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.

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