ABSTRACT Efficient reliability analysis of high‐dimensional and implicit limit‐state functions remains a major challenge in reliability‐based engineering design. Traditional Kriging‐based reliability methods often suffer from high computational cost and reduced efficiency when dealing with such problems. To address these challenges, a general two‐stage adaptive Kriging‐Monte Carlo simulation (AK‐MCS) method with a dynamic HU learning function is proposed in this study. In the proposed method, an accuracy index is introduced to divide the learning process into a global exploration stage and a local refinement stage, while a hybrid HU learning function dynamically integrates the H and U learning functions through an adaptive weighting coefficient to balance convergence efficiency and prediction accuracy. The effectiveness and accuracy of the proposed reliability analysis method are demonstrated through a machining accuracy reliability optimization problem of a five‐axis computer numerically controlled (CNC) machine tool, which serves as a representative engineering application. The results show that the proposed method significantly reduces the number of required sample points while maintaining high computational efficiency and low relative error in reliability estimation. Furthermore, the application results indicate that the method can effectively support reliability‐based design optimization by accurately evaluating both the mean and minimum reliability indices.
Liu et al. (Thu,) studied this question.
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