Single-loop cross-entropy-based directional importance sampling for efficient estimation of failure probability function

Abstract

Failure probability function (FPF) can not only reflect the effect of random input distribution parameter (DP) on structural safety degree, but also decouple reliability based design optimization. Nowadays, it still desires the efficient algorithms for FPF. Thus, this paper proposes an efficient and novel single-loop cross-entropy-based directional importance sampling method (SL-CE-DIS). The proposed SL-CE-DIS has two innovations. The first is constructing the transformation relationship (Tr-Re) of the samples on the limit state surface (LSS) in the standard normal space corresponding to different DP realizations. This Tr-Re is established by the property of the LSS in original physical space independent of DP, and it makes the LSS sample explored by single CE-DIS at a given DP realization can be shared by the CE-DIS at other DP realizations. The second is designing an inverse updating rule to reconstruct the quasi-optimal DIS density (DIS-D) corresponding to other DP realization, which is in the adjacent region of the given DP realization, based on CE principle, and this designed inverse updating rule can easily estimate the FPF values corresponding to other DP realization by matching the transformed LSS samples. Based on the designed LSS sample sharing strategy and inverse updating rule of DIS-D, the proposed SL-CE-DIS can use the LSS information explored by single CE-DIS at the given DP realization to estimate the FPF corresponding to the DP over the adjacent of the given DP realization, and the presented examples fully verify the superiority of the SL-CE-DIS over the other existing single-loop sampling methods for FPF.