Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation

• Published in: Reliability engineering & system safety Vol. 216; p. 107991
• Main Authors: El Masri, Maxime, Morio, Jérôme, Simatos, Florian
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.12.2021; Elsevier BV; Elsevier
• Subjects: Algorithms; Computer Science; Covariance matrix; Cross-entropy; Entropy; Entropy (Information theory); Failure probability; High dimension; Importance sampling; Mathematics; Modeling and Simulation; Probability; Projection; Rare event simulation; Reliability analysis; Reliability engineering; Sampling; Projection; High dimension; Rare event simulation; Failure probability; Cross-entropy; Importance sampling; Failure probablity
• ISSN: 0951-8320; 1879-0836; 1879-0836
• DOI: 10.1016/j.ress.2021.107991

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we propose a new cross-entropy-based importance sampling algorithm to improve rare event probability estimation in high dimension. We focus on the cross-entropy method with Gaussian auxiliary distributions and we suggest to update the Gaussian covariance matrix only in a one-dimensional subspace. For that purpose, the main idea is to consider the projection in the one-dimensional subspace spanned by the sample mean vector, which gives an influential direction for the variance estimation. This approach does not require any additional simulation budget compared to the basic cross-entropy algorithm and we show on different numerical test cases that it greatly improves its performance in high dimension. •We propose a Cross Entropy (CE) based algorithm for rare event estimation in high dimension.•We focus on the CE method with Gaussian auxiliary distributions, in unimodal problems.•The method relies on a projection in a one-dimensional subspace.•The proposed algorithm outperforms the basic CE algorithm in high dimensional examples.