Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty

authored by: Pengfei Wei, Fuchao Liu, Marcos Valdebenito, Michael Beer
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.
Organisation(s): Institute for Risk and Reliability
External Organisation(s): Northwestern Polytechnical University
Universidad Tecnica Federico Santa Maria
University of Liverpool
Tongji University
Type: Article
Journal: Mechanical Systems and Signal Processing
Volume: 149
ISSN: 0888-3270
Publication date: 15.02.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.ymssp.2020.107219 (Access: Closed)