非线性系统退化数据的小波熵序列及其应用
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摘要
用小波分解下各尺度上的能量信息熵计算了Lorenz系统退化数据的小波熵序列,计算结果表明退化前后两小波熵序列所蕴含的动力学特征基本一致;进一步讨论了窗口宽度对小波熵序列的影响,发现同一序号点的小波熵值退化增量随窗口宽度增大保持稳定,表明小波熵序列具有较强的抗退化能力,能够从退化数据中挖掘出非线性系统的动力学特征,为运用退化数据揭示复杂非线性系统的动力学特征提供了一种有效的方法;最后将该方法应用于南极中山站地磁场数据,获得了地磁场变化强度的演变特征,地磁场的磁暴区、平静区、稳定变化区在小波熵序列的波形中具有非常明显的特征.
The Lorenz system's time series and its degradated time series were decomposed by wavelet transform and turned into various components of different scales,then all components' energy and the signal's information entropy were calculated under a series of sliding windows,obtained the dynamic wavelet entropy-wavelet entropy sequence,the calculation results show that the two wavelet entropy sequences contain the very consistent dynamics characteristic;Further more we discussed the influence of window width on the wavelet entropy sequence,and found that the degradated incremental of the wavelet entropy value was stable along with the increasing window width,show that the wavelet entropy sequence has strong resistance to degradation,which could dig out the dynamic characteristics of the complex system from the degradated data,it was provided a effective method for using the degradated data to reveal the dynamic characteristics of the complex system;Finally, the method was applied to the geomagnetic data of the South Pole ZhongShan station,acquired the evolution characteristics of the geomagnetic variational intensity,in which the evolution characteristics of storms area,calm area,stable change area had the very obvious characteristics in the wavelet entropy sequence.
The Lorenz system's time series and its degradated time series were decomposed by wavelet transform and turned into various components of different scales,then all components' energy and the signal's information entropy were calculated under a series of sliding windows,obtained the dynamic wavelet entropy-wavelet entropy sequence,the calculation results show that the two wavelet entropy sequences contain the very consistent dynamics characteristic;Further more we discussed the influence of window width on the wavelet entropy sequence,and found that the degradated incremental of the wavelet entropy value was stable along with the increasing window width,show that the wavelet entropy sequence has strong resistance to degradation,which could dig out the dynamic characteristics of the complex system from the degradated data,it was provided a effective method for using the degradated data to reveal the dynamic characteristics of the complex system;Finally, the method was applied to the geomagnetic data of the South Pole ZhongShan station,acquired the evolution characteristics of the geomagnetic variational intensity,in which the evolution characteristics of storms area,calm area,stable change area had the very obvious characteristics in the wavelet entropy sequence.
引文
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[2]Shaw FZ,Chen RF,Tsao HW,et al.Algorithmic complexity as an index of cortical function in awake and pentobarbital-anesthetized rats[J].J Neurosci Meth,1999,93(2):101-110.
[3]Pincus SM.Approximate entropy as a measure of system complexity[J].Chaos,1991,88(6):2297- 2301.
[4]侯威,封国林,董文杰.基于复杂度分析logistic映射和Lorenz模型的研究[J].物理学报,2005,54(8): 3940-3945.
[5]杨建平.地磁场变化的小波熵复杂度分析方法[J].地球物理学进展,2010,25(5):1605-1611.
[6]Osvaldo A Rosso,Susana Blanco,Juliana Yordanova,et al.Wavelet entropy:a new tool for analysis of short duration brain electrical signals[J].Journal of Neuroscience Methods,2001,105(1): 65-75.
[7]封洲燕.应用小波熵分析大鼠脑电信号的动态特性[J].生物物理学报,2002,18(3):325-330.
[8]何正友,蔡玉梅,钱清泉.小波熵理论及其在电力系统故障检测中的应用研究[J].中国电机工程学报, 2005,25(5):38-43.
[9]李建勋,柯熙政,丁德强.一种基于小波熵的时间尺度算法[J].天文学报,2007,48(1):84-91.
[10]徐文耀,Henri-Claud Nataf,魏自刚等.地磁场长期变化速率的30年周期.地球物理学报,2006, 49(5):1329-1338.
[11]李琪,林云芳,曾小苹.应用小波变换提取张北地震的震磁效应[J].地球物理学报,2006,49(3):855-863.
[12]Mallat SG.A theory for multiresolution signal decomposition:the wavelet representation[J]. IEEE Transaction on Pattern Analysis and Machine Intelligence,1989,11:674-693.
[13]董爱英.地磁观测报告(2005)[M].北京:海洋出版社,2007.
[14]徐文耀.地磁活动指数的过去、现在和未来[J].地球物理学进展,2009,24(3):830-841.
[15]Bartels J,Heck N H,Johnston H F.The three hour range index measuring geomagnetic activity[J]. Terre.Mag.Atmos.Elec,1939,44:441-454.
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