基于奇异值分解的欠定盲信号分离新方法及应用

New Method of Blind Source Separation in Under-determined Mixtures Based on Singular Value Decomposition and Application

提出一种利用相空间重构和奇异值分解实现信号升维,从而对欠定信号进行盲分离的新方法。选择合理的时间延迟和嵌入维数对信号进行相空间重构而得到吸引子轨迹矩阵,对该矩阵进行奇异值分解,并根据不同信号的奇异值分布特性选择合适的奇异值进行逆变换,从而可以得到源信号的新的线性组合,实现了信号升维。随后对新混合信号与原混合信号之间的关系进行讨论,分析二者之间的相关性,证明了该方法的合理性。利用该方法首先分析几种常见信号如正弦信号、调频信号、调幅信号等的奇异值分布特性,研究这些信号与白噪声混合时的欠定盲分离,并将其用于实测齿轮故障信号的盲分离,研究表明该方法能够识别齿轮系统的典型故障,取得了较好效果。

A new method of blind source separation （BSS） in under-determined mixtures is presented, which is based on the reconstruction of phase space and singular value decomposition to increase dimensions. The first step is to obtain the track matrix of the attractor by reconstruction of phase space based on appropriate time delay and embedded dimension, and apply singular value decomposition to this matrix. Then the inverse transform is applied to the revised signal matrix and a new linear combination of the source signals can be obtained, so that the signal dimensions are increased. Moreover the connection of the new linear combination, obtained, of the source signals and the original one is discussed, and the relativity of these two signals is analyzed so as to verify the feasibility of this new method. This method is used to research the under-determined BSS composed of some common signals, such as sine signal, frequency modulation signal, amplitude modulation signal mixed with white noise based on the different distribution features of the singular values, and then applied in the fault diagnosis of the experimental gear bench to diagnose the typical faults of gear.