基于初始值和背景值改进的GM(1, 1)模型优化与应用

针对在现实生活中, 经典GM(1,1)模型预测精度不稳定, 且以往的优化方法大部分具有片面性的缺点, 文章对经典GM(1,1)模型背景值与初始值进行改进, 提出了一种组合优化方法:根据动态寻优原则, 将背景值设为变量, 其参数以及时间响应式由MRE取最小值时确定;同时, 采用差分方程取代以x⁽¹⁾(1)为固定点的静态方程。将初始值和背景值看作变量, 以系统地减少模型误差。结合国内石油年消费量数据, 分别应用经典和改进后的GM(1,1)模型进行计算和误差对比, 验证了改进后的模型精度要显著优于经典模型。

Optimization and Application of GM(1,1) Model Based on Initial Value and Background Value

In real life, the prediction accuracy of classical GM(1, 1) model is unstable, and most of the previous optimization methods are one-sided. In this paper, the background and initial values of classical GM(1, 1) model are improved, and a combined optimization method is proposed. According to the principle of dynamic optimization, the background value is set as a variable, and its parameters and time response formula are determined by the minimum value of MRE. At the same time, the difference equation is used to replace the static equation with x⁽¹⁾(1) as the fixed point.Initial and background values are taken as variables to systematically reduce model errors. Combining with the domestic annual oil consumption data, the classical GM(1, 1) model and the improved GM(1, 1) model are used to calculate and compare the errors, which proves that the improved model is significantly better than the classical model in accuracy.