TY - JOUR

T1 - Semi-Bayesian active learning quadrature for estimating extremely low failure probabilities

AU - Dang, Chao

AU - Beer, Michael

N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC) . Michael Beer would like to thank the support of the National Natural Science Foundation of China under grant number 72271025 .

PY - 2024/6

Y1 - 2024/6

N2 - 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.

AB - 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.

KW - Bayesian active learning

KW - Learning function

KW - Parallel computing

KW - Stopping criterion

KW - Structural reliability analysis

UR - http://www.scopus.com/inward/record.url?scp=85186765378&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2024.110052

DO - 10.1016/j.ress.2024.110052

M3 - Article

AN - SCOPUS:85186765378

VL - 246

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 110052

ER -