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 -