基于经验模态分解的故障诊断方法研究
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摘要
随着现代工业的发展及机械自动化程度提高，一些大型旋转机械设备应用越来越广泛，如何保证这些机械设备安全稳定运行成为一项重要课题，机械设备的故障诊断技术越来越受到重视，它是故障信号处理的关键技术。故障诊断技术一般采用时频分析方法，传统方法(如短时Fourier变换、小波变换等)在处理复杂的故障信号时具有一定的作用，但也存在局限性。信号的平稳性是传统信号处理方法的前提，信号特征只能分别通过时域或者频域反映，而信号的时域和频域的局部化特征和全貌无法同时兼顾,这就限制了传统时频分析方法的发展，它对复杂的信号特别是非平稳、非线性的故障信号不能进行自适应、有效地分析和进一步的处理。发展新的故障诊断技术成为当务之急，以现代信号处理技术为基础的故障分析方法应运而生，其在设备运行状态监测和保障机械安全运行，预防事故等方面具有重要的意义。
本文阐述了几种应用于故障诊断领域的时频分析方法，深入研究了经验模态分解方法，并针对经验模态分解算法存在的问题重点展开讨论，提出了解决这些问题的方法，本文的研究内容如下:
(1)对常用的机械故障信号时频分析方法进行了研究，如短时Fourier变换、Wigner-Ville分布、小波变换等，总结这些方法的特点及不足，在此基础上引出Hilbert-Huang变换(HHT)以及其精髓经验模态分解(EMD)，并指出EMD分解算法中有几个问题需要解决,如模态混叠、端点效应、包络线的拟合。
(2)提出一种高频信号辅助法来抑制EMD过程中的模态混叠问题。在筛分之前向信号中加入已知小幅高频的正弦信号，以此改变原始信号的极值分布即改变信号的包络，去“淹没”那些异常事件,使异常事件不再那么明显,从而使信号包络更自然,可以有效抑制模态混叠现象，提高EMD的整体分解效果。与传统的EMD方法对比，改进的方法能有效抑制模态混叠问题。
(3)利用线性外推法来处理信号端点处极值。经验模态分解需通过极值点描述信号上下包络线，但是信号两端边界的极大值和极小值不好估计，包络线就存在着变数，这样经验模态分解过程就会产生边界误差，随着分解进行边界误差会向内传播，从而污染内部数据，导致分解结果不合理。通过分析几种典型的抑制端点效应的方法，把线性外推法引入EMD,以获得观测区间边界极值点，这种方法简单而且可以有效地抑制端点效应。
(4)提出基于非均匀有理B样条曲线的信号包络拟合新方法。该方法通过弦长参数化，得到定义域内的节点矢量，利用信号极大值、极小值点反算得到非均匀B样条曲线的控制多边形，然后利用节点矢量和控制多边形一起构造非均匀B样条曲线，拟合信号包络。采用该方法可以获得精确的瞬时平均值，从而抑制没有意义的信号波动，避免了拟合出现过冲、欠冲以及不完全包络等问题。
(5)利用本文提出的改进的EMD方法，对实验室仿真信号和实际的故障信号分别进行分析，通过以上分析证明了改进EMD方法的有效性。
With the development of modern industry and the improvement of machinery automation, anumber of large rotating machines are used more and more widely, how to ensure the safe andstable operation of the equipment has become an important issue, the fault diagnosis technologyof mechanical equipment has been paid more and more attention, which is the key technology offault signal processing. Fault diagnosis technology usually adopts time-frequency analysismethod, the traditional method has a certain effect in the processing of complex fault signal, butalso has limitations. Signal stability is the premise of traditional signal processing method, signalcharacteristics can be respectively reflected through a time domain or frequency domain, whilelocal and the overall characteristics of the signal in time domain and frequency domain can notbe taken into account, which limits the development of traditional time-frequency analysismethod, because it is not adaptive, and efficient analysis and further processing for complexsignal, in particular nonlinear nonstationary fault signal can’t be realized.Therefore, It is urgentto develop a new fault diagnosis technology, and fault analysis methods based on modern signalprocessing emerge as the times require. It has important significance for monitoring equipmentoperation state, guarantee of safety of machinery operation and prevention of accidents.
