TY - JOUR

T1 - Refined parallel adaptive Bayesian quadrature for estimating small failure probabilities

AU - Wang, Lei

AU - Hu, Zhuo

AU - Dang, Chao

AU - Beer, Michael

N1 - Funding Information: This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFB2600900 ), the Graduate Student Research Innovation Project of Hunan Province (CSUST), China (Grant No. CX20200843 ), and China Scholarship Council .

PY - 2024/4

Y1 - 2024/4

N2 - Bayesian active learning methods have emerged for structural reliability analysis, showcasing more attractive features compared to existing active learning methods. The parallel adaptive Bayesian quadrature (PABQ) method, as a representative of them, allows to efficiently assessing small failure probabilities but faces the problem of empirically specifying several important parameters. The unreasonable parameter settings could lead to the inaccurate estimates of failure probability or the non-convergence of active learning. This study proposes a refined PABQ (R-PABQ) method by presenting three novel refinements to overcome the drawbacks of PABQ. Firstly, a sequential population enrichment strategy is presented and embedded into the importance ball sampling technique to solve the computer memory problem when involving large sample population. Secondly, an adaptive determination strategy for radius is developed to automatically adjust the sampling region during the active learning procedure. Lastly, an adaptive multi-point selection method is proposed to identify a batch of points to enable parallel computing. The effectiveness of the proposed R-PABQ method is demonstrated by four numerical examples. Results show that the proposed method can estimate small failure probabilities (e.g., 10−7∼10−9) with superior accuracy and efficiency over several existing active learning reliability methods.

AB - Bayesian active learning methods have emerged for structural reliability analysis, showcasing more attractive features compared to existing active learning methods. The parallel adaptive Bayesian quadrature (PABQ) method, as a representative of them, allows to efficiently assessing small failure probabilities but faces the problem of empirically specifying several important parameters. The unreasonable parameter settings could lead to the inaccurate estimates of failure probability or the non-convergence of active learning. This study proposes a refined PABQ (R-PABQ) method by presenting three novel refinements to overcome the drawbacks of PABQ. Firstly, a sequential population enrichment strategy is presented and embedded into the importance ball sampling technique to solve the computer memory problem when involving large sample population. Secondly, an adaptive determination strategy for radius is developed to automatically adjust the sampling region during the active learning procedure. Lastly, an adaptive multi-point selection method is proposed to identify a batch of points to enable parallel computing. The effectiveness of the proposed R-PABQ method is demonstrated by four numerical examples. Results show that the proposed method can estimate small failure probabilities (e.g., 10−7∼10−9) with superior accuracy and efficiency over several existing active learning reliability methods.

KW - Bayesian active learning

KW - Gaussian process

KW - Importance ball sampling

KW - Parallel computing

KW - Small failure probability

UR - http://www.scopus.com/inward/record.url?scp=85182888950&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2024.109953

DO - 10.1016/j.ress.2024.109953

M3 - Article

AN - SCOPUS:85182888950

VL - 244

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 109953

ER -