自适应形态滤波与局域波分解理论及滚动轴承故障诊断
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摘要
振动信号是滚动轴承运行状态的信息载体，周期性重复冲击及幅值调制是滚动轴承在缺陷与故障时的核心特征，这两者均有一个共同的特点，即不仅与时间有关，而且与频率也密切相关，因此如果割裂时频特征，仅仅从时域或频域的角度分析这类信号，则很难获得有关信号特征的全貌，而从联合的时频域的角度来识别这类信号，无疑会提高诊断的准确性和可靠性。另外强背景噪声及冲击振动也是滚动轴承振动信号不可忽视的特点，因此本文拟采用自适应形态滤波法，以滚动轴承的故障特征频率为判据构造自适应多结构多尺度形态滤波器进行背景噪声的滤除及冲击信号的提取，在此基础上结合局域波分解法对滚动轴承振动信号进行处理，进而提取有效的特征参量局域波相关尺度熵，最后利用模糊聚类的方法对滚动轴承的运行状态进行识别，主要工作如下：
（1）数学形态学摒弃了传统数值建模及分析的观点，从集合的角度刻画和分析被处理信号，设计了一个“探针”（结构元素）的来探测信号的信息，利用该探针在被处理信号中不断平移,完成信号与结构元素间的匹配,达到信号提取、细节保持和噪声抑制的目的。按照振动信号处理中频响函数测量原理，研究了结构元素宽度、采样频率、分析点数与滤波特性间的定量关系，给出了数学形态滤波器特性的定量描述。提出一种自适应多结构多尺度形态组合滤波方法，详细讨论自适应多结构多尺度结构元素的构造，以被处理信号的特征频率强度系数为判据，利用敏感的结构元素组合出多尺度多结构的自适应均值滤波器，取得了较好的低频信号提取效果。
（2）局域波法是基于信号局部特征的自适应时变分解算法，其分解过程就是把被处理信号分解成多个IMF分量和一个趋势项的和，且局域波分解的基函数是根据被处理信号自适应产生，因此具有良好的信号局部表征能力。在详细分析局域波分解产生端点效应机理的基础上，提出了端点匹配特征波延拓抑制端点效应的方法，该方法在波形匹配过程中充分考虑了被处理信号端点处的数据特性，将载入数据的首末端点处的数据作为匹配基元，从而改变了端点处不受约束的状况，仿真测试结果表明有效抑制了端点效应。
（3）按照局域波分解的完备性、能量守恒及虚假分量的性质，检验并去除虚假分量，抵消主导模态分量中的误差分量，针对局域波分解过程中虚假分量的产生机理，本文提出基于能量守恒及相关分析的抗虚假分量方法，利用相关分析判别信号的主导模态分量，结合能量守恒原理，给出了虚假分量属性判别依据及模态更新的原则；
（4）根据模态混叠不同的产生机理，本文提出形态运算及移频变换抗模态混叠方法，形态运算是有效提取间断信号、脉冲干扰强有力的工具，因此提出基于形态运算抗异常事件引起的模态混叠方法，仿真结果表明形态运算对脉冲干扰，间断信号引起的模态混叠能起到理想的效果；移频变换有效解决了由于信号间相互作用导致模态混叠问题，通过多组数据处理发现当复合信号满足局域波分解的充分条件二时，充分条件一可放宽到120.95，利用本文提出的方法都能有效提取出与原组分匹配的IMF分量，圆满完成局域波的分解过程。
（5）对实测的不同运行状态下滚动轴承的振动信号进行自适应形态滤波与局域波分解，在此基础上利用模糊聚类的方法，提取局域波相关特征尺度熵，进行极值归一化及标定处理，然后改造为等价模糊关系矩阵完成聚类分析。该方法简单实用，是滚动轴承故障诊断较为有效的方法。
以上研究工作在一定程度上丰富和完善了形态滤波与局域波分解方法，诊断应用表明本文提出的方法能有效区分不同运行状态，解决实际问题。
Vibration signal is the information carrier of rolling bearing of running state. Periodicallyrepeated impact and amplitude modulation are important characteristics of defects and fault inrolling bearings. They have a common characteristic that is not only related to time but alsoclosely related to frequency. It is difficult to obtain all of the signal characteristics if we splitthe time-frequency features and only analyze this kind of signals from the viewpoint of timeor frequency domain. On the contrary, it will undoubtedly improve the diagnostic accuracyand reliability if we identify the signal from the angle of the joint time-frequency domain. Inaddition, strong background noise and shock vibration are also characteristics of rollingbearing vibration signal that can not be ignored. So this paper adopts the method of adaptivemorphological filtering that filter out background noise and extract shock signal throughsetting up adaptive multi-structural and multi-scale morphological filter with the criterion ofrolling bearing fault characteristic frequency. Based on this, the method of local wavedecomposition is employed to process vibration signals of rolling bearing. Then thecharacteristic parameters of related scale entropy are extracted and finally the running statesof rolling bearing are identified with the method of fuzzy clustering. The main work is asfollows:
(1) Mathematical morphology abandons the view of traditional numerical modeling andanalysis. It depicts and analyzes signal from set. The “probe” named as a structure elementwas designed to collect the information of signal. It achieved signal matching, signalextracting, details keeping and noise suppression by moving the probe constantly. Accordingto the measurement principle of frequency response function in the vibration signalprocessing, the quantitative relationship between filtering characteristic and the width ofstructure the elements, sampling frequency, analysis point number was studied. A quantitativedescription of the mathematical morphological filter was given. The method of multi-scalemulti-structural adaptive mean filter was proposed. The construction of adaptive multi-scalemulti-structural element was discussed in detail. With frequency intensity coefficient ascriterion, the adaptive multi-scale multi-structural mean filter was constructed by using sensitive structure elements, which realized better extraction effects of the low-frequencysignal.
