Operator norm-based determination of failure probability of nonlinear oscillators with fractional derivative elements subject to imprecise stationary Gaussian loads
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 stocha...
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| Published in | Mechanical systems and signal processing Vol. 208; p. 111043 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
15.02.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0888-3270 1096-1216 |
| 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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| AbstractList | 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. |
| ArticleNumber | 111043 |
| Author | Beer, M. Valdebenito, M.A. Fragkoulis, V.C. Faes, M.G.R. Jerez, D.J. Ni, P. Mitseas, I.P. |
| Author_xml | – sequence: 1 givenname: D.J. orcidid: 0000-0003-2496-945X surname: Jerez fullname: Jerez, D.J. organization: Departamento de Ingeniería Civil, Universidad Técnica Federico Santa María, Avda. España 1680, Valparaíso 2390123, Chile – sequence: 2 givenname: V.C. orcidid: 0000-0001-9925-9167 surname: Fragkoulis fullname: Fragkoulis, V.C. email: vasileios.fragkoulis@liverpool.ac.uk organization: Department of Civil and Environmental Engineering, University of Liverpool, Liverpool L69 3GH, UK – sequence: 3 givenname: P. surname: Ni fullname: Ni, P. organization: Institute for Risk and Reliability, Leibniz Universität Hannover, Callinstr. 34, Hannover 30167, Germany – sequence: 4 givenname: I.P. orcidid: 0000-0001-5219-1804 surname: Mitseas fullname: Mitseas, I.P. organization: School of Civil Engineering, University of Leeds, Leeds LS2 9JT, UK – sequence: 5 givenname: M.A. orcidid: 0000-0002-5083-0454 surname: Valdebenito fullname: Valdebenito, M.A. organization: Chair for Reliability Engineering, TU Dortmund University, Leonard-Euler Straße 5, Dortmund 44227, Germany – sequence: 6 givenname: M.G.R. orcidid: 0000-0003-3341-3410 surname: Faes fullname: Faes, M.G.R. organization: Chair for Reliability Engineering, TU Dortmund University, Leonard-Euler Straße 5, Dortmund 44227, Germany – sequence: 7 givenname: M. orcidid: 0000-0002-0611-0345 surname: Beer fullname: Beer, M. organization: Institute for Risk and Reliability, Leibniz Universität Hannover, Callinstr. 34, Hannover 30167, Germany |
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| Keywords | Uncertainty quantification Imprecise probabilities First-passage probability Stochastic averaging Statistical linearization Fractional derivative |
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