基于循环平稳信号处理的滚动轴承故障诊断方法研究
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摘要
滚动轴承是机械设备中常用、关键的零部件,其工作状态是否正常直接关系到整台机组乃至整条生产线的生产质量和安全。研究滚动轴承的监测和诊断技术,对于避免重大事故及变革维修体制等具有重要的理论研究价值和实际应用意义。
本文在分析了滚动轴承现有诊断技术的基础上,根据滚动轴承近似对称的结构特征及其旋转的工作方式,针对当轴承元件出现损伤时,由损伤点引起冲击调制使观测到的振动信号表现出循环平稳性这一现象,深入研究了基于循环统平稳信号处理的滚动轴承振动信号特征提取方法。具体内容如下:
1)研究了一阶循环统计量。基于旋转机械振动中常见的调幅振动信号模型,证明了这类信号的循环平稳性。对比了循环均值和时域同步平均分析,指出这两者在提取信号中的一阶周期性特征信息方面具有相同的效果,但是二者的理论基石却完全不一样。对时域同步平均方法予以改进,得到循环时变同步平均方法,该方法能够更全面地反映一阶多周期信号中的多周期特征。研究还指出,循环均值不能实现对调幅信号的解调功能,因此不适合用来分析调幅信号。
2)深入研究了循环自相关函数的解调性能。对比循环自相关函数解调、基于Hilbert变换的包络解调及平方解调,指出了它们虽在解调时具有相似的功效,但却存在本质上的差异:循环自相关函数是通过非线性二次变换和循环因子的共同作用获取循环平稳信号中的周期成分,将调幅信息直接解调到循环频率轴上;包络解调法有解调功能,却忽略了载波信息;而平方解调则是通过平方变换,实现对信号解调。包络解调和平方解调都只是实现了循环自相关函数解调的局部功能。
3)对循环自相关函数在特定循环频率处的切片信息进行了研究。对比了循环自相关函数的模、实部和虚部切片分析。结果表明:循环自相关函数模的切片分析可以在不同循环频率处获取到调幅振动信号中的不同特征信息,并且在某些特定的循环频率处,可提取出单一的特征频率成分。在理论研究和仿真分析的基础上,找出了循环自相关函数模的切片分析的一般性规律。
4)研究了谱相关密度函数。引入时域平滑循环周期图法,用于获取循环平稳信号的谱相关密度函数。谱相关密度函数通常可以采用对称与非对称两种变换形式加以实现。不同的变换形式会对谱相关密度函数的信息具体表现形式产生影响。推导了谱相关密度函数的一般表达式,给出了一般换形式下谱相关密度函数分布规律图。同时研究指出尽管变换形式不同,但是谱相关密度函数反映的信息特征实质是一样的,都可以揭示出循环平稳信号中的全部信息。
5)针对故障滚动轴承冲击调幅振动信号的特点,改进了循环平稳度的定义,用于判别非平稳信号中包含周期成分强弱的程度。针对具有不同循环平稳度的非平稳信号,研究指出要采用不同的信号分析与处理方法,才能有效地识别和诊断。
6)噪声干扰是信号特征提取中会遇到的一个重要问题,本文探讨性研究了白噪声对循环谱密度的影响,指出了二阶循环统计量对加性白噪声的渐进免疫性能。
7)本文也研究了高阶循环统计量理论及其实现方法。在理论研究的基础上,本文对比了二阶统计量、高阶统计量和循环统计量的一些性能指标,指出高阶循环统计量具有更好的抗噪声干扰性能。将二阶循环统计量的切片分析理论引入到高阶循环统计量分析中,能够更加直观地将信号的高阶循环统计量分布表述出来,为高阶循环统计量的工程应用奠定了一定的基础。但是,高阶循环统计量具有算法复杂、计算效率低等缺陷,在一定的程度上限制了其实用性。
8)鉴于二阶循环平稳分析对白噪声的渐进免疫性、对有色噪声的敏感性以及高阶循环平稳分析的计算复杂性,传统的循环平稳分析方法对几乎循环平稳信号的循环平稳特征提取存在缺憾。本文根据Morlet小波自身的特点以及连续小波变换的优越性,针对弱冲击调制信号,采用最小熵Morlet匹配小波基选择原理选择适合提取冲击特征的小波基,利用最大似然估计阈值消噪方法,实现弱冲击信号的冲击特征强化。对于旋转机械早期故障而言,因为早期故障引起的弱冲击调制导致了几乎循环平稳现象,利用基于Morlet小波的弱冲击信号冲击特征强化方法,强化这类几乎循环平稳信号的循环平稳特征,从而为这类信号有效地进行循环平稳分析奠定了基础。
9)本文还研究了故障滚动轴承的循环平稳振动模型,在传统振动模型基础上,本文引入冲击的幅值、周期以及响应等三个时变量因子,得到了可以模拟内圈、外圈以及滚动体等故障的综合振动模型。新模型与传统模型相比,更加贴近故障滚动轴承的实际情况。并通过仿真实验,证明了该模型的循环平稳性。
10)最后,本文进行了大量的实验研究,对不同类型故障的滚动轴承,对比了传统功率谱分析、包络分析、平方解调分析、二阶循环平稳分析、循环双谱分析,基于Morlet小波的循环平稳特征强化分析等分析方法的分析结果,论证了理论研究成果的正确性和有效性。将循环统计量分析方法和改进的BP神经网络相结合,构建了一个滚动轴承故障智能诊断系统,为滚动轴承的智能诊断提供了一种新的解决思路。
Rolling element bearing is one of the most widely used components in almost all kinds of machinery. Its working condition has influence on product quality and working safety in industry directly. So it is very significant to research on bearing condition monitoring and fault diagnosis techniques, especially for bearing early fault.
