基于多尺度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
机械设备的状态监测与故障诊断对于保证设备的安全、可靠、高效运行具有重要的理论意义和实用价值。通过采用各种信号处理方法从机械设备故障振动信号中提取故障特征信息,是机械设备故障诊断的关键。机械故障振动信号通常为非平稳振动信号,选择合适的非平稳信号分析方法是有效诊断机械故障的前提。
变转速条件下,以等时间间隔拾取的齿轮振动信号通常为低信噪比的多分量非平稳信号,这使得采用目前常用的信号处理技术从中提取故障特征信息非常困难。另一方面,转子发生碰摩故障的早期阶段,故障特征信号非常微弱,常淹没于强大的工频背景信号中,使得故障难以实现早期检测。多尺度线调频小波路径追踪(Multi-scale Chirplet Path Pursuit, MCPP)方法是近年来提出的一种自适应的非平稳信号分析方法,该方法具有自适应匹配分析信号中能量最大的信号分量并准确估计其瞬时频率的能力,适合用于分析频率呈大范围变化的非平稳振动信号,因此可用于解决变转速下齿轮振动信号故障特征难以提取以及转子早期碰摩故障特征难以检测的问题。论文在国家自然科学基金项目(项目编号：50875078)和高等学校博士学科点专项科研基金项目(项目编号：20090161110006)的资助下,将MCCP方法引入旋转机械故障诊断中,深入研究了MCPP方法在变转速齿轮故障诊断及转子碰摩故障早期检测中的应用。
论文主要研究工作和创新性成果有：
(1)针对升、降速状态下拾取的齿轮振动信号具有非平稳性,频谱分析将产生频谱模糊,且不具有物理意义的问题,分析了FrFT方法用于处理升、降速状态下拾取的齿轮振动信号的可行性及存在的问题,提出基于MCPP与FrFT的升、降速齿轮故障诊断方法,该方法采用MCPP方法从升、降速阶段获得的齿轮振动信号中提取适合采用FrFT分析的齿轮振动信号段,并估计FrFT的最佳分析阶次,从而实现FrFT在升、降速阶段齿轮故障诊断中的应用。
(2)针对变转速下齿轮振动信号的调制边频带会随转速变化而变化,使得解调分析变得非常困难的问题,将MCPP方法用于齿轮转速估计,以实现齿轮振动信号的阶比分析；针对工程实际中获取的齿轮振动信号信噪比低的特点,将多尺度形态学分析这一具有良好抗噪性能的方法应用于齿轮振动信号分析,提出基于MCPP方法的多尺度形态学解调方法,研究表明该方法适合用于低信噪比非平稳振动信号的解调分析。
(3)针对齿轮发生故障时,由于存在噪声与调制现象,振动信号表现出一定的非线性和非高斯性,使得其状态难以准确判断的问题,将双谱分析和MCPP方法相结合,提出了基于MCPP的阶比双谱分析方法,并将其应用于诊断变转速状态下的齿轮故障。实验研究表明,该方法能正确区分不同状态的齿轮。
(4)合理设置频率偏置搜寻范围和调频率搜寻范围是MCPP方法成功应用的关键,针对如何合理设置频率偏置搜寻范围和调频率搜寻范围的问题,提出了基于奇异值分解(Singular Value Decomposition)的MCPP方法,该方法将SVD方法用于振动信号预处理,从预处理后信号的Winger-ville分布时频图上得到对振动信号频率偏置范围及调频率范围的估计,有效解决了MCPP方法中频率搜寻范围和调频率搜寻范围的合理设置问题。
(5)针对转子发生碰摩故障的早期阶段,故障特征信号非常微弱,容易被强大的工频信号所淹没的问题,将基于MCPP与信号稀疏分解的多尺度线调频基稀疏信号分解(Multi-scale Chirplet Sparse Signal Decompositon, MCSSD)方法用于转子早期碰摩故障检测,提出了基于MCSSD的转子碰摩故障早期检测方法。仿真和实验分析验证了基于MCSSD的转子碰摩故障早期检测方法的有效性和优越性。
MCPP方法能以具有线性频率的chirplet原子逐段自适应匹配分析信号中能量最大的信号分量并准确估计其瞬时频率,根据MCPP方法的这一性质,本文针对变转速条件下拾取的齿轮振动信号具有低信噪比、非平稳、非线性、非高斯等特点,将MCPP方法分别与FrFT、多尺度形态学分析、双谱分析、SVD方法相结合,应用于变转速条件下的齿轮故障诊断。仿真分析和应用实例表明：将MCPP方法与FRFT、多尺度形态学分析等信号处理方法相结合,可实现各种信号处理方法的优势互补,能有效诊断变转速条件下的齿轮故障。本文还针对转子早期碰摩故障特征微弱而难以检测的问题,将基于MCPP与稀疏信号分解的MCSSD方法应用于转子碰摩故障早期检测,仿真分析和应用实例验证了MCSSD方法应用于转子碰摩故障早期检测的有效性。
The mechanical fault diagnosis is very important to ensure the normal operation of the rotating machinery. Therefore, it has extremely significant reality meaning and practical merit. As we all know, extracting the fault feature from the vibration signals is the key of fault diagnosis. Most of the fault vibration signals of the rotating machinery are non-stationary. Consequently, selecting appropriate non-stationary signal processing methods is the precondition for the success of fault diagnosis.
