频率域盲信号分离理论研究
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摘要
信号特征提取是机械故障诊断的基础,直接影响到机械故障诊断的正确性,它的理论发展与技术进步与信号处理相关学科的研究发展密不可分。本文在分析传统信号处理方法不足的基础上,展开了对盲信号分离(一种新的信号处理技术)的理论研究。
本文首先在综述盲信号分离的发展史后,指出盲信号分离在应用中存在的两个主要难点,即源数估计以及相关源信号的盲分离,并提出了观测信号盲分离处理框架。
为了全面了解盲信号分离的理论基础,本文介绍了盲信号分离理论中所涉及到的基本概念、求解的限制条件以及盲信号分离三种混合模型,着重阐述了线性瞬时混合三个经典算法的盲分离原理。
针对独立源信号盲分离,本文在分析观测信号功率谱密度所包含的物理意义基础上,提出一种新的基于功率谱密度的算法。该算法最大的特点在于,当传感器数与源数关系不明确情况下(或大于、或小于、或等于),根据观测信号的功率谱密度函数的比值,得到混合矩阵。通过所得的混合矩阵判定观测信号是完备混合、超定混合还是欠定混合,并由此进一步获得分离矩阵。该算法避免了一般经典算法难以处理的问题,即源信号的概率密度函数估计以及优化过程中解的收敛性和不稳定性问题。
为了解决盲信号分离在应用中出现的源数估计问题,本文提出了两种源数估计方法。第一种是基于功率谱密度的源数估计法,它主要是通过聚类观测信号的功率谱密度矩阵的列向量来估计源数。这种算法具有目前所有其它源数估计算法所不具备的优势,即不需要在传感器数大于源数条件下估计源数,具有较强的实用性。但理论上在估计相关源信号时,该算法只能估计上下界,不能做出精确估计;第二种是基于非负矩阵分解(Non-negative Matrix Factorization: NMF)的源数估计法。它主要是利用NMF在分解矩阵时不受信号独立性影响的特性,直接通过观测信号的幅频系数矩阵估计任意源信号的数量,但该算法要求传感器数大于等于源数。这两种算法均通过仿真和实际观测信号加以验证。
对于相关源信号的盲分离,本文提出了2种算法。第一种是受限非负矩阵分解法。它同样是利用NMF不受信号独立性影响的优良性质,从混合信号幅频系数矩阵中求得混合矩阵,进而获得分离矩阵。针对NMF在分解矩阵过程中存在解的不唯一性,本文首先基于NMF确定源数,然后在对相关源信号盲分离实质研究的基础上,提出运用NMF分离混合信号时对目标函数加以源信号相关性约束,从而求得混合矩阵。该算法对相关源信号具有较强的分离性能;第二种是分步去共频法,该算法主要是利用共频与非共频在源信号相关矩阵非对角元素与对角元素的相对比值不同,分步从观测信号中找出共频并从中剔除,由非公共频率成分按独立源信号盲分离算法求分离矩阵,具有较好的分离性能。本文对这两种算法的分离性能进行了仿真对比,同时也进行了噪声干扰下的对比仿真,指出两种算法的优缺点。
本论文的研究不仅对盲信号分离理论的发展和完善具有重要的理论意义,而且对将该研究成果应用于实际观测信号的盲分离具有重要的现实意义和实用价值。
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.
本文首先在综述盲信号分离的发展史后,指出盲信号分离在应用中存在的两个主要难点,即源数估计以及相关源信号的盲分离,并提出了观测信号盲分离处理框架。
为了全面了解盲信号分离的理论基础,本文介绍了盲信号分离理论中所涉及到的基本概念、求解的限制条件以及盲信号分离三种混合模型,着重阐述了线性瞬时混合三个经典算法的盲分离原理。
针对独立源信号盲分离,本文在分析观测信号功率谱密度所包含的物理意义基础上,提出一种新的基于功率谱密度的算法。该算法最大的特点在于,当传感器数与源数关系不明确情况下(或大于、或小于、或等于),根据观测信号的功率谱密度函数的比值,得到混合矩阵。通过所得的混合矩阵判定观测信号是完备混合、超定混合还是欠定混合,并由此进一步获得分离矩阵。该算法避免了一般经典算法难以处理的问题,即源信号的概率密度函数估计以及优化过程中解的收敛性和不稳定性问题。
为了解决盲信号分离在应用中出现的源数估计问题,本文提出了两种源数估计方法。第一种是基于功率谱密度的源数估计法,它主要是通过聚类观测信号的功率谱密度矩阵的列向量来估计源数。这种算法具有目前所有其它源数估计算法所不具备的优势,即不需要在传感器数大于源数条件下估计源数,具有较强的实用性。但理论上在估计相关源信号时,该算法只能估计上下界,不能做出精确估计;第二种是基于非负矩阵分解(Non-negative Matrix Factorization: NMF)的源数估计法。它主要是利用NMF在分解矩阵时不受信号独立性影响的特性,直接通过观测信号的幅频系数矩阵估计任意源信号的数量,但该算法要求传感器数大于等于源数。这两种算法均通过仿真和实际观测信号加以验证。
对于相关源信号的盲分离,本文提出了2种算法。第一种是受限非负矩阵分解法。它同样是利用NMF不受信号独立性影响的优良性质,从混合信号幅频系数矩阵中求得混合矩阵,进而获得分离矩阵。针对NMF在分解矩阵过程中存在解的不唯一性,本文首先基于NMF确定源数,然后在对相关源信号盲分离实质研究的基础上,提出运用NMF分离混合信号时对目标函数加以源信号相关性约束,从而求得混合矩阵。该算法对相关源信号具有较强的分离性能;第二种是分步去共频法,该算法主要是利用共频与非共频在源信号相关矩阵非对角元素与对角元素的相对比值不同,分步从观测信号中找出共频并从中剔除,由非公共频率成分按独立源信号盲分离算法求分离矩阵,具有较好的分离性能。本文对这两种算法的分离性能进行了仿真对比,同时也进行了噪声干扰下的对比仿真,指出两种算法的优缺点。
本论文的研究不仅对盲信号分离理论的发展和完善具有重要的理论意义,而且对将该研究成果应用于实际观测信号的盲分离具有重要的现实意义和实用价值。
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.
引文
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