基于引力搜索算法的分数阶变异时序回归GSA-TSGM(1,1)模型
|
摘要
为了利用分数阶累加算子在灰色短期预测中的高效性能,首次将分数阶累加算子引入变异时序回归模型以期取得更高的预测精度。主要方法如下:首先取湖北省链子崖某监测点1978—1987年的十年数据作为训练集并使用引力搜索算法确定最佳分数阶累加阶数,而1988—1993年的六年数据作为验证集验证提出的模型;其次对比了经典灰色模型GM(1,1)、分数阶累加灰色模型、变异时序回归模型TSGM(1,1)三种灰色模型。结果如下:首先修正了陈西江等人变异时序回归模型仿真时出现的错误,其次表明了相比于其他的模型,基于引力搜索算法的分数阶累加时序回归模型在进行灰色长期预测中具有较高的预测精度。因此,通过分数阶累加算子提高了灰色理论中长期预测模型的精度,为灰色长期预测提供了指导。
In order to use the high performance of fractional accumulated generating operator( FAGO) in the short-term grey prediction,this paper firstly added FAGO in the time sequence variation grey model TSGM( 1,1) to get higher accuracy. The main method organized as follow. Firstly,it used the data of 1978 to 1987 from the monitoring station of"Lianziya"mountain in Hubei province as training data to optimal FAGO by using gravitational search algorithm and then used the data of 1988-1993 as verifying data to test the accuracy of the proposed grey model. Secondly,it compared other grey model GM( 1,1),fractional accumulated generating GM( 1,1) and TSGM( 1,1). The result was that as follow. Firstly,it corrected the error in the simulation of time sequence variation regression model. Moreover,it shows that the proposed model has higher prediction accuracy. Therefore,the novel model improves accuracy of the grey theory in long-term prediction by fractional accumulated generating operator and it provides the guide in the long-term prediction.
In order to use the high performance of fractional accumulated generating operator( FAGO) in the short-term grey prediction,this paper firstly added FAGO in the time sequence variation grey model TSGM( 1,1) to get higher accuracy. The main method organized as follow. Firstly,it used the data of 1978 to 1987 from the monitoring station of"Lianziya"mountain in Hubei province as training data to optimal FAGO by using gravitational search algorithm and then used the data of 1988-1993 as verifying data to test the accuracy of the proposed grey model. Secondly,it compared other grey model GM( 1,1),fractional accumulated generating GM( 1,1) and TSGM( 1,1). The result was that as follow. Firstly,it corrected the error in the simulation of time sequence variation regression model. Moreover,it shows that the proposed model has higher prediction accuracy. Therefore,the novel model improves accuracy of the grey theory in long-term prediction by fractional accumulated generating operator and it provides the guide in the long-term prediction.
引文
[1] Deng Julong. Control problems of grey systems[J]. Systems&Control Letters,1982,1(5):288-294.
[2] Frank E,Hall M,Trigg L,et al. Data mining in bioinformatics using Weka[J]. Bioinformatics,2004,20(15):2479-2481.
[3]肖新平,邓旅成,查金茂.灰色系统分析理论及其应用[M].大连:大连海事大学出版社,1997:203-267.(Xiao Xinping,Deng Lucheng,Cha Jinmao. Grey system analysis theory and its application[M]. Dalian:Dalian Maritime University Press,1997:203-267.)
[4]刘思峰. GM(1,1)模型的适用范围[J].系统工程理论与实践,2000,20(5):121-124.(Liu Sifeng. The range suitable for GM(1,1)[J]. Systems Engineering-Theory&Practice,2000,20(5):121-124.)
[5] Wen J C,Huang K H,Wen Kunli. The study of alpha in GM(1,1)model[J]. Journal of Chinese Institute of Engineers,2000,23(5):583-589.