In general, the gear vibration signals which measured at equal-time-interval are the multi-component non-stationary signals and have the low signal-to-noise ratio, which makes it is very difficult to extract the fault features from the gear vibration signals with the existing signal processing techniques. On the other hand, under the early stage of rotor's rub-impact failure, the fault feature is very weak and is always hidden in the strong power frequency signal component. Hence, it is very difficult to be detected. The multi-scale chirplet path pursuit (MCPP) method is a non-stationary signal processing method which is proposed in recent years. With the best path algorithm of the MCPP method, the signal component with the largest energy in the original vibration signal and its instantaneous frequency can be estimated by connecting the selected chirplets and their corresponding piecewise linear frequencies, respectively. For this reason, the MCPP method is suitable to analyze the non-stationary signals whose instantaneous frequencies change in wide range. In the early stage of rotor's rub-impact failure, the power frequency component whose energy is the maximal among all the components in the rotor vibration signal can be picked up from the original rotor vibration signals by MCPP method. Thus, the MCPP method can be used to fault diagnosis of the gears with time-varying rotational speed, and can also be used to detect the weak rubbing fault features from the rotor vibration signal. Supported by National Natural Science Foundation (No.50875078) and Specialized Research Foundation for the Doctoral Program of Higher Education (No.20090161110006), this dissertation takes deep researches on the fault diagnosis of gears with time-varying rotating speed and the early detection of the rubbing fault of rotors based on MCPP method.
The main researches and the acquired innovative achievements are as follows:
(1) The gear vibration signals which obtained under speed-up and speed-down process are non-stationary. Therefore, the FFT-based spectral analysis of these gear vibration signals will be blurring, and have no physical meaning. Aimed at this problem, whether or not the FrFT method can be used to process the gear vibration signals which measured under speed-up and speed-down process is discussed, and the difficulties existing in the application of FrFT is further studied. Then, based on MCPP and FrFT, a novel approach for gear fault detection under speed-up and speed-down process is proposed. For a given gear vibration signal which collected under speed-up and speed-down process, the gear vibration signal segment for which FrFT is useful can be extracted from it (with the MCPP method), and the best order of FrFT for the extracted gear vibration signal segment can be calculated out, simultaneously. This is then followed by the FrFT spectrum of the extracted gear vibration signal segment. If the modulation sidebands are visible in the FrFT spectrum, we can judge the existing fault on the gear.
(2) Under the time-varying rotational speed condition, the modulation sidebands of the gear vibration signals are always varying with the rotational speed, which makes the demodulation analysis of these gear vibration signals are very difficult. Because the MCPP method can estimate the instantaneous frequency of the signal component whose energy is the largest among all the components of the original gear vibration signal, it can be used to estimate the rotational speed of the gear. Then, the order-tracking of the gear vibration signal is feasible. Furthermore, the gear vibration signal which obtained from the engineering practice always has the low signal-to-noise ratio. Hence, the morphology analysis which is an effective tool to extract impulsive signal components of the vibration signal and has the robust anti-noise ability is introduced. Then the order multi-scale morphology modulation method based on multi-scale chirplet path is proposed.
(3) When the mechanical systems broke down, the vibration signals are always companied with noise and modulations, and that they are always showed determined nonlinearity and non-Gaussian, which makes it very difficult to discern the condition of mechanical systems. Aimed at this problem, by combining the bi-spectrum analysis and the MCPP method, a novel approach namely the order bi-spectrum analysis based on the MCPP method is proposed to detect the fault of the gears under the time-varying rotational speed condition. The experimental study indicates that the proposed method can distinguish different conditions of gears.
