基于振动信号特征提取与表达的旋转机械状态监测与故障诊断研究
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摘要
在机械设备状态监测与故障诊断研究中,故障特征的提取及表达关系到故障诊断的可靠性与准确性,因此是机械设备故障研究中的关键问题。本文应用时域绝对自相关统计分析、时频分析中小波的分形分析、基于高阶统计量的独立分量分析与盲分离,对旋转机械中的轴承与齿轮的不同状态的振动信号进行特征提取与表达、及分类研究。
第一章阐明了机械设备状态监测与故障诊断的选题意义及研究内容,回顾了现有的检测方案及技术手段。分析了现有的振动信号分析方法：时域统计分析、时频分析、基于高阶统计量分析的独立分量分析及盲信号分离。基于轴承、齿轮的振动分析,指出本论文的主要研究内容。
第二章提出了一种基于绝对自相关统计分析信号周期瞬态成分检测方法及故障特征极坐标增强表达方法,首先计算信号的时间平均函数,接着计算其自相关函数,再利用快速傅里叶变换计算自相关函数的频谱,根据频谱确定信号的主要频率成分,分别按照这些主要频率成分的周期建立极坐标映射,并将各映射表示在极坐标图上,当对应于周期极坐标图上出现增强的特征表示,即判定待检测信号中存在有此周期的瞬态成分。所提出的方法可以有效的分辨出轴承的状态以及其对应的故障。
第三章主要研究了小波变换分形方法在轴承状态分类中的应用。首先对信号进行小波变换,通过小波反变换得到不同尺度下的细节信号,并结合原始信号的功率谱特点,选取能够充分反映信号频率——能量特征的尺度,然后计算这些尺度下各细节信号的方差,再取对数,对这些对数值进行最小二乘法直线拟合,得到拟合直线的斜率,最后利用斜率计算出表征信号复杂程度的分形维数,通过分形维数对轴承状态进行分类研究。分析结果表明,此种方法可以有效的区分轴承的正常、外圈故障、滚珠故障状态。
第四章研究了独立分量分析的基本理论及其在-维振动信号特征提取的应用研究。首先对统计独立性及不相关性进行了说明,接着研究了独立分量分析的一般模型,并对其可解性、不确定性进行了探讨。之后着重研究了非高斯性度量的对照函数：峭度、负熵、互信息,以及在进行独立分量分析之前对信号进行的预处理方法：零均值化与白化。研究了独立分量分析快速算法(FastICA)及其实现,并利用仿真分析说明ICA的不确定性。在FastICA基础上研究了一维振动信号的高阶统计信息特征提取,利用ICA基滤波相关特征(IFC)对齿轮箱振动信号进行特征提取与状态模式分类,取得了良好的效果。
第五章研究了盲卷积分离的故障特征提取方法。首先建立了更能体现机械设备振动卷积混合特点的盲卷积混合及分离模型,接着推导了两信号源两传感器盲卷积系统的分离求解过程；然后在分离信号与源信号之间的交叉残余误差(RCTE)的分离性能评判基础上,提出了一种基于限值RCTE的控制迭代准则。并针对旋转机械振动信号的特点生成仿真信号,将该方法应用于旋转机械振动信号瞬态成分与噪声卷积混合问题,仿真试验结果表明了该算法的有效性。
第六章总结全文并提出了研究展望。
Fault feature extraction and representation is the most crucial problem for the reliability and accuracy in the mechanical condition monitoring and fault diagnosis. This dissertation explores the applications of the theories with absolute value of autocorrelation, wavelet fractal analysis, independent component analysis and blind source separation in the feature extraction, representation and classification of vibration signal for the rotary machinery, such as bearing and gear.
In chapter 1, at first, the significances and content of mechanical condition monitoring and fault diagnosis are pointed out, the current detection scheme and technical means are reviewed for the condition monitoring of bearing and gear, then the applications of the time domain statistical analysis, time-frequency representation, independent component analysis and blind source separation are reviewed as well, lastly, the contents, the focuses and the innovations of this dissertation are pointed out.
Detection of signal transients based on the absolute value of autocorrelation and the representation of enforced fault feature in the polar coordinates are proposed in chapter 2. The new method is done in four steps:first, calculates the time average function of the original signal; second calculates the autocorrelations of the time average function; third, calculates the spectrum of the autocorrelations by fast Fourier transform; fourth, the enforced fault feature is represented in the polar coordinates corresponding the possible periods of the transients. The experimental verification shows the effectiveness of the new proposed method for bearing condition monitoring.
The applications of the fractal analysis based on wavelet transform to the classification of bearing's vibration signals are studied in chapter 3. Firstly the acceleration signals are decomposed to detailed signals at different wavelet scales by using the discrete wavelet transform. The variances of detailed signals are calculated and then fractal dimensions of the acceleration signals are estimated from the slop of the variance progression. The fractal dimensions are significantly different among the different working conditions of the bearings and showes a high reproducibility. The results suggest that the wavelet-based fractal analysis is effective for classifying the working conditions of bearing.
The basic theory of independent component analysis and its application to feature extraction from one-dimension vibration signal are studied in chapter 4. Firstly, the ICA general model and the dissimilarity between statistical independence and uncorrelated property are reviewed, then the contrast functions:kurtosis, negentropy and mutual information for measures of nongaussianity are presented, also is the centering and whitening for preprocessing for ICA. Secondly, the FastICA algorithm is studied. Finally, a new feature called ICA filtered correlation feature is quantitatively calculated by the transformed coefficients. The new feature has the clear class property and can be applied for signal classification.
Blind source separation for convolutive mixtures and its application to machine vibrations are studied in chapter 5. First reviews the general concept of blind source separation, especially the theory for convolutive mixtures, the model of convolutive mixture and two deconvolution structures:Recursive and Direct structures, then presents a BSS algorithm for convolutive mixtures based on RCTE threshold control criteria, last the simulation testing points out good performance for simulated mixtures.
