基于形态分量分析和线调频小波路径追踪的机械故障诊断方法研究
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摘要
随着科学技术的发展，机械设备日益朝着大型化、高速化、连续化、自动化方向发展。为了保证机械设备的安全运行，设备状态监测与故障诊断技术越来越多的受到人们的重视。信号处理方法作为机械设备状态监测与故障诊断技术的核心，一直是国内外学者研究的重点。当机械设备发生故障时，其振动信号中包含了相应的故障信息，如何从振动信号中提取故障特征信息是机械设备状态监测和故障诊断研究的热点。
机械设备的振动信号通常是多个振源振动成分的混合体，对振动信号中各成分的有效分离，不仅可揭示各振源的振动形态，而且还可为机械设备故障的快速准确定位提供重要依据。形态分量分析(Morphological Component Analysis，MCA)方法通过构建不同形态的稀疏表示字典，能有效地实现信号中不同形态的信号成分的分离。另一方面，机械设备往往处于变转速下运行，直接对其振动信号进行分析，容易造成“频率模糊”现象。工程实际中通常采用阶次跟踪方法实现信号的平稳化。而在阶次跟踪方法中，如何获取转速信息则是关键。线调频小波路径追踪(Chirplet Path Pursuit，CPP)算法采用分段线性拟合的思想，能有效地估计出信号中的转速信息。论文在国家自然科学基金项目(项目编号：50875078，51275161)的资助下，研究用MCA方法和CPP算法从机械故障振动信号分离故障成分和提取故障特征。
论文主要研究工作和创新性成果有
(1)针对传统的包络解调方法不适合提取齿轮箱故障振动信号中多分量信号的调制信息的问题，提出了基于MCA的包络解调方法。该方法先用MCA方法将齿轮箱故障振动信号分解成谐振分量、冲击分量及噪声分量，再通过对谐振分量的解调分析诊断齿轮局部故障，同时，可通过对冲击分量的解调分析诊断轴承局部故障。利用该方法对齿轮箱滚动轴承局部故障振动信号进行分析，结果表明，该方法可有效提取信号中的调制信息，凸显故障特征；对包含齿轮和轴承局部故障的齿轮箱复合故障振动信号的分析表明，该方法可有效分离齿轮与轴承的局部故障特征。
(2)针对变转速下的齿轮故障调制信息具有时变特性，不能直接利用循环平稳解调分析从齿轮故障振动信号中提取调制信息的问题，提出了基于CPP算法的阶比循环平稳解调方法。该方法先用CPP算法从齿轮箱振动信号中估计转速信号，再根据估计出的转速信号对原始振动信号进行等角度重采样，最后对重采样信号进行循环平稳解调分析，提取齿轮箱振动信号中的调制信息。CPP算法在转速估计方面具有精度高和抗噪能力强的优点，而循环平稳解调则可以有效提取淹没在噪声中的周期性故障特征，因此该方法结合了二者的优点，适合于变转速齿轮故障振动信号中调制信息的提取。算法仿真和试验分析验证了该方法提取变转速下齿轮局部故障调制信息的有效性。
(3)针对变转速下齿轮箱复合故障调制信息提取的问题，提出了基于CPP的能量算子解调方法。该方法先采用CPP方法从齿轮箱振动信号中估计转速信号，以实现齿轮箱振动信号的等角度重采样；再利用能量算子解调对重采样信号进行解调分析，并根据解调谱中的调制信息来诊断变转速齿轮箱复合故障。通过算法仿真和应用实例对包含齿轮局部故障和轴承局部故障的变转速齿轮箱复合故障进行了分析，结果表明，该方法在无转速计的情况下能有效提取变转速齿轮箱中复合故障的故障特征。
(4)针对变转速齿轮箱中复合故障的故障特征分离的问题，提出了基于MCA与CPP的变速齿轮箱复合故障诊断方法。该方法利用MCA方法对齿轮箱复合故障振动信号进行分析，实现信号中各故障成分的分离；同时，采用CPP算法从齿轮箱振动信号中估计转速；再根据该转速信号对分离出的各故障成分进行包络阶次分析；最后，根据各故障成分的包络阶次谱进行故障诊断。对包含齿轮和轴承局部故障的变速齿轮箱复合故障的特征提取进行了算法仿真和应用实例分析，结果表明，该方法可在无转速计的情况下有效分离变速齿轮箱中复合故障的故障特征。
(5)针对齿轮早期故障时调制信息小，且正常的齿轮因几何形状和装配误差也会产生调制现象，从而出现误诊的问题，提出了基于瞬时频率和瞬时幅值的变转速齿轮故障诊断方法，该方法根据瞬时幅值和瞬时频率诊断变转速下的齿轮故障。利用该方法对变转速下的齿轮振动信号进行了分析，结果表明，该方法可有效地识别变转速下齿轮的健康状态。
MCA方法根据信号中各组成成分的形态差异，构建不同形态的稀疏表示字典，可有效分离信号中各组成成分。而CPP方法能从原始振动信号估计出转速信号，具有精度高和抗噪能力强的特点。本文结合MCA方法和CPP方法，将其应用于机械故障诊断中。算法仿真和应用实例表明，将MCA方法、CPP方法与循环平稳解调、能量算子解调等解调方法相结合应用于机械故障振动信号的分析，能有效地提取振动信号中的故障特征，具有良好的工程应用前景。
With the progress of science and technology, modern mechanical equipments aredeveloping toward large-scale, high-speed, continuum and automatization. Hence, toensure the normal operation of mechanical equipments, the condition monitoring andfault diagnosis technology receives more and more recognition. As the core ofcondition monitoring and fault diagnosis technology, signal processing method hasalways been the research focus for domestic and overseas scholars. When a localfailure occurs in a mechanical equipment, the fault information will be contained inits vibration signal. Therefore, how to extract the fault feature information from thevibration signal has become a hotspot in the area of machinery condition monitoringand fault diagnosis.
