An Adaptive Multiple Response Gaussian Process for Reliability Analysis of Multi-Output Systems

In engineering applications, computational models often have multiple outputs, meaning systems with various failure modes. The key to solving reliability analysis problems for such systems lies in efficiently approximating the limit state functions (LSFs) and robustly evaluating the failure probabilities. In this paper, an adaptive multiple response Gaussian process oriented weighted importance sampling (AMRGP-WIS) method is proposed for efficient reliability analysis of multi-output systems with a small failure probability. The multiple response Gaussian process (MRGP) model is used to approximate the expensive LSFs because the covariance matrix between outputs can correctly capture the correlation among output dimensions. Then, a two-stage sequential sampling method based on MRGP is proposed, which combines the global exploration of Hu with the local exploitation of Heff, reducing the number of real evaluation points and enhancing the robustness of the method. Furthermore, a weighted importance sampling (WIS) method is proposed, which robustly estimates small failure probabilities in multi-output structural systems. The robustness and efficiency of the proposed AMRGP-WIS method are demonstrated in four numerical examples and an engineering case. The results indicate that this method can significantly reduce the number of real evaluation samples and obtain more precise results for reliability analysis of multi-output systems.