基于混沌理论的电力推进船舶电力负荷预测
摘要
基于混沌理论对电力推进船舶电力负荷进行预测研究的目的是以研究混沌动力学为基础,结合电力推进船舶电力负荷的特点,从负荷的混沌特性分析、数据预处理到预测,为电力推进船舶初步建立一套负荷预测体系,进而提高船舶电力系统的安全稳定性和航行的经济性。
本文首先采用功率谱分析方法从定性的角度对电力推进船舶电力负荷进行混沌特性分析,同时对负荷的相关维数及最大Lyapunov指数进行定量计算,验证船舶电力负荷具有混沌特性,从而对电力推进船舶电力负荷序列有了新的认识,并可应用混沌理论对电力推进船舶电力负荷进行预测。
其次为提高电力推进船舶电力负荷数据质量,基于小波方法对负荷数据进行奇异性分析,并运用分形维数对负荷数据和由于冲击震荡、采样干扰等因素产生的噪声进行自适应分离,为预测提供良好的数据基础。
然后以自相似轨道搜寻为基础,建立混沌局域预测与关联度相结合的电力推船舶电力负荷单变量预测模型;同时提出采用相似日负荷作为样本应用于电力推进船舶电力负荷混沌局域预测模型。实例计算结果表明以上两种预测方法对电力推进船舶电力负荷单变量预测的准确性。
最后针对电力推进船舶电力负荷影响因素多的特点,以单变量时间序列的相空间重构为基础,进行多变量时间序列相空间重构,建立多变量混沌预测模型。并针对负荷的规律性变化,运用小波分解将其分解为固有负荷分量和载重量影响负荷分量,对固有负荷分量采用混沌局域关联模型进行重点预测;对载重量影响负荷分量采用线性回归模型进行预测,实现预测精度的进一步提高。
On the base of analying chaotic characterics, the aim is to establish a ship power load forecasting system combine with ship power load character, which did assure secure and economic operation of electric propulsion ship. The forecasting system covers three aspects: the chaos character analysis, the historial data beforehand processing and the forecasting of ship power load.
Chaos character of electric propulsion ship power load is analyzed through the quality and ration angle. Power spectrum approach to quality angle is presented, correlation dimension and the most Lyapunov exponent are computed to ration angle, which did validate chaos character of electric propulsion ship power load. So it gives us a new acquaintance to the complexity of ship power load time series, and the ship power load could be forecasted through chaos theory.
The reliability and reality of load historial data is the foundation of electric propulsion ship power load forecasting. But, the impact load in running ship power system, and the disturb data in collecting load data may cause fault data in load historial data. Focusing on beforehand processing historial load data, the singularity of ship power load is analyzed using wavelet method, and the ship power load data can be of self-adaptability to be apart from its noises based on fractal dimension, then fault data can be eliminated, which did provide better data basis for the electric propulsion ship power load forecasting.
The univariate time series of electric propulsion ship power load forecasting model is set up. The self-similar trajectory is looked for, and the correlation degree is acted on chaos local forecasting model. Moreover, the similar days load is input into chaos local forecasting model. The practical examples express that the above methods have more precision to univariate forecasting of ship power load.
To counter the influence of different factors on ship power load, the multivariate chaos forecasting model of electric propulsion ship power load is set up. Based on the phase space reconstruction of univariate time series, phase space of multivariate time series is reconstructed, and then chaos forecasting model of multivariate time series can be established to forecast the electric propulsion ship power load. Moreover, to cunter the varying rule of the ship power load itself, wavelet transform is applied to decompose electric propulsion ship power load. Ship power load is divided into normal load and dead weight influence load. A chaos local correlation forecasting model is built for normal load, and a polynomial regressive model is built for dead weight influence load. The practical examples express that the methods are effective and feasible.
本文首先采用功率谱分析方法从定性的角度对电力推进船舶电力负荷进行混沌特性分析,同时对负荷的相关维数及最大Lyapunov指数进行定量计算,验证船舶电力负荷具有混沌特性,从而对电力推进船舶电力负荷序列有了新的认识,并可应用混沌理论对电力推进船舶电力负荷进行预测。
其次为提高电力推进船舶电力负荷数据质量,基于小波方法对负荷数据进行奇异性分析,并运用分形维数对负荷数据和由于冲击震荡、采样干扰等因素产生的噪声进行自适应分离,为预测提供良好的数据基础。
然后以自相似轨道搜寻为基础,建立混沌局域预测与关联度相结合的电力推船舶电力负荷单变量预测模型;同时提出采用相似日负荷作为样本应用于电力推进船舶电力负荷混沌局域预测模型。实例计算结果表明以上两种预测方法对电力推进船舶电力负荷单变量预测的准确性。
最后针对电力推进船舶电力负荷影响因素多的特点,以单变量时间序列的相空间重构为基础,进行多变量时间序列相空间重构,建立多变量混沌预测模型。并针对负荷的规律性变化,运用小波分解将其分解为固有负荷分量和载重量影响负荷分量,对固有负荷分量采用混沌局域关联模型进行重点预测;对载重量影响负荷分量采用线性回归模型进行预测,实现预测精度的进一步提高。
On the base of analying chaotic characterics, the aim is to establish a ship power load forecasting system combine with ship power load character, which did assure secure and economic operation of electric propulsion ship. The forecasting system covers three aspects: the chaos character analysis, the historial data beforehand processing and the forecasting of ship power load.
Chaos character of electric propulsion ship power load is analyzed through the quality and ration angle. Power spectrum approach to quality angle is presented, correlation dimension and the most Lyapunov exponent are computed to ration angle, which did validate chaos character of electric propulsion ship power load. So it gives us a new acquaintance to the complexity of ship power load time series, and the ship power load could be forecasted through chaos theory.
The reliability and reality of load historial data is the foundation of electric propulsion ship power load forecasting. But, the impact load in running ship power system, and the disturb data in collecting load data may cause fault data in load historial data. Focusing on beforehand processing historial load data, the singularity of ship power load is analyzed using wavelet method, and the ship power load data can be of self-adaptability to be apart from its noises based on fractal dimension, then fault data can be eliminated, which did provide better data basis for the electric propulsion ship power load forecasting.
The univariate time series of electric propulsion ship power load forecasting model is set up. The self-similar trajectory is looked for, and the correlation degree is acted on chaos local forecasting model. Moreover, the similar days load is input into chaos local forecasting model. The practical examples express that the above methods have more precision to univariate forecasting of ship power load.
To counter the influence of different factors on ship power load, the multivariate chaos forecasting model of electric propulsion ship power load is set up. Based on the phase space reconstruction of univariate time series, phase space of multivariate time series is reconstructed, and then chaos forecasting model of multivariate time series can be established to forecast the electric propulsion ship power load. Moreover, to cunter the varying rule of the ship power load itself, wavelet transform is applied to decompose electric propulsion ship power load. Ship power load is divided into normal load and dead weight influence load. A chaos local correlation forecasting model is built for normal load, and a polynomial regressive model is built for dead weight influence load. The practical examples express that the methods are effective and feasible.
引文
[1]樊印海.电力推进自动控制.大连:大连海事大学出版社,1998.
[2]金德昌,姜孟文,云峻峰.船舶电力推进原理.北京:国防工业出版社,1993.
[3]徐纠佐,刘赞,顾海宏.船舶综合全电力推进系统.柴油机,2003,(2):17-20.
[4]李钷,李敏,刘涤尘.基于改进回归法的电力负荷预测.电网技术,2006,30(1):99-104.
