Denoising Method Based on Singular Spectrum Analysis and Its Applications in Calculation of Maximal Liapunov Exponent
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摘要: 基于奇异谱分析对信号的自适应滤波特性，提出了一种降低混沌信号噪声的算法，这个算法首先求得信号的各阶经验正交函数（EOF）和主分量（PC）,然后用经验正交函数和主分量重构信号，根据重构信号的奇异谱选择最优的重构阶次以获得降噪后的信号．在计算动力系统最大Liapunov指数时，由于噪声的存在会降低计算的精度，因此将提出的降噪算法应用于最大Liapunov指数的计算中．通过对Henon映射和Logistic映射这两个典型混沌系统最大Liapunov指数的计算，结果表明该算法能有效提高最大Liapunov指数计算的精度．
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关键词:
- 奇异谱分析 /
- 降噪 /
- 最大Liapunov指数 /
- 混沌系统
Abstract: An algorithm based on the data-adaptive filtering characteristics of singular spectrum analy sis (SSA) is proposed to denoise chaotic data.Firstly,the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated,reconstruct the signal using the EOFs and PCs,and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal.The noise of the signal can influence the calculating precision of maximal Liapunov exponents.The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system,Henon map and Logistic map.Some numerical results show that this denoising algo rithm could improve the calculating precision of maximal Liapunov exponent.-
Key words:
- singular spectrum analysis /
- denoising /
- maximal Liapunov exponent /
- chaotic system
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