A novel kriging-improved high-dimensional model representation metamodelling technique for approximating high-dimensional problems

Abstract

Aiming to address the issue of the ‘curse of dimensionality’ encountered in approximating high-dimensional problems using surrogate-based methods, high-dimensional model representation (HDMR), decomposing the high-dimensional problem into summands of different-order component functions, has been widely studied. To reduce the computational demands of the current HDMR metamodelling techniques, an improved high-dimensional model representation framework (iHDMR) is presented, taking full advantage of the relationships between the first-order and second-order component functions in the Cut-HDMR theory. then, a novel metamodelling technique, termed kriging (KRG)-iHDMR, is implemented by integrating the kriging technique and the suggested surface-axes alternating sampling strategy into the iHDMR framework. The accuracy and efficiency of KRG-iHDMR are demonstrated by various numerical and engineering examples with different dimensions. Finally, an optimization problem of the multi-stage solid launch vehicle propulsion system is introduced to verify the engineering feasibility of the KRG-iHDMR metamodelling technique.