简谐成分的盲源分离适用性研究

摘要

Most blind source separation ( BSS) problems are solved on the basis of the independence assumption of signals or the assumption of time structure. Inappropriate assumptions may result in algorithm overlearning, and fur-thermore lead to spurious identification of the signal source. The aim of this paper is to exploit the applicability of BSS methods used in blind separation of harmonic components, which are ubiquitous in mechanical systems. First-ly, two BSS methods, namely independent component analysis ( ICA) and second order blind identification ( SO-BI) , are described;then, the non-Gausianity of the harmonic signals is analyzed by kurtosis, finding that a signal with more intense non-Gausianity may be formed when the harmonic signals constitute a Fourier series;finally, the FastICA algorithm and SOBI algorithm are applied to the simulation of the blind separation of harmonic signals and the experimental research of mode identification of the simple-support structure. The results show that when the har-monic signals constitute a Fourier series, with the ICA method, the signal with more intense non-Gausianity will be separated in priority, which will lead to overlearning of the algorithm. However, the SOBI method may assure the accuracy and reliability of a blind separation process of the harmonic components.%盲源分离问题（ BSS）大多基于信源信号的独立性假设或者时间结构假设条件来展开研究，对信源的不当假设可能导致算法过学习，产生虚假的信源识别结果。针对机械系统中普遍存在的简谐成分，研究了BSS方法应用于简谐成分盲分离的适用性。简要介绍了2种典型的BSS方法---独立分量分析方法（ ICA）和二阶盲辨识方法（ SOBI），通过峭度分析简谐信号的非高斯性，发现当简谐信号构成傅里叶级数系时，有可能构成非高斯性更强的信号。应用FastICA算法和SOBI算法进行简谐信号盲分离的仿真研究以及简支梁结构模态识别的实验研究。结果表明：当简谐信号构成傅里叶级数系时， ICA方法会优先分离非高斯性更强的信号，导致方法过学习；而SOBI方法能确保简谐成分的盲分离过程准确可靠。