to represent the unknown distribution of the limit state function (LSF), which makes the mixture distribution adaptive. To specify the unknown parameters effectively, the Laplace transform at some discrete values is utilized, in which a set of nonlinear equations can be solved easily. An effective cubature rule is utilized to assess numerically the Laplace transform and the involved moments, which can guarantee the efficiency and precision for structural reliability computation. After the LSF’s distribution is attained, the failure probability can be evaluated readily via an integral over the distribution. Five numerical examples were provided to indicate the result of the proposed method.