Net-HDMR Metamodeling Method for High-Dimensional Problems

Metamodel technology provides an efficient method to approximate complex engineering design problems. However, the approximation for high-dimensional problems usually requires a large number of samples for most traditional metamodeling methods, which leads to the difficulty of curse of dimensionality. To address the aforementioned issue, this paper presents the Net-high dimension model representation (HDMR) method based on the Cut-HDMR framework. Compared with traditional HDMR modeling, the Net-HDMR method incorporates two novel modeling approaches that improve the modeling efficiency of high-dimensional problems. The first approach enhances the modeling accuracy of HDMR by using the net function interpolation method to decompose the component functions into a series of one-dimensional net functions. The second approach adopts the CV-Voronoi sequence sampling method to effectively represent one-dimensional net functions with limited samples. Overall, the proposed method transforms complex high-dimensional problems into fitting finite one-dimensional splines, thereby increasing the modeling efficiency while ensuring approximate accuracy. Six numerical benchmark examples with different dimensions are examined to demonstrate the accuracy and efficiency of the proposed Net-HDMR. An engineering problem of thermal stress and deformation analysis for a jet engine turbine blade was introduced to verify the engineering feasibility of the proposed Net-HDMR.

Automated summary

This paper proposes the Net-HDMR method based on the Cut-HDMR framework for approximating complex high-dimensional engineering design problems. The method incorporates two novel modeling approaches that enhance the accuracy and efficiency of HDMR. The proposed method is validated through numerical benchmark examples and an engineering problem of thermal stress and deformation analysis for a jet engine turbine blade.