[6]谭冠军,檀甲友,王加阳. GM(1,1)模型的背景值构造方法和应用(Ⅱ)[J].系统工程理论与实践,2000,20(5):125-128.(Tan Guanjun,Tan Jiayou,Wang Jiayang. The structure method and application of background value in grey model(Ⅱ)[J]. Systems Engineering-Theory&Practice,2000,20(5):125-128.)
[7]汪孔政.时变参数PGM(1,1)变形预测模型及其应用[J].武汉大学学报:信息科学版,2005,30(5):456-459.(Wang Kongzheng.Time-varying parameter PGM(1,1)deformation prediction model and its applications[J]. Geomatics and Information Science of Wuhan University,2005,30(5):456-459.)
[8] Hsu L. Using improved grey forecasting models to forecast the output of opto-electronics industry[J]. Expert Systems with Application,2011,38(11):13879-13885.
[9]李希灿,李丽.时序残差GM(1,1)模型[J].系统工程理论与实践,1998,18(10):59-63.(Li Xican,Li Li. GM(1,1)model of time sequence residual[J]. Systems Engineering-Theory&Practice,1998,18(10):59-63.)
[10]陈西江,鲁铁定.残差自适应回归MGM(1,n)[J].测绘科学,2012,37(2):36-37.(Chen Xijiang,Lu Tieding. MGN(1,n)based on adaptive regression of residual[J]. Science of Surveying and Mapping,2012,37(2):36-37.)
[11]陈西江,鲁铁定.变异时序回归GM(1,1)模型[J].测绘科学,2011,36(6):184-186.(Chen Xijiang,Lu Tieding. GM(1,1)model of time sequence variation regression[J]. Science of Surveying and Mapping,2011,36(6):184-186.)
[12]Kilbas A A,Srivastava H M,Trujillo J J. Theory and applications of fractional differential equations,volume 204,North-Holland mathematics studies[M].[S. l.]:Elsevier Science Publishers,2006:433-463.
[13]Wu Lifeng,Liu Sifeng,Yao Ligen,et al. Grey system model with the fractional order accumulation[J]. Communications in Nonlinear Science&Numerical Simulation,2013,18(7):1775-1785.
[14]Mao Shuhua,Zhu Min,Yan Xinping,et al. Modeling mechanism of a novel fractional grey model based on matrix analysis[J]. Journal of Systems Engineering and Electronics,2016,27(5):1040-1053.
[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 Shuhua,Gao Mingyun,Xiao Xinping. Fractional order accumulation time-lag GM(1,N,τ)model and its application[J]. Systems Engineering-Theory&Practice,2015,35(2):430-436.)
[16]Mao Shuhua,Gao Mingyun,Xiao Xinping,et al. A novel fractional grey system model and its application[J]. Applied Mathematical Modelling,2016,40(7-8):5063-5076.
[17] Rashedi E,Nezamabadi-pour H,Saryazdi S. GSA:a gravitational search algorithm[J]. Information Sciences,2009,179(13):2232-2248.
[18]Ma Weimin,Zhu Xiaoxi,Wang Miaomiao. Forecasting iron ore import and consumption of China using grey model optimized by particle swarm optimization algorithm[J]. Resources Policy,2013,38(4):613-620.
[19]Tofallis C. Erratum:a better measure of relative prediction accuracy for model selection and model estimation[J]. Journal of the Operational Research Society,2015,66(3):524-524.
[20] Li Chaoshun,Li Hongshun,Kou Pangao. Piecewise function based gravitational search algorithm and its application on parameter identification of AVR system[J]. Neurocomputing,2014,124(2):139-148.
[2] Frank E,Hall M,Trigg L,et al. Data mining in bioinformatics using Weka[J]. Bioinformatics,2004,20(15):2479-2481.
[3]肖新平,邓旅成,查金茂.灰色系统分析理论及其应用[M].大连:大连海事大学出版社,1997:203-267.(Xiao Xinping,Deng Lucheng,Cha Jinmao. Grey system analysis theory and its application[M]. Dalian:Dalian Maritime University Press,1997:203-267.)