[5]焦文玲,金佳宾,廉乐明.时间序列分析在城市天然气短期负荷预测中的应用.哈尔滨建筑大学学报,2001,34(4):79-82.
[6]李金颖,牛东晓.非线性季节性电力负荷灰色组合预测研究.电网技术,2003,27(5):26-28.
[7]严华,吴捷,马志强等.模糊集理论在电力系统短期负荷预测中的应用.电力系统自动化,2000,24(11):67-72.
[8]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究.中国电机工程学报,2002,22(7):85-89.
[9]潘峰,程浩忠,杨镜非等.基于支持向量机的电力系统短期负荷预测.电网技术,2004,28(21):39-42.
[10]顾洁.应用小波分析进行短期负荷预测.电力系统及其自动化学报,2003,15(2):40-44.
[11][美]洛伦兹E.N.著,刘式达,刘式适,严中伟译.混沌的本质.北京:气象出版社,1997.
[12]格莱克,张淑誉译.混沌:开创新科学.上海:上海译文出版社,1990.
[13]郝柏林.从抛物线谈起--混沌动力学引论.上海:上海科技教育出版社,1993.
[14]李辉.混沌数字通信.北京:清华大学出版社,2006.
[15]吴祥兴,陈忠.混沌学导论.上海:上海科学技术文献出版社,1996.
[16]Li T.Y,Yorke J.A.Period Three Implies Chaos.Amer Math Monthly,1975,82:985-992.
[17]C.Nicolis,G,Nicolis.Is There A Climatic Attractor,Nature,1984,391:529-532.
[18]K.Fraedrich.Estimating The Dimension of Weather and Climate Attractor.J.Atmo.Sci,1986,43(5):419-432.
[19]J.Kurths,H.Herzel.An Attractor in A Solar Time Series.Physica D,1987,25:165-172.
[20]A.Hense.On the Possible Existence of A Strange Attractor for The Southern Oscillation.Bectr,Phys.Atmosph,1987,60(1):34-47.
[21]I.Rodriguez-Iturbe et al.Chaos in Rainfall.Water Resources Res,1989,25(7):1667-1675.
[22]Grassberger P,Procaccia.I.Measuring The Strangeness of Strange Attractors.Phyasica D,1983,(9):189-208.
[23]李后强,汪富强.分形理论及其在分子科学中的应用.北京:科学出版社,1993.
[24]Breaford P,Wilcox et al.Searching for Chaotic Dynamics in Snowmelt Runoff.Water Resources Research,1991,27(6):1005-1010.
[25]Ajjarapu V,Lee B.Bifurcation.Theory and Its Application to Nonlinear Dynamical Phenomena in An Electrical Power System.IEEE Pwrs,1992,7(1):424-431.
[26]仲蔚,俞金寿.混沌与分形在化工过程控制中的应用.控制与决策,2001,16(1):1-6.
[27]赵汉青,文必洋.短时间序列的混沌检测方法及其在高频地波雷达海杂波混沌特性研究中的应用.信息处理,2003,19(1):92-94.
[28]L Chiang H.D,LIU C.C.et al.Chaos in A Simple Power System,IEEE PWRS,1993,8(4):1407-1417.
[29]A.W.Jayarwardena,Feizhou Lai.Analysis and Prediction of Chaos In Rainfall and Stream Flow Time Series.Journal of Hydrology,1994,(753):23-52.
[30]E.N.Lorenz.Deterministic Nonperiodic Flow.J.Atmos,Sci.,20,130-141.[
31]G.F.Feigenbaum.Universal Behavior in Nonlinear Systems.Los Alamos Sci.,1,4-27.
[32]O.Kaplan,L.Glass.Understanding nonlinear dynamics.New York:Springer-Verlag,1995.
[33]G.L.Baker,J.P.Gollub.Chaotic dynamics:an introduction.Cambridge:Cambridge University Press,1990.
[34]Su S-F,Lin C-B,Hsu Y-T.A High Precision Global Prediction Approach Based on Local Prediction Approaches.IEEE Transactions on Systems,Man and Cybernetics,Part C,2002,32(4):416-425.
[35]简相超,郑君里.一种正交多项式混沌全局建模方法.电子学报,2002,30(1):76-78.
[36]Kantz H,Schreiber T.Nonlinear time series analysis.Cambridge:Cambriging University Press,1997.
[37]李恒超,张家树.混沌时间序列局域零阶预测法性能比较.西南交通大学学报,2004,39(3):328-331.
[38]任晓林,胡光锐,徐雄.混沌时间序列局域线性预测方法.上海交通大学学报,1999,33(1):19-21.
[39]向小东,郭耀煌.基于混沌吸引子的时间序列预测方法及其应用.西南交通大学学报,2001,36(5):472-475.
[40]Jayawardena A W,Li W K,Xu P.Neighborhood Selection for Local Modeling and Prediction of Hydrological Time Series.Jounal of Hydrology,2002,258:40-57.
[41]Jianming Y.On Measuring and Correcting The Effects of Data Mining And Model Selection.J.Am stat.Assoc.,1998,93(441):120-131.
[42]Kasim K,Levent S,Orhan S.Nonlinear Time Series Prediction of 03 Concentration in Istanbul.Atmospheric Environment,2000,34(8):1267-1271.
[43]Fang F,Wang H Y.Local Polynomial Prediction Method of Multivrariate Chaotic Time Series and Its Application.Journal of Southeast University(English Edition),2005,21(2),229-232.
[44]丁涛,周惠成.混沌时间序列局域预测方法.系统工程与电子技术,2004,26(3):338-340.
[45]吕金虎,张锁春.加权一阶局域法在电力系统短期负荷预测中的应用.控制理论与应用,2002,19(5):767-770.
[46]Sugihara G,May R M.Nonlinear Forecasting as A Way of Distinguishing Chaos from Measurement Error in Time Series.Nature,1990,344:734-741.
[47]J.D.Farmer.Predicting chaotic time series.Physica Review Letters,1987,59:845-848.
[48]M.Casdagli.Nonlinear Prediction of Chaotic Time Series.Physica D,1989,35:335-356.
[49]梁志珊,王丽敏,付大鹏等.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报,1998,18(5):368-371.
[50]梁志珊,王丽敏,付大鹏.应用混沌理论的电力系统短期负荷预测.控制与决策,1998.13(1):87-90.
[51]Zhang J,Man K F,Ke J Y.Time series prediction using Lyapunov exponents in embedding phase space.IEEE International Conference on Systems,Man and Cybernetics,1998,1750-1755.
[52]张家树,肖先赐.混沌时间序列的Volterra自适应预测.物理学报,2000,49(3):403-408.
[53]张家树,肖先赐.用于混沌时间序列自适应预测的一种少参数二阶Volterra滤波器.物理学报,2001,50(7):1248-1254.
[54]甘建超,肖先赐.基于相空间领域的混沌时间序列自适应预测滤波器(1)线性自适应滤波.物理学报,2003,52(5):1096-1101.
[55]甘建超,肖先赐.基于相空间领域的混沌时间序列自适应预测滤波器(2)线性自适应滤波.物理学报,2003,52(5):1102-1107.
[56]郭双冰,肖先赐.混沌时间序列Volterra自适应滤波器定阶.电子与信息学报,2002,24(4):461-466.
[57]张家树,肖先赐.用于低维混沌时间序列预测的一种非线性自适应预测滤波器.通信学报,2001,22(10):93-98.
[58]Sifeng Zhu,Xihuai Wang.A svm approach to ship power load forecasting based on rbf kernel.IEEE Proceedings of the 5~(th) World Congress on Intelligent Control and Automation,2004:1824-1828.
