基于第二代小波的机械故障信号处理方法研究
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摘要
随着对安全生产和产品质量需求的不断提高，当机电设备偏离正常工作状态时，要求能够被及时发现并进行维修，因此设备的故障诊断技术成为当前国际国内研究的一大热点问题。第二代小波是近年来发展起来的一种新的小波构造理论，具有许多传统小波变换无法比拟的优点，在信号分析和处理领域得到了广泛应用。为此，本文以机械设备的故障监测和诊断为目的，系统地开展了第二代小波理论在信号压缩、信号消噪、故障检测以及故障模式分类方面的应用研究。
首先，研究了第二代小波滤波器的时频特性，指出了采用第二代小波对机械故障信号分析时存在的问题。研究表明，第二代小波的尺度滤波器和小波滤波器在时域中是紧支撑的、对称的，并且具有冲击特征，可以用来提取故障信号中的瞬态冲击特征；第二代小波滤波器在频域中不具备理想的频率特性，频带之间存在交叠；第二代小波具备分析非平稳信号的能力，但是分析结果存在频率混叠问题，因此在故障诊断中的应用存在局限性。
其次，研究了第二代小波变换的频率混叠问题，提出了抑制频率混叠的方法，为故障特征的有效提取提供了理论依据。分析了分裂操作、预测操作、更新操作以及合成操作的性质，指出了第二代小波产生频率混叠的原因和抑制频率混叠的方法；研究了冗余第二代小波的性质，结果表明，冗余第二代小波在变换过程中不进行分裂和合成操作，因此不仅可以抑制分析结果中的频率混叠成分，而且使变换具备了平移不变性。从滤波器频率响应的角度解释了冗余第二代小波包产生频带错位的原因，提出了消除冗余第二代小波包频带错位的修正方法。
再次，提出了一种基于二维第二代小波变换的旋转机械振动信号压缩方法。在第二代小波变换和混合熵编码的信号压缩框架下，分析了旋转机械振动信号的准周期特性及其二维描述方法，提出了首先按照回转周期将振动信号从一维信号转换为二维矩阵，然后再采用二维小波变换对其进行压缩和重构的方法。试验结果表明，有损压缩与无损压缩技术相结合可以在保证信号重构精度的同时，进一步提高信号的压缩比；对于旋转机械振动信号，采用二维小波变换进行压缩具有更好的压缩性能。
然后，提出了一种基于空间自适应冗余第二代小波变换的信号消噪方法。空间自适应第二代小波可以针对每一尺度上的每个样本选择最佳的预测器，从而能够更好地锁定信号的局部特征。冗余小波变换具有抑制混叠特性和平移不变特性，在信号消噪时能够更加准确地估计噪声强度，并且可以缓解消噪后信号在奇异点处的吉布斯振荡现象。因此，空间自适应冗余第二代小波可以更好地应用于信号消噪。试验结果表明，基于空间自适应冗余第二代小波的信号消噪方法不仅可以提高信噪比、降低均方误差，而且能够保留更多的瞬态故障特征。
最后，对冗余第二代小波包变换在机械故障检测和故障模式分类中的应用进行了研究。针对机械故障模式分类问题，提出了一种基于冗余第二代小波包的故障模式分类方法，该方法利用冗余第二代小波包提取故障特征参数，利用邻域粗糙集对特征参数进行属性选择。通过对滚动轴承微弱故障进行检测以及对齿轮箱和汽车发动机气门机构多种故障工况模式进行分类，试验结果表明，基于冗余第二代小波包可以有效地检测出机械振动信号中的微弱故障特征，并且可以提取出分类能力更强的故障特征参数进行模式分类，进而得到更高的故障分类精度。
Growing demand for operation safety and high quality production requires thatdeviation of machine conditions from its normal setting should be identified andfixed promptly to reduce costly machine downtime and maintain high productivity.Therefore, research on effective mechanical equipments health monitoring anddiagnosis has been enhanced in recently years. The second generation wavelettransform (SGWT) is new wavelet theory and possesses many distinct properties. Forthe purpose of condition monitoring and fault diagnosis for mechanical equipment,fault feature extraction, signal compression, signal denoising and faulty conditionidentification techniques based on SGWT were studied in this dissertation.
Firstly, the nonstationary properties of mechanical faulty signals were discussed,and the necessity and effectiveness of using SGWT for nonstationary signalsprocessing were demonstrated. Studies show that the wavelet function and scalingfunction of SGWT in time domain are compactly supported and symmetrical, at thesame time they have the signature of impact. But in frequency domain, they do notpossess the ideal cut-off property. The SGWT has the ability to process nonstationarysignal, but the frequency aliasing is inhering in its analysis results. Therefore, theapplication of SGWT has some limitations in the field of fault diagnosis.
