Efficient metamodeling method using recursive variable decomposition for high dimensional model

Abstract

Metamodel has been widely used to solve computationally expensive engineering problems, and there have been many studies on how to generate metamodels with limited number of samples to further improve efficiency and accuracy of the metamodels. However, applications of these methods could be limited in high dimensional problems since it is still challenging due to curse of dimensionality to generate accurate metamodels in high-dimensional design space. In this paper, recursive decomposition concept coupled with sequential sampling method is proposed to efficiently generate high dimensional metamodels. Whenever a new sample is added during the sequential sampling procedure, variable decomposition is repeatedly performed using interaction estimation from a full-dimension Kriging metamodel. When generating the new sample, the proposed method uses a two-step sampling strategy: The first step focuses on obtaining an accurate decomposition result and the second step focuses on improving accuracy of the metamodel. Using the proposed method, latent decomposability of function can be identified using reasonable samples, and high dimensional metamodel can be generated very accurately using the decomposability. Numerical examples using both decomposable and indecomposable problems show that the proposed method shows reasonable decomposition results, and thus improves metamodel accuracy using similar number of samples compared with conventional methods.