Kriging‐based reliability analysis for a multi‐output structural system with multiple response Gaussian process

This paper proposes an active learning Kriging (ALK) based reliability analysis method for a multi-output structural system by using a multiple response Gaussian process (MRGP) model. Firstly, various failure modes, including their interactions, are involved in a multi-output structural system. The MRGP model is used to construct the surrogate model directly because it can efficiently characterize the correlation between different failure modes. The particle swarm optimization (PSO) algorithm is integrated into the MRGP model to optimize the hyperparameter. Secondly, similar to ALK-based reliability method, three improved functions for these common learning functions (e.g., U-function, EFF-function, H-function) are proposed, which consider the distance requirement between the iteration sample point and training samples. Finally, the cross-validation methodology is employed as the stopping criterion and several numerical examples are provided to illustrate the effectiveness.