Efficient estimation procedure for failure probability function by an augmented directional sampling

Failure probability function (FPF) can reflect quantitative effects of random input distribution parameter (DP) on failure probability, and it is significant for decoupling reliability-based design optimization (RBDO). But the FPF estimation is time-consuming since it generally requires repeated reliability analyses at different DPs. For efficiently estimating FPF, an augmented directional sampling (A-DS) is proposed in this paper. By using the property that the limit state surface (LSS) in physical input space is independent of DP, the A-DS establishes transformation of LSS samples in standard normal spaces corresponding to different DPs. By the established transformation in different standard normal spaces, the LSS samples obtained by DS at a given DP can be transformed to those at other DPs. After simple interpolation post-processing on those transformed samples, the failure probability at other DPs can be estimated by DS simultaneously. The main novelty of A-DS is that a strategy of sharing DS samples is designed for estimating the failure probability at different DPs. The A-DS avoids repeated reliability analyses and inherits merit of DS suitable for solving problems with multiple failure modes and small failure probability. Compared with other FPF estimation methods, the examples sufficiently verify the accuracy and efficiency of A-DS.