TY - JOUR

T1 - Parallel Bayesian probabilistic integration for structural reliability analysis with small failure probabilities

AU - Hu, Zhuo

AU - Dang, Chao

AU - Wang, Lei

AU - Beer, Michael

N1 - Funding Information: This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFB2600900 ), and China Scholarship Council.

PY - 2024/1

Y1 - 2024/1

N2 - Bayesian active learning methods have emerged for structural reliability analysis and shown more attractive features than existing active learning methods. However, it remains a challenge to actively learn the failure probability by fully exploiting its posterior statistics. In this study, a novel Bayesian active learning method termed ‘Parallel Bayesian Probabilistic Integration’ (PBPI) is proposed for structural reliability analysis, especially when involving small failure probabilities. A pseudo posterior variance of the failure probability is first heuristically proposed for providing a pragmatic uncertainty measure over the failure probability. The variance amplified importance sampling is modified in a sequential manner to allow the estimations of posterior mean and pseudo posterior variance with a large sample population. A learning function derived from the pseudo posterior variance and a stopping criterion associated with the pseudo posterior coefficient of variance of the failure probability are then presented to enable active learning. In addition, a new adaptive multi-point selection method is developed to identify multiple sample points at each iteration without the need to predefine the number, thereby allowing parallel computing. The effectiveness of the proposed PBPI method is verified by investigating four numerical examples, including a turbine blade structural model and a transmission tower structure. Results indicate that the proposed method is capable of estimating small failure probabilities with superior accuracy and efficiency over several other existing active learning reliability methods.

AB - Bayesian active learning methods have emerged for structural reliability analysis and shown more attractive features than existing active learning methods. However, it remains a challenge to actively learn the failure probability by fully exploiting its posterior statistics. In this study, a novel Bayesian active learning method termed ‘Parallel Bayesian Probabilistic Integration’ (PBPI) is proposed for structural reliability analysis, especially when involving small failure probabilities. A pseudo posterior variance of the failure probability is first heuristically proposed for providing a pragmatic uncertainty measure over the failure probability. The variance amplified importance sampling is modified in a sequential manner to allow the estimations of posterior mean and pseudo posterior variance with a large sample population. A learning function derived from the pseudo posterior variance and a stopping criterion associated with the pseudo posterior coefficient of variance of the failure probability are then presented to enable active learning. In addition, a new adaptive multi-point selection method is developed to identify multiple sample points at each iteration without the need to predefine the number, thereby allowing parallel computing. The effectiveness of the proposed PBPI method is verified by investigating four numerical examples, including a turbine blade structural model and a transmission tower structure. Results indicate that the proposed method is capable of estimating small failure probabilities with superior accuracy and efficiency over several other existing active learning reliability methods.

KW - Bayesian active learning

KW - Bayesian probabilistic integration

KW - Gaussian process

KW - Importance sampling

KW - Parallel computing

KW - Small failure probability

UR - http://www.scopus.com/inward/record.url?scp=85177196686&partnerID=8YFLogxK

U2 - 10.1016/j.strusafe.2023.102409

DO - 10.1016/j.strusafe.2023.102409

M3 - Article

AN - SCOPUS:85177196686

VL - 106

JO - Structural safety

JF - Structural safety

SN - 0167-4730

M1 - 102409

ER -