An Efficient Kriging Modeling Method Based on Multidimensional Scaling for High-Dimensional Problems

Abstract

Kriging-based modeling has been widely used in computationally intensive simulations. However, the Kriging modeling of high-dimensional problems not only takes more time, but also leads to the failure of model construction. To this end, a Kriging modeling method based on multidimensional scaling (KMDS) is presented to avoid the “dimensional disaster”. Under the condition of keeping the distance between the sample points before and after the dimensionality reduction unchanged, the KMDS method, which mainly calculates each element in the inner product matrix due to the mapping relationship between the distance matrix and the inner product matrix, completes the conversion of design data from high dimensional to low dimensional. For three benchmark functions with different dimensions and the aviation field problem of aircraft longitudinal flight control, the proposed method is compared with other dimensionality reduction methods. The KMDS method has better modeling efficiency while meeting certain accuracy requirements.

Keywords

• surrogate model
• Kriging method
• multidimensional scaling
• high-dimensional problems