A dimension reduction-based Kriging modeling method for high-dimensional time-variant uncertainty propagation and global sensitivity analysis

Surrogate models have been widely used in the uncertainty propagation and global sensitivity analysis of complex evaluation -expensive engineering problems. However, the construction of high -accuracy surrogate models for time -variant problems with high -dimensional inputs and outputs using a small number of training samples remains a challenge. To address this challenge, we propose a dimension reduction -based Kriging modeling (KMDR) method for high -dimensional time -variant uncertainty propagation and global sensitivity analysis. Singular value decomposition is performed on the original time -variant response to extract principal components from high -dimensional outputs. And the improved sufficient dimension reduction (ISDR) is performed on high -dimensional inputs to identify the latent input space with respect to each principal component of outputs. A ladle estimator with a rigorous mathematical definition is then employed to determine the number of principal components of the outputs and the dimensionalities of the latent input spaces. The ladle estimator considers variabilities in both eigenvalues and eigenvectors of a matrix and can determine the latent dimensionality more accurately and efficiently than existing approaches. Subsequently, Kriging models between highdimensional inputs and each principal component of the outputs are constructed based on a newly devised Kriging kernel, which embeds the information of the ISDR into the kernel function and can achieve higher accuracy than directly constructing Kriging models between latent inputs and outputs. In addition, a generalized variance -based sensitivity index, which can quantify the effects of the inputs on the overall time -variant response, is defined and computed directly from Sobol' sensitivity indices of the inputs at each time node. Finally, the surrogate model of the timevariant system constructed by the KMDR is directly adopted for efficient time -variant uncertainty propagation and global sensitivity analysis. Several examples demonstrate that the proposed approach can construct more accurate surrogate models and obtain more accurate time -variant uncertainty propagation and global sensitivity analysis results than existing methods with a small training set.