CSP-free adaptive Kriging surrogate model method for reliability analysis with small failure probability

In the field of reliability engineering, the active learning reliability method that amalgamates Kriging model and Monte Carlo simulation has been devised and proven to be efficacious in reliability analysis. Nevertheless, the performance of this method is sensitive to the magnitude of candidate sample pool, particularly for systems with small failure probabilities. To surmount these limitations, this paper proposes an active learning method that obviates the need for candidate sample pools. The proposed method comprises two stages: construction of surrogate model and Monte Carlo simulation for failure probability estimation. During the surrogate model construction stage, the surrogate model is iteratively refined based on the representative samples selected by solving the optimization problem facilitated by the particle swarm optimization algorithm. To achieve an optimal balance between solution accuracy and efficiency, the penalty intensity control and the density control for the experimental design points are incorporated to modify the objective function in optimization. The performance of the proposed method is evaluated using numerical examples, and results indicate that by leveraging an optimization algorithm to select representative samples, the proposed method overcomes the limitations of traditional active learning methods based on candidate sample pool and exhibits exceptional performance in addressing small failure probabilities.