(4) Setting up the suitable searching range of the frequency offset and the frequency slope rate is the key for a successful application of the MCPP method. In order to acquire the suitable searching range of the frequency offset and the frequency slope rate, the singular value decomposition (SVD) method is introduced, and then the MCPP method based on SVD is presented. The proposed method uses the SVD method for preprocessing the vibration signal, and then from the Wigner-ville spectrogram of the preprocessed signal, the scopes of the frequency offset and the frequency slope rate of the vibration signal can be roughly estimated.
(5) In the early stage of rotor's rub-impact failure, the fault feature is very weak, which is always hidden in the strong power frequency signal component. A new signal decomposition method, i.e. the multi-scale chirplet sparse signal decomposition (MCSSD) method which is proposed by combing MCPP and the sparse signal decomposition method is used for early detecting the rub-impact fault of the rotor systems. Then, an early detection method of the rubbing fault for rotors which based on the MCSSD method is proposed. The simulations and the experiments confirmed the validity and the superiority of the proposed method.
The MCPP method can use the chirplet atoms whose instantaneous frequency curves are linear straight lines to adaptively match the signal component with the largest energy in a multi-component vibration signal. Meanwhile, the instantaneous frequency of this signal component with the largest energy can be estimated by jointing the piecewise linear frequencies of the chirplets which is used by the MCPP method. Owing to the above ability, the MCPP method is suitable for processing non-stationary signals. Under the time-varying rotational speed condition, the gear vibration signals which measured at equal-time-interval always have low signal-to-noise ratio and possess some properties, such as non-stationarity, nonlinearity and non-Gaussianity, which makes the fault diagnosis more complex. Therefore, as a novel non-stationary signal processing technique, the MCPP method is introduced in and combined with FrFT, multi-scale morphology analysis, bi-spectrum, and SVD. Then, various combination methods are proposed and applied for fault diagnosis of gears under time-varying rotating speed. The results of the simulations and experiments indicate that the combination methods can be effectively applied to the fault diagnosis of gears under the variable rotational speed condition. Furthermore, considering at the early stage of rotor's rub-impact failure, the rub-impact fault feature is too weak to be detected directly. The MSCCD method which proposed by joining MCPP and the sparse signal decomposition method is applied to detect the feeble fault feature. The simulations and experiments show that the MSCCD method is feasible for characteristics detection of the rub-impact fault in the rotor system.
变转速条件下,以等时间间隔拾取的齿轮振动信号通常为低信噪比的多分量非平稳信号,这使得采用目前常用的信号处理技术从中提取故障特征信息非常困难。另一方面,转子发生碰摩故障的早期阶段,故障特征信号非常微弱,常淹没于强大的工频背景信号中,使得故障难以实现早期检测。多尺度线调频小波路径追踪(Multi-scale Chirplet Path Pursuit, MCPP)方法是近年来提出的一种自适应的非平稳信号分析方法,该方法具有自适应匹配分析信号中能量最大的信号分量并准确估计其瞬时频率的能力,适合用于分析频率呈大范围变化的非平稳振动信号,因此可用于解决变转速下齿轮振动信号故障特征难以提取以及转子早期碰摩故障特征难以检测的问题。论文在国家自然科学基金项目(项目编号：50875078)和高等学校博士学科点专项科研基金项目(项目编号：20090161110006)的资助下,将MCCP方法引入旋转机械故障诊断中,深入研究了MCPP方法在变转速齿轮故障诊断及转子碰摩故障早期检测中的应用。
论文主要研究工作和创新性成果有：
(1)针对升、降速状态下拾取的齿轮振动信号具有非平稳性,频谱分析将产生频谱模糊,且不具有物理意义的问题,分析了FrFT方法用于处理升、降速状态下拾取的齿轮振动信号的可行性及存在的问题,提出基于MCPP与FrFT的升、降速齿轮故障诊断方法,该方法采用MCPP方法从升、降速阶段获得的齿轮振动信号中提取适合采用FrFT分析的齿轮振动信号段,并估计FrFT的最佳分析阶次,从而实现FrFT在升、降速阶段齿轮故障诊断中的应用。
