改进嵌入维数和时间延迟计算的GP预测算法
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摘要
改进了混沌系统中的两个重要特征量:嵌入维数和时间延迟的计算,根据计算得出的上述两个参数重构相空间;然后在相空间中作轨迹的线性拟合,选择轨迹中的最近邻点作一次性的预测。提出的算法在相空间中很好地把轨迹的线性拟合与最近邻方法结合起来,解决了现有的时间序列分析和预测算法中主观性太强的缺点,通过对话务量时间序列和太阳黑子时间序列的验证,与其它算法相比,该算法的分析结果稳定而准确、预测精度高、运行时间比较短。
This paper improved the computing of two important characteristic measure embedding dimension and time delay in chaos system,and reconstructed phase space based on these two parameter.And then it simulated track li-nearly in phase space,selecting nearest neighbor for one time predicate.The new algorithm combines the linear track simulation and the nearest neighbor method well,sloving disadvantage that the subjectivity is too strong in existing time serials and predicate method.By validating the phone number time serials and sunspot serials,comparing other algorithm,the analysis result of our method is steady and exact,predicate precision of it is high and the running time of it is short.
This paper improved the computing of two important characteristic measure embedding dimension and time delay in chaos system,and reconstructed phase space based on these two parameter.And then it simulated track li-nearly in phase space,selecting nearest neighbor for one time predicate.The new algorithm combines the linear track simulation and the nearest neighbor method well,sloving disadvantage that the subjectivity is too strong in existing time serials and predicate method.By validating the phone number time serials and sunspot serials,comparing other algorithm,the analysis result of our method is steady and exact,predicate precision of it is high and the running time of it is short.
引文
[1]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002
[2]Grassberger P,Procaccia I.Di mension and Entropy of Strange Attractors froma Fluctuating Dynamic Approach[J].Physica,1984,13D:34-54
[3]李信富,李小凡,武晔.分形理论在地震学中的应用研究[J].地球物理学进展,2007(2)
[4]王德明,曾丹苓,刘娟芳.利用分形理论研究气液界面特性[J].工程热物理学报,2004(5)
[5]杨新宇,曾明,赵瑞,等.分形理论在网络流量分析中的应用综述[J].计算机工程,2004(23)
[6]Mansurov K.Forecasting currency crises byfractal analysis te-chniques[J].Studies on Russian Economic Development,2008,19(1):96-103
[7]Schertzera D,Lovejoy S.Space-ti me complexity and multifrac-tal predictability[J].Physica A:Statistical Mechanics and its Applications,2004,338:173-186
[8]候越先,可丕廉,王雷.适用于高必要嵌入维的混沌时间序列预测算法[J].天津大学学报,1999,32(5):594-598
[9]郑会永,刘华强,戴冠中.时间序列分维的改进GP算法[J].西北工业大学学报.1998,16(1):28-32
[10]Albano A M,Muench J,Schwartz C,et al.Singular-value de-composition and the Grassberger-Procaccia algorithm[J].Phys.Rev.A,1993,38:3017-3026
[11]Kennel,Mathew B,Brown R,et al.Determining embedding di-mension for phase-space reconstruction using a geometrical con-struction[J].Phy Rev A,1992,45:3403-3411
[12]Broomhead D,King G.Extracting qualitative dynamics from experi mental data[J].Physica D,1986,20:217-236
[13]Fraser A M,Swinney HI.Independent coordinates for strange attractors from mutual information[J].Phys.Rev.A,1986,33:1134-1140
[14]Rosenstein M T,Collins J J,Carlo D L J.Reconstruction ex-pansion as a geometry-based framework for choosing proper de-lay ti mes[J].Physica D,1994,73:82-98
[2]Grassberger P,Procaccia I.Di mension and Entropy of Strange Attractors froma Fluctuating Dynamic Approach[J].Physica,1984,13D:34-54
[3]李信富,李小凡,武晔.分形理论在地震学中的应用研究[J].地球物理学进展,2007(2)
[4]王德明,曾丹苓,刘娟芳.利用分形理论研究气液界面特性[J].工程热物理学报,2004(5)
[5]杨新宇,曾明,赵瑞,等.分形理论在网络流量分析中的应用综述[J].计算机工程,2004(23)
[6]Mansurov K.Forecasting currency crises byfractal analysis te-chniques[J].Studies on Russian Economic Development,2008,19(1):96-103
[7]Schertzera D,Lovejoy S.Space-ti me complexity and multifrac-tal predictability[J].Physica A:Statistical Mechanics and its Applications,2004,338:173-186
[8]候越先,可丕廉,王雷.适用于高必要嵌入维的混沌时间序列预测算法[J].天津大学学报,1999,32(5):594-598
[9]郑会永,刘华强,戴冠中.时间序列分维的改进GP算法[J].西北工业大学学报.1998,16(1):28-32
[10]Albano A M,Muench J,Schwartz C,et al.Singular-value de-composition and the Grassberger-Procaccia algorithm[J].Phys.Rev.A,1993,38:3017-3026
[11]Kennel,Mathew B,Brown R,et al.Determining embedding di-mension for phase-space reconstruction using a geometrical con-struction[J].Phy Rev A,1992,45:3403-3411
[12]Broomhead D,King G.Extracting qualitative dynamics from experi mental data[J].Physica D,1986,20:217-236
[13]Fraser A M,Swinney HI.Independent coordinates for strange attractors from mutual information[J].Phys.Rev.A,1986,33:1134-1140
[14]Rosenstein M T,Collins J J,Carlo D L J.Reconstruction ex-pansion as a geometry-based framework for choosing proper de-lay ti mes[J].Physica D,1994,73:82-98
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