含分数阶微积分的非等间距灰色模型及其应用  

Non-equigap grey model with fractional order calculus and its applications

作　　者：涂乐平 党耀国 王俊杰 TU Leping;DANG Yaoguo;WANG Junjie(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学经济管理学院,南京211106

出　　处：《系统工程理论与实践》2023年第12期3636-3652,共17页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(72001107,72271120);中国博士后科学基金(2020T130297,2019M660119)。

摘　　要：相比于等间距灰色模型,非等间距灰色预测模型适用范围更广.然而,现有的非等间距灰色模型的预测响应值容易受到主观数据的干扰,导致预测结果出现偏差.因此,本文提出了具有分数阶微积分的非等间距灰色残差修正模型.首先,基于非等间距分数阶积分序列得到非等间距灰色模型的参数估计.然后,对时间响应函数进行分数阶求导得到模型的预测还原式.最后,使用不累加的非等间距灰色模型对积分残差进行修正.在一定条件下,本文改进模型与传统非等间距灰色模型是近似的.案例分析结果表明,具有分数阶微积分的非等间距灰色残差修正模型可以有效用于非等间距序列的预测建模,具有很高的模型精度和预测响应性.Compared with the equally spaced grey models,the non-equigap grey forecasting models have a wider applicability range.However,the predicted response values of existing nonequigap grey models are easily disturbed by subjective data,which leads to biased prediction results.Therefore,this paper proposes a non-equigap grey residual correction model with fractional order calculus.First,the parameter estimates of the non-equigap grey model are obtained based on the non-equigap fractional order integration series.Then,the fractional order derivative of the time response function is used to obtain the prediction reduction of the grey model.Finally,the integral residuals are corrected using the non-accumulative non-equigap grey model.In certain conditions,the improved model is approximate to the traditional non-equigap grey model.The results of the case study show that the non-equigap grey residual correction model with fractional order calculus can be effectively used for prediction modeling of non-equidistant sequence with high model accuracy and predictive responsiveness.

关 键 词：非等间距数据 灰色预测建模 分数阶求导 PSO优化算法 残差修正 

分 类 号：N941.5[自然科学总论—系统科学]