An enhanced Kriging surrogate modeling technique for high-dimensional problems

Surrogate modeling techniques are widely used to simulate the behavior of manufactured and engineering systems. The construction of such surrogate models may become intractable in cases when input spaces have high dimensions, because the large number of model responses is typically required to estimate model parameters. In this paper, we proposed a new Kriging modeling technique combined with dimension reduction method to address the issue. In the proposed method, the sliced inverse regression technique is utilized to achieve a dimension reduction by constructing a new projection vector which reduces the dimension of the original input vector without losing the essential information of the model response quantify of interest. In the dimension reduction subspace, a new correlation function of Kriging is constructed by means of the tensor product of several correlation functions with respect to each projection direction. The proposed method is especially promising for high-dimensional problems. In examples including finite element model (FEM) pertinent to low cycle fatigue life (LCF) of a aero-engine compressor disc, the enhanced Kriging is found to outperform several well-established surrogate models when small sample sizes are used.