[4]刘思峰. GM(1,1)模型的适用范围[J].系统工程理论与实践,2000,20(5):121-124.(Liu Sifeng. The range suitable for GM(1,1)[J]. Systems Engineering-Theory&Practice,2000,20(5):121-124.)
[5] Wen J C,Huang K H,Wen Kunli. The study of alpha in GM(1,1)model[J]. Journal of Chinese Institute of Engineers,2000,23(5):583-589.
[6]谭冠军,檀甲友,王加阳. GM(1,1)模型的背景值构造方法和应用(Ⅱ)[J].系统工程理论与实践,2000,20(5):125-128.(Tan Guanjun,Tan Jiayou,Wang Jiayang. The structure method and application of background value in grey model(Ⅱ)[J]. Systems Engineering-Theory&Practice,2000,20(5):125-128.)
[7]汪孔政.时变参数PGM(1,1)变形预测模型及其应用[J].武汉大学学报:信息科学版,2005,30(5):456-459.(Wang Kongzheng.Time-varying parameter PGM(1,1)deformation prediction model and its applications[J]. Geomatics and Information Science of Wuhan University,2005,30(5):456-459.)
[8] Hsu L. Using improved grey forecasting models to forecast the output of opto-electronics industry[J]. Expert Systems with Application,2011,38(11):13879-13885.
[9]李希灿,李丽.时序残差GM(1,1)模型[J].系统工程理论与实践,1998,18(10):59-63.(Li Xican,Li Li. GM(1,1)model of time sequence residual[J]. Systems Engineering-Theory&Practice,1998,18(10):59-63.)
[10]陈西江,鲁铁定.残差自适应回归MGM(1,n)[J].测绘科学,2012,37(2):36-37.(Chen Xijiang,Lu Tieding. MGN(1,n)based on adaptive regression of residual[J]. Science of Surveying and Mapping,2012,37(2):36-37.)
[11]陈西江,鲁铁定.变异时序回归GM(1,1)模型[J].测绘科学,2011,36(6):184-186.(Chen Xijiang,Lu Tieding. GM(1,1)model of time sequence variation regression[J]. Science of Surveying and Mapping,2011,36(6):184-186.)
[12]Kilbas A A,Srivastava H M,Trujillo J J. Theory and applications of fractional differential equations,volume 204,North-Holland mathematics studies[M].[S. l.]:Elsevier Science Publishers,2006:433-463.
[13]Wu Lifeng,Liu Sifeng,Yao Ligen,et al. Grey system model with the fractional order accumulation[J]. Communications in Nonlinear Science&Numerical Simulation,2013,18(7):1775-1785.
[14]Mao Shuhua,Zhu Min,Yan Xinping,et al. Modeling mechanism of a novel fractional grey model based on matrix analysis[J]. Journal of Systems Engineering and Electronics,2016,27(5):1040-1053.
[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 Shuhua,Gao Mingyun,Xiao Xinping. Fractional order accumulation time-lag GM(1,N,τ)model and its application[J]. Systems Engineering-Theory&Practice,2015,35(2):430-436.)
[16]Mao Shuhua,Gao Mingyun,Xiao Xinping,et al. A novel fractional grey system model and its application[J]. Applied Mathematical Modelling,2016,40(7-8):5063-5076.
[17] Rashedi E,Nezamabadi-pour H,Saryazdi S. GSA:a gravitational search algorithm[J]. Information Sciences,2009,179(13):2232-2248.
[18]Ma Weimin,Zhu Xiaoxi,Wang Miaomiao. Forecasting iron ore import and consumption of China using grey model optimized by particle swarm optimization algorithm[J]. Resources Policy,2013,38(4):613-620.
[19]Tofallis C. Erratum:a better measure of relative prediction accuracy for model selection and model estimation[J]. Journal of the Operational Research Society,2015,66(3):524-524.
[20] Li Chaoshun,Li Hongshun,Kou Pangao. Piecewise function based gravitational search algorithm and its application on parameter identification of AVR system[J]. Neurocomputing,2014,124(2):139-148.