Some techniques of condition monitoring for rolling element bearing have been analyzed in the thesis. Since symmetry or approximately symmetry of working parts of a bearing and its uniquely periodical rotating working mode, vibration of a destroyed bearing generally exhibits strong periodicity. These periodical pulses bring amplitude modulation (AM) characteristic. Considering the above reasons, a new signal processing method for bearing condition monitoring is studied in this thesis.
Firstly, first-order cyclic statistics, named Cyclic Mean (CM) value, is studied. An example result has been obtained by cyclic mean for the amplitude modulation signal, which proved the signal exhibit cyclostationarity. The results of CM analysis and Synchronous Average (SA) analysis are compared. It is pointed out that the two methods possess similar performance for identifying the first-order periodical feature of the signal. However, their basis theories are different, the CM is based on sine-wave generating algorithm, but the SA is just based on the average estimate. A modified Cyclic Temporary Synchronous Average (CTSA) method is put forward. The CTSA analysis method can exhibit the first-order multi-periodical characteristics of the signal much more clearly. Our research also indicates that cyclic mean does not possess demodulation function.
A further conclusion is introduced that Cyclic Autocorrelation Function (CAF) possesses demodulation capability. Comparing CAF with envelope demodulation and square demodulation, it is proved that the three methods have a similar performance on extracting feature frequencies of an AM signal. However, the three methods also have essential difference. CAF can obtain the periodical information for a cyclostationary signal by nonlinear transform and cyclic factor. It demodulates the AM components to cyclic frequency axis directly. Envelop demodulation technique only extracts AM frequencies from the original signal, and does not obtain any information about carrier wave. Square demodulation technique is just a special part of the CAF when time lag is equal to zero.
Further study focuses on the slices of amplitude of CAF at different cyclic frequencies. The results show that the slices of the module of CAF can extract different information corresponding to different cyclic frequencies. At some certain cyclic frequencies, the module of CAF even can extract pure feature frequency. Several examples have been analyzed and common rules are summarized.
