Jerez, D.J. orcid.org/0000-0003-2496-945X, Fragkoulis, V.C. orcid.org/0000-0001-9925-9167, Ni, P. et al. (4 more authors) (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. 111043. ISSN 0888-3270
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2023 Elsevier Ltd. This is an author produced version of an article published in Mechanical Systems and Signal Processing. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Uncertainty quantification; First-passage probability; Imprecise probabilities; Fractional derivative; Stochastic averaging; Statistical linearization |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Civil Engineering (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Jan 2024 09:38 |
Last Modified: | 17 Dec 2024 01:13 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ymssp.2023.111043 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206725 |
Download
Filename: Jerez_Fragkoulis_Ni_Mitseas_Valdebenito_Faes_Beer_Journal_MSSP_2024_no template.pdf
Licence: CC-BY-NC-ND 4.0