基于扰动因子的GM(1,N)模型数值算法
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摘要
文章通过研究几类灰色模型,提出Newton-cotes GM(1,N)数值算法,通过实例分析,Newton-cotes GM(1,N)模型比其他几类GM(1,N)模型预测精度高。为了克服这种灰色建模算法不能更改参数的缺点,提出了基于扰动因子改进的灰色模型;通过扰动因子的数值变化对参数的影响,达到改变特征因素的最优预测值;依据平均相对误差指标,对预测的结果进行误差分析和比较,得到新算法的拟合精度比原有算法的拟合精度有明显的改进。
Based on the study of several types of gray models, this paper proposes Newton-cotes GM(1, N) numerical algorithm. Case analyses show that Newton-cotes GM(1, N) model has higher prediction accuracy than other GM(1, N) models. In order to overcome the disadvantage that parameters can not be changed in the grey modeling algorithm, the paper proposes a new grey model based on perturbation factor improvement, and the proposed model is able to achieve the optimal prediction value of changing characteristic factors through the influence of the numerical change of the perturbation factor on the parameters. Finally,according to the average relative error index, the paper carries out error analysis and comparison of the predicted results, indicating that the fitting accuracy of the new algorithm is significantly improved than that of the original algorithm.
Based on the study of several types of gray models, this paper proposes Newton-cotes GM(1, N) numerical algorithm. Case analyses show that Newton-cotes GM(1, N) model has higher prediction accuracy than other GM(1, N) models. In order to overcome the disadvantage that parameters can not be changed in the grey modeling algorithm, the paper proposes a new grey model based on perturbation factor improvement, and the proposed model is able to achieve the optimal prediction value of changing characteristic factors through the influence of the numerical change of the perturbation factor on the parameters. Finally,according to the average relative error index, the paper carries out error analysis and comparison of the predicted results, indicating that the fitting accuracy of the new algorithm is significantly improved than that of the original algorithm.
引文
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[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).
[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).
[4]王钟羡等.非等间距序列的灰色模型[J].数学的实践认识,2003,33(10).
[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).
[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).
[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).
[8]邓聚龙.多维灰色规划[M].武汉:华中理工大学出版社,1989.
[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).
[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).
[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).
[9]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).
[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]中华人民共和国国家统计局.中国统计年鉴2009[M].北京:中国统计出版社,2009.
[15]浙江省统计局.浙江统计年鉴2009[M].北京:中国统计出版社,2009.
[16]刘思峰,郭天榜.灰色系统理论及其应用[J].郑州:河南大学出版社,1991.
[17]詹棠森等.基于模糊层次分析的陶瓷艺术品价格预测模型研究[J].中国陶瓷工业,2014,21(2).