(2)针对变转速下齿轮振动信号的调制边频带会随转速变化而变化,使得解调分析变得非常困难的问题,将MCPP方法用于齿轮转速估计,以实现齿轮振动信号的阶比分析；针对工程实际中获取的齿轮振动信号信噪比低的特点,将多尺度形态学分析这一具有良好抗噪性能的方法应用于齿轮振动信号分析,提出基于MCPP方法的多尺度形态学解调方法,研究表明该方法适合用于低信噪比非平稳振动信号的解调分析。
(3)针对齿轮发生故障时,由于存在噪声与调制现象,振动信号表现出一定的非线性和非高斯性,使得其状态难以准确判断的问题,将双谱分析和MCPP方法相结合,提出了基于MCPP的阶比双谱分析方法,并将其应用于诊断变转速状态下的齿轮故障。实验研究表明,该方法能正确区分不同状态的齿轮。
(4)合理设置频率偏置搜寻范围和调频率搜寻范围是MCPP方法成功应用的关键,针对如何合理设置频率偏置搜寻范围和调频率搜寻范围的问题,提出了基于奇异值分解(Singular Value Decomposition)的MCPP方法,该方法将SVD方法用于振动信号预处理,从预处理后信号的Winger-ville分布时频图上得到对振动信号频率偏置范围及调频率范围的估计,有效解决了MCPP方法中频率搜寻范围和调频率搜寻范围的合理设置问题。
(5)针对转子发生碰摩故障的早期阶段,故障特征信号非常微弱,容易被强大的工频信号所淹没的问题,将基于MCPP与信号稀疏分解的多尺度线调频基稀疏信号分解(Multi-scale Chirplet Sparse Signal Decompositon, MCSSD)方法用于转子早期碰摩故障检测,提出了基于MCSSD的转子碰摩故障早期检测方法。仿真和实验分析验证了基于MCSSD的转子碰摩故障早期检测方法的有效性和优越性。
MCPP方法能以具有线性频率的chirplet原子逐段自适应匹配分析信号中能量最大的信号分量并准确估计其瞬时频率,根据MCPP方法的这一性质,本文针对变转速条件下拾取的齿轮振动信号具有低信噪比、非平稳、非线性、非高斯等特点,将MCPP方法分别与FrFT、多尺度形态学分析、双谱分析、SVD方法相结合,应用于变转速条件下的齿轮故障诊断。仿真分析和应用实例表明：将MCPP方法与FRFT、多尺度形态学分析等信号处理方法相结合,可实现各种信号处理方法的优势互补,能有效诊断变转速条件下的齿轮故障。本文还针对转子早期碰摩故障特征微弱而难以检测的问题,将基于MCPP与稀疏信号分解的MCSSD方法应用于转子碰摩故障早期检测,仿真分析和应用实例验证了MCSSD方法应用于转子碰摩故障早期检测的有效性。
The mechanical fault diagnosis is very important to ensure the normal operation of the rotating machinery. Therefore, it has extremely significant reality meaning and practical merit. As we all know, extracting the fault feature from the vibration signals is the key of fault diagnosis. Most of the fault vibration signals of the rotating machinery are non-stationary. Consequently, selecting appropriate non-stationary signal processing methods is the precondition for the success of fault diagnosis.
In general, the gear vibration signals which measured at equal-time-interval are the multi-component non-stationary signals and have the low signal-to-noise ratio, which makes it is very difficult to extract the fault features from the gear vibration signals with the existing signal processing techniques. On the other hand, under the early stage of rotor's rub-impact failure, the fault feature is very weak and is always hidden in the strong power frequency signal component. Hence, it is very difficult to be detected. The multi-scale chirplet path pursuit (MCPP) method is a non-stationary signal processing method which is proposed in recent years. With the best path algorithm of the MCPP method, the signal component with the largest energy in the original vibration signal and its instantaneous frequency can be estimated by connecting the selected chirplets and their corresponding piecewise linear frequencies, respectively. For this reason, the MCPP method is suitable to analyze the non-stationary signals whose instantaneous frequencies change in wide range. In the early stage of rotor's rub-impact failure, the power frequency component whose energy is the maximal among all the components in the rotor vibration signal can be picked up from the original rotor vibration signals by MCPP method. Thus, the MCPP method can be used to fault diagnosis of the gears with time-varying rotational speed, and can also be used to detect the weak rubbing fault features from the rotor vibration signal. Supported by National Natural Science Foundation (No.50875078) and Specialized Research Foundation for the Doctoral Program of Higher Education (No.20090161110006), this dissertation takes deep researches on the fault diagnosis of gears with time-varying rotating speed and the early detection of the rubbing fault of rotors based on MCPP method.
