差分方程灰色DEGM(2,1)模型的优化及应用

Optimization and Application of Grey DEGM(2,1) Model of Difference Equation

传统灰色GM(2,1)模型从差分方程到微分方程的跨越,缺乏充分的科学基础,也会因两种结构间的转换带来额外误差。文章引入差分方程DEGM(2,1)模型,该模型的定义、参数估计、拟合值生成,全部使用差分方程完成,避免了GM(2,1)模型的转换问题。为解决初始值数据对拟合精度的不利影响,采用一种反向修正方法,给DEGM(2,1)模型的两个迭代初始值各增加一个修正参数,通过修正参数来反向抵消初始值带来的偏差。结果表明,改进后的DEGM(2,1)模型,单个数据的最大相对误差和整体数据的平均绝对误差,都明显小于传统GM(2,1)模型。

The traditional grey GM(2,1) jumping from difference to differential equation lacks sufficient scientific basis, and will also give rise to additional errors due to the transformation between the two structures. This paper introduces the DEGM(2,1)model of difference equation, whose definition, parameter estimation and fitting value generation of GM(2,1) model are all completed by using difference equation, avoiding the conversion problem of GM(2,1) model. In order to solve the adverse effect of the initial value data on the fitting accuracy, this paper adopts a reverse correction method to add a correction parameter to each of the initial values of two iterations of the DEGM(2,1) model, so as to reversely offset the deviation from the initial value by modifying the parameters. The results show that the maximum relative error of the single data and the average absolute error of the whole data in the improved DEGM(2,1) model are significantly smaller than in the traditional GM(2,1) model.