地球科学进展 ›› 1999, Vol. 14 ›› Issue (6): 559 -565. doi: 10.11867/j.issn.1001-8166.1999.06.0559

综述与评述 上一篇    下一篇

非线性时间序列分析的最新进展及其在地球科学中的应用前景
洪时中   
  1. 成都市地震局,四川 成都 610015
  • 收稿日期:1999-03-19 修回日期:1999-06-07 出版日期:1999-12-01
  • 通讯作者: 洪时中,男,1943年8月出生于安徽安庆,高级工程师,主要从事非线性科学在地震科学中应用的研究。
  • 基金资助:

    国家自然科学基金项目“地震预测的非线性时间序列方法研究”(编号:49474209)资助。

NONLINEAR TIME SERIES ANALYSIS AND ITS APPLICATIONS TO GEOSCIENCE

HONG Shizhong   

  1. Seismological Bureau of Chengdu,Chengdu 610015,China
  • Received:1999-03-19 Revised:1999-06-07 Online:1999-12-01 Published:1999-12-01

评述了非线性时间序列分析的最新进展,包括相空间重构、序列性质的鉴别、建模与预报,同时介绍了非线性时间序列分析在地球科学中的应用概况。

Recent developments in nonlinear time series analysis are reviewed,including phase space reconstruction,estimating embedding dimension and time delay,distinguishing chaos from noise,modeling and prediction of nonlinear time series.Applications of nonlinear time series analysis for geoscience are also
commented.

中图分类号: 

〔1〕Paciard N H,Grutchfield J P,Farmer J D,et al.Geometry from a time series〔J〕.Phys Rev Lett,1980,45(9):712~716.
〔2〕Takens F.Detecting strange attractors in turbulence〔J〕.Lecture Notes in Mathematics,1981,898:336.
〔3〕Grassberger P Procaccia. Measuring the strangeness of strange attractors〔J〕.Physica D,1983,9:189~208.
〔4〕Wolf A,Swift J B,Swinney H L,et al. Determing Lyapunov exponents from a time series〔J〕.Physica D,1985,16:285~317.
〔5〕Farmer J D, Sidorowich J J.Predicting chaotic time series〔J〕.Phys Rev Lett,1987,59(8):845~848.
〔6〕Casdagli M. Nonlinear prediction of chaotic time series〔J〕.Physica D,1989,35:335~356.
〔7〕Sauer T,Yorke J A, Casdagli M.Embedology〔J〕.Journal of Statistical Physics,1991,65(3~4):579~616.
〔8〕Weigend A S. Paradigm change in prediction〔A〕.In:Tong H,ed.Chaos and Forecasting〔C〕. Singapore: World Scientific,1995.145~160.
〔9〕Tong H. Nonlinear Time Series: A Dynamical System Approach〔M〕.Oxford:Oxford University Press,1990.
〔10〕Tong H.Some comments on a bridge between nonlinear dynamicits and statisticans〔J〕.Physica D,1992,58:299~303.
〔11〕Grassbeger P,Schreiber T, Schaffrath C.Nonlinear time sequence analysis〔J〕. International Journal of Bifurcation and Chaos,1991,1(3):521~547.
〔12〕Tong H.Dimension Estimation and Models (Nonlinear Time Series and Chaos Vol1)〔C〕. Singapore: World Scientific,1993.
〔13〕Tong H.Chaos and Forecasting (Nonlinear Time Series and Chaos Vol2)〔C〕.Singapore:World Scientific ,1995.
〔14〕Abarbanel H D I,Brown R,Sidorowich J J,et al.The Analysis of observed chaotic data in physical systems〔J〕.Rev Mod Phys,1993,65(4):1 331~1 392.
〔15〕Casdagli M,Tardins D D,Eubank S,et al.Nonlinear modeling of chaotic time series:theory and applications〔C〕.LA-UR-91-1637,1991.
〔16〕Hao Bailin.Elementary Symbolic Dynamics,and Chaos in Dissipative Systems〔M〕.Singapore:World Scientific,1989.
〔17〕Schroer C G,Sauer T,Ott E,et al.Predicting chaos most of the time from embeddings with self-intersections〔J〕.Phys Rev Lett,1998,80(7):1 410~1 413.
〔18〕Broomhead D S, King G P. Extracting qualitative dynamics from experimental data〔J〕.Physica D,1986,20:217~336.
〔19〕Kennel M B,Brown R, Abarbanel H D I.Determing embedding dimension for phase-space reconstruction using a geometrical construction〔J〕.Phys Rev A,1992,45(6):3 403~3411.
〔20〕Cao Liangyue.Practical method for determining the minimum embedding dimension of a scalar time series〔J〕.Physica D,1997,110:43~50.
〔21〕Sugihara G, May R M.Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series〔J〕.Nature,1990,344:734~741.
〔22〕Kaplan D T, Glass L.Direct test for determinism in a time series〔J〕.Phys Rev Lett,1992.68(4):427~430.
〔23〕Rosenstein M T,Collins J J, De Luca C J.Reconstruction expansion as a geometry-based framework for choosing proper delay times〔J〕.Physica D,1994,73:82~98.
〔24〕Fraser A M, Swinney H L. Independent coordinates for strange attractors from mutual information〔J〕.Phys Rev A,1986,33(2):1 134~1 140.
〔25〕Wayland R,Bromley D,Pickett D,et al.Recognizing determinism in a time series〔J〕.Phys Rev Lett,1993,70(5):580~582.
〔26〕Martinerie J M,Albano A M,Mees A I,et al.Mutual information,strange attractors,and the optimal estimation of dimension〔J〕.Phys Rev A,1992,45(10):7 058~7 064.
〔27〕Kugiumtzis D.State space reconstruction parameters in the analysis of chaotic time series—the role of the time window length〔J〕.Physica D,1996,95:13~28.
〔28〕Gibson J F,Farmer J D,Casdagli M,et al.An analytic approcah to practical state space reconstuction〔J〕,Physica D,1992,57:1~30.
〔29〕洪时中,赵永龙,袁坚.非线性时间序列分析中几个具体问题的初步研究——以太阳黑子序列为例〔A〕.中国地球物理学会年刊(1997)〔C〕.上海:同济大学出版社,1997.
〔30〕Lao Yingcheng, Lerner D.Effective scaling regime for computing the correlation dimension from chaotic time series〔J〕.Physica D,1998,115:1~18.
〔31〕郝柏林.分岔、混沌、奇怪吸引子、湍流及其它——关于确定论系统中的内在随机性〔J〕.物理学进展,1983,3(3):329~416.
〔32〕Theiler J,Eubank S,Longtin A,et al.Testing for nonlinearity in time series:the method of surrogate data〔J〕.Physica D,1992,58:77~94.
〔33〕Osborne A R, Rrovenzale A.Finite corrlation dimension for stochastic systems with power-1aw spectra〔J〕.Physica D,1989,35:357~381.
〔34〕Tanaka T,Aihara K, Taki M.Analysis of positive Lyapunov exponents from random time series〔J〕.Physica D,1998,111:42~50.
〔35〕袁坚,肖先赐.非线性时间序列的高阶奇异谱分析〔J〕.物理学报,1998,47(6):897~905.
〔36〕Schittenkopf C, Deco G. Testing nonlinear Markovian hypotheses in dynamical systems〔J〕.Physica D,1997,104:61~74.
〔37〕Weigend A S, Gershenfeld A.Time Series Prediction:Forecasting the Future and Understanding the Past〔A〕.Proceeding Santa Fe Institute Studies in the Sciences of Complexity (Vol XV)〔C〕.Reading:Addison-Welsley,1994.

