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Risk and Reliability Analysis: Theory and Applications pp 143–168Cite as

Estimate of Small First Passage Probabilities of Nonlinear Random Vibration Systems

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

Estimates of the small probabilities of failure, i.e., small first passage probabilities, of nonlinear random vibration systems is of great importance in the structural reliability analysis and reliability-based design. Some methods have been developed for estimating the small probabilities, but their computational efficiency is not high enough for analyzing the large-scale systems. In order to overcome the challenge of the computational efficiency of the estimate of the small probabilities, a new method is developed. The method mainly consists of two uncoupled procedures, i.e., modeling the distribution tails of the extreme values of the responses of nonlinear random vibration systems and constructing the Copula of the extreme values of the nonlinear responses. The former is used to estimate the small first passage probabilities of the scalar response processes, while the latter is used to estimate the small first passage probabilities of the vector response processes. Some numerical examples are presented to demonstrate the accuracy and efficiency of the developed method.

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Authors and Affiliations

  1. Department of Civil Engineering, Shanghai Jiao Tong University, Minhang, China

    Jun He

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  1. Jun He
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Correspondence to Jun He .

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Editors and Affiliations

  1. Civil and Environmental Engineering, 3118 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    Paolo Gardoni

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He, J. (2017). Estimate of Small First Passage Probabilities of Nonlinear Random Vibration Systems. In: Gardoni, P. (eds) Risk and Reliability Analysis: Theory and Applications. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-52425-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-52425-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52424-5

  • Online ISBN: 978-3-319-52425-2

  • eBook Packages: EngineeringEngineering (R0)

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