Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading

Ni, Peihua, Jerez, Danko J, Fragkoulis, Vasileios C ORCID: 0000-0001-9925-9167, Faes, Matthias GR, Valdebenito, Marcos A and Beer, Michael ORCID: 0000-0002-0611-0345 (2022) Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading. ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING, 8 (1). 04021086-.

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Official URL: http://dx.doi.org/10.1061/ajrua6.0001217

Abstract

This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic Gaussian loads. Typically, such computations involve solving a nested double-loop problem, where the propagation of the aleatory uncertainty has to be performed for each realization of the epistemic parameters. Apart from near-trivial cases, such computation is generally intractable without resorting to surrogate modeling schemes, especially in the context of performing nonlinear dynamical simulations. The recently introduced operator norm framework allows for breaking this double loop by determining those values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. However, the method in its current form is only applicable to linear models due to the adopted assumptions in the derivation of the involved operator norms. In this paper, the operator norm framework is extended and generalized by resorting to the statistical linearization methodology to account for nonlinear systems. Two case studies are included to demonstrate the validity and efficiency of the proposed approach.

Item Type:	Article
Uncontrolled Keywords:	Uncertainty quantification, Imprecise probabilities, Operator norm theorem, Statistical linearization
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	18 Jan 2022 08:12
Last Modified:	15 Mar 2024 05:27
DOI:	10.1061/AJRUA6.0001217
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3147033