基于灰作用量和灰导数优化的DGM(2,1)模型  

DGM(2,1)Model Based on Grey Action and Grey Derivative Optimization

作　　者：胥俊林 陈友军[1] Xu Junlin;Chen Youjun(School of Mathematics and Information,China West Normal University,Nanchong 637002,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637002

出　　处：《洛阳师范学院学报》2023年第5期1-8,共8页Journal of Luoyang Normal University

基　　金：四川省教育厅自然科学基金资助项目(18ZA0469)。

摘　　要：为解决原始DGM(2,1)模型中灰作用量存在的灰色不确定性问题,以及直接以差商代替微商选取灰导数会产生较大误差的问题,首先利用变换的一阶中心差商替换积分项以优化灰导数,再将线性时变灰作用量引入DGM(2,1)模型,进而推导出基于线性时变灰作用量和优化灰导数的DGM(2,1)模型的时间响应序列.通过实证分析得出新模型较其他几类模型精度更高,具有一定的可行性与有效性.新模型不仅适用于非齐次指数序列的预测,并且也适用于摆动序列的短期预测.This research aims to solve the grey uncertainty of grey action in the original DGM(2,1)model and the large error in selecting the gray derivative caused by replacing the derivative directly with difference quotient.The research process first implied the first-order central difference quotient to optimize the gray derivative,then introduced the linear time-varying gray action into DGM(2,1)model,and deduced the time response series of DGM(2,1)model based on linear time-varying grey action and optimization of grey derivative.The results show that the present model has higher accuracy than other models through theoretical and empirical analysis,and the model presents certain feasibility and effectiveness.This model is not only suitable for the prediction of non-homogeneous index series but also has higher accuracy for the short-term prediction of swing series.

关 键 词：DGM(2 1)模型 灰导数 线性时变灰作用量 灰色预测 

分 类 号：N941.5[自然科学总论—系统科学]