Details
| Original language | English |
|---|---|
| Article number | 107219 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 149 |
| Early online date | 24 Aug 2020 |
| Publication status | Published - 15 Feb 2021 |
Abstract
Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack of information. In this work, a new methodology framework, named as “Non-intrusive Imprecise Probabilistic Integration (NIPI)”, is developed for achieving the above target, and specifically, the distributional probability-box model and the estimation of the corresponding probabilistic moments of model responses are of concern. The NIPI owns two attractive characters. First, the spatial correlation information in both aleatory and epistemic uncertainty spaces, revealed by the Gaussian Process Regression (GPR) model, is fully integrated for deriving NIPI estimations of high accuracy by using Bayesian inference. Second, the numerical errors are regarded as a kind of epistemic uncertainty, by analytically propagating them, the posterior variances are derived for indicating the errors of the NIPI estimations. Further, an adaptive experiment design strategy is developed to accelerate the convergence of NIPI by making full use of the information of “contribution to posterior variance” revealed by the GPR model. The performance of the proposed methods is demonstrated by numerical and engineering examples.
Keywords
- Active learning, Bayesian inference, Epistemic uncertainty, Gaussian process regression, Imprecise probabilities, Probabilistic integration, Uncertainty quantification
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 149, 107219, 15.02.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty
AU - Wei, Pengfei
AU - Liu, Fuchao
AU - Valdebenito, Marcos
AU - Beer, Michael
N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (NSFC 51905430). The first author is also supported by the Alexander von Humboldt Foundation of Germany and the Top International University Visiting Program for Outstanding Young Scholars of Northwestern Polytechnical University. The third author would also like to acknowledge the support from ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271.
PY - 2021/2/15
Y1 - 2021/2/15
N2 - Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack of information. In this work, a new methodology framework, named as “Non-intrusive Imprecise Probabilistic Integration (NIPI)”, is developed for achieving the above target, and specifically, the distributional probability-box model and the estimation of the corresponding probabilistic moments of model responses are of concern. The NIPI owns two attractive characters. First, the spatial correlation information in both aleatory and epistemic uncertainty spaces, revealed by the Gaussian Process Regression (GPR) model, is fully integrated for deriving NIPI estimations of high accuracy by using Bayesian inference. Second, the numerical errors are regarded as a kind of epistemic uncertainty, by analytically propagating them, the posterior variances are derived for indicating the errors of the NIPI estimations. Further, an adaptive experiment design strategy is developed to accelerate the convergence of NIPI by making full use of the information of “contribution to posterior variance” revealed by the GPR model. The performance of the proposed methods is demonstrated by numerical and engineering examples.
AB - Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack of information. In this work, a new methodology framework, named as “Non-intrusive Imprecise Probabilistic Integration (NIPI)”, is developed for achieving the above target, and specifically, the distributional probability-box model and the estimation of the corresponding probabilistic moments of model responses are of concern. The NIPI owns two attractive characters. First, the spatial correlation information in both aleatory and epistemic uncertainty spaces, revealed by the Gaussian Process Regression (GPR) model, is fully integrated for deriving NIPI estimations of high accuracy by using Bayesian inference. Second, the numerical errors are regarded as a kind of epistemic uncertainty, by analytically propagating them, the posterior variances are derived for indicating the errors of the NIPI estimations. Further, an adaptive experiment design strategy is developed to accelerate the convergence of NIPI by making full use of the information of “contribution to posterior variance” revealed by the GPR model. The performance of the proposed methods is demonstrated by numerical and engineering examples.
KW - Active learning
KW - Bayesian inference
KW - Epistemic uncertainty
KW - Gaussian process regression
KW - Imprecise probabilities
KW - Probabilistic integration
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=85089747769&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2020.107219
DO - 10.1016/j.ymssp.2020.107219
M3 - Article
AN - SCOPUS:85089747769
VL - 149
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 107219
ER -