 

[1] 原世伟, 李新, 杜二虎. 多主体建模在水资源管理中的应用:进展与展望[J]. 地球科学进展, 2021, 36(9): 899-910.
[2] 刘雷钧, 何建刚, 涂海波, 郎骏健, 柳林涛. 载体垂向扰动对轴对称型金属弹簧海洋重力仪的影响[J]. 地球科学进展, 2021, 36(5): 520-527.
[3] 陈仁升, 沈永平, 毛炜峄, 张世强, 吕海深, 刘永强, 刘章文, 房世峰, 张伟, 陈春艳, 韩春坛, 刘俊峰, 赵求东, 郝晓华, 李如琦, 秦艳, 黄维东, 赵成先, 王书峰. 西北干旱区融雪洪水灾害预报预警技术:进展与展望[J]. 地球科学进展, 2021, 36(3): 233-244.
[4] 马雷鸣. 天气预报中的人工智能技术进展[J]. 地球科学进展, 2020, 35(6): 551-560.
[5] 梅双丽,李勇,马杰. 热带季节内振荡在延伸期预报中的应用进展[J]. 地球科学进展, 2020, 35(12): 1222-1231.
[6] 郭彦龙,赵泽芳,乔慧捷,王然,卫海燕,王璐坤,顾蔚,李新. 物种分布模型面临的挑战与发展趋势[J]. 地球科学进展, 2020, 35(12): 1292-1305.
[7] 金荣花,马杰,任宏昌,尹姗,蔡芗宁,黄威. 我国 1030天延伸期预报技术进展与发展对策[J]. 地球科学进展, 2019, 34(8): 814-825.
[8] 高丽,陈静,郑嘉雯,陈权亮. 极端天气的数值模式集合预报研究进展[J]. 地球科学进展, 2019, 34(7): 706-716.
[9] 朱月佳,邢蕊,朱明佳,王东勇,邱学兴. 联合概率方法在安徽强对流潜势预报中的应用和检验[J]. 地球科学进展, 2019, 34(7): 731-746.
[10] 黄亦鹏,李万彪,赵玉春,白兰强. 基于雷达与卫星的对流触发观测研究和临近预报技术进展[J]. 地球科学进展, 2019, 34(12): 1273-1287.
[11] 郭恺. 基于局部层析的 TTI各向异性参数初始建模方法研究[J]. 地球科学进展, 2019, 34(10): 1060-1068.
[12] 念达, 邓琪敏, 付遵涛. 相对湿度及其变化的年循环研究进展[J]. 地球科学进展, 2018, 33(7): 762-774.
[13] 安俊岭, 陈勇, 屈玉, 陈琦, 庄炳亮, 张平文, 吴其重, 徐勤武, 曹乐, 姜海梅, 陈学舜, 郑捷. 全耦合空气质量预报模式系统[J]. 地球科学进展, 2018, 33(5): 445-454.
[14] 杨秋明. 长江下游夏季低频温度和高温天气的延伸期预报研究[J]. 地球科学进展, 2018, 33(4): 385-395.
[15] 李江峰, 蔡晓军, 王文, 李倩文, 雷彦森. 偏最小二乘回归在水汽和地面气温多模式集成预报中的应用研究[J]. 地球科学进展, 2018, 33(4): 404-415.
阅读次数
全文


摘要