An improved AK-IS based on the adaptive radial-based importance sampling for reliability analysis

Reliability analysis remains a cornerstone for quantifying uncertainty in probabilistic engineering, yet its practical implementation is constrained by the prohibitive computational cost of repeatedly evaluating limit-state functions. To address this challenge, Importance Sampling (IS) emerges as a variance reduction technique that significantly enhances assessment efficiency. Building upon the hybrid meta-modeling paradigm of the Adaptive Kriging Importance Sampling (AK-IS) method, this research proposes an advanced computational framework through the development of a novel adaptive radial-based sampling strategy. The proposed methodology advances the field in three key aspects. Firstly, a general formulation for radial sampling is derived to ensure dimensional invariance and scalability across high-dimensional spaces. Secondly, a non-intrusive adaptive procedure termed secondary sorting is introduced to accurately determine the optimal sampling radius ${\beta }^{\text{opt}}$ through iterative refinement. Finally, a systematic algorithmic architecture is established for integrative reliability analysis. Extensive numerical validation demonstrates that the proposed approach achieves superior sampling efficiency compared to conventional techniques, with significant reductions in computational burden while maintaining comparable accuracy levels. The results confirm that this adaptive radial sampling strategy effectively balances exploration-exploitation trade-offs, leading to enhanced robustness and generalizability in probabilistic reliability assessments.