The failure probability concerning specified design parameters, termed the failure probability function (FPF), is essential in reliability-based design. Conventional methods require high computational costs for complex systems due to repeated expensive simulations. Although single-loop methods with active learning Kriging (AK) have been proposed to reduce these costs, their efficiency remains limited by suboptimal sampling and inaccurate kernel density estimation (KDE). To address these challenges, this work introduces a novel multi-purpose K-nearest neighbor (KNN) framework integrated with an enhanced AK in an augmented space, termed the SL-AK-KNN method. The method leverages the adaptive capabilities of KNN in two key aspects: (1) as a spatial-information-guided learning function that improves both global and local efficiency of AK by exploring and exploiting sample density variations across different regions, and (2) as an adaptive nonparametric density estimator for approximating the conditional joint probability density function (PDF), thereby mitigating KDE’s edge region inaccuracies without relying on kernel functions and fixed bandwidth. It is intuitively well-suited for exploratory analysis of unknown density distributions. Numerical examples demonstrate that the proposed framework significantly reduces computational costs while enhancing FPF estimation accuracy, enabling robust reliability design for the engineering applications of the bracket structure and hydraulic pipeline system.
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