基于初始条件优化的非等间距多变量灰色预测模型研究
|
摘要
为了进一步提高非等间距多变量灰色预测模型MGM(1,m)的预测精确度,根据新信息优先原理,本文提出了一种初始值末点优化的非等间距多变量灰色预测模型。通过对模型初始点的优化,给出了优化模型的计算公式和时间响应函数,从而使模型更符合灰色预测建模时新信息优先的原则。最后,通过算例验证了所提出模型的实用性,同时表明优化后的模型可以提高模型的模拟、预测精度。
In order to further improve prediction accuracy of multi-variable grey prediction model, by the principle of new information should be given priority, an optimized non-equidistant multi-variable grey prediction model based on the optimization of the initial value is proposed in this paper. Through optimizing the initial value of the model, the optimized formula and time response function of the model is deduced, therefore, it is more suitable for the optimized grey prediction model that new information should be first considered. Finally, a numerical example is presented to illustrate the practicability of the proposed model, and it also shows that the optimized model can improve the simulation and prediction accuracy.
In order to further improve prediction accuracy of multi-variable grey prediction model, by the principle of new information should be given priority, an optimized non-equidistant multi-variable grey prediction model based on the optimization of the initial value is proposed in this paper. Through optimizing the initial value of the model, the optimized formula and time response function of the model is deduced, therefore, it is more suitable for the optimized grey prediction model that new information should be first considered. Finally, a numerical example is presented to illustrate the practicability of the proposed model, and it also shows that the optimized model can improve the simulation and prediction accuracy.
引文
[1] 杨蒙蒙,钱伟.基于神经网络预测的网络化控制系统故障检测[J].信息与控制,2018,47(1):36～40.
[2] Zeng B,Luo C M,Liu S F,Li C.A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing[J].Computers & Industrial Engineering,2016,101:479～489.
[3] Xu N,Dang Y G,Gong Y D.Novel grey prediction model with nonlinear optimized time response method for forecasting of electricity consumption in China[J].Energy,2017,118:473～480.
[4] Wu L F,Liu S F,Liu D L,Fang Z G,Xu H Y.Modelling and forecasting CO2 emissions in the BRICS(Brazil,Russia,India,China,and South Africa) countries using a novel multi-variable grey model[J].Energy,2015,79:489～495.
[5] 王利东,赵敏,刘静霞.基于灰色关联分析和证据理论的语言值群决策模型[J].模糊系统与数学,2017,31(1):86～92.
[6] 陈挚,文军,谢政.灰色预测模型在汇率分析中的应用[J].模糊系统与数学,2001,15(3):98～101.
[7] Yuan C Q,Liu S F,Fang Z G.Comparison of China’s primary energy consumption forecasting by using ARIMA (the autoregressive integrated moving average) model and GM(1,1) model[J].Energy,2016,100:384～390.
[8] Tien T L.A research on the grey prediction model GM(1,n)[J].Applied Mathematics and Computation,2012,218:4903～4916.
[9] 翟军,盛建明.MGM(1,n)灰色模型及应用[J].系统工程理论与实践,1997,(5):109～113.
[10] 熊萍萍,党耀国,王正新.MGM(1,m)模型背景值的优化[J].控制与决策,2011,26(6):806～810+815.
[11] Han Y,Xu S G.Multi-variable grey model(MGM(1,n,q)) based on genetic algorithm and its application in urban water consumption simulation[J].Journal of System Simulation,2008,20(17):4533～4536.
[12] Guo X J,Liu S F,Wu L F,Gao Y B,Yang Y J.A multi-variable grey model with a self-memory component and its application on engineering prediction[J].Engineering Applications of Artificial Intelligence,2015,42:82～93.
[13] 刘笑冰,陈建成,何忠伟.基于MGM(1,n)模型的北京创意农业发展灰色预测[J].中国人口资源与环境,2013,(4):62～66.
[14] 王正新.无偏GM(1,1)幂模型初始条件的优化[J].系统工程与电子技术,2013,35(3):569～573.
[15] 熊萍萍,党耀国,姚天祥.基于初始条件优化的一种非等间距GM(1,1)建模方法[J].控制与决策,2015,30(11):2097～2102.
[16] Xie N M,Liu S F.Discrete grey forecasting model and its optimization[J].Applied Mathematical Modelling,2009,33(2):1173～1186.
[17] 郭金海,杨锦伟.GM(1,1)模型初始条件和初始点的优化[J].系统工程理论与实践,2015,35(9):2333～2338.
[18] 熊萍萍,党耀国,朱晖.基于非等间距的多变量模型[J].控制与决策,2011,26(1):49～53.
[2] Zeng B,Luo C M,Liu S F,Li C.A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing[J].Computers & Industrial Engineering,2016,101:479～489.
[3] Xu N,Dang Y G,Gong Y D.Novel grey prediction model with nonlinear optimized time response method for forecasting of electricity consumption in China[J].Energy,2017,118:473～480.
[4] Wu L F,Liu S F,Liu D L,Fang Z G,Xu H Y.Modelling and forecasting CO2 emissions in the BRICS(Brazil,Russia,India,China,and South Africa) countries using a novel multi-variable grey model[J].Energy,2015,79:489～495.
[5] 王利东,赵敏,刘静霞.基于灰色关联分析和证据理论的语言值群决策模型[J].模糊系统与数学,2017,31(1):86～92.
[6] 陈挚,文军,谢政.灰色预测模型在汇率分析中的应用[J].模糊系统与数学,2001,15(3):98～101.
[7] Yuan C Q,Liu S F,Fang Z G.Comparison of China’s primary energy consumption forecasting by using ARIMA (the autoregressive integrated moving average) model and GM(1,1) model[J].Energy,2016,100:384～390.
[8] Tien T L.A research on the grey prediction model GM(1,n)[J].Applied Mathematics and Computation,2012,218:4903～4916.
[9] 翟军,盛建明.MGM(1,n)灰色模型及应用[J].系统工程理论与实践,1997,(5):109～113.
[10] 熊萍萍,党耀国,王正新.MGM(1,m)模型背景值的优化[J].控制与决策,2011,26(6):806～810+815.
[11] Han Y,Xu S G.Multi-variable grey model(MGM(1,n,q)) based on genetic algorithm and its application in urban water consumption simulation[J].Journal of System Simulation,2008,20(17):4533～4536.
[12] Guo X J,Liu S F,Wu L F,Gao Y B,Yang Y J.A multi-variable grey model with a self-memory component and its application on engineering prediction[J].Engineering Applications of Artificial Intelligence,2015,42:82～93.
[13] 刘笑冰,陈建成,何忠伟.基于MGM(1,n)模型的北京创意农业发展灰色预测[J].中国人口资源与环境,2013,(4):62～66.
[14] 王正新.无偏GM(1,1)幂模型初始条件的优化[J].系统工程与电子技术,2013,35(3):569～573.
[15] 熊萍萍,党耀国,姚天祥.基于初始条件优化的一种非等间距GM(1,1)建模方法[J].控制与决策,2015,30(11):2097～2102.
[16] Xie N M,Liu S F.Discrete grey forecasting model and its optimization[J].Applied Mathematical Modelling,2009,33(2):1173～1186.
[17] 郭金海,杨锦伟.GM(1,1)模型初始条件和初始点的优化[J].系统工程理论与实践,2015,35(9):2333～2338.
[18] 熊萍萍,党耀国,朱晖.基于非等间距的多变量模型[J].控制与决策,2011,26(1):49～53.