Blind Signal Separation Methods In The Frequency Domain

The signal feature extraction is the base of machinery fault diagnosis, directly influences the diagnosis correctness. And its theory development and technology improvement are correlative deeply with signal processing. In this thesis, after the defects of traditional signal processing are analyzed, blind signal separation, a new signal processing technical, is made theoretical researches on.First the development history about blind signal separation (BSS) is summarized in the thesis. Then the two main difficulties, i.e. the estimation of the number of sources and the blind separation of correlated source, are pointed out in the application of BSS. And the processing frame of BSS is proposed.The basic concepts, the limit conditions and three mixture models are introduced, in order to understand the theory of BSS overall. The blind separation principles of three classical algorithms for the linear, instantaneous combinations are importantly described.On the base of analyzing the physics meaning of power spectral density (PSD) for observation signal, a new BSS method based on PSD for blind separation of independent source is proposed. The best characteristic of this algorithm is that when the relation between the number of sensors and of sources is unknown (either greater than or smaller than or equal to), the mixture matrix is got by the ratio of observation signal PSD. According to the matrix, it can be assured that the observation signal belongs to one of three mixtures, namely the complete mixture, over-determined mixture and under-determined mixture, and the separation matrix is found. The algorithm avoids some difficult questions for some classical algorithms, that is, the estimation of probability density function for source, the convergence and un-stableness in the optimization and so on.Two algorithms are proposed to solve the estimation of the number of sources in application BSS. One is the method based on PSD, namely, through clustering the column vector of PSD matrix for observation signals, the number of sources is estimated. The algorithm needs not the condition that the number of sensors is greater than the number of the sources, which the other algorithms need. Hence, it has good practicability. However, the round of the number of correlated sources can be estimated theoretically, and the exact value can not be got. The second is the method based on non-negative matrix factorization (NMF). Applying the feature of NMF which is not influenced by source signal independence, the number of any sources can be directly estimates by the frequency amplitude matrix of observation signals. However the algorithm requires that the number of sensors must be greater than the number of sources. The effectiveness of the proposed two methods is verified by simulation and real experiments data.Two algorithms are proposed for the blind separation of correlated source. One is the method based on constrained non-negative matrix factorization. It takes advantage of the good feature of NMF and finds the mixture matrix from the frequency amplitude matrix of source. Due to non-uniqueness of solution for NMF, after the blind separation nature of correlated source is studied, adding the aim function to the constraint for the correlation of sources, the mixture matrix is got by NMF. The algorithm has good separation performance for the correlated source. The second is the method that the common frequencies are removed from observation signals step by step and the non-common frequencies are applied to separate observation signals. Comparing the ratio values of non-diagonal and diagonal element for common frequency and non-common frequency, the common frequency is found and removed from mixture signal one by one. At last, through the non-common frequencies, the separation matrix is got and the sources are extracted by the classical BSS algorithms. The method is without the limitation which the second has, and has good separation performance. The two algorithms are compared by simulation in the thesis, and the influence of noise on the estimation of number of sources is done. The advantages and shortcomings for these methods are pointed out.The achievements of this thesis are significant for the development of the BSS theory. Also, it is practical and valuable to apply these achievements to the blind separation for real signals.