In general, the measured vibration signal is usually a mixture with manyvibration components generated by different vibration sources. It is significant toseparate each component from vibration signal effectively, which can not only rev ealeach source’s vibration mode, but also provide the basis for fast and accurate faultlocating. As a newly proposed signal processing method, the morphologicalcomponent analysis (MCA) method can effectively separate each signal componentwith distinct morphology from a vibration signal by constructing different sparsedictionaries with different forms. On the other hand, the mechanical equipment oftenoperates under changing rotating speed. In such a case, the frequency blurring oftenhappens when the vibration signal is directly analyzed by FFT-based spectrumanalysis. For this reason, the order tracking method is often applied to transformnon-stationary signal into stationary signal in engineering applications, and the key oforder tracking method is how to acquire an exact rotating speed. The chirplet pathpursuit (CPP) algorithm is another newly presented signal processing method. Byadopting the thought of piecewise linear approximation, the CPP algorithm canestimate a precise rotating speed signal from vibration signals. Supported by NationalNatural Science Foundation (No.50875078,51275161), this dissertation takes deepresearches on separating fault component and extracting fault characteristics frommechanical vibration signals by joint application of MCA method and CPP algorithm.
The main researches and innovative achievements of this dissertation are asfollows:
(1) Due to the limitation of traditional envelop demodulating method, which isnot suitable to extract modulation information from multi-component signals, a newenvelop demodulating method based on MCA is proposed. The vibration signal of agearbox can be decomposed into harmonic component, impulse component and noisecomponent by using MCA, and then the gear local failure can be dia gnosed in termsof the demodulation analysis of harmonic component, simultaneously, according tothe demodulation result of impulse component, the bearing local failure can also bediagnosed. The results, obtained by the analysis of vibration signals of a gearbox withfaulted bearings, show that the proposed method can effectively extract the faultdemodulation information and highlight the fault characteristic as well. The outcomes,acquired by the analysis of vibration signals of a gearbox with compound faultsconsisted of gear local failure and bearing local failure, indicate that the proposedmethod can separate the fault characteristics of gear and bearing effectively.
