一种基于相空间重构的动态离散时间序列参数自适应求取算法
|
摘要
提出了自适应确定动态离散时间序列的最佳重构相空间嵌入维方法,为数据量不断变动的动态离散时间序列数据库实现自动连续分析提供了可能.讨论了在应用Wolf算法计算最大Lyapunov指数时遇到的因追踪轨线追踪到相空间终点而使计算意外终止的问题,提出最大Lyapunov指数的改进求解方法.基于最大Lyapunov指数进行验证性预测,说明了算法的有效性,并进一步分析了算法对实时分析短期稳定的混沌系统具有积极意义.
This paper presents a method for calculating and automatically determining the optimal embed- ding dimension of the reconstructed phase-space of a dynamic discrete time series.Thus it will be possible to automatically analyze the dynamic discrete time series whose data varies continually.We discuss the prob- lem that the calculation of the largest Lyapunov exponent,using the Wolf algorithm,may be accidentally interrupted by the trace trajectory that reaches the end of the phase-space.The presented method in this paper is confirmed feasible by using the time series proof-prediction based on the largest Lyapunov exponent. Finally,a further discussion shows that the presented method for the real-time analysis of the short-time stable Shanghai Composite Index is positive.
This paper presents a method for calculating and automatically determining the optimal embed- ding dimension of the reconstructed phase-space of a dynamic discrete time series.Thus it will be possible to automatically analyze the dynamic discrete time series whose data varies continually.We discuss the prob- lem that the calculation of the largest Lyapunov exponent,using the Wolf algorithm,may be accidentally interrupted by the trace trajectory that reaches the end of the phase-space.The presented method in this paper is confirmed feasible by using the time series proof-prediction based on the largest Lyapunov exponent. Finally,a further discussion shows that the presented method for the real-time analysis of the short-time stable Shanghai Composite Index is positive.
引文
[1]TAKENS F.Determining strange attractors in tur- bulence[J].Lecture Notes in Math,1981,898:361- 381.
[2]GRASSBERGER P,PROCACCIA I.Characterization of strange attractors[J].Phys Rev Lett,1983,50: 346.
[3]靳伍银，徐健学，洪灵，等．一种求解嵌入在混沌吸引子中不稳定周期轨道的新方法[J]．兰州大学学报：自然科学版，2004，40(4)：24-27．
[4]马红光，韩崇昭，孔祥玉，等．基于Lyapunov指数的非线性模拟电路故障诊断方法[J]．电路与系统学报，2004，9(4)：71-75．
[5]丁方允，丁睿．粘弹性柱的若干动力学性质——数值实验[J]．兰州大学学报：自然科学版，1997，33(1)：22-27．
[6]杨绍清，章新华，赵长安．一种最大李雅普诺夫指数估计的稳健算法[J]．物理学报，2000，49(4)：636-640．
[7]王卫宁，汪秉宏，史晓平．股票价格波动的混沌行为分析[J]．数量经济技术经济研究，2004，21(4)：141-147．
[8]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，2002：67-68，106-108．
[9]WOLF A,SWIFT J B,SWINNEY L,et al.Deter- mining Lyapunov exponents from a time series[J]. Physics D,1985,16:285-317.
[10]MICHAEL T R,JAMES J C.A practical method for calculating largest Lyapunov exponents from small data sets[J].Physics D,1993,65:117-134.
[11]马军海．复杂非线性系统的重构技术[M]．天津：大津大学出版社，2005：64-69，134-140．
[12]李强，徐桂明，黄耘．地下水位的混沌和多重分形特征演化及其中短期预报意义[J]．地震，1999, 19(3)：274-280．
[2]GRASSBERGER P,PROCACCIA I.Characterization of strange attractors[J].Phys Rev Lett,1983,50: 346.
[3]靳伍银，徐健学，洪灵，等．一种求解嵌入在混沌吸引子中不稳定周期轨道的新方法[J]．兰州大学学报：自然科学版，2004，40(4)：24-27．
[4]马红光，韩崇昭，孔祥玉，等．基于Lyapunov指数的非线性模拟电路故障诊断方法[J]．电路与系统学报，2004，9(4)：71-75．
[5]丁方允，丁睿．粘弹性柱的若干动力学性质——数值实验[J]．兰州大学学报：自然科学版，1997，33(1)：22-27．
[6]杨绍清，章新华，赵长安．一种最大李雅普诺夫指数估计的稳健算法[J]．物理学报，2000，49(4)：636-640．
[7]王卫宁，汪秉宏，史晓平．股票价格波动的混沌行为分析[J]．数量经济技术经济研究，2004，21(4)：141-147．
[8]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，2002：67-68，106-108．
[9]WOLF A,SWIFT J B,SWINNEY L,et al.Deter- mining Lyapunov exponents from a time series[J]. Physics D,1985,16:285-317.
[10]MICHAEL T R,JAMES J C.A practical method for calculating largest Lyapunov exponents from small data sets[J].Physics D,1993,65:117-134.
[11]马军海．复杂非线性系统的重构技术[M]．天津：大津大学出版社，2005：64-69，134-140．
[12]李强，徐桂明，黄耘．地下水位的混沌和多重分形特征演化及其中短期预报意义[J]．地震，1999, 19(3)：274-280．
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心