Consecutive adaptive Kriging method for high-dimensional reliability analysis based on multi-fidelity framework

Reliability is a critical factor in the design of engineering systems. Consequently, numerous adaptive Kriging methods have been investigated to efficiently calculate the probability of failure in reliability analysis. However, these methods face limitations when applied to high-dimensional reliability analysis problems due to the curse of dimensionality. To overcome this issue, this research proposes a novel adaptive Kriging framework for high-dimensional reliability analysis based on a multi-fidelity metamodelling approach. The proposed method utilizes consecutive adaptive Kriging methods. In the first step, the adaptive Kriging approach is applied to the first-order high-dimensional model representation (HDMR) using univariate samples. This leads to the construction of a hybrid HDMR model based on the univariate samples obtained in the first step. The proposed method assumes that the hybrid HDMR can provide a rough approximation of the high-dimensional space. In the second step, a hierarchical Kriging model is constructed, considering the hybrid HDMR model as a low-fidelity model. An adaptive Kriging method for hierarchical Kriging is then conducted using multivariate samples. These multivariate samples are utilized not only to correct the low-fidelity model as high-fidelity samples in hierarchical Kriging but also to estimate the hybridity parameter of the hybrid HDMR. This allows the hybrid HDMR model to adapt to different types of reliability analysis problems. The results of numerical examples and engineering applications demonstrate that the proposed method can efficiently evaluate the accurate probabilities of failure by adjusting to the specific features of the given problems.