[59]王锡淮,朱思锋.基于支持向量机的船舶电力负荷预测.中国电机工程学报,2004,24(10):36-40.
[60]高普云.非线性动力学--分叉、混沌与孤立子.长沙:国防科技大学出版社,2005.
[61]黄润生.混沌及其应用.武汉:武汉大学出版社,2000.
[62]刘式达,刘式适.孤波和湍流.上海:上海科技教育出版社.1995.
[63]陈予恕,唐云.非线性动力学中的现代分析方法.北京:科学出版社,2000.
[64]刘式达,刘式适.分形和分维引论.北京:气象出版社,1993.
[65]Abarbanel H D Iet al.Rev.Mod.Phys,1993,65,33.
[66]Tsonis A A.Chaos:from theory to application.New York:Plenum Press,1992.
[67]Kantz H,Schreiber T.Nonlinear time series analysis.Cambrige:Cambrige University Press,1997.
[68]Takens F.Dynamical systems and turbulence.In:Rand D,Young L S,eds.Lecture notes in mathematics.Berlin:Springer,1981:366-381.
[69]Packard N H,Crutchfield J P,Farmer J D,et al.Geometry from a time series.Phys Rev Lett,1980,45(9):712-716.
[70]Mane R.On the Dimension of The Compact Invariant Sets of Certain Nonlinear Maps.In:Rand D,Young L S editors.Dynamic systems and turbulence,warwick,1980,Lecture Notes in Mathematics,Springer-Yerlag,1981,898:230.
[71]Kennel L M B,Brown R,Abarbanel H D I.Determining embedding dimension for phase space reconstruction using a geometrical construction.Phys Rev.A.1992,45:3402-3411.
[72]Broomhead D S,King G P,Extracting Qualitative Dynamics from Experimental Data.Physica D.1986,20:217-236.
[73]Kugiumtzis D.State Space Reconstruction Parameters in The Analysis of Chaotic Time Series-The Role of the Time Window Length.Physica D,1996,95:13.
[74]Fraser A M,Swinney H L.Independent coordinates for strange attractor from mutual information.Phys.Rev.A,1986,33:1134.
[75]Lai Y C,Lerner D.Effective Scaling Regime for Computing The Correlation Dimension from Chaotic Time Series,Physica D,1998,115:1-18.
[76]蒋培,胡晓棠.一种新的选择相空间重构参数的方法.机械科学与技术,2001,20(3):364-366.
[77]林嘉宇,黄芝平,王跃科等.语音信号相空间重构中时间延迟选择的改进的平均位移法.国防科技大学学报,1999,21(3):59-62.
[78]林嘉宇,王跃科,黄芝萍等.语音信号相空间重构中时间延迟的选择--复自相关法.信号处理,1999.15(3)220-225.
[79]Abarbanel H D I,Masuda N,Rabinovich M I,et al.Distribution of Mutual Information.Physics Letters A,2001,281(5-6):368-373.
[80]Luis A A.A Nonlinear Correlation Functions for Selecting The Delay Time in Dynamical Reconstructions.Physics Letters A,1995,127:48-60.
[81]Rosenstein M T,Collins J J,Deluca C J.Reconstruction Expansion As A Geometry-Based Framework for Choosing Proper Delay Time.Physica D,1994,73:82-98.
[82]Albano A M,Passamane A,Farrell M E.Using Higher-Order Correlation to Define An Embedding Window.Physica D,1991,54:85-97.
[83]Buzug T,Pfister G.Optimal delay time and embedding dimension for delay time coordinates by analysis of the global static and local dynamic behavior of strange attractors.Physical Review A,1992,45(10):7072-7084.
[84]Kantz H,Schreiber T.Nonlinear time series and their singularities:The characterization of strange sets.Phys.Rev.A,1986,33:1134.
[85]吕金虎,陆君安,陈世华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002.
[86]Henry D.I.Abrbanel.The analysis of observed chaotic data in physical system.Reviews of Modern Physics,1993,65(4):1331-1392.
[87]M.T.Rosenstein,J.J.Collins,C.J.De luca.A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets.Physica D,1993,65:117-134.
[88]Fraser A M,Information and Entroy in Strange Attractors.IEEE Trans.Inf.Theory,1989,35:245-262.
[89]Henry D.I.Abarbanel,Naoki Masuda,M.I.Rabinovich,et al.Distribution of mutual information.Physics Letters A,2001,(281):368-373.
[90]刘延柱,陈立群.非线性动力学.上海:上海交通大学出版社,2000.
[91]P.Grassberger,I.Prcaccia.Measuring The Strangeness of Strange Attractors.Physica D,1983(9):189-208.
[92]P.Grassberger,I.Prcaccia.Characterization of strange attractors.Physical Review Letters,1983,50(5):346-349.
[93]P.Grassberger,I.Prcaccia.Dimension and Entropy of Strange Attractors from A Fluctuating Dynamics Approach.Physica,1984,13D:34.
[94]Grassberger,Procaccia I.Estimation of the kolmogorov entropy from a chaotic signal.Phys.Rev.A,1983,28:2591-2893.
[95]Galka A,Maa B T,Pfister G.Estimating The Dimension of High-Dimensional Attractors:A Comparison between Two Algorithms.Physica D,1998,121(3-4):237-251.
[96]Abarbanel H D I,Brown R,Sidorowich J J,et al.The analysis of observed data in physical systems.Rev.Mod.Phy,1993,65(4):1331-1392.
[97]Taiye B,Sangoyomi et al.Nonlinear Dynamics of The Grear Salt Lake:Dimension Estimation.Water Resources Research,1996,32(1):149-159.
[98]Martinerie J M,Albano A M,Mees A I,et al.Mutual information,strange attractors,and the optimal estimation of dimension.Pbys Rev A,1992(45):7058-7064.
[99]Kugiumtzis D.State Space Reconstruction Parameters in The Analysis of Chaotic Time Series-The Role of The Time Window Length.Physica D,1996(65):117-134.
[100]D.S.Broomhead,Gregory P,King.Extracting Qualitative Dynamics from Experimental Data.Physica D,1986,(20).
[101]H.S.Kim,R.Eykholt,J.D.Salas.Nonlinear Dynamics,Delay Times and Embedding Windows,Physica D,1999,127:48-60.
[102]Peter D W.The Use of Fast Fourier Transform for The Estimation of Power Spectra:A Method Based on Time Averaging Over Short,Modified Periodograms.IEEE Transactions on Audio and Electroacoustics,1967,15(2):70-73.
[103]王兴元.复杂非线性系统中的混沌.北京:电子工业出版社,2003.
[104]黄润生,黄浩.混沌及其应用.湖北:武汉大学出版社,2005.
[105]马红光,韩崇昭.电路中的混沌与故障诊断.北京:国防工业出版社,2006.
[106]Michael T.Rosentein,James J.Collins,Carlo J.De Luca.A Practical Method for Calculating Largest Lyapunov Exponent from Small Data Sets.Physica D,1993,65:117-134.
[107]赵贵兵,石炎福.从混沌时间序列同时计算关联维和Kolmogorov熵.计算物理,1999,16(3):309-315.
[108]Lai Yc,Lerner D.Effective Scaling Regime for Computing The Correlation Dimension form Chaotic Time Series.Physica D,1998,115:21-18.
[109]Esteller R,Vachtsevanos G,Echauz J,Litt B.A Comparison of Waveform Fractal Dimension Algorithms.IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Application,2001,48(2):177-183.