This paper expounds several time-frequency analysis methods used in the field of faultdiagnosis, deeply studies the empirical mode decomposition method, spreads out discussionaccording to the problems of empirical mode decomposition algorithm, and puts forward thesolutions to these problems, the research contents of this paper are as follows:
(1)The commonly used time-frequency analysis methods of machine fault signal are studied,such as short time Fourier transform, Wigner-Ville distribution, wavelet transform. Thecharacteristics and disadvantages of these methods are summarized. On the basis of this,Hilbert-Huang transform (HHT) as well as the essence of the empirical mode decomposition(EMD) have been introduced, and several problems of EMD algorithm which need to be solved,such as the mode mixing, end effect, and envelope fitting are pointed out.
(2)A high frequency signal auxiliary method is put forward to inhibit mode mixing of EMDprocess. A known small high frequency sinusoidal signal is added to the original signal beforescreening in order to change the extreme value distribution of the original signal-the signalenvelope. In this way, which the abnormal events are no longer so obvious, and the signalenvelope becomes more natural, which can effectively suppress the mode mixing phenomenonand improve the overall efficiency of EMD. Compared with the traditional EMD method, theimproved method can effectively suppress problem of the mode mixing.
(3) Linear extrapolation method is employed to process the signal at the end of extremevalue. Empirical mode decomposition describes upper and lower envelope of the signal throughextreme points, but the maximum and the minimum value of the signal at both ends of the border are hard to estimate, so the envelope has variables, which will produce a boundary error inempirical mode decomposition process. As the decomposition goes, boundary error willpropagate inward, thereby contaminating the internal data and causing decomposition results tobe unreasonable. Through the analysis of several typical methods of suppression of end effect,the linear extrapolation is introduced into EMD to obtain the extreme points of observationinterval boundary. This method is simple and can effectively suppress the end effect.
(4)A new Envelop fitting method based on non-uniform rational B-splines curve isproposed. With this method, the node vector in the domain is obtained through chord lengthparameterization, using of backcalculation signal maxima and minima points, the controlpolygon of non-uniform rational B-splines curve is obtained. Then the node vector and controlpolygon are used to construct non-uniform rational B-splines curve which fits signal envelope.Using this method, accurate instantaneous average value can be obtained, thereby suppressingmeaningless signal fluctuations and avoiding problems such as overshoot, undershoot andincomplete envelope.
(5)Using the improved EMD method proposed by this paper, the laboratory simulationsignal and the actual fault signals are analyzed respectively. Through the above analysis, it isproved that the improved EMD method is effective.
本文阐述了几种应用于故障诊断领域的时频分析方法，深入研究了经验模态分解方法，并针对经验模态分解算法存在的问题重点展开讨论，提出了解决这些问题的方法，本文的研究内容如下:
(1)对常用的机械故障信号时频分析方法进行了研究，如短时Fourier变换、Wigner-Ville分布、小波变换等，总结这些方法的特点及不足，在此基础上引出Hilbert-Huang变换(HHT)以及其精髓经验模态分解(EMD)，并指出EMD分解算法中有几个问题需要解决,如模态混叠、端点效应、包络线的拟合。
(2)提出一种高频信号辅助法来抑制EMD过程中的模态混叠问题。在筛分之前向信号中加入已知小幅高频的正弦信号，以此改变原始信号的极值分布即改变信号的包络，去“淹没”那些异常事件,使异常事件不再那么明显,从而使信号包络更自然,可以有效抑制模态混叠现象，提高EMD的整体分解效果。与传统的EMD方法对比，改进的方法能有效抑制模态混叠问题。
(3)利用线性外推法来处理信号端点处极值。经验模态分解需通过极值点描述信号上下包络线，但是信号两端边界的极大值和极小值不好估计，包络线就存在着变数，这样经验模态分解过程就会产生边界误差，随着分解进行边界误差会向内传播，从而污染内部数据，导致分解结果不合理。通过分析几种典型的抑制端点效应的方法，把线性外推法引入EMD,以获得观测区间边界极值点，这种方法简单而且可以有效地抑制端点效应。
(4)提出基于非均匀有理B样条曲线的信号包络拟合新方法。该方法通过弦长参数化，得到定义域内的节点矢量，利用信号极大值、极小值点反算得到非均匀B样条曲线的控制多边形，然后利用节点矢量和控制多边形一起构造非均匀B样条曲线，拟合信号包络。采用该方法可以获得精确的瞬时平均值，从而抑制没有意义的信号波动，避免了拟合出现过冲、欠冲以及不完全包络等问题。
(5)利用本文提出的改进的EMD方法，对实验室仿真信号和实际的故障信号分别进行分析，通过以上分析证明了改进EMD方法的有效性。
