An efficient surrogate-aided importance sampling framework for reliability analysis. (September 2019) - Liu, Wang-Sheng; Cheung, Sai Hung; Cao, Wen-Jun
Highlights: A new and efficient two-stage framework for reliability analysis called Surrogates for Importance Sampling (S4IS) is proposed, which is very efficient in building the surrogate by selecting support points adaptively. The basic idea is to dynamically balance the exploration and exploitation capability of the selected support points. The proposed S4IS has been validated by five illustrative examples for different types of reliability analysis problems. For the example studied, S4IS is shown to be efficient and robust to the number of random variables up to 50. Despite the Gaussian Process surrogate used in this paper, the proposed framework is applicable to other types of surrogates. Abstract: Surrogates in lieu of expensive-to-evaluate performance functions can accelerate the reliability analysis greatly. This paper proposes a new two-stage framework for surrogate-aided reliability analysis named Surrogates for Importance Sampling (S4IS). In the first stage, a coarse surrogate is built to gain the information about failure regions. The second stage zooms into the important regions and improves the accuracy of the failure probability estimator by adaptively selecting support points. The learning functions are proposed to guide the selection of support points such that the exploration and exploitation can be dynamically balanced. As a generic framework, S4IS has the potential to incorporate different types of surrogates (Gaussian Processes, Support Vector Machines, Neural Network, etc.). The effectiveness and efficiency of S4IS are validated by five illustrative examples, which involve system reliability, highly nonlinear limit-state functions, small failure probability and moderately high dimensionality. The implementation of S4IS is made available to download at https://sites.google.com/site/josephsaihungcheung/ .