AMSS-KG: an improved Kriging model with adaptive multi-scale sampling

To address inefficiencies in Kriging modeling caused by traditional single/multi-point sampling approaches, this paper proposes an adaptive multi-scale sampling method that dynamically adjusts sample quantities using the change rates of the coefficient of determination and mean absolute percentage error change rates. The enhanced Kriging model combines this adaptive sampling with sequential Kriging sampling to progressively reduce sample acquisition as accuracy improves. Tests on four standard functions demonstrate that the proposed model matches classical methods in accuracy for low-dimensional weakly nonlinear problems while significantly outperforming them in three challenging cases: low-dimensional strong nonlinearity (lower prediction errors), high-dimensional weak nonlinearity, and high-dimensional strong nonlinearity (better goodness-of-fit). Remarkably, it achieves these results with only 36.68% of the samples required by conventional expected improvement methods, substantially cutting computational costs. Additionally, a computationally demanding aeroacoustic noise reduction optimization study for a natural gas orifice plate validates the method's practical effectiveness. The results confirm its strong suitability for engineering applications. The adaptive sampling mechanism allows automatic sample reduction in later stages without accuracy loss, overcoming the dual challenges of slow single-point convergence and excessive computational demands in fixed multi-point approaches. This improvement enhances Kriging's applicability for high-precision modeling of complex engineering problems.