Operator norm-based determination of failure probability of nonlinear oscillators with fractional derivative elements subject to imprecise stationary Gaussian loads

Jerez, DJ, Fragkoulis, VC ORCID: 0000-0001-9925-9167, Ni, P, Mitseas, IP, Valdebenito, MA, Faes, MGR and Beer, M ORCID: 0000-0002-0611-0345 (2024) Operator norm-based determination of failure probability of nonlinear oscillators with fractional derivative elements subject to imprecise stationary Gaussian loads. Mechanical Systems and Signal Processing, 208. p. 111043.

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Abstract

An approximate analytical technique is developed for bounding the first-passage probability of lightly damped nonlinear and hysteretic oscillators endowed with fractional derivative elements and subjected to imprecise stationary Gaussian loads. In particular, the statistical linearization and stochastic averaging methodologies are integrated with an operator norm-based approach to formulate a numerically efficient proxy for the first-passage probability. This proxy is employed to determine the realizations of the interval-valued parameters of the excitation model that yield the extrema of the failure probability function. Ultimately, each failure probability bound is determined in a fully decoupled manner by solving a standard optimization problem followed by a single evaluation of the first-passage probability. The proposed approximate technique can be construed as an extension of a recently developed operator norm scheme to account for oscillators with fractional derivative elements. In addition, it can readily treat a wide range of nonlinear and hysteretic behaviors. To illustrate the applicability and effectiveness of the proposed technique, a hardening Duffing and a bilinear hysteretic nonlinear oscillators with fractional derivative elements subject to imprecise stationary Gaussian loads are considered as numerical examples.

Item Type:	Article
Additional Information:	Source info: MSSP23-3270
Uncontrolled Keywords:	Uncertainty Quantification, First-passage probability, Imprecise probabilities, Fractional derivative, Stochastic averaging, Statistical linearization
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	10 Jan 2024 10:27
Last Modified:	10 Jan 2024 10:28
DOI:	10.1016/j.ymssp.2023.111043
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3177656