基于频域约束独立成分分析的经验模态分解去噪方法

EMD denoising method based on frequency domain constrained independent component analysis

噪声污染是煤岩动力灾害电磁监测应用中需要解决的重要问题,去噪效果的好坏直接影响灾害预测的准确性。经验模态分解(Empirical Mode Decomposition,EMD)是目前电磁信号去噪中应用最多的一种方法,但当信号与噪声时频特征相近时,该算法存在严重的内蕴模态函数(Intrinsic Mode Function,IMF)混叠现象(即部分模态函数仍为信号与噪声的组合)。针对该问题,提出一种基于经验模态分解和频域约束独立成分分析的去噪方法,首先利用EMD将电磁信号分解为多个IMF分量,通过计算各分量与原信号间的互相关系数判断存在模态混叠现象过渡IMF,再以过渡IMF后续分量的频域为约束条件,对过渡IMF进行独立成分分析,去除过渡分量中的噪声;最后将去噪后的过渡分量与其后续分量进行重构,得到去噪后的信号。分别以含噪Ricker子波和现场电磁信号为例,利用信噪比定量验证了上述方法对处理现场电磁信号模态混叠问题的有效性,同时频域约束条件下的独立成分分析去噪收敛快、效率高,适合海量实时监测信号快速去噪使用。

Noise pollution is an important issue to be solved in the application of coal or rock dynamic disasters electromagnetic monitoring.Denoising effect directly affect the disaster prediction accuracy.Empirical Mode Decomposition（EMD） is the most widely method used in electromagnetic signal denoising.But when the frequency characteristics of the signal and noise are similar,the algorithm exists serious noise aliasing of intrinsic mode function（ IMF）.Some IMFs are the combination of signal and noise.To solve this problem,this paper proposes a denoising method based on EMD and frequency domain constrained independent component analysis. Firstly,the noisy signal is decomposed to a series of IMFs by EMD.Secondly,calculate the correlation coefficients of each IMF and the original signal,identify the transition IMF between noise and signal.Then the high frequency noise IMFs above the transition IMF are removed.Thirdly,independent component analysis of the transition IMF based on frequency-domain constraints（ the frequency domain of transition IMF follow-up component） to remove noise.Finally,the denoised transition IMF and its subsequent IMFs are reconstructed to the denoised signal. Take noisy Ricker wavelet and field electromagnetic signals as the example,use signal-noise ratio quantitatively verify the validity of the denoising method described above to process electromagneticsignal mode aliasing problem.Frequency domain constrained independent component analysis has the advantages of denoising fast convergence and high efficiency.The denoising method is suitable for mass rapid real-time monitoring signals.