[110]E N Lorenz.The essence of chaos.Washion:The University of Washington Press,1993.
[111]Li Yin-shan,Zhang Nian-mei,Yang Gui - tong.1/3 Sub-Harmonic Solution of Elliptical Sandwich Plates.Applied Mathematics and Mechanics,2003,24(10):1147-1157.
[112]Li Yin-shan,Yang Gui - tong,Zhang Shan-yuan et al.Experiments on Super-Harmonic Bifurcation and Chaotic Motion of A Circular Plate Oscillator.Journal of Experimental Mechanics,2001,16(4):347-358.
[113]Li Yin-shan,Chen Yu-shu,Xue Yu-sheng.Stability Margin of Unbalance Elastic Rotor in Short Bearings under A Nonlinear Oil-Film Force Model.Journal of Mechanical Engineering,2002,38(9):27-32.
[114]Wolf A,Swift JB,Swinney HL,etc.Determining Lyapunov Exponents from A Time Series.Physica-D.1985,16:285-317.
[115]J.Theiler.Estimating Fractal Dimension.J.Opt.Soc.Am.A,1990,7(6):1055-1073.
[116]Ott E.Chaos in dynamic systems.Cambridge:Cambridge University Press,1993.
[117]Vicsek T.Fractal growth phenomena.Singapore:Springer-Verlag,1989.
[118]Pesin Y B.On Rigorous Mathematical Definitions of Correlation Dimension and Generalized Spectrum for Dimension.Journal of Statistical Physics,1993,71(3/4):529-547.
[119]Schepers H E,Van Beck J n G M,Bassingthwaighte J B.Four Method to Estimation The Fractal Dimension from Self-Affine Signals.IEEE Engineering in Medicine and Biology,1992,11(3):57-64.
[120]方锦清.驾驭混沌与发展高新技术.北京:原子能出版社,2002.
[121]刘春生,张晓春.实用小波分析.徐州:中国矿业大学出版社.2002.
[122]张晓春,李富全.小波变换及其在岩石超声检测中的应用.黑龙江矿业学院学报,2000(1):46-49.
[123]S.Malat.Characterization of Signal from Multiscale Edges.IEEE Trans.PAMI,1992,14(7):710-732.
[124]沙震,阮火军.分形与拟和.杭州:浙江大学出版社,2005.
[125]谢和平等编译.分形几何:数学基础与应用.重庆:重庆大学出版社,1991.
[126]胡航.语音信号处理.哈尔滨:哈尔滨工业大学出版社,2000.
[127][英]肯尼思·法尔科内.分形几何--数学基础及其应用.沈阳:东北大学出版社,2001.
[128]Paul S,Addison.Fractals and Chaos:an Illustrated Course.Bristol,UK,1997.
[129]张济忠.分形[M].北京:清华大学出版社,1995.
[130]文志英.分形几何的数学基础.上海:上海科技教育出版社,2000.
[131]谢和平,薛秀谦.分形应用中的数学基础与方法.北京:科学出版社,1997.
[132]游荣义,陈忠等.基于小波变换的混沌信号相空间中小波变换方法研究.物理学报,2004,53(9):2882-2888.
[133]Friedhelm Schwenker,Hans A.Kestler,Guther Palm.Three learning Phase for Radial Basis Function Net-Works,Neural Networks,2001,14:439-458.
[134]侯祥林,张春晖,徐心和.多层神经网络共轭梯度优化算法及其在模式识别中的应用.东北大学学报(自然科学版),2002,23(1):20一23.
[135]Enis Cetin A.Signal Recovery from Wavelet Transforms Maxima.IEEE Trans M I,1982,10(1):81-101.
[136]Donoho D L.De-noising by Soft-Thresholding.IEEE Trans.on Information Theory,1995,41(3):613-627.
[137]Medina C A,Alcaim A,Apolinario,et al.Wavelet De-noising of Speech Using Neural Networks for Threshold Selection.IEE Electronic Letters,2003,39(25):1869-1871.
[138]Dafis C J,Nwankpa C O,Petropulu A.Analysis of power system transient disturbances using an EPRIT-based method.2000 IEEE Power Engineer Society Summer Meeting.Seattle,WA,USA,2000.437-442.
[139]任晓林,胡光锐,徐雄.混沌时间序列局域线性预测方法.上海交通大学学报,1999,33(1):19-21.
[140]丁涛,周惠成.混沌时间序列局域预测方法.系统工程与电子技术,2004,26(3):338-340.
[141]Kugiumtzis D,Lingjaerde C,Christophersen N.Regularized Local Linear Prediction of Chaotic Time Series.Physica D,1998,112(3-4):334-360.
[142]Sugi hara G,May R M.Nonlinear Forecasting as A Way of Distinguishing Chaos from Measurement Error in Time Series.Nature,1990,344:734-741.
[143]李恒超,张家树.混沌时间序列局域零阶预测法性能比较.西南交通大学学报,2004,39(3):328-331.
[144]Kantz H,Schreiber T.Nonlinear time series analysis.Cambridge:Cambridge University Press,1997.
[145]王永忠,曾昭磐.混沌时间序列的局域线性回归预测方法.厦门大学学报(自然科学版),1999,38(4):636-340.
[146]Zhang J,Man K F,Ke J Y.Time Series Prediction Using Lyapunov Exponents in Embedding Phase Space.IEEE International Conference on Systems,Man and Cybernetics,1998,1750-1755.
[147]梁志珊,王丽敏,付大鹏,张化光.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报,1998,1750-1755.
[148]吕金虎,占勇,陆君安.电力系统短期负荷预测的非线性混沌改进模型.中国电机工程学报,2000,20(12):80-83.
[149]Sivakumar B.A Phase-Space Reconstruction Approach to Prediction of Suspended Sediment Concentration in Rivers.Journal of Hydrology,2002,258:149-162.
[150]Sivakumar B,Jayawardena A W,Fernando T M K G.River Flow Forecasting:Using of Phase-Space Reconstruction and Artificial Neural Networks Approaches.Journal of hydrology,2002,265:225-245.
[151]向小东,郭耀煌.基于混沌吸引子的时间序列预测方法及其应用.西南交通大学学报,2001,36(5):472-475.
[152]张家树.混沌信号的非线性自适应预测技术及其应用研究:(博士学位论文).成都:电子科技大学,2001.
[153]Schreiber T.Interdisciplinary Application of Nonlinear Time Series Methods.Physics Reports,1999,(8):1-64.
[154]Fridman S V,Yeh K C,Franke S J.Linear and Nonlinear Prediction Techniques for Short-Term Forecasting of HF Fading Signals.Radio Science,1997,22(3):989-998.
[155]Bakirtzis A G,Theocharis J B,Papadakis S E,et al.Short Term Load Forecasting Using Fuzzy Neural Networks.IEEE Trans on Power System,1995,10(3):1518-1524.
[156]hiang Z S.The Short Term Load Forecasting of Power System Based on Adaptive Neural Network.Journal of Northeast China Institute of Electric Power Engineer,1994,14(1):27-35.
[157]Chen nong,A.Canizares Claudio,Ajit Singh.Ann-based Short-Term Load Forecasting in Electricity Markets.IEEE Power Engineer Society Winter Meeting.Ohio USA,2001.
[158]马军海,贾湖,盛昭瀚.非线性混沌经济时序的预测方法及其应用研究.管理科学学报,2001,4(4):49-53.
