  In the field of reliability engineering, the Active learning reliability
method combining Kriging and Monte Carlo Simulation (AK-MCS) has been developed
and demonstrated to be effective in reliability analysis. However, the
performance of AK-MCS is sensitive to the size of Candidate Sample Pool (CSP),
particularly for systems with small failure probabilities. To address the
limitations of conventional AK-MCS that relies on CSP, this paper proposes a
CSP-free AK-MCS. The proposed methodology consists of two stages: surrogate
model construction and Monte Carlo simulation for estimating the failure
probability. In the stage of surrogate model construction, the surrogate model
is iteratively refined based on the representative samples selected by solving
the optimization problem facilitated by Particle Swarm Optimization (PSO)
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 introduced to modify the objective function in
optimization. The performance of the proposed methodology is evaluated using
numerical examples, and results indicate that by leveraging an optimization
algorithm to select representative samples, the proposed CSP-free AK-MCS
overcomes the limitations of conventional CSP-based AK-MCS and exhibits
exceptional performance in addressing small failure probabilities.
