基于扰动因子GM(1,N)模型优化算法及其应用
|
摘要
基于Simpson公式的GM(1,N)建模的算法不能更改参数的缺点,提出了基于扰动因子改进Simpson GM(1,N)模型。通过扰动因子变化影响参数值,以达到特征因素的最优预测值。依据平均相对误差指标对一些时间序列数据进行了不同模型的实证分析和比较,得到本算法的拟合精度比原有算法有明显的改进,从而验证了该算法对一些时间序列的有效性。所提出的新算法是GM(1,N)模型进行预测时值得尝试的一个方法,对GM(1,N)预测模型的合理应用具有一定的现实意义。
A new improved Simpson GM( 1,N) modeling is proposed through imported perturbation factor,basing on the defect on unchanging parameters of GM( 1,N) modeling in Simpson formula.The parameters can be changed with the change of the perturbation factor,in order to achieve the optimal predictive value,based on the average relative error index,some time series data are empirically analysized and compared,and there are gained that the fitting precision of this algorithm is significantly improved. thus,the validity of the algorithm is proved. The new algorithm proposed is a trying method in predicting the GM( 1,N) model. The reasonable application of prediction model of GM( 1,N) is of practical significance.
A new improved Simpson GM( 1,N) modeling is proposed through imported perturbation factor,basing on the defect on unchanging parameters of GM( 1,N) modeling in Simpson formula.The parameters can be changed with the change of the perturbation factor,in order to achieve the optimal predictive value,based on the average relative error index,some time series data are empirically analysized and compared,and there are gained that the fitting precision of this algorithm is significantly improved. thus,the validity of the algorithm is proved. The new algorithm proposed is a trying method in predicting the GM( 1,N) model. The reasonable application of prediction model of GM( 1,N) is of practical significance.
引文
[1]邓聚龙.灰色系统理论教程[M].武汉:华中理工大学出版社,1992.
[2]罗佑新,周继荣.非等间距GM_1_1_模型及其在疲劳试验数据处理和疲劳试验在线监测中的应用[J].机械强度,1996,18(3):60-63.
[3]戴文战,李俊峰.非等间距GM(1,1)模型建模研究[J].系统工程理论与实践,2005(9):89-93.
[4]王钟羡,旲春笃,史雪荣.非等间距序列的灰色模型[J].数学的实践认识,2003,33(10):16-20.
[5]蒋卫东,李夕兵,赵国彦.非等时序列预测的时数分离研究[J].系统工程理论与实践,2003,23(1):68-71.
[6]曾祥艳,曾玲.非等间距GM(1,1)模型的改进与应用[J].数学的实践与认知,2011,41(2):90-95.
[7]韩晋,杨岳,陈峰,等.基于非等时距加权灰色模型与神经网络的组合预测算法[J].应用数学和力学,2013,34(4):408-419.
[8]邓聚龙.多维灰色规划[M].武汉:华中理工大学出版社,1989:17-23.
[9]叶舟,陈康民.基于自相关理论的GM(1,1)和GM(1,N)联合预测[J].上海理工大学学报,2002,24(1):17-20
[10]黄继.灰色多变量GM(1,N|Γ,r)模型及其粒子群优化算法[J].系统工程理论与实践,2009,29(10):145-151.
[11]仇伟杰,刘思峰.GM(1,N)模型的离散化结构解[J].系统工程与电子技术,2006,28(11):1679-1681
[12]何满喜,王勤.基于Simpson公式的GM(1,N)建模的新算法[J].系统工程理论与实践,2013,33(1):199-202.
[13]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2001.
[14]刘思峰,郭天榜.灰色系统理论及其应用[M].郑州:河南大学出版社,1991:175-180.
[2]罗佑新,周继荣.非等间距GM_1_1_模型及其在疲劳试验数据处理和疲劳试验在线监测中的应用[J].机械强度,1996,18(3):60-63.
[3]戴文战,李俊峰.非等间距GM(1,1)模型建模研究[J].系统工程理论与实践,2005(9):89-93.
[4]王钟羡,旲春笃,史雪荣.非等间距序列的灰色模型[J].数学的实践认识,2003,33(10):16-20.
[5]蒋卫东,李夕兵,赵国彦.非等时序列预测的时数分离研究[J].系统工程理论与实践,2003,23(1):68-71.
[6]曾祥艳,曾玲.非等间距GM(1,1)模型的改进与应用[J].数学的实践与认知,2011,41(2):90-95.
[7]韩晋,杨岳,陈峰,等.基于非等时距加权灰色模型与神经网络的组合预测算法[J].应用数学和力学,2013,34(4):408-419.
[8]邓聚龙.多维灰色规划[M].武汉:华中理工大学出版社,1989:17-23.
[9]叶舟,陈康民.基于自相关理论的GM(1,1)和GM(1,N)联合预测[J].上海理工大学学报,2002,24(1):17-20
[10]黄继.灰色多变量GM(1,N|Γ,r)模型及其粒子群优化算法[J].系统工程理论与实践,2009,29(10):145-151.
[11]仇伟杰,刘思峰.GM(1,N)模型的离散化结构解[J].系统工程与电子技术,2006,28(11):1679-1681
[12]何满喜,王勤.基于Simpson公式的GM(1,N)建模的新算法[J].系统工程理论与实践,2013,33(1):199-202.
[13]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2001.
[14]刘思峰,郭天榜.灰色系统理论及其应用[M].郑州:河南大学出版社,1991:175-180.