[159]Berndt Pilgram,Kevin Judd,Alistair Mees.Modelling The Dynamics Of Nonlinear Time Series Using Canonical Variate Analysis.Physica D,2002,170(2):103- 117.
[160]Sanjay Vasant Dudul.Prediction of A Lorenz Chaotic Attractor Using Two-Layer Perceptron Neural Network.Applied Soft Computing,2005,5(4):333 -355.
[161]王海燕.多变量非线性时间序列的复杂性分析研究:(博士学位论文).南京:东南大学,2001.
[162]Abarbanel H D I,Brown R,Sidorowich J Jet al.The analysis of observed data in physical systems.Reviews of Modern Physics,1993,65(4):1331-1392.
[163]Yang Hongming,Duan Xianzhong.Chaotic characteristics of electricity price and its forecasting model.IEEE CCECE 2003,Montreal:659-662.
[164]A Porporato,L Ridolfi.Multivariate Nonlinear Prediction of River Flows.Journal of Hydrology,2001,248:109-122.
[165]王海燕,盛照瀚,张进.多变量时间序列复杂系统的相空间重构.东南大学学报(自然科学版),2003,33(1):115-118.
[166]Wang Haiyan,Zhu Mei.A Prediction Comparison between Univariate and Multivariate Chaotic Time Series.Journal of Southeast University(English Edition),2003,19(4):414-417.
[167]Christian H.Reick,Bernd Page.Time series prediction by multivariate next neighbor methods with application to zooplankton forecasts.Mathematics and Computers in Simulation,2000,52:289- 310.
[168]盛昭翰,姚洪兴,王海燕等.混沌动力系统的重构预测与控制.北京:中国经济出版社,2003.
[169]Tomoya Suzuki,Tohru Ikeguchi,Masuo Suzuki.Multivariable Nonlinear Analysis of Foreign Exchange Rates.Physica A,2003,323:591-660.
[170]Anthony Stathopoulos,Matthew G.Karlaftis.A Multivariate State Space Approach for Urban Traffic Flow Modeling and Prediction.Transportation research part C,2003,11(2):121-135.
[171]Prichard D,Theiler J.Generating surrogate data for time series with several simultaneously measured variables.Physical Review Letters,1994,73(7):951-954.
[172]Rombowts S A R B,Keunen R W M,Stom C J.Investigation of Nonlinear Structure in Multichannel EEG.Physics Letters A,1995,202:352-358.
[173]Dvorak I.Takens Versus Multichannel Reconstruction in EEG Correlation Exponent Estimates.Physics Letters A,1990,151(5):225-233.
[174]Cao L Y,Mees A,Judd K.Dynamics from Multivariate Time Series.Physica D,1998,121:75-88.
[175]Boccaletti S,Valladares D L.Reconstructing embedding spaces of coupled dynamical systems from multivariate data.Physical Review E,2002,65:1-4.
[176]杨绍清,贾传荧.两种实用的相空间重构方法.物理学报,2002,51(11):2452-2456.
[177]卢山.基于非线性动力学的金融时间序列预测技术研究:(博士学位论文).南京:东南大学,2006.
[178]吴耿 锋,周佩玲,储阅春等.基于相空间重构的预测方法及其在天气预报中的应用.自然杂志,1999,21(2):107-110.
[179]Jianming Y.On Measuring and Correcting The Effects Of Data Mining and Model Selection.J.Am Stat.Assoc.,1998,93(441):120-131.
[180]Kasim K,Levent S,Orhan S.Nonlinear Time Series Prediction of 03 Concentration in Istanbul.Atmospheric environment,2000,34(8):1267-1271.
[2]金德昌,姜孟文,云峻峰.船舶电力推进原理.北京:国防工业出版社,1993.
[3]徐纠佐,刘赞,顾海宏.船舶综合全电力推进系统.柴油机,2003,(2):17-20.
[4]李钷,李敏,刘涤尘.基于改进回归法的电力负荷预测.电网技术,2006,30(1):99-104.
[5]焦文玲,金佳宾,廉乐明.时间序列分析在城市天然气短期负荷预测中的应用.哈尔滨建筑大学学报,2001,34(4):79-82.
[6]李金颖,牛东晓.非线性季节性电力负荷灰色组合预测研究.电网技术,2003,27(5):26-28.
[7]严华,吴捷,马志强等.模糊集理论在电力系统短期负荷预测中的应用.电力系统自动化,2000,24(11):67-72.
[8]谢开贵,李春燕,周家启.基于神经网络的负荷组合预测模型研究.中国电机工程学报,2002,22(7):85-89.
[9]潘峰,程浩忠,杨镜非等.基于支持向量机的电力系统短期负荷预测.电网技术,2004,28(21):39-42.
[10]顾洁.应用小波分析进行短期负荷预测.电力系统及其自动化学报,2003,15(2):40-44.
[11][美]洛伦兹E.N.著,刘式达,刘式适,严中伟译.混沌的本质.北京:气象出版社,1997.
[12]格莱克,张淑誉译.混沌:开创新科学.上海:上海译文出版社,1990.
[13]郝柏林.从抛物线谈起--混沌动力学引论.上海:上海科技教育出版社,1993.
[14]李辉.混沌数字通信.北京:清华大学出版社,2006.
[15]吴祥兴,陈忠.混沌学导论.上海:上海科学技术文献出版社,1996.
[16]Li T.Y,Yorke J.A.Period Three Implies Chaos.Amer Math Monthly,1975,82:985-992.
[17]C.Nicolis,G,Nicolis.Is There A Climatic Attractor,Nature,1984,391:529-532.
[18]K.Fraedrich.Estimating The Dimension of Weather and Climate Attractor.J.Atmo.Sci,1986,43(5):419-432.
[19]J.Kurths,H.Herzel.An Attractor in A Solar Time Series.Physica D,1987,25:165-172.
[20]A.Hense.On the Possible Existence of A Strange Attractor for The Southern Oscillation.Bectr,Phys.Atmosph,1987,60(1):34-47.
[21]I.Rodriguez-Iturbe et al.Chaos in Rainfall.Water Resources Res,1989,25(7):1667-1675.
[22]Grassberger P,Procaccia.I.Measuring The Strangeness of Strange Attractors.Phyasica D,1983,(9):189-208.
[23]李后强,汪富强.分形理论及其在分子科学中的应用.北京:科学出版社,1993.
[24]Breaford P,Wilcox et al.Searching for Chaotic Dynamics in Snowmelt Runoff.Water Resources Research,1991,27(6):1005-1010.
[25]Ajjarapu V,Lee B.Bifurcation.Theory and Its Application to Nonlinear Dynamical Phenomena in An Electrical Power System.IEEE Pwrs,1992,7(1):424-431.
[26]仲蔚,俞金寿.混沌与分形在化工过程控制中的应用.控制与决策,2001,16(1):1-6.
[27]赵汉青,文必洋.短时间序列的混沌检测方法及其在高频地波雷达海杂波混沌特性研究中的应用.信息处理,2003,19(1):92-94.
[28]L Chiang H.D,LIU C.C.et al.Chaos in A Simple Power System,IEEE PWRS,1993,8(4):1407-1417.
[29]A.W.Jayarwardena,Feizhou Lai.Analysis and Prediction of Chaos In Rainfall and Stream Flow Time Series.Journal of Hydrology,1994,(753):23-52.
[30]E.N.Lorenz.Deterministic Nonperiodic Flow.J.Atmos,Sci.,20,130-141.[
31]G.F.Feigenbaum.Universal Behavior in Nonlinear Systems.Los Alamos Sci.,1,4-27.
