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

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

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

Externe Organisationen

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

OriginalspracheEnglisch
Aufsatznummer111043
FachzeitschriftMechanical Systems and Signal Processing
Jahrgang208
Frühes Online-Datum17 Dez. 2023
PublikationsstatusVeröffentlicht - 15 Feb. 2024

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.

ASJC Scopus Sachgebiete

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Operator norm-based determination of failure probability of nonlinear oscillators with fractional derivative elements subject to imprecise stationary Gaussian loads. / Jerez, D. J.; Fragkoulis, V. C.; Ni, P. et al.
in: Mechanical Systems and Signal Processing, Jahrgang 208, 111043, 15.02.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Jerez DJ, Fragkoulis VC, Ni P, Mitseas IP, Valdebenito MA, Faes MGR et al. 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. 2024 Feb 15;208:111043. Epub 2023 Dez 17. doi: 10.1016/j.ymssp.2023.111043
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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.",
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T1 - Operator norm-based determination of failure probability of nonlinear oscillators with fractional derivative elements subject to imprecise stationary Gaussian loads

AU - Jerez, D. J.

AU - Fragkoulis, V. C.

AU - Ni, P.

AU - Mitseas, I. P.

AU - Valdebenito, M. A.

AU - Faes, M. G.R.

AU - Beer, M.

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N2 - 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.

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