Refined parallel adaptive Bayesian quadrature for estimating small failure probabilities

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.