[32]O.Kaplan,L.Glass.Understanding nonlinear dynamics.New York:Springer-Verlag,1995.
[33]G.L.Baker,J.P.Gollub.Chaotic dynamics:an introduction.Cambridge:Cambridge University Press,1990.
[34]Su S-F,Lin C-B,Hsu Y-T.A High Precision Global Prediction Approach Based on Local Prediction Approaches.IEEE Transactions on Systems,Man and Cybernetics,Part C,2002,32(4):416-425.
[35]简相超,郑君里.一种正交多项式混沌全局建模方法.电子学报,2002,30(1):76-78.
[36]Kantz H,Schreiber T.Nonlinear time series analysis.Cambridge:Cambriging University Press,1997.
[37]李恒超,张家树.混沌时间序列局域零阶预测法性能比较.西南交通大学学报,2004,39(3):328-331.
[38]任晓林,胡光锐,徐雄.混沌时间序列局域线性预测方法.上海交通大学学报,1999,33(1):19-21.
[39]向小东,郭耀煌.基于混沌吸引子的时间序列预测方法及其应用.西南交通大学学报,2001,36(5):472-475.
[40]Jayawardena A W,Li W K,Xu P.Neighborhood Selection for Local Modeling and Prediction of Hydrological Time Series.Jounal of Hydrology,2002,258:40-57.
[41]Jianming Y.On Measuring and Correcting The Effects of Data Mining And Model Selection.J.Am stat.Assoc.,1998,93(441):120-131.
[42]Kasim K,Levent S,Orhan S.Nonlinear Time Series Prediction of 03 Concentration in Istanbul.Atmospheric Environment,2000,34(8):1267-1271.
[43]Fang F,Wang H Y.Local Polynomial Prediction Method of Multivrariate Chaotic Time Series and Its Application.Journal of Southeast University(English Edition),2005,21(2),229-232.
[44]丁涛,周惠成.混沌时间序列局域预测方法.系统工程与电子技术,2004,26(3):338-340.
[45]吕金虎,张锁春.加权一阶局域法在电力系统短期负荷预测中的应用.控制理论与应用,2002,19(5):767-770.
[46]Sugihara G,May R M.Nonlinear Forecasting as A Way of Distinguishing Chaos from Measurement Error in Time Series.Nature,1990,344:734-741.
[47]J.D.Farmer.Predicting chaotic time series.Physica Review Letters,1987,59:845-848.
[48]M.Casdagli.Nonlinear Prediction of Chaotic Time Series.Physica D,1989,35:335-356.
[49]梁志珊,王丽敏,付大鹏等.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报,1998,18(5):368-371.
[50]梁志珊,王丽敏,付大鹏.应用混沌理论的电力系统短期负荷预测.控制与决策,1998.13(1):87-90.
[51]Zhang J,Man K F,Ke J Y.Time series prediction using Lyapunov exponents in embedding phase space.IEEE International Conference on Systems,Man and Cybernetics,1998,1750-1755.
[52]张家树,肖先赐.混沌时间序列的Volterra自适应预测.物理学报,2000,49(3):403-408.
[53]张家树,肖先赐.用于混沌时间序列自适应预测的一种少参数二阶Volterra滤波器.物理学报,2001,50(7):1248-1254.
[54]甘建超,肖先赐.基于相空间领域的混沌时间序列自适应预测滤波器(1)线性自适应滤波.物理学报,2003,52(5):1096-1101.
[55]甘建超,肖先赐.基于相空间领域的混沌时间序列自适应预测滤波器(2)线性自适应滤波.物理学报,2003,52(5):1102-1107.
[56]郭双冰,肖先赐.混沌时间序列Volterra自适应滤波器定阶.电子与信息学报,2002,24(4):461-466.
[57]张家树,肖先赐.用于低维混沌时间序列预测的一种非线性自适应预测滤波器.通信学报,2001,22(10):93-98.
[58]Sifeng Zhu,Xihuai Wang.A svm approach to ship power load forecasting based on rbf kernel.IEEE Proceedings of the 5~(th) World Congress on Intelligent Control and Automation,2004:1824-1828.
[59]王锡淮,朱思锋.基于支持向量机的船舶电力负荷预测.中国电机工程学报,2004,24(10):36-40.
[60]高普云.非线性动力学--分叉、混沌与孤立子.长沙:国防科技大学出版社,2005.
[61]黄润生.混沌及其应用.武汉:武汉大学出版社,2000.
[62]刘式达,刘式适.孤波和湍流.上海:上海科技教育出版社.1995.
[63]陈予恕,唐云.非线性动力学中的现代分析方法.北京:科学出版社,2000.
[64]刘式达,刘式适.分形和分维引论.北京:气象出版社,1993.
[65]Abarbanel H D Iet al.Rev.Mod.Phys,1993,65,33.
[66]Tsonis A A.Chaos:from theory to application.New York:Plenum Press,1992.
[67]Kantz H,Schreiber T.Nonlinear time series analysis.Cambrige:Cambrige University Press,1997.
[68]Takens F.Dynamical systems and turbulence.In:Rand D,Young L S,eds.Lecture notes in mathematics.Berlin:Springer,1981:366-381.
[69]Packard N H,Crutchfield J P,Farmer J D,et al.Geometry from a time series.Phys Rev Lett,1980,45(9):712-716.
[70]Mane R.On the Dimension of The Compact Invariant Sets of Certain Nonlinear Maps.In:Rand D,Young L S editors.Dynamic systems and turbulence,warwick,1980,Lecture Notes in Mathematics,Springer-Yerlag,1981,898:230.
[71]Kennel L M B,Brown R,Abarbanel H D I.Determining embedding dimension for phase space reconstruction using a geometrical construction.Phys Rev.A.1992,45:3402-3411.
[72]Broomhead D S,King G P,Extracting Qualitative Dynamics from Experimental Data.Physica D.1986,20:217-236.
[73]Kugiumtzis D.State Space Reconstruction Parameters in The Analysis of Chaotic Time Series-The Role of the Time Window Length.Physica D,1996,95:13.
[74]Fraser A M,Swinney H L.Independent coordinates for strange attractor from mutual information.Phys.Rev.A,1986,33:1134.
[75]Lai Y C,Lerner D.Effective Scaling Regime for Computing The Correlation Dimension from Chaotic Time Series,Physica D,1998,115:1-18.
[76]蒋培,胡晓棠.一种新的选择相空间重构参数的方法.机械科学与技术,2001,20(3):364-366.
[77]林嘉宇,黄芝平,王跃科等.语音信号相空间重构中时间延迟选择的改进的平均位移法.国防科技大学学报,1999,21(3):59-62.
[78]林嘉宇,王跃科,黄芝萍等.语音信号相空间重构中时间延迟的选择--复自相关法.信号处理,1999.15(3)220-225.
[79]Abarbanel H D I,Masuda N,Rabinovich M I,et al.Distribution of Mutual Information.Physics Letters A,2001,281(5-6):368-373.
[80]Luis A A.A Nonlinear Correlation Functions for Selecting The Delay Time in Dynamical Reconstructions.Physics Letters A,1995,127:48-60.
[81]Rosenstein M T,Collins J J,Deluca C J.Reconstruction Expansion As A Geometry-Based Framework for Choosing Proper Delay Time.Physica D,1994,73:82-98.
[82]Albano A M,Passamane A,Farrell M E.Using Higher-Order Correlation to Define An Embedding Window.Physica D,1991,54:85-97.
