The single-loop Kriging model combined with Bayes’ formula for time-dependent failure probability based global sensitivity

Time-dependent failure probability based global sensitivity (TDFP-GS) analysis quantifies the effect of input uncertainty on the failure probability for the time-dependent structure, which is usually time-consuming to be performed. For alleviating this issue, a method by combining the single-loop Kriging (SILK) model with Bayes’ formula is proposed in this work. After transformed by Bayes’ formula, the estimation of the conditional failure probability in the TDFP-GS expression is converted to that of conditional probability density function (PDF) of the input on the failure domain, which eliminates the dimensionality dependence in the calculation process. The SILK model is established to estimate the failure probability of the structure. When all the failure samples are accurately recognized by the converged SILK model, the conditional PDF can be estimated by the kernel density estimation (KDE), which doesn't require any performance function evaluation. The TDFP-GS can be estimated by the difference between the original PDF and the conditional PDF of the input on the failure domain. Four examples are presented for validating the effectiveness and the efficiency of the proposed method.