灰色模型GM(1,1)直接优化建模

摘要

灰色模型GM(1,1)是预测中常用的模型,但有时误差较大,有个重要原因是模型的基本形式(用于估计参数)和模型的白化方程(用于预测)结构不一致.为了提高模型的预测精度,该文仅从模型的白化方程出发,按照某个准则,直接对其解(时间响应函数)优化,如按照平均相对误差绝对值最小准则建模.优化函数的初始值,该文选择三和法和三点法.实例表明灰色模型GM(1,1)直接优化建模精度很高.%The gray model GM(1,1) is a commonly used model in prediction,but it has rather big errors some-times,because its basic form (used to estimate parameters) is not consistent with that of whitenization equation (used for prediction). In order to improve prediction accuracy of models,this paper started with whitenization equation and optimized its solution (time response function ) directly according to some criteria ,such as the mini-mum criterion of average absolute relative errors. This paper selected three-harmony and three-point methods to optimize the initial value of functions. The examples indicate that the directly optimized gray model GM (1,1) has very high accuracy in modeling.