Augmented reliability analysis for estimating imprecise first excursion probabilities in stochastic linear dynamics

authored by: Matthias G.R. Faes, Marcos A. Valdebenito, Xiukai Yuan, Pengfei Wei, Michael Beer
Abstract: Imprecise probability allows quantifying the level of safety of a system taking into account the effect of both aleatory and epistemic uncertainty. The practical estimation of an imprecise probability is usually quite demanding from a numerical viewpoint, as it is necessary to propagate separately both types of uncertainty, leading in practical cases to a nested implementation in the so-called double loop approach. In view of this issue, this contribution presents an alternative approach that avoids the double loop by replacing the imprecise probability problem by an augmented, purely aleatory reliability analysis. Then, with the help of Bayes’ theorem, it is possible to recover an expression for the failure probability as an explicit function of the imprecise parameters from the augmented reliability problem, which ultimately allows calculating the imprecise probability. The implementation of the proposed framework is investigated within the context of imprecise first excursion probability estimation of uncertain linear structures subject to imprecisely defined stochastic quantities and crisp stochastic loads. The associated augmented reliability problem is solved within the context of Directional Importance Sampling, leading to an improved accuracy at reduced numerical costs. The application of the proposed approach is investigated by means of two examples. The results obtained indicate that the proposed approach can be highly efficient and accurate.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): KU Leuven
Universidad Adolfo Ibanez
Xiamen University
Northwestern Polytechnical University
University of Liverpool
Tongji University
Type: Article
Journal: Advances in Engineering Software
Volume: 155
ISSN: 0141-1195
Publication date: 05.2021
Publication status: Published
ASJC Scopus subject areas: Software, Engineering(all)
Electronic version(s): https://doi.org/10.1016/j.advengsoft.2021.102993 (Access: Closed)