Semi-Bayesian active learning quadrature for estimating extremely low failure probabilities

Chao Dang and Michael Beer

Reliability Engineering and System Safety, 2024, vol. 246, issue C

Abstract: The Bayesian failure probability inference (BFPI) framework provides a sound basis for developing new Bayesian active learning reliability analysis methods. However, it is still computationally challenging to make use of the posterior variance of the failure probability. This study presents a novel method called ‘semi-Bayesian active learning quadrature’ (SBALQ) for estimating extremely low failure probabilities, which builds upon the BFPI framework. The key idea lies in only leveraging the posterior mean of the failure probability to design two crucial components for active learning — the stopping criterion and learning function. In this context, a new stopping criterion is introduced through exploring the structure of the posterior mean. Besides, we also develop a numerical integration technique named ‘hyper-shell simulation’ to estimate the analytically intractable integrals inherent in the stopping criterion. Furthermore, a new learning function is derived from the stopping criterion and by maximizing it a single point can be identified in each iteration of the active learning phase. To enable multi-point selection and facilitate parallel computing, the proposed learning function is modified by incorporating an influence function. Through five numerical examples, it is demonstrated that the proposed method can assess extremely small failure probabilities with desired efficiency and accuracy.

Keywords: Structural reliability analysis; Bayesian active learning; Stopping criterion; Learning function; Parallel computing (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0951832024001273
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:246:y:2024:i:c:s0951832024001273

DOI: 10.1016/j.ress.2024.110052

Access Statistics for this article

Reliability Engineering and System Safety is currently edited by Carlos Guedes Soares

More articles in Reliability Engineering and System Safety from Elsevier
Bibliographic data for series maintained by Catherine Liu ().