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

verfasst von

D. J. Jerez, V. C. Fragkoulis, P. Ni, I. P. Mitseas, M. A. Valdebenito, M. G.R. Faes, M. Beer

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.

Organisationseinheit(en)

Institut für Risiko und Zuverlässigkeit

Externe Organisation(en)

Universidad Tecnica Federico Santa Maria
The University of Liverpool
University of Leeds
Nationale Technische Universität Athen (NTUA)
Technische Universität Dortmund
Tongji University

Typ

Artikel

Journal

Mechanical Systems and Signal Processing

Band

208

ISSN

0888-3270

Publikationsdatum

15.02.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Steuerungs- und Systemtechnik, Signalverarbeitung, Tief- und Ingenieurbau, Luft- und Raumfahrttechnik, Maschinenbau, Angewandte Informatik

Elektronische Version(en)

https://doi.org/10.1016/j.ymssp.2023.111043 (Zugang: Geschlossen)