Efficient Metamodeling Strategy Using Multivariate Linear Interpolation for High Dimensional Problems

Metamodeling method has been widely used to solve engineering problems which require significant computation, and there have been a large number of studies to propose efficient metamodeling methods in the last two decades. However, researches on practical metamodeling method dealing with high dimensional design space are insufficient. There sometimes exist high dimensional, expensive and black-box (HEB) problems, and handling these HEB problems with metamodeling method is challenging because of computational burden and complexity. In this paper, the efficient metamodeling strategy is proposed to handle HEB problems. The proposed strategy decomposes high dimensional design space into multiple less dimensional design spaces based on the coefficient of the multivariate linear interpolation equation. After the decomposition, sub-metamodels are generated using a sequential sampling method in each design space, and the final metamodel is constructed using these sub-metamodels. Engineering example verifies that the proposed strategy reduces required number of samples to satisfy the specified target accuracy compared to existing metamodeling methods.