近非齐次指数离散灰色直接模型的适用范围及拓展
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摘要
文章基于近非齐次指数离散灰色模型的直接建模,得到了一个新灰色预测模型。新模型不仅对近非齐次指数序列提高了建模精度,而且将适用范围拓展到近非齐次指数增减序列与线性增减序列的组合序列、抛物型增减序列等情形。推导了待定系数的求解公式,从理论上证明了新模型对严格非齐次指数增减序列与线性增减序列的组合序列、近抛物型增减序列都具有白化指数、系数重合性,从而对近似于这些类型的序列都有较高的模拟预测精度;其次通过优化初始条件,再次提高模拟精度;最后通过实例验证了方法的有效性和可行性。
Based on the direct modeling of the approximate non-homogeneous exponential discrete grey model, this paper constructs a new grey forecasting model, which not only improves the modeling accuracy of approximate non-homogeneous exponential sequences, but also extends the application scope to such cases as the combination of the increasing-decreasing sequence of approximate non-homogeneous exponential and linear increasing-decreasing sequence, parabolic increasing-decreasing sequence and so forth. The paper derives the formula for undetermined coefficient, and theoretically proves that the new model has whitening index and coefficient coincidence with the combination sequence of increasing-decreasing sequence of strict non-homogeneous exponential and linear increasing-or-decreasing sequence, parabolic increasing-or-decreasing sequence, hence relatively higher simulation prediction accuracy on these types of sequences. In addition, by optimizing the initial conditions, the paper improves the accuracy of simulation once more. Finally, examples are employed to verify the effectiveness and feasibility of the proposed method.
Based on the direct modeling of the approximate non-homogeneous exponential discrete grey model, this paper constructs a new grey forecasting model, which not only improves the modeling accuracy of approximate non-homogeneous exponential sequences, but also extends the application scope to such cases as the combination of the increasing-decreasing sequence of approximate non-homogeneous exponential and linear increasing-decreasing sequence, parabolic increasing-decreasing sequence and so forth. The paper derives the formula for undetermined coefficient, and theoretically proves that the new model has whitening index and coefficient coincidence with the combination sequence of increasing-decreasing sequence of strict non-homogeneous exponential and linear increasing-or-decreasing sequence, parabolic increasing-or-decreasing sequence, hence relatively higher simulation prediction accuracy on these types of sequences. In addition, by optimizing the initial conditions, the paper improves the accuracy of simulation once more. Finally, examples are employed to verify the effectiveness and feasibility of the proposed method.
引文
[1]邓聚龙.灰预测与决策[M].武汉:华中科技大学出版社,2002.
[2]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社,2004.
[3]Liu S F,Forrest J.The Role and Position of Grey System Theo-ry in Science Development[J].The Journal of Grey System(UK),1997,9(4).
[4]余逗,魏勇.非齐次指数序列的GM模型[A].第16届全国灰色系统学术会议论文集[C].北京:中国高等科学技术中心,2008.
[5]刘常丽,屈绍建.一类GM(1,1)模型白化方程的优化[J].数学的实践与认识,2015,45(4).
[6]陈芳,魏勇.近非齐次指数序列GM(1,1)模型灰导数的优化[J].系统工程理论与实践,2013,33(11).
[7]崔兴凯,路秀英.基于NGM(1,1,k)模型的农产品产量预测方法[J].微电子学与计算机,2011,28(8).
[8]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009,24(11).
[9]王正新,党耀国,刘思峰.基于离散指数函数优化的GM(1,1)模型[J].系统工程理论与实践,2008,(2).
[10]谢乃明,刘思峰.离散灰色模型的拓展及其最优化求解[J].系统工程理论与实践,2006,28(11).
[11]战立青,施化吉.近似非齐次指数数据的灰色建模方法与模型[J].系统工程理论与实践,2013,33(3).
[12]姜爱平,张启敏.非等间距近似非齐次指数序列的灰色建模方法及其优化[J].系统工程理论与实践,2014,32(12).
[13]童明余,周孝华,曾波.基于直接估计法的NGM(1,1)模型拓展[J].控制与决策,2015,30(10).
[14]高明.一种适用于非齐次指数增长序列的接型离散灰色模型[J].统计与信息论坛,2010,25(4).
[15]曾波,刘思峰.近似非齐次指数序列的DGM(1,1)模型直接建模法[J].系统工程理论与实践,2011,2(31).
[16]王义闹.GM(1,1)逐步优化直接建模方法的推广[J].系统工程理论与实践,2003,23(2).
[17]Xie N M,Liu S F.Interval Grey Number Sequence Prediction by Us-ing Non-homogenous Exponential Discrete Grey Forecasting Model[J].Journal of Systems Engineering and Electronics,2015,26(1).
[2]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社,2004.
[3]Liu S F,Forrest J.The Role and Position of Grey System Theo-ry in Science Development[J].The Journal of Grey System(UK),1997,9(4).
[4]余逗,魏勇.非齐次指数序列的GM模型[A].第16届全国灰色系统学术会议论文集[C].北京:中国高等科学技术中心,2008.
[5]刘常丽,屈绍建.一类GM(1,1)模型白化方程的优化[J].数学的实践与认识,2015,45(4).
[6]陈芳,魏勇.近非齐次指数序列GM(1,1)模型灰导数的优化[J].系统工程理论与实践,2013,33(11).
[7]崔兴凯,路秀英.基于NGM(1,1,k)模型的农产品产量预测方法[J].微电子学与计算机,2011,28(8).
[8]崔杰,党耀国,刘思峰.一种新的灰色预测模型及其建模机理[J].控制与决策,2009,24(11).
[9]王正新,党耀国,刘思峰.基于离散指数函数优化的GM(1,1)模型[J].系统工程理论与实践,2008,(2).
[10]谢乃明,刘思峰.离散灰色模型的拓展及其最优化求解[J].系统工程理论与实践,2006,28(11).
[11]战立青,施化吉.近似非齐次指数数据的灰色建模方法与模型[J].系统工程理论与实践,2013,33(3).
[12]姜爱平,张启敏.非等间距近似非齐次指数序列的灰色建模方法及其优化[J].系统工程理论与实践,2014,32(12).
[13]童明余,周孝华,曾波.基于直接估计法的NGM(1,1)模型拓展[J].控制与决策,2015,30(10).
[14]高明.一种适用于非齐次指数增长序列的接型离散灰色模型[J].统计与信息论坛,2010,25(4).
[15]曾波,刘思峰.近似非齐次指数序列的DGM(1,1)模型直接建模法[J].系统工程理论与实践,2011,2(31).
[16]王义闹.GM(1,1)逐步优化直接建模方法的推广[J].系统工程理论与实践,2003,23(2).
[17]Xie N M,Liu S F.Interval Grey Number Sequence Prediction by Us-ing Non-homogenous Exponential Discrete Grey Forecasting Model[J].Journal of Systems Engineering and Electronics,2015,26(1).