Parameter global reliability sensitivity analysis with meta-models: A probability estimation-driven approach

Parameter global reliability sensitivity (PGRS) reflects the influence of imprecise distribution parameters of basic model input variables on the variation of failure probability. It can be measured by the variance decomposition item of the failure probability function (FPF). The variance decomposition item of FPF can be expanded to the mean square of the difference between the unconditional expectation of the FPF and the conditional expectation of the FPF. To simplify the calculation, this paper uses the absolute value item of the difference to replace the square item of the difference. They both can reflect accumulation of the differences. To transform the direct triple-loop estimation of PGRS into a single-loop calculation, this paper firstly uses Bayes formula to transform the calculation of PGRS into a single-loop sample classification process and a failure-conditional probability density function (PDF) estimation. Secondly, by using the interval-conditional feature to approximate the point-conditional feature, the estimation of failure-conditional PDF for the conditional imprecise distribution parameter is substituted by estimating the interval conditional probability. Finally, the adaptive Kriging model widely used in reliability analysis is introduced in the proposed algorithm to classify samples efficiently. The proposed method only requires one matrix of samples to analyze the PGRS of all imprecise distribution parameters. The effectiveness of the proposed method is verified by three examples.