Parallel adaptive Bayesian quadrature for rare event estimation

Chao Dang, Pengfei Wei, Matthias G.R. Faes, Marcos A. Valdebenito, Michael Beer

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Various numerical methods have been extensively studied and used for reliability analysis over the past several decades. However, how to understand the effect of numerical uncertainty (i.e., numerical error due to the discretization of the performance function) on the failure probability is still a challenging issue. The active learning probabilistic integration (ALPI) method offers a principled approach to quantify, propagate and reduce the numerical uncertainty via computation within a Bayesian framework, which has not been fully investigated in context of probabilistic reliability analysis. In this study, a novel method termed ‘Parallel Adaptive Bayesian Quadrature’ (PABQ) is proposed on the theoretical basis of ALPI, and is aimed at broadening its scope of application. First, the Monte Carlo method used in ALPI is replaced with an importance ball sampling technique so as to reduce the sample size that is needed for rare failure event estimation. Second, a multi-point selection criterion is proposed to enable parallel distributed processing. Four numerical examples are studied to demonstrate the effectiveness and efficiency of the proposed method. It is shown that PABQ can effectively assess small failure probabilities (e.g., as low as 10−7) with a minimum number of iterations by taking advantage of parallel computing.

Original languageEnglish
Article number108621
JournalReliability Engineering and System Safety
StatePublished - Sep 2022
Externally publishedYes


  • Bayesian quadrature
  • Gaussian process
  • Numerical uncertainty
  • Parallel computing
  • Reliability analysis


Dive into the research topics of 'Parallel adaptive Bayesian quadrature for rare event estimation'. Together they form a unique fingerprint.

Cite this