New analytical solution of the first-passage reliability problem for linear oscillators

S. Ghazizadeh, M. Barbato, E. Tubaldi

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29 Citations (Scopus)


The classical first-passage reliability problem for linear elastic single-degree-of-freedom (SDOF) oscillators subjected to stationary and nonstationary Gaussian excitations is explored. Several analytical approximations are available in the literature for this problem: the Poisson, classical Vanmarcke, and modified Vanmarcke approximations. These analytical approximations are widely used because of their simplicity and their lower computational cost compared with simulation techniques. However, little is known about their accuracy in estimating the time-variant first-passage failure probability (FPFP) for varying oscillator properties, failure thresholds, and types of loading. In this paper, a new analytical approximation of the FPFP for linear SDOF systems is proposed by modifying the classical Vanmarcke hazard function. This new approximation is verified by comparing its failure probability estimates with the results obtained using existing analytical approximations and the importance sampling using elementary events method for a wide range of oscillator properties, threshold levels, and types of input excitations. It is shown that the newly proposed analytical approximation of the hazard function yields a significantly more accurate estimate of the FPFP compared with the Poisson, classical Vanmarcke, and modified Vanmarcke approximations.
Original languageEnglish
Pages (from-to)695-706
Number of pages12
JournalJournal of Engineering Mechanics
Issue number6
Publication statusPublished - 2012


  • nonstationary process
  • reliability problems
  • stochastic dynamics
  • structural reliability
  • time variant
  • estimation
  • hazards
  • loading
  • comparative study
  • computer simulation
  • estimation method
  • mechanics
  • oscillation
  • probability
  • reliability analysis
  • approximation theory
  • accuracy assessment

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