Response and reliability analysis of nonlinear uncertain dynamical structures by the probability density evolution method

Søren R. K. Nielsen, Yongbo Peng, Mahdi Teimouri Sichani

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

8 Citationer (Scopus)

Abstract

The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which reduces the number of basic random variables to merely a single one. Correspondingly, the response and reliability problems reduce to the solution of one-dimensional quadratures.
OriginalsprogEngelsk
Artikelnummer12
TidsskriftInternational Journal of Dynamics and Control
Vol/bind4
Udgave nummer2
Sider (fra-til)221-232
ISSN2195-268X
DOI
StatusUdgivet - 2016

Emneord

  • Evolutionary phase model
  • Nonlinear dynamical systems
  • Probability density evolution method
  • Reliability analysis
  • Stochastic response

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