Secondly, the viewpoint of constructing redundant SGWT (RSGWT) to suppressfrequency aliasing was proposed, which provided the basis of effective fault featureextraction. Based on the analysis of split operation, prediction operation, updateoperation and merging operation of SGWT, the reasons and the suppressingapproach for frequency aliasing were pointed out. The anti-aliasing property,translation invariability property and the computational complexity of RSGWT wereanalyzed in detail. The frequency band derangement of redundant second generationwavelet packet transform (RSGWPT) was presented and also a modified version wasproposed.
Thirdly, a real-time signal compression method based on SGWT and hybridentropy coding was proposed. Within the framework of the proposed method, thequasi-periodic characteristic of rotating machinery vibration signal and the twodimension description for such data were analyzed. Based on this investigation, atwo dimension wavelet compression algorithm for such vibration data was proposed.Testing results show that combining both lossy and lossless compression techniquescan achieve higher compression ratio while maintaining the same reconstructionaccuracy. Also, as to rotating machinery vibration signal, employing two dimension wavelet transform can simultaneously eliminate the redundancy in both intra-cycleand inter-cycle effectively.
Fourthly, a signal denoising method based on the space-adaptive RSGWT wasproposed. The space-adaptive construction approach for SGWT is able to designwavelet function for each sample point in the signal. The redundant transform is ableto obtain a more accuracy noise intensity estimation and to suppress pseudo-Gibbsphenomena on the singularity points of the denoised signal. So using the space-adaptive RSGWT to signal denoising can get a better result than those obtained byusing other wavelet-based methods. The proposed denoising method wasinvestigated by applying to denoise both simulated signals and practical signals.Testing results show that the proposed method can not only improve the ratio ofsignal to noise and decrease the mean square error, but also reserve more faultyfeatures of the raw signal.
Finally, the application of RSGWPT in fault detection and fault conditionidentification was studied. As to mechanical fault condition identification, aRSGWPT based method was proposed. The RSGWPT was employed to extract faultfeature and the neighborhood rough set theory was used to select fault features forreducing the decision table and improving the learning efficiency of the classifier.The RSGWPT were applied to detect incipient fault feature of a faulty ball bearingand the testing results showed that it could detect the weak faulty feature from thevibration signal effectively. The proposed fault condition identification method wasverified by applying to classify different working conditions of gearbox and valvetrains on a car engine. Testing results show that using the proposed method canextract more effective and distinguished statistical features for classification, andtherefore higher classification accuracy can be obtained.
首先，研究了第二代小波滤波器的时频特性，指出了采用第二代小波对机械故障信号分析时存在的问题。研究表明，第二代小波的尺度滤波器和小波滤波器在时域中是紧支撑的、对称的，并且具有冲击特征，可以用来提取故障信号中的瞬态冲击特征；第二代小波滤波器在频域中不具备理想的频率特性，频带之间存在交叠；第二代小波具备分析非平稳信号的能力，但是分析结果存在频率混叠问题，因此在故障诊断中的应用存在局限性。
其次，研究了第二代小波变换的频率混叠问题，提出了抑制频率混叠的方法，为故障特征的有效提取提供了理论依据。分析了分裂操作、预测操作、更新操作以及合成操作的性质，指出了第二代小波产生频率混叠的原因和抑制频率混叠的方法；研究了冗余第二代小波的性质，结果表明，冗余第二代小波在变换过程中不进行分裂和合成操作，因此不仅可以抑制分析结果中的频率混叠成分，而且使变换具备了平移不变性。从滤波器频率响应的角度解释了冗余第二代小波包产生频带错位的原因，提出了消除冗余第二代小波包频带错位的修正方法。
再次，提出了一种基于二维第二代小波变换的旋转机械振动信号压缩方法。在第二代小波变换和混合熵编码的信号压缩框架下，分析了旋转机械振动信号的准周期特性及其二维描述方法，提出了首先按照回转周期将振动信号从一维信号转换为二维矩阵，然后再采用二维小波变换对其进行压缩和重构的方法。试验结果表明，有损压缩与无损压缩技术相结合可以在保证信号重构精度的同时，进一步提高信号的压缩比；对于旋转机械振动信号，采用二维小波变换进行压缩具有更好的压缩性能。
然后，提出了一种基于空间自适应冗余第二代小波变换的信号消噪方法。空间自适应第二代小波可以针对每一尺度上的每个样本选择最佳的预测器，从而能够更好地锁定信号的局部特征。冗余小波变换具有抑制混叠特性和平移不变特性，在信号消噪时能够更加准确地估计噪声强度，并且可以缓解消噪后信号在奇异点处的吉布斯振荡现象。因此，空间自适应冗余第二代小波可以更好地应用于信号消噪。试验结果表明，基于空间自适应冗余第二代小波的信号消噪方法不仅可以提高信噪比、降低均方误差，而且能够保留更多的瞬态故障特征。
最后，对冗余第二代小波包变换在机械故障检测和故障模式分类中的应用进行了研究。针对机械故障模式分类问题，提出了一种基于冗余第二代小波包的故障模式分类方法，该方法利用冗余第二代小波包提取故障特征参数，利用邻域粗糙集对特征参数进行属性选择。通过对滚动轴承微弱故障进行检测以及对齿轮箱和汽车发动机气门机构多种故障工况模式进行分类，试验结果表明，基于冗余第二代小波包可以有效地检测出机械振动信号中的微弱故障特征，并且可以提取出分类能力更强的故障特征参数进行模式分类，进而得到更高的故障分类精度。