Spectrum Correlation Density Function (SCDF) is studied in this thesis. The time smoothed and frequency smoothed cyclic periodogram are imported to obtain SCDF. Slices of SCDF for some cyclic frequencies are analyzed, and the similar rules are obtained as CAF. There are many kinds of transform modes of SCDF. The symmetrical and nonsymmetrical transformations are commonly used. The result of SCDF via a usual transformation is deducted. The result shows that different transform will affect information expression for SCDF. However, the essences which the SCDF provided are the same.
Degree of Cyclostationary (DCS) is discussed, and a special DCS definition for engineering application is provided. It is a scale for the intensity of periodical information for non-stationary signal. A viewpoint is referred that corresponding signal processing technique should be adopted to analyze signal with different DCS.
Higher-order cyclic statistics (HOCS) theory is also discussed. Some performances have been compared with second-order statistics, higher-order statistics and higher-order cyclic statistics. The conclusion is that HOCS has better anti-interference performance. The slice analysis method of SOCS is extended to HOCS domain, which can express the results of HOCS more clearly. However, HOCS has some limitations, such as the implement method is complexly and the calculation data is too long.
A new cyclostationary characteristic strengthening method of weak cyclostationary signal based on Morlet Continuous Wavelet Transform (CWT) is advanced. This method uses the characteristics of Morlet Wavelet and the advantage of CWT, according to the minimum of entropy principle and the threshold maximum likelihood estimate method, and at last can strengthen the cyclostationary characteristics of the weak cyclostationary signal.
The traditional vibration model of fault rolling element bearings is modified and gets a new cyclic model. The new model uses three random time-varying parameters to simulate the time-varying of the amplitude, the period of the impulse and the response of the system to this impulse. These improvements make the new model approach to the real work condition of rolling element bearings much more closely.
Experimental research is well done at last. Several different kinds of rolling element bearing local faults are investigated. The vibration data are acquired and analyzed, the results verifies the accuracy of corresponding theoretical research in the present study and demonstrates its availability and feasibility in engineering practices. An intelligence diagnosis system of rolling element bearings based on cyclic statistics and BP Neural Networks is established, which provides a new kind of method to solve the intelligence diagnosis problem of rolling element bearings.