[83]Buzug T,Pfister G.Optimal delay time and embedding dimension for delay time coordinates by analysis of the global static and local dynamic behavior of strange attractors.Physical Review A,1992,45(10):7072-7084.
[84]Kantz H,Schreiber T.Nonlinear time series and their singularities:The characterization of strange sets.Phys.Rev.A,1986,33:1134.
[85]吕金虎,陆君安,陈世华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002.
[86]Henry D.I.Abrbanel.The analysis of observed chaotic data in physical system.Reviews of Modern Physics,1993,65(4):1331-1392.
[87]M.T.Rosenstein,J.J.Collins,C.J.De luca.A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets.Physica D,1993,65:117-134.
[88]Fraser A M,Information and Entroy in Strange Attractors.IEEE Trans.Inf.Theory,1989,35:245-262.
[89]Henry D.I.Abarbanel,Naoki Masuda,M.I.Rabinovich,et al.Distribution of mutual information.Physics Letters A,2001,(281):368-373.
[90]刘延柱,陈立群.非线性动力学.上海:上海交通大学出版社,2000.
[91]P.Grassberger,I.Prcaccia.Measuring The Strangeness of Strange Attractors.Physica D,1983(9):189-208.
[92]P.Grassberger,I.Prcaccia.Characterization of strange attractors.Physical Review Letters,1983,50(5):346-349.
[93]P.Grassberger,I.Prcaccia.Dimension and Entropy of Strange Attractors from A Fluctuating Dynamics Approach.Physica,1984,13D:34.
[94]Grassberger,Procaccia I.Estimation of the kolmogorov entropy from a chaotic signal.Phys.Rev.A,1983,28:2591-2893.
[95]Galka A,Maa B T,Pfister G.Estimating The Dimension of High-Dimensional Attractors:A Comparison between Two Algorithms.Physica D,1998,121(3-4):237-251.
[96]Abarbanel H D I,Brown R,Sidorowich J J,et al.The analysis of observed data in physical systems.Rev.Mod.Phy,1993,65(4):1331-1392.
[97]Taiye B,Sangoyomi et al.Nonlinear Dynamics of The Grear Salt Lake:Dimension Estimation.Water Resources Research,1996,32(1):149-159.
[98]Martinerie J M,Albano A M,Mees A I,et al.Mutual information,strange attractors,and the optimal estimation of dimension.Pbys Rev A,1992(45):7058-7064.
[99]Kugiumtzis D.State Space Reconstruction Parameters in The Analysis of Chaotic Time Series-The Role of The Time Window Length.Physica D,1996(65):117-134.
[100]D.S.Broomhead,Gregory P,King.Extracting Qualitative Dynamics from Experimental Data.Physica D,1986,(20).
[101]H.S.Kim,R.Eykholt,J.D.Salas.Nonlinear Dynamics,Delay Times and Embedding Windows,Physica D,1999,127:48-60.
[102]Peter D W.The Use of Fast Fourier Transform for The Estimation of Power Spectra:A Method Based on Time Averaging Over Short,Modified Periodograms.IEEE Transactions on Audio and Electroacoustics,1967,15(2):70-73.
[103]王兴元.复杂非线性系统中的混沌.北京:电子工业出版社,2003.
[104]黄润生,黄浩.混沌及其应用.湖北:武汉大学出版社,2005.
[105]马红光,韩崇昭.电路中的混沌与故障诊断.北京:国防工业出版社,2006.
[106]Michael T.Rosentein,James J.Collins,Carlo J.De Luca.A Practical Method for Calculating Largest Lyapunov Exponent from Small Data Sets.Physica D,1993,65:117-134.
[107]赵贵兵,石炎福.从混沌时间序列同时计算关联维和Kolmogorov熵.计算物理,1999,16(3):309-315.
[108]Lai Yc,Lerner D.Effective Scaling Regime for Computing The Correlation Dimension form Chaotic Time Series.Physica D,1998,115:21-18.
[109]Esteller R,Vachtsevanos G,Echauz J,Litt B.A Comparison of Waveform Fractal Dimension Algorithms.IEEE Transactions on Circuits and Systems Ⅰ:Fundamental Theory and Application,2001,48(2):177-183.
[110]E N Lorenz.The essence of chaos.Washion:The University of Washington Press,1993.
[111]Li Yin-shan,Zhang Nian-mei,Yang Gui - tong.1/3 Sub-Harmonic Solution of Elliptical Sandwich Plates.Applied Mathematics and Mechanics,2003,24(10):1147-1157.
[112]Li Yin-shan,Yang Gui - tong,Zhang Shan-yuan et al.Experiments on Super-Harmonic Bifurcation and Chaotic Motion of A Circular Plate Oscillator.Journal of Experimental Mechanics,2001,16(4):347-358.
[113]Li Yin-shan,Chen Yu-shu,Xue Yu-sheng.Stability Margin of Unbalance Elastic Rotor in Short Bearings under A Nonlinear Oil-Film Force Model.Journal of Mechanical Engineering,2002,38(9):27-32.
[114]Wolf A,Swift JB,Swinney HL,etc.Determining Lyapunov Exponents from A Time Series.Physica-D.1985,16:285-317.
[115]J.Theiler.Estimating Fractal Dimension.J.Opt.Soc.Am.A,1990,7(6):1055-1073.
[116]Ott E.Chaos in dynamic systems.Cambridge:Cambridge University Press,1993.
[117]Vicsek T.Fractal growth phenomena.Singapore:Springer-Verlag,1989.
[118]Pesin Y B.On Rigorous Mathematical Definitions of Correlation Dimension and Generalized Spectrum for Dimension.Journal of Statistical Physics,1993,71(3/4):529-547.
[119]Schepers H E,Van Beck J n G M,Bassingthwaighte J B.Four Method to Estimation The Fractal Dimension from Self-Affine Signals.IEEE Engineering in Medicine and Biology,1992,11(3):57-64.
[120]方锦清.驾驭混沌与发展高新技术.北京:原子能出版社,2002.
[121]刘春生,张晓春.实用小波分析.徐州:中国矿业大学出版社.2002.
[122]张晓春,李富全.小波变换及其在岩石超声检测中的应用.黑龙江矿业学院学报,2000(1):46-49.
[123]S.Malat.Characterization of Signal from Multiscale Edges.IEEE Trans.PAMI,1992,14(7):710-732.
[124]沙震,阮火军.分形与拟和.杭州:浙江大学出版社,2005.
[125]谢和平等编译.分形几何:数学基础与应用.重庆:重庆大学出版社,1991.
[126]胡航.语音信号处理.哈尔滨:哈尔滨工业大学出版社,2000.
[127][英]肯尼思·法尔科内.分形几何--数学基础及其应用.沈阳:东北大学出版社,2001.
[128]Paul S,Addison.Fractals and Chaos:an Illustrated Course.Bristol,UK,1997.
[129]张济忠.分形[M].北京:清华大学出版社,1995.
[130]文志英.分形几何的数学基础.上海:上海科技教育出版社,2000.
[131]谢和平,薛秀谦.分形应用中的数学基础与方法.北京:科学出版社,1997.
[132]游荣义,陈忠等.基于小波变换的混沌信号相空间中小波变换方法研究.物理学报,2004,53(9):2882-2888.
[133]Friedhelm Schwenker,Hans A.Kestler,Guther Palm.Three learning Phase for Radial Basis Function Net-Works,Neural Networks,2001,14:439-458.
[134]侯祥林,张春晖,徐心和.多层神经网络共轭梯度优化算法及其在模式识别中的应用.东北大学学报(自然科学版),2002,23(1):20一23.
