机械系统振动源的盲分离方法研究
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摘要
机械振动源信号的分离与分析对于机械系统的状态监测与故障诊断具有重要理论意义和实用价值。本论文结合国家自然科学基金项目(编号50675194,50505016),开展了机械振动源的盲源分离方法(Blind Source Separation,BSS)研究。论文在分析机械系统振动源及其混合机理的基础上,研究了机械振动源数的估计、基于二阶统计量和基于高阶统计量的机械振动源盲分离方法,并进行了仿真和试验验证。论文的主要研究工作和章节安排如下:
第1章概述了机械系统振动分析与诊断方法,分析了振动信号源分析技术及其不足,论述了引入盲源分离技术进行机械源信号分离的重要性。综述了盲源分离技术及其在机械故障诊断领域的研究现状,给出了一种基于盲源分离的多机械故障诊断架构。最后给出了本文的选题背景、研究内容、总体结构及创新点。
第2章从盲源分离的角度分析了机械系统中“源”的概念,给出了机械振动BSS中源信号的定义。以齿轮箱为例,研究了机械系统中振动源产生的机理和振动源信号的混合机理,分析了机械系统内本底振源的来源、振动模型及其相关特征。研究了齿轮箱的振动模型和振动测量模型。该模型可用于构建仿真源,以对比不同源分离算法的性能;也可作为机械故障源先验知识,为获得准确的源分离结果提供帮助。
第3章阐述和分析了基于特征值的源数估计方法的原理和实现方法。分析了源数和观测数不等的源数估计方法以及机械振动源检测中的源数估计问题。提出了在源数大于观测数的条件下,针对瞬时混合模型的基于FFT的源数估计方法,分析了该方法在卷积混合模型下的适用性。针对多频信号卷积混合模型提出了基于EMD-SVD-DE和基于EMD-SVD-BIC的源数估计方法,它们可应用于分析源数大于观测数的问题。这两种方法通过EMD方法对振动观测信号进行分解,获得源信号的内在特征振动形式,把1个传感器观测信号拓展为多个源信号内在特征的组合;然后通过奇异值分解获得反映源数信息的特征值分布;再采用占优特征值(DE)法和BIC信息准则,判断源信号的数目。
第4章在分析现有的二阶统计量的盲源分离方法基础上,提出了一种改进的基于二阶统计量的盲源分离算法。采用一组由不同时滞的协方差矩阵的平均时滞相关矩阵代替联合矩阵,获取混合矩阵的平均特征结构,从而将联合矩阵的联合对角化转化为平均矩阵的对角化问题,大大简化了算法,而对算法的稳健性和精确度影响不大。同时在对角化实施过程中,利用单位时滞协方差矩阵进行白化矩阵的计算,降低了噪声对分离结果的影响。
第5章阐述了高阶统计量方法,重点研究了利用非线性函数引入高阶统计量的时域BSS方法。给出了机械振动源卷积混合系统的时域模型,分析了时域BSS方法过程和分离原理,提出了多振源卷积混合盲源分离算法。算法的分离过程分为两个自适应过程:一个过程是滤波器系数的估计。在这个过程中对滤波器系数进行了合理简化,以独立性为评判准则,采用反向学习的方式进行滤波器系数的学习。另一个过程是源信号的估计。通过基于独立性原则得到的滤波器消除其它源信号对混合信号的影响,可得到互相耦合的同时间点的信号,通过联立等式消除信号之间的耦合,获得信号点的估计。该方法解决了多于两源卷积混合的分离问题。
第6章给出了多机系统振动源盲源分离系统解决方案,设计和构建了基于盲源分离的多机试验系统,开发了数据采集程序,并对采集的信号进行了分析和处理。进行源数估计方法有效性、快速二阶盲分离算法以及基于高阶统计量的多振源卷积混合盲源分离算法分离性能的有效性验证。提出了卷积混合情况下的实时信号的分离性能指标,采用不同时延的相关系数评定BSS算法的分离效果。
第7章给出本文工作的主要结论,并对未来的研究工作进行展望。
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.
第1章概述了机械系统振动分析与诊断方法,分析了振动信号源分析技术及其不足,论述了引入盲源分离技术进行机械源信号分离的重要性。综述了盲源分离技术及其在机械故障诊断领域的研究现状,给出了一种基于盲源分离的多机械故障诊断架构。最后给出了本文的选题背景、研究内容、总体结构及创新点。
第2章从盲源分离的角度分析了机械系统中“源”的概念,给出了机械振动BSS中源信号的定义。以齿轮箱为例,研究了机械系统中振动源产生的机理和振动源信号的混合机理,分析了机械系统内本底振源的来源、振动模型及其相关特征。研究了齿轮箱的振动模型和振动测量模型。该模型可用于构建仿真源,以对比不同源分离算法的性能;也可作为机械故障源先验知识,为获得准确的源分离结果提供帮助。
第3章阐述和分析了基于特征值的源数估计方法的原理和实现方法。分析了源数和观测数不等的源数估计方法以及机械振动源检测中的源数估计问题。提出了在源数大于观测数的条件下,针对瞬时混合模型的基于FFT的源数估计方法,分析了该方法在卷积混合模型下的适用性。针对多频信号卷积混合模型提出了基于EMD-SVD-DE和基于EMD-SVD-BIC的源数估计方法,它们可应用于分析源数大于观测数的问题。这两种方法通过EMD方法对振动观测信号进行分解,获得源信号的内在特征振动形式,把1个传感器观测信号拓展为多个源信号内在特征的组合;然后通过奇异值分解获得反映源数信息的特征值分布;再采用占优特征值(DE)法和BIC信息准则,判断源信号的数目。
第4章在分析现有的二阶统计量的盲源分离方法基础上,提出了一种改进的基于二阶统计量的盲源分离算法。采用一组由不同时滞的协方差矩阵的平均时滞相关矩阵代替联合矩阵,获取混合矩阵的平均特征结构,从而将联合矩阵的联合对角化转化为平均矩阵的对角化问题,大大简化了算法,而对算法的稳健性和精确度影响不大。同时在对角化实施过程中,利用单位时滞协方差矩阵进行白化矩阵的计算,降低了噪声对分离结果的影响。
第5章阐述了高阶统计量方法,重点研究了利用非线性函数引入高阶统计量的时域BSS方法。给出了机械振动源卷积混合系统的时域模型,分析了时域BSS方法过程和分离原理,提出了多振源卷积混合盲源分离算法。算法的分离过程分为两个自适应过程:一个过程是滤波器系数的估计。在这个过程中对滤波器系数进行了合理简化,以独立性为评判准则,采用反向学习的方式进行滤波器系数的学习。另一个过程是源信号的估计。通过基于独立性原则得到的滤波器消除其它源信号对混合信号的影响,可得到互相耦合的同时间点的信号,通过联立等式消除信号之间的耦合,获得信号点的估计。该方法解决了多于两源卷积混合的分离问题。
第6章给出了多机系统振动源盲源分离系统解决方案,设计和构建了基于盲源分离的多机试验系统,开发了数据采集程序,并对采集的信号进行了分析和处理。进行源数估计方法有效性、快速二阶盲分离算法以及基于高阶统计量的多振源卷积混合盲源分离算法分离性能的有效性验证。提出了卷积混合情况下的实时信号的分离性能指标,采用不同时延的相关系数评定BSS算法的分离效果。
第7章给出本文工作的主要结论,并对未来的研究工作进行展望。
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.
引文
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