This study introduces a novel adaptive surrogate model methodology for the reliability analysis of systems exhibiting small failure probabilities. To circumvent the limitations inherent in conventional adaptive Kriging surrogate model methodologies reliant on candidate sample pools, an adaptive Kriging surrogate model methodology incorporating the Particle Swarm Optimization (PSO) algorithm is proposed. During implementation, the surrogate model is iteratively refined and high-value samples are selected to update the surrogate model through an optimization solution facilitated by PSO. Meanwhile, two modified learning functions that account for local neighborhood effects and distribution distance of samples for experimental design are introduced to achieve an optimal balance between solution accuracy and efficiency for the proposed methodology. The computational performance of the proposed methodology is assessed using numerical examples. The results indicate that the integration of PSO not only enhances the probability of obtaining high-value samples but also markedly improves the solution accuracy of the adaptive Kriging surrogate model methodology for reliability analysis. By leveraging an optimization algorithm to determine high-value samples, the proposed methodology transcends the limitations of conventional candidate pool-based selection methods, exhibiting exceptional performance in addressing small failure probabilities.

翻译：本研究提出了一种新颖的自适应代理模型方法，用于分析具有小失效概率系统的可靠性。为规避传统依赖候选样本池的自适应Kriging代理模型方法的固有局限性，本文提出了一种融合粒子群优化算法的自适应Kriging代理模型方法。在实施过程中，通过PSO驱动的优化求解，迭代优化代理模型并选取高价值样本以更新模型。同时，引入两种改进的学习函数——分别考虑局部邻域效应和实验设计样本的分布距离，以实现所提方法在求解精度与效率之间的最优平衡。通过数值算例评估了所提方法的计算性能。结果表明，PSO的集成不仅提升了获取高价值样本的概率，还显著提高了自适应Kriging代理模型方法在可靠性分析中的求解精度。通过利用优化算法确定高价值样本，所提方法突破了传统基于候选池样本选择方法的局限性，在处理小失效概率问题时展现出卓越性能。