小波及奇异值分解在混沌特征计算中的综合去噪研究
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摘要
观测时间序列的非线性动力学混沌特征研究在电力、气象、地震、边坡等工程领域的应用日益广泛,但观测序列的噪声对研究结果具有重要的影响,人们通常采用傅立叶或者小波变换方法去噪。但对于混沌序列来说,这种去噪方法具有一定的局限性,会造成观测数据一定程度的破坏,对混沌分析结果会产生一定的影响。本文探讨运用小波变换结合奇异值分解(SVD)方法来解决观测时间序列在混沌特征分析时的去噪问题,该方法针对混沌分析过程中的源观测数据特点,首先用小波方法对一维观测序列去噪,并对去噪后的序列计算混沌特征分析中的重要参数-相空间重构参数m,τ,根据m,τ对源一维观测序列进行重构,得到重构的相空间矩阵A,然后对矩阵A采用SVD方法进行处理,通过这两种方法相结合的方式来达到更好的去噪目的。结果表明其去噪效果是明显的,数据经过小波变换和SVD联合处理后其观测序列的混沌特征更明显和易于提取,提高了观测时间序列混沌分析的可靠性。
Chaotic feature research of non-linearity dynamics to observation series has comprehensively applications in electric power,weather,earthquake and etc.Noises of observation series have an important effect on the research results.Fourier or wavelet transform is usually adopted for eliminating noises of observation series,but this method will make data of observation series distortion,therefore it has definite localization and has an effect on results of chaotic analysis.A synthetical method which uses wavelet transform and strange value decomposition to eliminate noises in course of chaotic analysis of observation series is discussed.Firstly,the method uses wavelet transform to eliminate the noises of one-dimension observation series and calculates important reconstruction parameter m,τof phase space of this series,then reconstructs phase space of original one-dimension observation series by m,τand get reconstruction matrix A of phase space,and then transform matrix A using method of strange value decomposition.Finally achieve the aim of eliminating noises.The results show effect of eliminating noises is obvious.The chaotic feature of observation series is more obvious and easier to be abstracted using method of wavelet and strange value decomposition to eliminate noises of observation series.The reliability of chaotic analysis of observation series is improved.
Chaotic feature research of non-linearity dynamics to observation series has comprehensively applications in electric power,weather,earthquake and etc.Noises of observation series have an important effect on the research results.Fourier or wavelet transform is usually adopted for eliminating noises of observation series,but this method will make data of observation series distortion,therefore it has definite localization and has an effect on results of chaotic analysis.A synthetical method which uses wavelet transform and strange value decomposition to eliminate noises in course of chaotic analysis of observation series is discussed.Firstly,the method uses wavelet transform to eliminate the noises of one-dimension observation series and calculates important reconstruction parameter m,τof phase space of this series,then reconstructs phase space of original one-dimension observation series by m,τand get reconstruction matrix A of phase space,and then transform matrix A using method of strange value decomposition.Finally achieve the aim of eliminating noises.The results show effect of eliminating noises is obvious.The chaotic feature of observation series is more obvious and easier to be abstracted using method of wavelet and strange value decomposition to eliminate noises of observation series.The reliability of chaotic analysis of observation series is improved.
引文
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[3]吕金虎,陆君安,陈士华.混沌时间序列及其分析[M].武汉:武汉大学出版社,2002.
[4]胡昌华,张军波.基于MATLAB的系统分析与设计-小波分析[M].西安:西安电子科技大学出版社,2001.
[5]CasdagliM artin.Non linear pred iction of chaotic tim e series[J].Phys D,1989,35(11):335-356.
[6]M artin C.Non linear pred iction of chaotic tim e series[J].Phys.D,1989,35(7):335-356.
[7]马军海,盛昭瀚.低维混沌时序的预测方法及其应用研究[J].东南大学学报,1999,29(5):65-69.
[8]尹泽明,丁春利.精通MATLAB 6[M].北京:清华大学出版社,2002.
[9]徐仲,张凯院,陆全,等.矩阵论简明教程[M].北京:科学出版社,2001.
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