(2) The fault modulation information of a local failure gear has the character oftime-varying, thus, it cannot be directly extracted from the vibration signal by usingcyclostationary demodulating. Aimed at this problem, an order cyclostationarydemodulating approach based on CPP is proposed. Firstly, the rotating speed isestimated from the gearbox vibration signal by using CPP. And then, according to theestimated rotating speed, the angular domain resampling signal is got by even anglesampling the original signal. Finally, the modulation information of gearbox vibrationsignal can be extracted by using cyclostationary demodulating analysis to the angulardomain resampling signal. The CPP algorithm has the advantages of high accuracyand good anti-noise ability, moreover, the cyclostationary demodulating can extractthe cycle fault feature from noisy signal, hence, the proposed approach inherit themerit of both, and is suitable for extracting fault feature from vibration signal of faultgear with variable rotating speed. Simulation and application examples indicate thatthe proposed approach is an effectively way to extract the gear fault characteristicfrom vibration signal of a changing rotating speed gearbox.
(3) Aiming at the problem of extracting modulation information from vibrationsignal of a gearbox with compound faults under changing rotate speed, an energyoperator demodulating approach based on CPP is proposed. Firstly, the rotating speedis estimated using CPP algorithm so as to resample the gearbox vibration signal ineven angle. Then, the energy operator demodulating is employed to analyze theangular domain resampling signal. Finally, the compound faults diagnosis of achanging-speed gearbox is implemented in terms of the modulation information in the demodulating spectrum. The vibration signals of a changing-speed gearbox withcompound faults consisted of gear local failure and bearing local failure are analyzedby both simulation and example applications, and the analysis results demonstrate thatthe proposed method can effectively extract fault characteristic from achanging-speed gearbox with compound faults under the condition of lack oftachometer.
(4) Aiming at the problem of separating fault characteristics from a changingrotating speed gearbox with compound faults, a compound faults diagnosis methodbased on MCA and CPP is proposed. Firstly, each component with fault information isseparated from the gearbox vibration signal by using MCA; simultaneously, therotating speed is estimated from the gearbox vibration signal by using CPP. Secondly,according to the estimated rotating speed, each component is analyzed by envelopeorder spectrum. Lastly, the compound faults diagnosis are carried out according to theenvelop order spectrum of each component. The results, obtained by the analysis ofsimulation and application examples to the changing-speed gearbox with compoundfaults consisted of gear local failure and bearing local failure, prove that the proposedmethod can effectively separate fault characteristic from a changing rotating speedgearbox with compound faults.
(5) In the early stage of gear failure, the fault modulation information isrelatively weak, moreover, due to the geometric shape and assembly errors, thevibration signal of a normal gear can also generate amplitude modulation andfrequency modulation (AM-FM) phenomenon, consequently, the misdiagnosis mayhappens. In view of this problem, a fault diagnosis method for changing-speed gearbased on instantaneous frequency and instantaneous amplitude is proposed, and it isapplied to diagnose the local failure gear with variable rotating speed in terms ofinstantaneous frequency and instantaneous amplitude. The results, acquired by theanalysis of the gear vibration signal under variable rotating speed, exhibit that thehealth condition of a changing rotating speed gear can be effectively identified by theproposed approach.
According to the morphological difference of each component in the vibrationsignal, the MCA approach can effectively separate each component from the vibrationsignal by building different sparse dictionaries with different forms. While the CPPmethod can estimate rotating speed signal from the original vibration signal, and hasthe characters of high accuracy and good anti-noise ability. Therefore, thisdissertation combines the MCA and CPP approach and employs them to diagnose mechanical faults. Simulation and application examples indicate that the combinationmethods, which are obtained by combinating MCA and CPP with the demodulatingmethods such as cyclostationary demodulating and energy operator demodulating, canextract the fault feature from the mechanical fault vibration signals effectively, andconsequently have a good engineering application prospect.