本文在分析了滚动轴承现有诊断技术的基础上,根据滚动轴承近似对称的结构特征及其旋转的工作方式,针对当轴承元件出现损伤时,由损伤点引起冲击调制使观测到的振动信号表现出循环平稳性这一现象,深入研究了基于循环统平稳信号处理的滚动轴承振动信号特征提取方法。具体内容如下:
1)研究了一阶循环统计量。基于旋转机械振动中常见的调幅振动信号模型,证明了这类信号的循环平稳性。对比了循环均值和时域同步平均分析,指出这两者在提取信号中的一阶周期性特征信息方面具有相同的效果,但是二者的理论基石却完全不一样。对时域同步平均方法予以改进,得到循环时变同步平均方法,该方法能够更全面地反映一阶多周期信号中的多周期特征。研究还指出,循环均值不能实现对调幅信号的解调功能,因此不适合用来分析调幅信号。
2)深入研究了循环自相关函数的解调性能。对比循环自相关函数解调、基于Hilbert变换的包络解调及平方解调,指出了它们虽在解调时具有相似的功效,但却存在本质上的差异:循环自相关函数是通过非线性二次变换和循环因子的共同作用获取循环平稳信号中的周期成分,将调幅信息直接解调到循环频率轴上;包络解调法有解调功能,却忽略了载波信息;而平方解调则是通过平方变换,实现对信号解调。包络解调和平方解调都只是实现了循环自相关函数解调的局部功能。
3)对循环自相关函数在特定循环频率处的切片信息进行了研究。对比了循环自相关函数的模、实部和虚部切片分析。结果表明:循环自相关函数模的切片分析可以在不同循环频率处获取到调幅振动信号中的不同特征信息,并且在某些特定的循环频率处,可提取出单一的特征频率成分。在理论研究和仿真分析的基础上,找出了循环自相关函数模的切片分析的一般性规律。
4)研究了谱相关密度函数。引入时域平滑循环周期图法,用于获取循环平稳信号的谱相关密度函数。谱相关密度函数通常可以采用对称与非对称两种变换形式加以实现。不同的变换形式会对谱相关密度函数的信息具体表现形式产生影响。推导了谱相关密度函数的一般表达式,给出了一般换形式下谱相关密度函数分布规律图。同时研究指出尽管变换形式不同,但是谱相关密度函数反映的信息特征实质是一样的,都可以揭示出循环平稳信号中的全部信息。
5)针对故障滚动轴承冲击调幅振动信号的特点,改进了循环平稳度的定义,用于判别非平稳信号中包含周期成分强弱的程度。针对具有不同循环平稳度的非平稳信号,研究指出要采用不同的信号分析与处理方法,才能有效地识别和诊断。
6)噪声干扰是信号特征提取中会遇到的一个重要问题,本文探讨性研究了白噪声对循环谱密度的影响,指出了二阶循环统计量对加性白噪声的渐进免疫性能。
7)本文也研究了高阶循环统计量理论及其实现方法。在理论研究的基础上,本文对比了二阶统计量、高阶统计量和循环统计量的一些性能指标,指出高阶循环统计量具有更好的抗噪声干扰性能。将二阶循环统计量的切片分析理论引入到高阶循环统计量分析中,能够更加直观地将信号的高阶循环统计量分布表述出来,为高阶循环统计量的工程应用奠定了一定的基础。但是,高阶循环统计量具有算法复杂、计算效率低等缺陷,在一定的程度上限制了其实用性。
8)鉴于二阶循环平稳分析对白噪声的渐进免疫性、对有色噪声的敏感性以及高阶循环平稳分析的计算复杂性,传统的循环平稳分析方法对几乎循环平稳信号的循环平稳特征提取存在缺憾。本文根据Morlet小波自身的特点以及连续小波变换的优越性,针对弱冲击调制信号,采用最小熵Morlet匹配小波基选择原理选择适合提取冲击特征的小波基,利用最大似然估计阈值消噪方法,实现弱冲击信号的冲击特征强化。对于旋转机械早期故障而言,因为早期故障引起的弱冲击调制导致了几乎循环平稳现象,利用基于Morlet小波的弱冲击信号冲击特征强化方法,强化这类几乎循环平稳信号的循环平稳特征,从而为这类信号有效地进行循环平稳分析奠定了基础。
9)本文还研究了故障滚动轴承的循环平稳振动模型,在传统振动模型基础上,本文引入冲击的幅值、周期以及响应等三个时变量因子,得到了可以模拟内圈、外圈以及滚动体等故障的综合振动模型。新模型与传统模型相比,更加贴近故障滚动轴承的实际情况。并通过仿真实验,证明了该模型的循环平稳性。
10)最后,本文进行了大量的实验研究,对不同类型故障的滚动轴承,对比了传统功率谱分析、包络分析、平方解调分析、二阶循环平稳分析、循环双谱分析,基于Morlet小波的循环平稳特征强化分析等分析方法的分析结果,论证了理论研究成果的正确性和有效性。将循环统计量分析方法和改进的BP神经网络相结合,构建了一个滚动轴承故障智能诊断系统,为滚动轴承的智能诊断提供了一种新的解决思路。
Rolling element bearing is one of the most widely used components in almost all kinds of machinery. Its working condition has influence on product quality and working safety in industry directly. So it is very significant to research on bearing condition monitoring and fault diagnosis techniques, especially for bearing early fault.
Some techniques of condition monitoring for rolling element bearing have been analyzed in the thesis. Since symmetry or approximately symmetry of working parts of a bearing and its uniquely periodical rotating working mode, vibration of a destroyed bearing generally exhibits strong periodicity. These periodical pulses bring amplitude modulation (AM) characteristic. Considering the above reasons, a new signal processing method for bearing condition monitoring is studied in this thesis.