With the development of modern industry and the improvement of machinery automation, anumber of large rotating machines are used more and more widely, how to ensure the safe andstable operation of the equipment has become an important issue, the fault diagnosis technologyof mechanical equipment has been paid more and more attention, which is the key technology offault signal processing. Fault diagnosis technology usually adopts time-frequency analysismethod, the traditional method has a certain effect in the processing of complex fault signal, butalso has limitations. Signal stability is the premise of traditional signal processing method, signalcharacteristics can be respectively reflected through a time domain or frequency domain, whilelocal and the overall characteristics of the signal in time domain and frequency domain can notbe taken into account, which limits the development of traditional time-frequency analysismethod, because it is not adaptive, and efficient analysis and further processing for complexsignal, in particular nonlinear nonstationary fault signal can’t be realized.Therefore, It is urgentto develop a new fault diagnosis technology, and fault analysis methods based on modern signalprocessing emerge as the times require. It has important significance for monitoring equipmentoperation state, guarantee of safety of machinery operation and prevention of accidents.
This paper expounds several time-frequency analysis methods used in the field of faultdiagnosis, deeply studies the empirical mode decomposition method, spreads out discussionaccording to the problems of empirical mode decomposition algorithm, and puts forward thesolutions to these problems, the research contents of this paper are as follows:
(1)The commonly used time-frequency analysis methods of machine fault signal are studied,such as short time Fourier transform, Wigner-Ville distribution, wavelet transform. Thecharacteristics and disadvantages of these methods are summarized. On the basis of this,Hilbert-Huang transform (HHT) as well as the essence of the empirical mode decomposition(EMD) have been introduced, and several problems of EMD algorithm which need to be solved,such as the mode mixing, end effect, and envelope fitting are pointed out.
(2)A high frequency signal auxiliary method is put forward to inhibit mode mixing of EMDprocess. A known small high frequency sinusoidal signal is added to the original signal beforescreening in order to change the extreme value distribution of the original signal-the signalenvelope. In this way, which the abnormal events are no longer so obvious, and the signalenvelope becomes more natural, which can effectively suppress the mode mixing phenomenonand improve the overall efficiency of EMD. Compared with the traditional EMD method, theimproved method can effectively suppress problem of the mode mixing.
(3) Linear extrapolation method is employed to process the signal at the end of extremevalue. Empirical mode decomposition describes upper and lower envelope of the signal throughextreme points, but the maximum and the minimum value of the signal at both ends of the border are hard to estimate, so the envelope has variables, which will produce a boundary error inempirical mode decomposition process. As the decomposition goes, boundary error willpropagate inward, thereby contaminating the internal data and causing decomposition results tobe unreasonable. Through the analysis of several typical methods of suppression of end effect,the linear extrapolation is introduced into EMD to obtain the extreme points of observationinterval boundary. This method is simple and can effectively suppress the end effect.
(4)A new Envelop fitting method based on non-uniform rational B-splines curve isproposed. With this method, the node vector in the domain is obtained through chord lengthparameterization, using of backcalculation signal maxima and minima points, the controlpolygon of non-uniform rational B-splines curve is obtained. Then the node vector and controlpolygon are used to construct non-uniform rational B-splines curve which fits signal envelope.Using this method, accurate instantaneous average value can be obtained, thereby suppressingmeaningless signal fluctuations and avoiding problems such as overshoot, undershoot andincomplete envelope.
(5)Using the improved EMD method proposed by this paper, the laboratory simulationsignal and the actual fault signals are analyzed respectively. Through the above analysis, it isproved that the improved EMD method is effective.
引文
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