Details
| Original language | English |
|---|---|
| Article number | 102993 |
| Journal | Advances in Engineering Software |
| Volume | 155 |
| Early online date | 31 Mar 2021 |
| Publication status | Published - May 2021 |
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.
Keywords
- Augmented reliability problem, Directional Importance Sampling, Imprecise first excursion probability, stochastic loading, Uncertain Linear Structure
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- General Engineering
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In: Advances in Engineering Software, Vol. 155, 102993, 05.2021.
Research output: Contribution to journal › Article › Research
}
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 - Funding Information: Matthias Faes gratefully acknowledges the financial support of the Research Foundation Flanders (FWO) under grant number 12P3519N. Matthias Faes and Pengfei Wei acknowledge the support of the Alexander von Humboldt foundation. Marcos Valdebenito acknowledges the support of ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271.
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 - stochastic loading
KW - Uncertain Linear Structure
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
VL - 155
JO - Advances in Engineering Software
JF - Advances in Engineering Software
SN - 0141-1195
M1 - 102993
ER -