机械设备的振动信号通常是多个振源振动成分的混合体，对振动信号中各成分的有效分离，不仅可揭示各振源的振动形态，而且还可为机械设备故障的快速准确定位提供重要依据。形态分量分析(Morphological Component Analysis，MCA)方法通过构建不同形态的稀疏表示字典，能有效地实现信号中不同形态的信号成分的分离。另一方面，机械设备往往处于变转速下运行，直接对其振动信号进行分析，容易造成“频率模糊”现象。工程实际中通常采用阶次跟踪方法实现信号的平稳化。而在阶次跟踪方法中，如何获取转速信息则是关键。线调频小波路径追踪(Chirplet Path Pursuit，CPP)算法采用分段线性拟合的思想，能有效地估计出信号中的转速信息。论文在国家自然科学基金项目(项目编号：50875078，51275161)的资助下，研究用MCA方法和CPP算法从机械故障振动信号分离故障成分和提取故障特征。
论文主要研究工作和创新性成果有
(1)针对传统的包络解调方法不适合提取齿轮箱故障振动信号中多分量信号的调制信息的问题，提出了基于MCA的包络解调方法。该方法先用MCA方法将齿轮箱故障振动信号分解成谐振分量、冲击分量及噪声分量，再通过对谐振分量的解调分析诊断齿轮局部故障，同时，可通过对冲击分量的解调分析诊断轴承局部故障。利用该方法对齿轮箱滚动轴承局部故障振动信号进行分析，结果表明，该方法可有效提取信号中的调制信息，凸显故障特征；对包含齿轮和轴承局部故障的齿轮箱复合故障振动信号的分析表明，该方法可有效分离齿轮与轴承的局部故障特征。
(2)针对变转速下的齿轮故障调制信息具有时变特性，不能直接利用循环平稳解调分析从齿轮故障振动信号中提取调制信息的问题，提出了基于CPP算法的阶比循环平稳解调方法。该方法先用CPP算法从齿轮箱振动信号中估计转速信号，再根据估计出的转速信号对原始振动信号进行等角度重采样，最后对重采样信号进行循环平稳解调分析，提取齿轮箱振动信号中的调制信息。CPP算法在转速估计方面具有精度高和抗噪能力强的优点，而循环平稳解调则可以有效提取淹没在噪声中的周期性故障特征，因此该方法结合了二者的优点，适合于变转速齿轮故障振动信号中调制信息的提取。算法仿真和试验分析验证了该方法提取变转速下齿轮局部故障调制信息的有效性。
(3)针对变转速下齿轮箱复合故障调制信息提取的问题，提出了基于CPP的能量算子解调方法。该方法先采用CPP方法从齿轮箱振动信号中估计转速信号，以实现齿轮箱振动信号的等角度重采样；再利用能量算子解调对重采样信号进行解调分析，并根据解调谱中的调制信息来诊断变转速齿轮箱复合故障。通过算法仿真和应用实例对包含齿轮局部故障和轴承局部故障的变转速齿轮箱复合故障进行了分析，结果表明，该方法在无转速计的情况下能有效提取变转速齿轮箱中复合故障的故障特征。
(4)针对变转速齿轮箱中复合故障的故障特征分离的问题，提出了基于MCA与CPP的变速齿轮箱复合故障诊断方法。该方法利用MCA方法对齿轮箱复合故障振动信号进行分析，实现信号中各故障成分的分离；同时，采用CPP算法从齿轮箱振动信号中估计转速；再根据该转速信号对分离出的各故障成分进行包络阶次分析；最后，根据各故障成分的包络阶次谱进行故障诊断。对包含齿轮和轴承局部故障的变速齿轮箱复合故障的特征提取进行了算法仿真和应用实例分析，结果表明，该方法可在无转速计的情况下有效分离变速齿轮箱中复合故障的故障特征。
(5)针对齿轮早期故障时调制信息小，且正常的齿轮因几何形状和装配误差也会产生调制现象，从而出现误诊的问题，提出了基于瞬时频率和瞬时幅值的变转速齿轮故障诊断方法，该方法根据瞬时幅值和瞬时频率诊断变转速下的齿轮故障。利用该方法对变转速下的齿轮振动信号进行了分析，结果表明，该方法可有效地识别变转速下齿轮的健康状态。
MCA方法根据信号中各组成成分的形态差异，构建不同形态的稀疏表示字典，可有效分离信号中各组成成分。而CPP方法能从原始振动信号估计出转速信号，具有精度高和抗噪能力强的特点。本文结合MCA方法和CPP方法，将其应用于机械故障诊断中。算法仿真和应用实例表明，将MCA方法、CPP方法与循环平稳解调、能量算子解调等解调方法相结合应用于机械故障振动信号的分析，能有效地提取振动信号中的故障特征，具有良好的工程应用前景。
With the progress of science and technology, modern mechanical equipments aredeveloping toward large-scale, high-speed, continuum and automatization. Hence, toensure the normal operation of mechanical equipments, the condition monitoring andfault diagnosis technology receives more and more recognition. As the core ofcondition monitoring and fault diagnosis technology, signal processing method hasalways been the research focus for domestic and overseas scholars. When a localfailure occurs in a mechanical equipment, the fault information will be contained inits vibration signal. Therefore, how to extract the fault feature information from thevibration signal has become a hotspot in the area of machinery condition monitoringand fault diagnosis.
