基于主成分分析的经验模态分解消噪方法.docVIP

基于主成分分析的经验模态分解消噪方法* 摘 要: 针对非线性非平稳信号的去噪问题,提出一种基于主成分分析(PCA)的经验模态分解(EMD)消噪方法.该方法根据EMD的分解特性,利用PCA对噪声信号经EMD分解后的内蕴模态函数(IMF)进行去噪处理：首先利用 “3法则”对第一层IMF进行细节信息提取,并估计每层IMF中所含噪声的能量；然后对IMF进行PCA变换,根据IMF中所含噪声的能量选择合适数目的主成分分量进行重构,以去除IMF中的噪声.为验证本文方法的有效性,进行了数字仿真与实例应用实验. 实验结果均表明,所提方法的消噪效果整体上优于Bayesian小波阈值消噪方法和基于模态单元的EMD阈值消噪方法,是一种有效的信号消噪新方法. 关键词: 经验模态分解; 信号消噪; 主成分分析; 噪声能量 Empirical Mode Decomposition De-noising Method Based on Principal component Analysis* Abstract: In order to solve the problem of nonlinear and nonstationary signal de-noising, a novel de-noising method is proposed by combining the principal component analysis(PCA) and empirical mode decomposition(EMD). The method removes noise of intrinsic mode functions(IMFs) using PCA, after the noisy signal is decomposed by EMD. Firstly, the signal details of the first IMF are extracted by using of 3 criterion, and the noise energy of each level IMF is estimated. Secondly, the PCA is implementated on each IMF, and the part of principle components are selected to reconstruct the IMF according with noise energy of IMFs, then the noise of IMF is removed efficiently. Numercial simulation and real data test were carried out to evluate the performance of the proposed method. The experimental results showed that the proposed method outperformed the Baysian wavelet threshold de-noising algorithm and mode cell EMD de-noising algorithm in whole, so it is a novel effective signal de-noising method. Key words: empirical mode decomposition; signal de-noising; principle component analysis; noise energy 中图法分类号: TP301　　　文献标识码: A 从被噪声污染的信号中对原信号进行复原是信号处理中的经典问题之一,特别是在加性高斯白噪声条件下,提出了很多算法,例如中值滤波、Wiener滤波、小波滤波等[1].小波分析由于良好的时频分析特性,在信号去噪中得到了广泛的应用[2,3],但在应用小波变换对信号去噪时,需要预先选定小波基和分解的层数.已有的研究表明[4,5],相同条件下选用不同的小波基和分解层数,对去噪结果影响很大,特别是小波基函数的选择,对去噪结果有决定性的影响.这给利用小波进行信号去噪带来了很大的不便.近年来,为了分析非线性和非稳态信号,Huang等人提出了一种新的时频分解算法—经验模态分解(Empirical mode decomposition, EMD)[6].EMD是一种数据驱动的自适应信号分解方法,可以把数据分解成具有物理意义的一组内蕴模态函数(Intrinsic mode function, IMF)分量.EMD与小波变换相比最大优点是：小波分解需要事先给定小波基（