TY - JOUR

T1 - Augmented reliability analysis for estimating imprecise first excursion probabilities in stochastic linear dynamics

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Yuan, Xiukai

AU - Wei, Pengfei

AU - Beer, Michael

N1 - Publisher Copyright:
© 2021 Elsevier Ltd

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

KW - Augmented reliability problem

KW - Directional Importance Sampling

KW - Imprecise first excursion probability

KW - Uncertain Linear Structure

KW - stochastic loading

UR - http://www.scopus.com/inward/record.url?scp=85104963912&partnerID=8YFLogxK

U2 - 10.1016/j.advengsoft.2021.102993

DO - 10.1016/j.advengsoft.2021.102993

M3 - Article

AN - SCOPUS:85104963912

SN - 0965-9978

VL - 155

JO - Advances in Engineering Software

JF - Advances in Engineering Software

M1 - 102993

ER -