Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds

Dang, Chao, Wei, Pengfei, Faes, Matthias GR and Beer, Michael ORCID: 0000-0002-0611-0345 (2022) Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds. COMPUTERS & STRUCTURES, 270. p. 106860.

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Official URL: http://dx.doi.org/10.1016/j.compstruc.2022.106860

Abstract

Uncertainties existing in physical and engineering systems can be characterized by different kinds of mathematical models according to their respective features. However, efficient propagation of hybrid uncertainties via an expensive-to-evaluate computer simulator is still a computationally challenging task. In this contribution, estimation of response expectation function (REF), its variable importance and bounds under hybrid uncertainties in the form of precise probability models, parameterized probability-box models and interval models is investigated through a Bayesian approach. Specifically, a new method, termed “Parallel Bayesian Quadrature Optimization” (PBQO), is developed. The method starts by treating the REF estimation as a Bayesian probabilistic integration (BPI) problem with a Gaussian process (GP) prior, which in turn implies a GP posterior for the REF. Then, one acquisition function originally developed in BPI and other two in Bayesian global optimization are introduced for Bayesian experimental designs. Besides, an innovative strategy is also proposed to realize multi-point selection at each iteration. Overall, a novel advantage of PBQO is that it is capable of yielding the REF, its variable importance and bounds simultaneously via a pure single-loop procedure allowing for parallel computing. Three numerical examples are studied to demonstrate the performance of the proposed method over some existing methods.

Item Type:	Article
Uncontrolled Keywords:	Hybrid uncertainties, Response expectation function, Bayesian probabilistic integration, Bayesian global optimization, Bayesian experimental design, Parallel computing
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	21 Jul 2022 15:27
Last Modified:	06 Jul 2023 01:30
DOI:	10.1016/j.compstruc.2022.106860
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3159076