Firstly, first-order cyclic statistics, named Cyclic Mean (CM) value, is studied. An example result has been obtained by cyclic mean for the amplitude modulation signal, which proved the signal exhibit cyclostationarity. The results of CM analysis and Synchronous Average (SA) analysis are compared. It is pointed out that the two methods possess similar performance for identifying the first-order periodical feature of the signal. However, their basis theories are different, the CM is based on sine-wave generating algorithm, but the SA is just based on the average estimate. A modified Cyclic Temporary Synchronous Average (CTSA) method is put forward. The CTSA analysis method can exhibit the first-order multi-periodical characteristics of the signal much more clearly. Our research also indicates that cyclic mean does not possess demodulation function.
A further conclusion is introduced that Cyclic Autocorrelation Function (CAF) possesses demodulation capability. Comparing CAF with envelope demodulation and square demodulation, it is proved that the three methods have a similar performance on extracting feature frequencies of an AM signal. However, the three methods also have essential difference. CAF can obtain the periodical information for a cyclostationary signal by nonlinear transform and cyclic factor. It demodulates the AM components to cyclic frequency axis directly. Envelop demodulation technique only extracts AM frequencies from the original signal, and does not obtain any information about carrier wave. Square demodulation technique is just a special part of the CAF when time lag is equal to zero.
Further study focuses on the slices of amplitude of CAF at different cyclic frequencies. The results show that the slices of the module of CAF can extract different information corresponding to different cyclic frequencies. At some certain cyclic frequencies, the module of CAF even can extract pure feature frequency. Several examples have been analyzed and common rules are summarized.
Spectrum Correlation Density Function (SCDF) is studied in this thesis. The time smoothed and frequency smoothed cyclic periodogram are imported to obtain SCDF. Slices of SCDF for some cyclic frequencies are analyzed, and the similar rules are obtained as CAF. There are many kinds of transform modes of SCDF. The symmetrical and nonsymmetrical transformations are commonly used. The result of SCDF via a usual transformation is deducted. The result shows that different transform will affect information expression for SCDF. However, the essences which the SCDF provided are the same.
Degree of Cyclostationary (DCS) is discussed, and a special DCS definition for engineering application is provided. It is a scale for the intensity of periodical information for non-stationary signal. A viewpoint is referred that corresponding signal processing technique should be adopted to analyze signal with different DCS.
Higher-order cyclic statistics (HOCS) theory is also discussed. Some performances have been compared with second-order statistics, higher-order statistics and higher-order cyclic statistics. The conclusion is that HOCS has better anti-interference performance. The slice analysis method of SOCS is extended to HOCS domain, which can express the results of HOCS more clearly. However, HOCS has some limitations, such as the implement method is complexly and the calculation data is too long.
A new cyclostationary characteristic strengthening method of weak cyclostationary signal based on Morlet Continuous Wavelet Transform (CWT) is advanced. This method uses the characteristics of Morlet Wavelet and the advantage of CWT, according to the minimum of entropy principle and the threshold maximum likelihood estimate method, and at last can strengthen the cyclostationary characteristics of the weak cyclostationary signal.
The traditional vibration model of fault rolling element bearings is modified and gets a new cyclic model. The new model uses three random time-varying parameters to simulate the time-varying of the amplitude, the period of the impulse and the response of the system to this impulse. These improvements make the new model approach to the real work condition of rolling element bearings much more closely.
Experimental research is well done at last. Several different kinds of rolling element bearing local faults are investigated. The vibration data are acquired and analyzed, the results verifies the accuracy of corresponding theoretical research in the present study and demonstrates its availability and feasibility in engineering practices. An intelligence diagnosis system of rolling element bearings based on cyclic statistics and BP Neural Networks is established, which provides a new kind of method to solve the intelligence diagnosis problem of rolling element bearings.
引文
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