An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

Xuefei Guan, Jingjing He, Ratneshwar Jha, Yongming Liu

Research output: Contribution to journalArticle

36 Scopus citations

Abstract

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalReliability Engineering and System Safety
Volume97
Issue number1
DOIs
StatePublished - Jan 1 2012
Externally publishedYes

Keywords

  • Bayesian
  • FORM
  • First-order reliability method
  • Inverse FORM
  • Inverse reliability method
  • Laplace
  • Reliability updating

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering

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