基于上凸序列建模的DGM(1,1)模型优化

On the Improved DGM(1,1) Model Based on Concave Sequence

首先定义了序列凸性,证明了DGM(1,1)模型的还原序列为下凸序列,分析了其对上凸序列建模时的残差变化规律,提出了通过对称变换把上凸序列转化为下凸序列再建DGM(1,1)模型的一种新方法。实例也证实了新方法对于上凸序列建模比直接建立DGM(1,1)模型具有更高拟合精度。

Firstly,the convexity of sequence was defined and the restoring sequence of DGM( 1,1) model was proved to be a convex sequence. Then,the change rule of residual error for modeling based on the concave sequence was analyzed. Symmetry transformations are introduced to transform a concave sequence into a convex sequence for building the GM( 1,1) model. Examples also confirm that the new method has higher fitting precision for modeling than that of directly building the DGM( 1,1) model based on a concave sequence.