An adaptive partitioning Sobol sampling strategy based on an active learning kriging model for small failure probability reliability analysis

Purpose To address the critical challenges in reliability analysis of complex systems with high-dimensional nonlinear implicit performance functions including prohibitive computational costs, inefficient failure boundary exploration for small failure probability events, and the accuracy efficiency trade-off in surrogate models. Design/methodology/approach First, an adaptive partitioned Sobol sampling (APSS) strategy is proposed to enhance the exploration capability and uniformity of initial samples, efficiently probing failure boundaries while maintaining computational feasibility. Second, an expected uncertainty (EU) learning function is developed to adaptively refine surrogate models near failure interfaces with minimal function evaluations. Third, an active learning kriging (AK) method incorporating composite stopping criteria is designed. Finally, the proposed APSS framework is embedded into the enhanced surrogate model to assess reliability, achieving an optimal balance between accuracy and computational efficiency. Findings Numerical examples and engineering case studies demonstrate that the proposed approach reduces computational costs while maintaining controlled error levels compared to traditional methods. These results validate the method’s robustness in handling high-dimensional nonlinear implicit performance functions and small failure probability events, providing an engineering solution for the reliability-driven design of complex systems. Originality/value The proposed AK-APSS-EU framework addresses the challenges of small probability events and multiple failure regions by leveraging APSS to generate critical samples across the entire failure domain. By integrating a novel EU learning function with a composite stopping criterion, the method dynamically augments sample points to precisely refine the surrogate model at the failure boundary. Consequently, the framework rapidly approximates the true failure boundary without relying on complex conditional sampling or design point data.