基于驱动因素控制的DFCGM(1,N)及其拓展模型构建与应用
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摘要
针对一类驱动因素具有复杂变化特征的系统行为预测问题,将驱动因素序列对系统的作用函数引入经典GM(1,N)模型的灰色作用量,构建驱动因素控制的DFCGM(1,N)模型及其拓展模型,并探讨参数估计方法;从白化信息充分和匮乏两个角度,利用经验分析法和智能优化算法探索驱动因素控制参数的识别方法,并给出模型建模预测步骤;最后,通过对我国粮食产量进行预测,验证了模型的有效性和实用性,表明所提出模型能够有效解决多驱动因素影响的系统预测问题.
To solve the forecasting problems of system behavior affected by driving factors with a complicated changing patterns, a driving foctor control grey model of N variables driving foctor control grey model of N variables(DFCGM(1,N)) model based on driving factors control and its derived model are designed by introducing a driver function into the construction of the grey action item in the conventional GM(1,N) model, and subsequently the method of estimating the parameters is discussed. According to the sufficient and insufficient information about the driving factors, empirical analysis and intelligent optimization algorithms are used to explore the estimation of driving factors control parameters, respectively, and subsequently the modeling procedure is given with a flowchart. Finally, the effectiveness and practicality of the proposed model are verified by forecasting the grain production in China. Results show that the proposed model can effectively solve the forecasting problems on the system affected by multiple driving factors.
To solve the forecasting problems of system behavior affected by driving factors with a complicated changing patterns, a driving foctor control grey model of N variables driving foctor control grey model of N variables(DFCGM(1,N)) model based on driving factors control and its derived model are designed by introducing a driver function into the construction of the grey action item in the conventional GM(1,N) model, and subsequently the method of estimating the parameters is discussed. According to the sufficient and insufficient information about the driving factors, empirical analysis and intelligent optimization algorithms are used to explore the estimation of driving factors control parameters, respectively, and subsequently the modeling procedure is given with a flowchart. Finally, the effectiveness and practicality of the proposed model are verified by forecasting the grain production in China. Results show that the proposed model can effectively solve the forecasting problems on the system affected by multiple driving factors.
引文
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[2]肖新平,毛树华.灰预测与决策方法[M].北京:科学出版社,2013:272-277.(Xiao X P,Mao S H.Grey forecasting and decision making method[M].Beijing:Science Press,2013:272-277.)
[3]Guo H,Xiao X P,Forrest J.A research on a comprehensive adaptive grey prediction model CAGM(1,N)[J].Applied Mathematics and Computation,2013,225(1):216-227.
[4]Guo X J,Liu S F,Wu L F,et al.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.
[5]Zeng B,Luo C M,Liu S F,et al.Development of an optimization method for the GM(1,N)model[J].Engineering Applications of Artificial Intelligence,2016,55:353-362.
[6]Zeng B,Luo C M,Li C,et al.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.
[7]丁松,党耀国,徐宁.基于驱动变量增长趋势的TGM(1,N)预测模型[J].系统工程,2015,33(3):149-153.(Ding S,Dang Y G,Xu N.TGM(1,N)prediction model based on trends of driving variables[J].Systems Engineering,2015,33(3):149-153.)
[8]王正新.灰色多变量GM(1,N)幂模型及其应用[J].系统工程理论与实践,2014,34(9):2357-2363.(Wang Z X.Grey multivariable power model GM(1,N)and its application[J].Systems Engineering—Theory&Practice,2014,34(9):2357-2363.)
[9]Ding S,Dang Y G,Li X M,et al.Forecasting Chinese CO2 emissions from fuel combustion using a novel grey multivariable model[J].J of Cleaner Production,2017,162:1527-1538.
[10]Tien T L.The indirect measurement of tensile strength of material by the grey prediction model GMC(1,N)[J].Measurement Science Technology,2005,16(6):1322–1328.
[11]Tien T L.Forecasting CO2 output from gas furnace by grey model IGMC(1,N)[J].J of the Chinese Society of Mechanical Engineers,2010,31(1):55–65.
[12]Tien T L.The indirect measurement of tensile strength by the new model FGMC(1,N)[J].Measurement,2011,44(10):1884–1897.
[13]Wang Z X,Hao P.An improved grey multivariable model for predicting industrial energy consumption in China[J].Applied Mathematical Modelling,2016,40(11):5745-5758.
[14]张可,曲品品.时滞多变量离散灰色模型及其应用[J].系统工程理论与实践,2015,35(8):2092-2103.(Zhang K,Qu P P.Delay multi-variables discrete grey model and its application[J].Systems Engineering—Theory&Practice,2015,35(8):2092-2103.)
[15]毛树华,高明运,肖新平.分数阶累加时滞GM(1,N,τ)模型及其应用[J].系统工程理论与实践,2015,35(2):430-436.(Mao S H,Gao M Y,Xiao X P.Fractional order accumulation time-lag GM(1,N,τ)model and its application[J].Systems Engineering—Theory&Practice,2015,35(2):430-436.)
[16]王正新.多变量时滞GM(1,N)模型及其应用[J].控制与决策,2015,30(12):2298-2304.(Wang Z X.Multivariable time-delayed GM(1,N)model and its application[J].Control and Decision,2015,30(12):2298-2304.)
[17]Xie N M,Liu S.F.Discrete grey forecasting model and its optimization[J].Applied Mathematical Modelling,2009,33(2):1173-1186.
[18]Ma X,Liu Z.Research on the novel recursive discrete multivariate grey prediction model and its applications[J].Applied Mathematical Modelling,2016,40(8):4876-4890.
[19]Wu L,Liu S,Liu D,et al.Modelling and forecasting CO2emissions in the BRICS(Brazil,Russia,India,China,and South Africa)countries using a novel multi-variable grey model[J].Energy,2015,79:489-495.