Regional reliability sensitivity analysis based on dimension reduction technique

Reliability sensitivity analysis is crucial for efficient design optimisation based on parametric modelling. A common fact in applications is that reliability shows different degrees of sensitivity to changes in the ranges of design parameters within a design space. Therefore, a regional reliability sensitivity analysis (RRSA) is proposed to study how the reliability-based sensitivity indexes change when the local ranges of the design parameters are modified. In this study, a method combining the Bayesian formula and the sampling simulation method is utilised to obtain the derivative of the failure probability in an augmented space without the need to fit a function. Based on the idea of averaging the square of the local gradients in the entire parameter space, a covariance matrix is constructed using the average outer product of the gradient of the failure probability function (FPF) for the RRSA. As an emerging dimension-reduction technique, the active subspace method (ASM) is employed to identify the important directions of design variables to perform a reliability-based sensitivity analysis. The covariance matrix for the high-dimensional reliability analysis is estimated using the dynamic propagation sampling (DPS) method. Finally, we demonstrate the effectiveness and efficiency of the proposed RRSA through a numerical example wherein a Monte Carlo simulation (MCS) is employed for comparison.