Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

Faes, Matthias GR, Valdebenito, Marcos A, Moens, David and Beer, Michael ORCID: 0000-0002-0611-0345 (2021) Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities. Mechanical Systems and Signal Processing, 152. p. 107482.

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Official URL: http://dx.doi.org/10.1016/j.ymssp.2020.107482

Abstract

This paper presents a highly efficient and effective approach to bound the responses and probability of failure of linear systems where the model parameters are subjected to combinations of epistemic and aleatory uncertainty. These combinations can take the form of imprecise probabilities or hybrid uncertainties. Typically, such computations involve solving a nested double loop problem, where the propagation of the aleatory uncertainty has to be performed for each realisation of the epistemic uncertainty. Apart from near-trivial cases, such computation is intractable without resorting to surrogate modeling schemes. In this paper, a method is presented to break this double loop by virtue of the operator norm theorem. Indeed, in case linear models are considered and under the restriction that the model definition cannot be subject to aleatory uncertainty, the paper shows that the computational efficiency, quantified by the required number of model evaluations, of propagating these parametric uncertainties can be improved by several orders of magnitude. Two case studies involving a finite element model of a clamped plate and a six-story building are included to illustrate the application of the developed technique, as well as its computational merit in comparison to existing double-loop approaches.

Item Type:	Article
Uncontrolled Keywords:	Uncertainty Quantification, Imprecise probabilities, Operator norm theorem, Linear models, Decoupling
Depositing User:	Symplectic Admin
Date Deposited:	13 Jan 2021 09:35
Last Modified:	18 Jan 2023 23:03
DOI:	10.1016/j.ymssp.2020.107482
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3113399