(2) Local wave method is an adaptive variable decomposition algorithm based on localsignal characteristics. The method decomposes signal into numbers of IMF and a trend term.Because the basis functions were generated by adaptive signal processing, it has good localcharacterization capabilities. By detailed analysis of the mechanism of the endpoint effect, amethod of endpoint effect suppression that is based on the endpoint matching characteristicwave extension was put forward. In the process of wave matching, the characteristics of thesignal at the endpoints were taken into full consideration. With the signal at the endpoint asbasic matching element, the unconstrained situation at the endpoint was changed whicheffectively suppressed the end effect according to the simulation test results.
(3) The completeness of the local wave decomposition, the nature of energyconservation and the false component of local wave decomposition was employed forinspection and removal of false component, offset error component in the dominant modalcomponent. The method of anti-false component based on conservation of energy and relatedanalysis was put forward and the principle of false component attribute discrimination andmodal updating was proposed by using correlation analysis discriminant signal first dominantmode component combining with the principle of conservation of energy.
(4) According to different generation mechanisms of the mode mixing, the paperproposed anti-mode mixing method of using morphological operations and frequency shift.Morphological operation was an effectively powerful tool to extract the intermittent signaland interfere with pulse. Therefore, on the basis of the morphological operations, the methodof anti-mode mixing caused by abnormal incidents was proposed. The simulation results showthat morphological operations had a great effect on mode mixing caused by pulse interferenceand intermittent signals; Frequency shift effectively solved the problem of mode mixing dueto interaction between signals. When the second sufficient condition of the local wavedecomposition was satisfied, the First sufficient condition can be up to120.95. Withthe method proposed in this paper, the local wave decomposition process, extracting IMFcomponents matching the original component, could be realized successfully.
(5) By analyzing rolling bearing vibration signals measured under different conditionswith the method of adaptive morphological filter and the local wave decomposition and by using fuzzy clustering method. The feature scale entropy of the local wave extracted wastransformed into fuzzy equivalence relation matrix by the normalization processing andcalibration and then underwent clustering analysis. The method proved to be simple, practicaland with great detection precision, being an effective method of rolling bearing faultdiagnosis.
The study above, to a great extent, enriched and improved the morphological filteringand local wave decomposition method. Diagnostic applications indicated the methodsproposed in the paper could distinguish between different working conditions and solvepractical problems.
（1）数学形态学摒弃了传统数值建模及分析的观点，从集合的角度刻画和分析被处理信号，设计了一个“探针”（结构元素）的来探测信号的信息，利用该探针在被处理信号中不断平移,完成信号与结构元素间的匹配,达到信号提取、细节保持和噪声抑制的目的。按照振动信号处理中频响函数测量原理，研究了结构元素宽度、采样频率、分析点数与滤波特性间的定量关系，给出了数学形态滤波器特性的定量描述。提出一种自适应多结构多尺度形态组合滤波方法，详细讨论自适应多结构多尺度结构元素的构造，以被处理信号的特征频率强度系数为判据，利用敏感的结构元素组合出多尺度多结构的自适应均值滤波器，取得了较好的低频信号提取效果。
（2）局域波法是基于信号局部特征的自适应时变分解算法，其分解过程就是把被处理信号分解成多个IMF分量和一个趋势项的和，且局域波分解的基函数是根据被处理信号自适应产生，因此具有良好的信号局部表征能力。在详细分析局域波分解产生端点效应机理的基础上，提出了端点匹配特征波延拓抑制端点效应的方法，该方法在波形匹配过程中充分考虑了被处理信号端点处的数据特性，将载入数据的首末端点处的数据作为匹配基元，从而改变了端点处不受约束的状况，仿真测试结果表明有效抑制了端点效应。
（3）按照局域波分解的完备性、能量守恒及虚假分量的性质，检验并去除虚假分量，抵消主导模态分量中的误差分量，针对局域波分解过程中虚假分量的产生机理，本文提出基于能量守恒及相关分析的抗虚假分量方法，利用相关分析判别信号的主导模态分量，结合能量守恒原理，给出了虚假分量属性判别依据及模态更新的原则；
（4）根据模态混叠不同的产生机理，本文提出形态运算及移频变换抗模态混叠方法，形态运算是有效提取间断信号、脉冲干扰强有力的工具，因此提出基于形态运算抗异常事件引起的模态混叠方法，仿真结果表明形态运算对脉冲干扰，间断信号引起的模态混叠能起到理想的效果；移频变换有效解决了由于信号间相互作用导致模态混叠问题，通过多组数据处理发现当复合信号满足局域波分解的充分条件二时，充分条件一可放宽到120.95，利用本文提出的方法都能有效提取出与原组分匹配的IMF分量，圆满完成局域波的分解过程。
（5）对实测的不同运行状态下滚动轴承的振动信号进行自适应形态滤波与局域波分解，在此基础上利用模糊聚类的方法，提取局域波相关特征尺度熵，进行极值归一化及标定处理，然后改造为等价模糊关系矩阵完成聚类分析。该方法简单实用，是滚动轴承故障诊断较为有效的方法。
以上研究工作在一定程度上丰富和完善了形态滤波与局域波分解方法，诊断应用表明本文提出的方法能有效区分不同运行状态，解决实际问题。
Vibration signal is the information carrier of rolling bearing of running state. Periodicallyrepeated impact and amplitude modulation are important characteristics of defects and fault inrolling bearings. They have a common characteristic that is not only related to time but alsoclosely related to frequency. It is difficult to obtain all of the signal characteristics if we splitthe time-frequency features and only analyze this kind of signals from the viewpoint of timeor frequency domain. On the contrary, it will undoubtedly improve the diagnostic accuracyand reliability if we identify the signal from the angle of the joint time-frequency domain. Inaddition, strong background noise and shock vibration are also characteristics of rollingbearing vibration signal that can not be ignored. So this paper adopts the method of adaptivemorphological filtering that filter out background noise and extract shock signal throughsetting up adaptive multi-structural and multi-scale morphological filter with the criterion ofrolling bearing fault characteristic frequency. Based on this, the method of local wavedecomposition is employed to process vibration signals of rolling bearing. Then thecharacteristic parameters of related scale entropy are extracted and finally the running statesof rolling bearing are identified with the method of fuzzy clustering. The main work is asfollows:
