Bayesian inversion for imprecise probabilistic models using a novel entropy-based uncertainty quantification metric

Yang, Lechang, Bi, Sifeng, Faes, Matthias GR, Broggi, Matteo and Beer, Michael ORCID: 0000-0002-0611-0345 (2022) Bayesian inversion for imprecise probabilistic models using a novel entropy-based uncertainty quantification metric. Mechanical Systems and Signal Processing, 162. p. 107954.

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Official URL: http://dx.doi.org/10.1016/j.ymssp.2021.107954

Abstract

Uncertainty quantification metrics have a critical position in inverse problems for dynamic systems as they quantify the discrepancy between numerically predicted samples and collected observations. Such metric plays its role by rewarding the samples for which the norm of this discrepancy is small and penalizing the samples otherwise. In this paper, we propose a novel entropy-based metric by utilizing the Jensen–Shannon divergence. Compared with other existing distance-based metrics, some unique properties make this entropy-based metric an effective and efficient tool in solving inverse problems in presence of mixed uncertainty (i.e. combinations of aleatory and epistemic uncertainty) such as encountered in the context of imprecise probabilities. Implementation-wise, an approximate Bayesian computation method is developed where the proposed metric is fully embedded. To reduce the computation cost, a discretized binning algorithm is employed as a substitution of the conventional multivariate kernel density estimates. For validation purpose, a static case study is first demonstrated where comparisons towards three other well-established methods are made available. To highlight its potential in complex dynamic systems, we apply our approach to the NASA LaRC Uncertainty Quantification challenge 2014 problem and compare the obtained results with those from 6 other research groups as found in literature. These examples illustrate the effectiveness of our approach in both static and dynamic systems and show its promising perspective in real engineering cases such as structural health monitoring in conjunction with dynamic analysis.

Item Type:	Article
Uncontrolled Keywords:	Uncertainty quantification, Bayesian inverse problem, Imprecise probability, Entropy, Jensen-Shannon divergence, Approximate Bayesian computation
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	02 Aug 2021 07:53
Last Modified:	18 Jan 2023 21:34
DOI:	10.1016/j.ymssp.2021.107954
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3131935