In general, the measured vibration signal is usually a mixture with manyvibration components generated by different vibration sources. It is significant toseparate each component from vibration signal effectively, which can not only rev ealeach source’s vibration mode, but also provide the basis for fast and accurate faultlocating. As a newly proposed signal processing method, the morphologicalcomponent analysis (MCA) method can effectively separate each signal componentwith distinct morphology from a vibration signal by constructing different sparsedictionaries with different forms. On the other hand, the mechanical equipment oftenoperates under changing rotating speed. In such a case, the frequency blurring oftenhappens when the vibration signal is directly analyzed by FFT-based spectrumanalysis. For this reason, the order tracking method is often applied to transformnon-stationary signal into stationary signal in engineering applications, and the key oforder tracking method is how to acquire an exact rotating speed. The chirplet pathpursuit (CPP) algorithm is another newly presented signal processing method. Byadopting the thought of piecewise linear approximation, the CPP algorithm canestimate a precise rotating speed signal from vibration signals. Supported by NationalNatural Science Foundation (No.50875078,51275161), this dissertation takes deepresearches on separating fault component and extracting fault characteristics frommechanical vibration signals by joint application of MCA method and CPP algorithm.
The main researches and innovative achievements of this dissertation are asfollows:
(1) Due to the limitation of traditional envelop demodulating method, which isnot suitable to extract modulation information from multi-component signals, a newenvelop demodulating method based on MCA is proposed. The vibration signal of agearbox can be decomposed into harmonic component, impulse component and noisecomponent by using MCA, and then the gear local failure can be dia gnosed in termsof the demodulation analysis of harmonic component, simultaneously, according tothe demodulation result of impulse component, the bearing local failure can also bediagnosed. The results, obtained by the analysis of vibration signals of a gearbox withfaulted bearings, show that the proposed method can effectively extract the faultdemodulation information and highlight the fault characteristic as well. The outcomes,acquired by the analysis of vibration signals of a gearbox with compound faultsconsisted of gear local failure and bearing local failure, indicate that the proposedmethod can separate the fault characteristics of gear and bearing effectively.