[135]Enis Cetin A.Signal Recovery from Wavelet Transforms Maxima.IEEE Trans M I,1982,10(1):81-101.
[136]Donoho D L.De-noising by Soft-Thresholding.IEEE Trans.on Information Theory,1995,41(3):613-627.
[137]Medina C A,Alcaim A,Apolinario,et al.Wavelet De-noising of Speech Using Neural Networks for Threshold Selection.IEE Electronic Letters,2003,39(25):1869-1871.
[138]Dafis C J,Nwankpa C O,Petropulu A.Analysis of power system transient disturbances using an EPRIT-based method.2000 IEEE Power Engineer Society Summer Meeting.Seattle,WA,USA,2000.437-442.
[139]任晓林,胡光锐,徐雄.混沌时间序列局域线性预测方法.上海交通大学学报,1999,33(1):19-21.
[140]丁涛,周惠成.混沌时间序列局域预测方法.系统工程与电子技术,2004,26(3):338-340.
[141]Kugiumtzis D,Lingjaerde C,Christophersen N.Regularized Local Linear Prediction of Chaotic Time Series.Physica D,1998,112(3-4):334-360.
[142]Sugi hara G,May R M.Nonlinear Forecasting as A Way of Distinguishing Chaos from Measurement Error in Time Series.Nature,1990,344:734-741.
[143]李恒超,张家树.混沌时间序列局域零阶预测法性能比较.西南交通大学学报,2004,39(3):328-331.
[144]Kantz H,Schreiber T.Nonlinear time series analysis.Cambridge:Cambridge University Press,1997.
[145]王永忠,曾昭磐.混沌时间序列的局域线性回归预测方法.厦门大学学报(自然科学版),1999,38(4):636-340.
[146]Zhang J,Man K F,Ke J Y.Time Series Prediction Using Lyapunov Exponents in Embedding Phase Space.IEEE International Conference on Systems,Man and Cybernetics,1998,1750-1755.
[147]梁志珊,王丽敏,付大鹏,张化光.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报,1998,1750-1755.
[148]吕金虎,占勇,陆君安.电力系统短期负荷预测的非线性混沌改进模型.中国电机工程学报,2000,20(12):80-83.
[149]Sivakumar B.A Phase-Space Reconstruction Approach to Prediction of Suspended Sediment Concentration in Rivers.Journal of Hydrology,2002,258:149-162.
[150]Sivakumar B,Jayawardena A W,Fernando T M K G.River Flow Forecasting:Using of Phase-Space Reconstruction and Artificial Neural Networks Approaches.Journal of hydrology,2002,265:225-245.
[151]向小东,郭耀煌.基于混沌吸引子的时间序列预测方法及其应用.西南交通大学学报,2001,36(5):472-475.
[152]张家树.混沌信号的非线性自适应预测技术及其应用研究:(博士学位论文).成都:电子科技大学,2001.
[153]Schreiber T.Interdisciplinary Application of Nonlinear Time Series Methods.Physics Reports,1999,(8):1-64.
[154]Fridman S V,Yeh K C,Franke S J.Linear and Nonlinear Prediction Techniques for Short-Term Forecasting of HF Fading Signals.Radio Science,1997,22(3):989-998.
[155]Bakirtzis A G,Theocharis J B,Papadakis S E,et al.Short Term Load Forecasting Using Fuzzy Neural Networks.IEEE Trans on Power System,1995,10(3):1518-1524.
[156]hiang Z S.The Short Term Load Forecasting of Power System Based on Adaptive Neural Network.Journal of Northeast China Institute of Electric Power Engineer,1994,14(1):27-35.
[157]Chen nong,A.Canizares Claudio,Ajit Singh.Ann-based Short-Term Load Forecasting in Electricity Markets.IEEE Power Engineer Society Winter Meeting.Ohio USA,2001.
[158]马军海,贾湖,盛昭瀚.非线性混沌经济时序的预测方法及其应用研究.管理科学学报,2001,4(4):49-53.
[159]Berndt Pilgram,Kevin Judd,Alistair Mees.Modelling The Dynamics Of Nonlinear Time Series Using Canonical Variate Analysis.Physica D,2002,170(2):103- 117.
[160]Sanjay Vasant Dudul.Prediction of A Lorenz Chaotic Attractor Using Two-Layer Perceptron Neural Network.Applied Soft Computing,2005,5(4):333 -355.
[161]王海燕.多变量非线性时间序列的复杂性分析研究:(博士学位论文).南京:东南大学,2001.
[162]Abarbanel H D I,Brown R,Sidorowich J Jet al.The analysis of observed data in physical systems.Reviews of Modern Physics,1993,65(4):1331-1392.
[163]Yang Hongming,Duan Xianzhong.Chaotic characteristics of electricity price and its forecasting model.IEEE CCECE 2003,Montreal:659-662.
[164]A Porporato,L Ridolfi.Multivariate Nonlinear Prediction of River Flows.Journal of Hydrology,2001,248:109-122.
[165]王海燕,盛照瀚,张进.多变量时间序列复杂系统的相空间重构.东南大学学报(自然科学版),2003,33(1):115-118.
[166]Wang Haiyan,Zhu Mei.A Prediction Comparison between Univariate and Multivariate Chaotic Time Series.Journal of Southeast University(English Edition),2003,19(4):414-417.
[167]Christian H.Reick,Bernd Page.Time series prediction by multivariate next neighbor methods with application to zooplankton forecasts.Mathematics and Computers in Simulation,2000,52:289- 310.
[168]盛昭翰,姚洪兴,王海燕等.混沌动力系统的重构预测与控制.北京:中国经济出版社,2003.
[169]Tomoya Suzuki,Tohru Ikeguchi,Masuo Suzuki.Multivariable Nonlinear Analysis of Foreign Exchange Rates.Physica A,2003,323:591-660.
[170]Anthony Stathopoulos,Matthew G.Karlaftis.A Multivariate State Space Approach for Urban Traffic Flow Modeling and Prediction.Transportation research part C,2003,11(2):121-135.
[171]Prichard D,Theiler J.Generating surrogate data for time series with several simultaneously measured variables.Physical Review Letters,1994,73(7):951-954.
[172]Rombowts S A R B,Keunen R W M,Stom C J.Investigation of Nonlinear Structure in Multichannel EEG.Physics Letters A,1995,202:352-358.
[173]Dvorak I.Takens Versus Multichannel Reconstruction in EEG Correlation Exponent Estimates.Physics Letters A,1990,151(5):225-233.
[174]Cao L Y,Mees A,Judd K.Dynamics from Multivariate Time Series.Physica D,1998,121:75-88.
[175]Boccaletti S,Valladares D L.Reconstructing embedding spaces of coupled dynamical systems from multivariate data.Physical Review E,2002,65:1-4.
[176]杨绍清,贾传荧.两种实用的相空间重构方法.物理学报,2002,51(11):2452-2456.
[177]卢山.基于非线性动力学的金融时间序列预测技术研究:(博士学位论文).南京:东南大学,2006.
[178]吴耿 锋,周佩玲,储阅春等.基于相空间重构的预测方法及其在天气预报中的应用.自然杂志,1999,21(2):107-110.
[179]Jianming Y.On Measuring and Correcting The Effects Of Data Mining and Model Selection.J.Am Stat.Assoc.,1998,93(441):120-131.
[180]Kasim K,Levent S,Orhan S.Nonlinear Time Series Prediction of 03 Concentration in Istanbul.Atmospheric environment,2000,34(8):1267-1271.