Blind Separation Method Of Multi-fault Sources Based On Canonical Correlation Analysis

This dissertation is supported by the National Natural Science Foundation ofChina(No.51075372,51261024,51265039), Science and Technology Projects ofEducation Department of Jiangxi Province, China(No. GJJ12405), The Open Fund ofKey Laboratory of Machanical Equipment Health of Hunan Province (No.201204) andthe Innovation Fund Designated for Graduate Students of Jiangxi Province, China(No.YC2013-S214). Based on the deficiencies of the traditional blind source separation ofmechanical sources. This article introducing canonical correlation analysis algorithm tothe blind source separation of mechanical sources. Blind source separation methodbased on canonical correlation analysis is deeply discussed, some innovative results areobtained. The research contents in this paper is mainly as follows1. The research status of blind separation of mechanical fault sources and theirshortcomings are be summarized. The development and application of canonicalcorrelation analysis is also discussed. the basic theory of canonical correlation analysis,which mainly including mathematical description of the canonical correlation analysisand parsing algorithm, is introduced. Based on the above comments, the significance ofthis paper is briefly given.2. Based on the uniqueness of canonical correlation analysis, a blind sourceseparation method of machine fault diagnosis based on canonical correlation analysis.Compared with the blind source separation method of machine fault diagnosis based onindependent component analysis (ICA), the traditional blind source separation methodonly considers the statistical distribution of the sample values, without regard to thetime and spatial relationship between the source signals. However, the proposed methodovercome this defect, and the autocorrelation of source signal is used to separate themixture signals. The simulation results show that the proposed method obtain thesatisfactory separation performance, and has much more computational efficiency thanthe traditional ICA method. Finally, the proposed method is applied to the faultdiagnosis of rolling bearing. The experiment results further validate the effectiveness ofthe proposed method.3. Based on the deficiency in the traditional blind separation method of statisticallycorrelated sources, a new blind separation method of nonlinear mixture from correlatedsources is proposed. In the proposed method, the nonlinear problem between the data can be processed by the kernel method, and the correlated sources can be effectivelyseparated using the correlate of source signals. The proposed method is compared withtraditional blind separation method of statistically correlated sources. The simulationresults show that the proposed method is obviously superior to the traditional blindseparation method of statistically correlated, and the performance index of separationcan be reflected. Finally the proposed method is applied to blind separation of themisalignment of rotary and rotor rub-impact, the experiment results further validate theeffectiveness of the proposed method.4. Combining the advantages of wavelet analysis and kernel canonical correlationanalysis (KCCA)，an underdetermined blind source separation method of nonlinearmixture based on wavelet decomposition and kernel canonical correlation analysis,which is named as Wavelet-BSS method, is proposed. In the proposed method， thenonlinear mixture signals are firstly decomposed a series of approximate components bywavelet transform，these approximate components and original observation construct anew observation signal. Secondly new observation signal is mapped from lowdimensional space to high dimensional kernel feature space. Then the blind sourceseparation algorithm in kernel feature space is performed by canonical correlationanalysis. The simulation results show that the Wavelet-BSS method is superior totraditional blind source separation of nonlinear mixtures，and has satisfactory separationperformance.5. Dynamic blind source separation is a focus in the blind separation of multi-faultsources. Traditional blind source separation (BSS) is restricted to the stable statisticalcharacteristics and static mixture system, and ignores the sequential information. Basedon this deficiency, combining to canonical variate analysis (CVA) and independentcomponent analysis (ICA)，an dynamic blind source separation method based oncanonical variate analysis and independent component analysis, which is named asCVA-ICA method, is proposed. In the proposed method, the source signal is regarded asstate variable in the state space, observation signal as output variable, thus the dynamicsICA is transform into the state space ICA. The proposed method employs CVA as areduction tool to construct a state space, from where statistically independent sourcesare separated by the conventional ICA algorithm. The simulation results show that theCVA-ICA method is superior to traditional blind source separation in the dynamic blindsource separation，and has satisfactory separation performance. Finally the proposedmethod is applied to blind separation of bearing inner and ball, the experiment results further validate the effectiveness of the proposed method.