(2) The fault modulation information of a local failure gear has the character oftime-varying, thus, it cannot be directly extracted from the vibration signal by usingcyclostationary demodulating. Aimed at this problem, an order cyclostationarydemodulating approach based on CPP is proposed. Firstly, the rotating speed isestimated from the gearbox vibration signal by using CPP. And then, according to theestimated rotating speed, the angular domain resampling signal is got by even anglesampling the original signal. Finally, the modulation information of gearbox vibrationsignal can be extracted by using cyclostationary demodulating analysis to the angulardomain resampling signal. The CPP algorithm has the advantages of high accuracyand good anti-noise ability, moreover, the cyclostationary demodulating can extractthe cycle fault feature from noisy signal, hence, the proposed approach inherit themerit of both, and is suitable for extracting fault feature from vibration signal of faultgear with variable rotating speed. Simulation and application examples indicate thatthe proposed approach is an effectively way to extract the gear fault characteristicfrom vibration signal of a changing rotating speed gearbox.
(3) Aiming at the problem of extracting modulation information from vibrationsignal of a gearbox with compound faults under changing rotate speed, an energyoperator demodulating approach based on CPP is proposed. Firstly, the rotating speedis estimated using CPP algorithm so as to resample the gearbox vibration signal ineven angle. Then, the energy operator demodulating is employed to analyze theangular domain resampling signal. Finally, the compound faults diagnosis of achanging-speed gearbox is implemented in terms of the modulation information in the demodulating spectrum. The vibration signals of a changing-speed gearbox withcompound faults consisted of gear local failure and bearing local failure are analyzedby both simulation and example applications, and the analysis results demonstrate thatthe proposed method can effectively extract fault characteristic from achanging-speed gearbox with compound faults under the condition of lack oftachometer.
(4) Aiming at the problem of separating fault characteristics from a changingrotating speed gearbox with compound faults, a compound faults diagnosis methodbased on MCA and CPP is proposed. Firstly, each component with fault information isseparated from the gearbox vibration signal by using MCA; simultaneously, therotating speed is estimated from the gearbox vibration signal by using CPP. Secondly,according to the estimated rotating speed, each component is analyzed by envelopeorder spectrum. Lastly, the compound faults diagnosis are carried out according to theenvelop order spectrum of each component. The results, obtained by the analysis ofsimulation and application examples to the changing-speed gearbox with compoundfaults consisted of gear local failure and bearing local failure, prove that the proposedmethod can effectively separate fault characteristic from a changing rotating speedgearbox with compound faults.
(5) In the early stage of gear failure, the fault modulation information isrelatively weak, moreover, due to the geometric shape and assembly errors, thevibration signal of a normal gear can also generate amplitude modulation andfrequency modulation (AM-FM) phenomenon, consequently, the misdiagnosis mayhappens. In view of this problem, a fault diagnosis method for changing-speed gearbased on instantaneous frequency and instantaneous amplitude is proposed, and it isapplied to diagnose the local failure gear with variable rotating speed in terms ofinstantaneous frequency and instantaneous amplitude. The results, acquired by theanalysis of the gear vibration signal under variable rotating speed, exhibit that thehealth condition of a changing rotating speed gear can be effectively identified by theproposed approach.
According to the morphological difference of each component in the vibrationsignal, the MCA approach can effectively separate each component from the vibrationsignal by building different sparse dictionaries with different forms. While the CPPmethod can estimate rotating speed signal from the original vibration signal, and hasthe characters of high accuracy and good anti-noise ability. Therefore, thisdissertation combines the MCA and CPP approach and employs them to diagnose mechanical faults. Simulation and application examples indicate that the combinationmethods, which are obtained by combinating MCA and CPP with the demodulatingmethods such as cyclostationary demodulating and energy operator demodulating, canextract the fault feature from the mechanical fault vibration signals effectively, andconsequently have a good engineering application prospect.
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