Chapter 6 gives the conclusions and the prospect about this study.
第一章阐明了机械设备状态监测与故障诊断的选题意义及研究内容,回顾了现有的检测方案及技术手段。分析了现有的振动信号分析方法：时域统计分析、时频分析、基于高阶统计量分析的独立分量分析及盲信号分离。基于轴承、齿轮的振动分析,指出本论文的主要研究内容。
第二章提出了一种基于绝对自相关统计分析信号周期瞬态成分检测方法及故障特征极坐标增强表达方法,首先计算信号的时间平均函数,接着计算其自相关函数,再利用快速傅里叶变换计算自相关函数的频谱,根据频谱确定信号的主要频率成分,分别按照这些主要频率成分的周期建立极坐标映射,并将各映射表示在极坐标图上,当对应于周期极坐标图上出现增强的特征表示,即判定待检测信号中存在有此周期的瞬态成分。所提出的方法可以有效的分辨出轴承的状态以及其对应的故障。
第三章主要研究了小波变换分形方法在轴承状态分类中的应用。首先对信号进行小波变换,通过小波反变换得到不同尺度下的细节信号,并结合原始信号的功率谱特点,选取能够充分反映信号频率——能量特征的尺度,然后计算这些尺度下各细节信号的方差,再取对数,对这些对数值进行最小二乘法直线拟合,得到拟合直线的斜率,最后利用斜率计算出表征信号复杂程度的分形维数,通过分形维数对轴承状态进行分类研究。分析结果表明,此种方法可以有效的区分轴承的正常、外圈故障、滚珠故障状态。
第四章研究了独立分量分析的基本理论及其在-维振动信号特征提取的应用研究。首先对统计独立性及不相关性进行了说明,接着研究了独立分量分析的一般模型,并对其可解性、不确定性进行了探讨。之后着重研究了非高斯性度量的对照函数：峭度、负熵、互信息,以及在进行独立分量分析之前对信号进行的预处理方法：零均值化与白化。研究了独立分量分析快速算法(FastICA)及其实现,并利用仿真分析说明ICA的不确定性。在FastICA基础上研究了一维振动信号的高阶统计信息特征提取,利用ICA基滤波相关特征(IFC)对齿轮箱振动信号进行特征提取与状态模式分类,取得了良好的效果。
第五章研究了盲卷积分离的故障特征提取方法。首先建立了更能体现机械设备振动卷积混合特点的盲卷积混合及分离模型,接着推导了两信号源两传感器盲卷积系统的分离求解过程；然后在分离信号与源信号之间的交叉残余误差(RCTE)的分离性能评判基础上,提出了一种基于限值RCTE的控制迭代准则。并针对旋转机械振动信号的特点生成仿真信号,将该方法应用于旋转机械振动信号瞬态成分与噪声卷积混合问题,仿真试验结果表明了该算法的有效性。
第六章总结全文并提出了研究展望。
Fault feature extraction and representation is the most crucial problem for the reliability and accuracy in the mechanical condition monitoring and fault diagnosis. This dissertation explores the applications of the theories with absolute value of autocorrelation, wavelet fractal analysis, independent component analysis and blind source separation in the feature extraction, representation and classification of vibration signal for the rotary machinery, such as bearing and gear.
In chapter 1, at first, the significances and content of mechanical condition monitoring and fault diagnosis are pointed out, the current detection scheme and technical means are reviewed for the condition monitoring of bearing and gear, then the applications of the time domain statistical analysis, time-frequency representation, independent component analysis and blind source separation are reviewed as well, lastly, the contents, the focuses and the innovations of this dissertation are pointed out.
Detection of signal transients based on the absolute value of autocorrelation and the representation of enforced fault feature in the polar coordinates are proposed in chapter 2. The new method is done in four steps:first, calculates the time average function of the original signal; second calculates the autocorrelations of the time average function; third, calculates the spectrum of the autocorrelations by fast Fourier transform; fourth, the enforced fault feature is represented in the polar coordinates corresponding the possible periods of the transients. The experimental verification shows the effectiveness of the new proposed method for bearing condition monitoring.
The applications of the fractal analysis based on wavelet transform to the classification of bearing's vibration signals are studied in chapter 3. Firstly the acceleration signals are decomposed to detailed signals at different wavelet scales by using the discrete wavelet transform. The variances of detailed signals are calculated and then fractal dimensions of the acceleration signals are estimated from the slop of the variance progression. The fractal dimensions are significantly different among the different working conditions of the bearings and showes a high reproducibility. The results suggest that the wavelet-based fractal analysis is effective for classifying the working conditions of bearing.
The basic theory of independent component analysis and its application to feature extraction from one-dimension vibration signal are studied in chapter 4. Firstly, the ICA general model and the dissimilarity between statistical independence and uncorrelated property are reviewed, then the contrast functions:kurtosis, negentropy and mutual information for measures of nongaussianity are presented, also is the centering and whitening for preprocessing for ICA. Secondly, the FastICA algorithm is studied. Finally, a new feature called ICA filtered correlation feature is quantitatively calculated by the transformed coefficients. The new feature has the clear class property and can be applied for signal classification.
Blind source separation for convolutive mixtures and its application to machine vibrations are studied in chapter 5. First reviews the general concept of blind source separation, especially the theory for convolutive mixtures, the model of convolutive mixture and two deconvolution structures:Recursive and Direct structures, then presents a BSS algorithm for convolutive mixtures based on RCTE threshold control criteria, last the simulation testing points out good performance for simulated mixtures.
Chapter 6 gives the conclusions and the prospect about this study.
引文
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