A Kriging-HDMR Combined with Adaptive Proportional Sampling for Multi-Parameter Approximate Modeling

Abstract

High-dimensional complex multi-parameter problems are commonly in engineering, while the traditional approximate modeling is limited to low or medium dimensional problems, which cannot overcome the dimensional disaster and greatly reduce the modelling accuracy with the increase of design parameter space. Therefore, this paper combined Kriging with Cut-HDMR, proposed a developed Kriging-HDMR method based on adaptive proportional sampling strategy, and made full use of Kriging's own interpolation prediction advantages and corresponding errors to improve modelling efficiency. Three numerical tests including coupling test, high-dimensional nonlinear test and calculation cost test were used to verify the effectiveness of the algorithm, and compared with the traditional Kriging-HDMR and RBF-HDMR in R2 , REEA and RMEA measuring the approximate accuracy, results show that the improved Kriging-HDMR greatly reduces the sampling cost and avoids falling into local optima. In addition, at the same calculation cost, when the scale coefficient is 1/2, Kriging-HDMR has higher global approximate accuracy and stronger algorithm robustness, while preserving the hierarchical characteristics of coupling between input variables.