Growing demand for operation safety and high quality production requires thatdeviation of machine conditions from its normal setting should be identified andfixed promptly to reduce costly machine downtime and maintain high productivity.Therefore, research on effective mechanical equipments health monitoring anddiagnosis has been enhanced in recently years. The second generation wavelettransform (SGWT) is new wavelet theory and possesses many distinct properties. Forthe purpose of condition monitoring and fault diagnosis for mechanical equipment,fault feature extraction, signal compression, signal denoising and faulty conditionidentification techniques based on SGWT were studied in this dissertation.
Firstly, the nonstationary properties of mechanical faulty signals were discussed,and the necessity and effectiveness of using SGWT for nonstationary signalsprocessing were demonstrated. Studies show that the wavelet function and scalingfunction of SGWT in time domain are compactly supported and symmetrical, at thesame time they have the signature of impact. But in frequency domain, they do notpossess the ideal cut-off property. The SGWT has the ability to process nonstationarysignal, but the frequency aliasing is inhering in its analysis results. Therefore, theapplication of SGWT has some limitations in the field of fault diagnosis.
Secondly, the viewpoint of constructing redundant SGWT (RSGWT) to suppressfrequency aliasing was proposed, which provided the basis of effective fault featureextraction. Based on the analysis of split operation, prediction operation, updateoperation and merging operation of SGWT, the reasons and the suppressingapproach for frequency aliasing were pointed out. The anti-aliasing property,translation invariability property and the computational complexity of RSGWT wereanalyzed in detail. The frequency band derangement of redundant second generationwavelet packet transform (RSGWPT) was presented and also a modified version wasproposed.
Thirdly, a real-time signal compression method based on SGWT and hybridentropy coding was proposed. Within the framework of the proposed method, thequasi-periodic characteristic of rotating machinery vibration signal and the twodimension description for such data were analyzed. Based on this investigation, atwo dimension wavelet compression algorithm for such vibration data was proposed.Testing results show that combining both lossy and lossless compression techniquescan achieve higher compression ratio while maintaining the same reconstructionaccuracy. Also, as to rotating machinery vibration signal, employing two dimension wavelet transform can simultaneously eliminate the redundancy in both intra-cycleand inter-cycle effectively.
Fourthly, a signal denoising method based on the space-adaptive RSGWT wasproposed. The space-adaptive construction approach for SGWT is able to designwavelet function for each sample point in the signal. The redundant transform is ableto obtain a more accuracy noise intensity estimation and to suppress pseudo-Gibbsphenomena on the singularity points of the denoised signal. So using the space-adaptive RSGWT to signal denoising can get a better result than those obtained byusing other wavelet-based methods. The proposed denoising method wasinvestigated by applying to denoise both simulated signals and practical signals.Testing results show that the proposed method can not only improve the ratio ofsignal to noise and decrease the mean square error, but also reserve more faultyfeatures of the raw signal.
Finally, the application of RSGWPT in fault detection and fault conditionidentification was studied. As to mechanical fault condition identification, aRSGWPT based method was proposed. The RSGWPT was employed to extract faultfeature and the neighborhood rough set theory was used to select fault features forreducing the decision table and improving the learning efficiency of the classifier.The RSGWPT were applied to detect incipient fault feature of a faulty ball bearingand the testing results showed that it could detect the weak faulty feature from thevibration signal effectively. The proposed fault condition identification method wasverified by applying to classify different working conditions of gearbox and valvetrains on a car engine. Testing results show that using the proposed method canextract more effective and distinguished statistical features for classification, andtherefore higher classification accuracy can be obtained.
引文
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