Research On Blind Source Separation Of The Vibration Signals Of Mechanical System

The separation and analysis of the mechanical vibration signal is important to machine monitoring and faults diagnosis. Based on the National Nature Science Fund Project—"Research on new method for rotating machine faults diagnosis based on independent component analysis" (No: 50205025) and "Research on method for mechanical vibration source semi-blind source separation and reconstruction" (No: 50675194), research on blind source separation (BSS) of the vibration signals of mechanical system was carried out. The mechanism of the mechanical vibration, the method to estimate the number of vibration sources, the algorithms of BSS for mechanical vibration signals base on second-order statistics (SOS) and high-order statistics (HOS) were researched. The details were as follows:In Chapter one: The techniques to analyze the vibration sources were discussed. The problems existed in the technique of vibration analysis were analyzed. The essentiality of introducing BSS to obtain the useful signals which were related to the situation of the machine was addressed. The works of BSS methods and the application in the field of fault diagnosis of the machine were reviewed. A frame of the fault diagnosis for multi-machine based on BSS was presented. At the end of this chapter, the background to carry out this research and its details, the scheme and the innovation points of this dissertation were presented.In Chapter two: The concept of the "source" in the mechanical system for BSS was analyzed, and the source signals were defined for the BSS issues of mechanical vibration. The mechanism of how vibration sources came in to being and how vibration sources were mixed was researched. The source of the base vibration source signals of the mechanical system and their characters were analyzed. On the base of analyzing the vibration of the component of the mechanical system contributed to the measurement, the vibration signal model of the gear box was researched. The vibration model of the gearbox was present. According to the vibration model, the simulation signal can be constructed to compare the performances of the algorithm of BSS. For the more important, the model can be useful for choosing appropriate algorithm for the BSS of the vibration signals to get the ideal result.In Chapter three: The principles and the realization methods of the source number estimation method based on eigenvalue were analyzed. The problems of the source number estimation when the number of sources is differ from the number of measurements and the problems to detect the vibration sources in the mechanical systems were analyzed. A method based on FFT which can be used to estimate the number of the sources in the case of fewer sources than mixtures. The method can be used in the instantaneous model and the convolutive model which was mixed by simple sources. The source number estimation method based on EMD-SVD-DE(Empirical Mode Decomposition, EMD; Singular Value Decomposition, SVD; Dominant Eigenvalue, DE) and the method based on EMD-SVD-BIC(Empirical Mode Decomposition, EMD; Singular Value Decomposition, SVD; Bayesian Information Criterion, BIC) are presented to get the source number for the convolutive model of complex signals. They can be used in the case of fewer sources than mixtures. The characteristic forms of vibration sources were obtained through the EMD of the mixtures. One mixture signal was decompose to inherence character of several sources. The relation matrix of the characteristic forms of different mixtures was used to get the eigenvalues of sources which were used to determine the number of sources by means of the method DE and BIC.In Chapter four: The algorithms of BSS based on second order statistics (SOS) were discussed. A rapid second-order blind identification algorithm was developed to separate temporally correlated sources with different normalized spectra based on the origin algorithm of blind source separation. The set of covariance matrices of the origin algorithm was substituted for their average matrix to obtain their 'average eigenstructure'. And the problem of joint diagonalization of several matrices was reduced to one matrix diagonalization. So the cost of the computation was reduced. In contrast to the origin algorithm, the modified algorithm, especially for the approximate diagonalization algorithm, enhances the speed of the algorithm obviously without leading to the degeneration of the separation performance. The unit delay of the covariance matrix was used to get the whitened matrix, which reduces the noise effect to the separation result.In Chapter five: The algorithms of BSS based on high order statistics (HOS) were discussed. The temporal BSS algorithm which introduced the HOS by means of nonlinear function was researched. The temporal model of the convolutive mixtures of mechanical vibration signals was described. The process and the principle of the temporal BSS algorithm were analyzed. A convolutive temporal BSS algorithm of multi (more than two) sources and mixtures was presented based on the algorithm of two sources and two mixtures. The new algorithm was carried out by means of two iterative procedures: One was the procedure to estimate the coefficients of the filters. The independence criterion was used and the unknown filters were gotten by a back propagation procedure by means of simplifying the coefficients of filters in a rational way. The other one was the estimation of source signals. The coupled signals were gotten by means of the filters obtained by means the former procedure and the estimation sources were obtained through decoupled procedure. This improved algorithm can be used to separate convolutive mixtures with multi (more than two) mechanical vibrations.In Chapter six: A scheme to separation the vibration signals in multi-machine by means of BSS is presented. A test-bed which composed of two motors was constructed. The program for data sampling was designed. The sampled data were analyzed to evaluate the validity of the method of source number estimation, the rapidity of the improved algorithm based on SOS and the validity of the convolutive temporal BSS algorithm of multi (more than two) sources and mixtures. An index which is Different Delay Correlation Coefficient (DDCC) was put forward to measure the separation performance of the algorithm of BSS of the real signals.In Chapter seven: The concolusions are presented and some advanced topics in the proposed methodology that needs further investigation in future are presented and addressed.