基于小波-KCCA的非线性欠定盲分离方法研究

Study on underdetermined blind source separation method of nonlinear mixture based on wavelet and Kernel Canonical Correlation Analysis

结合小波分析和核典型相关分析(KCCA)各自的特点,提出一种基于小波-KCCA非线性欠定盲源分离方法。该方法的基本思想是利用小波分析对观测信号进行分解,将分解后的小波系数与原来的观测信号重新组合,构成新的观测信号,从而将欠定盲分离转换为超定或正定盲分离。然后把新的非线性观测信号从低维空间映射到高维核特征空间,将非线性盲源分离问题转化为特征空间中的线性盲源分离问题,最后用典型相关分析对混合信号进行盲源分离,得到源信号的估计。仿真结果表明,与传统的非线性盲分离方法相比较,提出的方法具有明显的优势,得到了满意的分离效果。最后,轴承内外圈故障非线性欠定混合盲分离实验进一步验证了小波-KCCA方法的有效性。

Combining the advantages of wavelet analysis and kernel canonical correlation analysis （KCCA）,an underdetermined blind source separation method of nonlinear mixture based on wavelet decomposition and kernel canonical correlation analysis,which is named as Wavelet-BSS method,is proposed.In the proposed method,the nonlinear mixture signals are firstly decomposed to a series of approximate components with wavelet transform; these approximate components and original observation signals are combined to construct a new observation signal,and the underdetermined blind source separation problem is transformed to determined or overdetermined blind source separation problems.Secondly,the new observation signal is mapped from low dimensional space to high dimensional kernel feature space; and the nonlinear blind source separation problem is transformed to linear blind source separation problem in the feature space.Then the canonical correlation analysis method is used to conduct blind source separation of the mixture signals,and the blind signal estimation is achieved.The simulation results show that the WaveletBSS method is superior to traditional blind source separation of nonlinear mixtures,and satisfactory separation performance is achieved.The proposed method was applied to the underdetermined blind separation of the nonlinear mixtures for the bearing inner and outer faults.The experiment results further verify the effectiveness of the proposed method.