核独立分量分析在机械振动信号分离中的应用

Applying Kernel Independent Component Analysis(KICA) to Obtaining Better Blind Separation of Mechanical Vibration Signals

针对旋转机械振动信号成分复杂,甚至表现出非线性特征,文章采用核独立分量分析(KICA)对其进行预处理。与独立分量分析(ICA)不同,KICA是通过非线性映射在高维特征空间上构建了核化的目标函数,并引入核方法实现该目标函数的优化操作。仿真实验中通过比较KICA、ICA和传统KICA(DKICA)的分离信号与源信号之间的相关系数,文中介绍的KICA对混合信号分离处理具有更高的准确性和鲁棒性;实测数据实验验证,经过KICA处理的机械振动信号,其表征的振动信息更为单一,使得隐含的特征频率得到凸显,为进一步处理和分析奠定良好基础。

Aim. In the final paragraph of the introduction of the full paper, we point out what we believe to be the advantages of applying KICA to blind separation. Sections 1 and 2 explain how to apply KICA. Section 1 briefs ICA （independent component analysis）. Section 2 is entitled KICA; subsection 2. 1 briefs the kernel method; subsec- tion 2.2 explains how to apply Refs. 6 and 7, both of which deal with KICA, to the blind separation of mechanical vibration signals; its core is that we use KICA to construct the objective function pf, whose mathematical expression is given in eq. （5）, in the high-dimension characteristic space through nonlinear mapping and to optimize the ob- jective function kernelled by the nonlinear characteristic space. The core of section 3 consists of： （ 1 ） we apply KI- CA to the blind separation of cosine signal and measurement data respectively and compare the correlation coeffi- cient of source signal with that of the signal thus separated; （2） the~.simulation results, given in Figs. 1, 2 and 3 and Table 1, show preliminarily that our KICA method is more precise and robust for blind separation of mechanical vibration signals than the conventional ICA method and the traditional DKICA method.