基于奇异值分解的信号特征提取方法研究

奇异值反映了信号中有用信号和噪声的能量分布情况，通过奇异值分解可以将隐含在噪声中的特征信号提取出来。本文提出了在强背景噪声中基于奇异值分解的特征提取方法。研究发现，随着信号信噪比的降低，奇异值的分布趋于直线，特征信号难以分离和提取。通过增加奇异值分解阶次，可以使反映噪声能量的奇异值的分布范围扩大，使得噪声的能量相对分散，凸显出了反映有用信号能量的奇异值，从而有利于特征信号的提取。仿真试验和故障分析实例都验证了该方法的可行性。

Feature extraction methods based on singular value decomposition

The feature extraction method for the signal with strong background noise based on singular value decomposition (SVD) was presented. The study results show that the singular values tend to be of linear distribution with the decrease of signal noise ratio (SNR), so the characteristic signal is difficult to be separated and extracted. The distribution range of the singular values which reflects the energy of noise will be extended by increasing the singular value decomposition order , so the energy of noise is dispersed, and the singular values which reflect the energy of wanted signal will be apparent markedly, and so it is favourable to extraction of characteristic signal. The feasibility of the method was validated by simulation testing and fault analysis example.