Fixed sampling distribution determination method for structural reliability assessment with parameter uncertainty

The uncertainty of distribution parameters significantly impacts the outcomes of structural reliability analysis. Considering these uncertainties, the failure probability becomes uncertain and the estimation of its distribution often encounters burdensome computational effort. In this paper, to avoid repeated sampling of input random vector and performance function calls, an efficient quantitative estimation method for determining the distribution and quantiles of failure probability is developed through fixing the sampling distribution of input random vector. The fixed sampling distribution is innovatively designed to cover the majority of important failure domains across varying distribution parameter values, after investigating the propagation relation of uncertainty between distribution parameters and design point. Using only one sample set of input vector and iterating the weights associated with the uncertain distribution parameters, the distribution of failure probability can be obtained. In the proposed method, the repeated reliability analysis is avoided and the computational effort approximates that of a single reliability analysis. The efficiency and accuracy of the method are verified by four examples involving unimodal/bimodal distribution, low/high reliability, low/high variability, and nonlinear/high-dimensional performance functions.