基于独立成分分析和经验模态分解的混沌信号降噪

基于经验模态分解和独立成分分析去噪的特点,提出了一种联合独立成分分析和经验模态分解的混沌信号降噪方法. 利用经验模态分解对混沌信号进行分解,根据平移不变经验模态分解的思想构造多维输入向量, 通过所构造的多维输入向量和独立成分分析对混沌信号的各层内蕴模态函数进行自适应去噪处理; 将处理后的所有内蕴模态函数进行累加重构,从而得到降噪后的混沌信号. 仿真实验中分别对叠加不同强度高斯噪声的Lorenz混沌信号及实际观测的月太阳黑子混沌序列进行了研究, 结果表明本文方法能够对混沌信号进行有效的降噪,而且能够较好地校正相空间中点的位置, 逼近真实的混沌吸引子轨迹. 关键词： 独立成分分析 经验模态分解 混沌信号 降噪

Chaotic signal denoising method based on independent component analysis and empirical mode decomposition

According to the characteristics of empirical mode decomposition and denoise of independent component analysis, an adaptive denoising method of chaotic signal is proposed based on independent component analysis and empirical mode decomposition. First, the chaotic signal is decomposed into a set of intrinsic mode functions by empirical mode decomposition; then, the multi-dimensional input vectors are constructed based on the translation invariant empirical mode decomposition, and the noise of each intrinsic mode function is removed through the constructed multi-dimensional input vectors and the independent component analysis; finally, the denoisied chaotic signal is obtained by accumulating and reconstructing all the processed intrinsic mode functions. Both the chaotic signal generated by Lorenz map with different level Gaussian noises, and the observed monthly series of sunspots are respectively used for noise reduction using the proposed method. The results of numerical experiments show that the proposed method is efficient. It can better correct the positions of data points in phase space and approximate the real chaotic attractor trajectories more closely．