TY - JOUR

T1 - Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities

AU - Faes, Matthias G.R.

AU - Valdebenito, Marcos A.

AU - Moens, David

AU - Beer, Michael

N1 - Funding Information: Matthias Faes acknowledges the financial support of the Research Foundation Flanders (FWO) in the context of his post-doctoral grant under Grant No. 12P3519N. Matthias Faes furthermore acknowledges the financial support of the Alexander von Humboldt foundation. Marcos Valdebenito acknowledges the support of ANID (National Agency for Research and Development, Chile) under its program FONDECYT, Grant No. 1180271.

PY - 2021/5/1

Y1 - 2021/5/1

N2 - 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.

AB - 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.

KW - Decoupling

KW - Imprecise probabilities

KW - Linear models

KW - Operator norm theorem

KW - Uncertainty Quantification

UR - http://www.scopus.com/inward/record.url?scp=85097719064&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2020.107482

DO - 10.1016/j.ymssp.2020.107482

M3 - Article

AN - SCOPUS:85097719064

VL - 152

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 107482

ER -