基于非齐次指数函数的灰色预测模型背景值重构方法研究

Study on the reconstructed method of background value in gray predictive model based on non-homogeneous exponential function

灰色模型背景值重构是从变形数据本身出发,考虑数据波动性而引起的模型偏差对预测结果的影响,对背景值的构造形式加以改进。本文针对齐次指数函数的背景值拟合法存在的不足,提出了一种基于非齐次指数函数的背景值重构方法。其核心思想是充分考虑u/a的影响,将原始数据的1-AGO序列抽象为非齐次指数函数。该方法建模简单,计算方便,能够有效地提高拟合、预测精度。且不受0<-a<2的限制,在-a≥2的情况下也能保持良好的拟合、预测效果。

The reconstruction of gray model background value is starting from the deformation data itself, considering the data volatility to cause the offset of data model and its influence on prediction result,to improve the structure forms of background value. This paper aims at shortcomings of the background value fitting method with homogeneous exponential function and proposes a reconstructed method of background value based on non-homogeneous exponential function. The core idea is to fully consider the u / a impact, make 1-AGO sequence of the original data as the abstract non-homogeneous exponential function. The method is simple for modeling and convenient for calculation,which can effectively improve the fitting and prediction accuracy. And it doesn't subject to the 0 <- a < 2 limitation,and in the case of- a≥2,it also maintain a good fitting and prediction.