The main researches and the acquired innovative achievements are as follows:
(1) The gear vibration signals which obtained under speed-up and speed-down process are non-stationary. Therefore, the FFT-based spectral analysis of these gear vibration signals will be blurring, and have no physical meaning. Aimed at this problem, whether or not the FrFT method can be used to process the gear vibration signals which measured under speed-up and speed-down process is discussed, and the difficulties existing in the application of FrFT is further studied. Then, based on MCPP and FrFT, a novel approach for gear fault detection under speed-up and speed-down process is proposed. For a given gear vibration signal which collected under speed-up and speed-down process, the gear vibration signal segment for which FrFT is useful can be extracted from it (with the MCPP method), and the best order of FrFT for the extracted gear vibration signal segment can be calculated out, simultaneously. This is then followed by the FrFT spectrum of the extracted gear vibration signal segment. If the modulation sidebands are visible in the FrFT spectrum, we can judge the existing fault on the gear.
(2) Under the time-varying rotational speed condition, the modulation sidebands of the gear vibration signals are always varying with the rotational speed, which makes the demodulation analysis of these gear vibration signals are very difficult. Because the MCPP method can estimate the instantaneous frequency of the signal component whose energy is the largest among all the components of the original gear vibration signal, it can be used to estimate the rotational speed of the gear. Then, the order-tracking of the gear vibration signal is feasible. Furthermore, the gear vibration signal which obtained from the engineering practice always has the low signal-to-noise ratio. Hence, the morphology analysis which is an effective tool to extract impulsive signal components of the vibration signal and has the robust anti-noise ability is introduced. Then the order multi-scale morphology modulation method based on multi-scale chirplet path is proposed.
(3) When the mechanical systems broke down, the vibration signals are always companied with noise and modulations, and that they are always showed determined nonlinearity and non-Gaussian, which makes it very difficult to discern the condition of mechanical systems. Aimed at this problem, by combining the bi-spectrum analysis and the MCPP method, a novel approach namely the order bi-spectrum analysis based on the MCPP method is proposed to detect the fault of the gears under the time-varying rotational speed condition. The experimental study indicates that the proposed method can distinguish different conditions of gears.
(4) Setting up the suitable searching range of the frequency offset and the frequency slope rate is the key for a successful application of the MCPP method. In order to acquire the suitable searching range of the frequency offset and the frequency slope rate, the singular value decomposition (SVD) method is introduced, and then the MCPP method based on SVD is presented. The proposed method uses the SVD method for preprocessing the vibration signal, and then from the Wigner-ville spectrogram of the preprocessed signal, the scopes of the frequency offset and the frequency slope rate of the vibration signal can be roughly estimated.
(5) In the early stage of rotor's rub-impact failure, the fault feature is very weak, which is always hidden in the strong power frequency signal component. A new signal decomposition method, i.e. the multi-scale chirplet sparse signal decomposition (MCSSD) method which is proposed by combing MCPP and the sparse signal decomposition method is used for early detecting the rub-impact fault of the rotor systems. Then, an early detection method of the rubbing fault for rotors which based on the MCSSD method is proposed. The simulations and the experiments confirmed the validity and the superiority of the proposed method.
The MCPP method can use the chirplet atoms whose instantaneous frequency curves are linear straight lines to adaptively match the signal component with the largest energy in a multi-component vibration signal. Meanwhile, the instantaneous frequency of this signal component with the largest energy can be estimated by jointing the piecewise linear frequencies of the chirplets which is used by the MCPP method. Owing to the above ability, the MCPP method is suitable for processing non-stationary signals. Under the time-varying rotational speed condition, the gear vibration signals which measured at equal-time-interval always have low signal-to-noise ratio and possess some properties, such as non-stationarity, nonlinearity and non-Gaussianity, which makes the fault diagnosis more complex. Therefore, as a novel non-stationary signal processing technique, the MCPP method is introduced in and combined with FrFT, multi-scale morphology analysis, bi-spectrum, and SVD. Then, various combination methods are proposed and applied for fault diagnosis of gears under time-varying rotating speed. The results of the simulations and experiments indicate that the combination methods can be effectively applied to the fault diagnosis of gears under the variable rotational speed condition. Furthermore, considering at the early stage of rotor's rub-impact failure, the rub-impact fault feature is too weak to be detected directly. The MSCCD method which proposed by joining MCPP and the sparse signal decomposition method is applied to detect the feeble fault feature. The simulations and experiments show that the MSCCD method is feasible for characteristics detection of the rub-impact fault in the rotor system.
引文
[1]钟秉林,黄仁.机械故障诊断学.北京：机械工业出版社,2002.
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