A dimension-wise analysis driven active learning paired-Kriging (DWA-ALK) method for the hybrid reliability analysis

Abstract

Hybrid reliability analysis (HRA) has been extensively explored and mainly performed based on two categories of models. Mathematical properties on these models are given and proven in a rigorous manner, providing insights into HRA problems. Potential obstacles of the most appealing Kriging-based method available in literature for HRA include: metamodeling in an augmented-dimensional space spanned by both random and interval parameters resulting in substantial inversion of a large correlation matrix, an absence of distance metric in learning functions causing sample clustering, repeated interval analysis mainly completed by either the sampling-based or optimization-based algorithm leading to excessive computational cost and memory requirements especially for high-dimensional interval inputs. In this sense, a dimension-wise analysis driven active learning paired-Kriging method is proposed, where a paired-Kriging metamodel is constructed solely in the random input space and, at each training point, the interval analysis is conducted by a dimension-wise analysis method. A new learning function and termination criterion are conceived for refining the paired-Kriging model. It is concluded that the proposed method outperforms the common-in-use ones for HRA with high-dimensional interval inputs while its accuracy and efficiency are comparable in the case of low-dimensional interval inputs after validating its numerical performance by typical issues.