(1) Mathematical morphology abandons the view of traditional numerical modeling andanalysis. It depicts and analyzes signal from set. The “probe” named as a structure elementwas designed to collect the information of signal. It achieved signal matching, signalextracting, details keeping and noise suppression by moving the probe constantly. Accordingto the measurement principle of frequency response function in the vibration signalprocessing, the quantitative relationship between filtering characteristic and the width ofstructure the elements, sampling frequency, analysis point number was studied. A quantitativedescription of the mathematical morphological filter was given. The method of multi-scalemulti-structural adaptive mean filter was proposed. The construction of adaptive multi-scalemulti-structural element was discussed in detail. With frequency intensity coefficient ascriterion, the adaptive multi-scale multi-structural mean filter was constructed by using sensitive structure elements, which realized better extraction effects of the low-frequencysignal.
(2) Local wave method is an adaptive variable decomposition algorithm based on localsignal characteristics. The method decomposes signal into numbers of IMF and a trend term.Because the basis functions were generated by adaptive signal processing, it has good localcharacterization capabilities. By detailed analysis of the mechanism of the endpoint effect, amethod of endpoint effect suppression that is based on the endpoint matching characteristicwave extension was put forward. In the process of wave matching, the characteristics of thesignal at the endpoints were taken into full consideration. With the signal at the endpoint asbasic matching element, the unconstrained situation at the endpoint was changed whicheffectively suppressed the end effect according to the simulation test results.
(3) The completeness of the local wave decomposition, the nature of energyconservation and the false component of local wave decomposition was employed forinspection and removal of false component, offset error component in the dominant modalcomponent. The method of anti-false component based on conservation of energy and relatedanalysis was put forward and the principle of false component attribute discrimination andmodal updating was proposed by using correlation analysis discriminant signal first dominantmode component combining with the principle of conservation of energy.
(4) According to different generation mechanisms of the mode mixing, the paperproposed anti-mode mixing method of using morphological operations and frequency shift.Morphological operation was an effectively powerful tool to extract the intermittent signaland interfere with pulse. Therefore, on the basis of the morphological operations, the methodof anti-mode mixing caused by abnormal incidents was proposed. The simulation results showthat morphological operations had a great effect on mode mixing caused by pulse interferenceand intermittent signals; Frequency shift effectively solved the problem of mode mixing dueto interaction between signals. When the second sufficient condition of the local wavedecomposition was satisfied, the First sufficient condition can be up to120.95. Withthe method proposed in this paper, the local wave decomposition process, extracting IMFcomponents matching the original component, could be realized successfully.
(5) By analyzing rolling bearing vibration signals measured under different conditionswith the method of adaptive morphological filter and the local wave decomposition and by using fuzzy clustering method. The feature scale entropy of the local wave extracted wastransformed into fuzzy equivalence relation matrix by the normalization processing andcalibration and then underwent clustering analysis. The method proved to be simple, practicaland with great detection precision, being an effective method of rolling bearing faultdiagnosis.
The study above, to a great extent, enriched and improved the morphological filteringand local wave decomposition method. Diagnostic applications indicated the methodsproposed in the paper could distinguish between different working conditions and solvepractical problems.
引文
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