WO2019205826A1 - 基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法 - Google Patents
基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法 Download PDFInfo
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- G01M13/00—Testing of machine parts
- G01M13/04—Bearings
- G01M13/045—Acoustic or vibration analysis
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- the invention relates to the field of mechanical equipment condition monitoring and fault diagnosis, in particular to a rolling bearing fault diagnosis method based on wavelet packet and modulation bispectrum analysis.
- Rolling bearings are one of the most widely used universal parts in various rotating machinery. Its operating state often directly affects the performance of the whole machine. Therefore, the fault diagnosis of rolling bearings has important research and application value.
- Wavelet packet energy spectrum is a time-frequency analysis method. It can analyze the vibration signal of each frequency band by wavelet packet energy spectrum analysis of the vibration signal, and extract the characteristic signal that can reflect the bearing fault information, which is more accurate and effective. Diagnose and identify early failures of mechanical equipment. In recent years, some scholars have carried out a lot of research work on wavelet packet transform. Tang Guiji et al. (Tang Guiji, Cai Wei. Fault Diagnosis of Rolling Bearings Using Wavelet Packet and Envelope Analysis[J]. Vibration, Testing and Diagnosis, 2009, 29(2): 201-204.) Wavelet Packet Energy Spectrum and Envelope Analyze the combined method and apply it to the fault detection of rolling bearings. Nikolaou et al.
- a technical problem to be solved by the present invention is to provide a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis.
- the technical solution of the present invention to solve the technical problem is to provide a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis, characterized in that the method comprises the following steps:
- Step 1 measuring the vibration signal of the detected rolling bearing
- Step 2 performing wavelet packet decomposition on the vibration signal to obtain each frequency band of the wavelet packet
- Step 3 Find the wavelet packet energy spectrum of each frequency band and normalize it to obtain normalized frequency bands
- Step 4 Select a frequency band in which the energy is concentrated from the normalized frequency bands to reconstruct the signal
- Step 5 Perform modulation bispectral analysis on the frequency band of the reconstructed signal to obtain the fault characteristic frequency of the rolling bearing.
- the present invention has the following advantages:
- the wavelet packet energy spectrum can effectively extract the transient signal, but the effect of extracting the fault characteristic frequency is not good.
- the method combines the transient characteristics of WPE with the periodic characteristics of MSB, effectively improves the effect of bearing fault diagnosis, can accurately extract the fault characteristic frequency and has high signal-to-noise ratio, and has a good application in the field of rotating machinery fault diagnosis. prospect.
- wavelet packet energy spectrum analysis can effectively extract the weak feature information of faulty bearings in strong background noise, and can effectively screen out the most effective wavelet packet coefficients for signal reconstruction. Conducive to the early failure of the bearing.
- Embodiment 1 is a time-domain waveform diagram of Embodiment 1 of a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis;
- Embodiment 2 is a wavelet packet energy spectrum diagram of Embodiment 1 of a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis;
- Embodiment 3 is a waveform diagram of a reconstructed signal of Embodiment 1 of a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis;
- FIG. 4 is a result diagram of an MSB of Embodiment 1 of a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis according to the present invention
- the invention provides a rolling bearing fault diagnosis method (referred to as a method) based on wavelet packet energy spectrum and modulation bispectrum analysis, characterized in that the method comprises the following steps:
- Step 1 measuring the vibration signal of the detected rolling bearing by the vibration sensor
- Step 2 performing wavelet packet decomposition on the vibration signal to obtain each frequency band of the wavelet packet
- Step 3 Find the wavelet packet energy spectrum of each frequency band and normalize it to obtain normalized frequency bands
- Step 4 Select a frequency band in which the energy is concentrated from the normalized frequency bands to reconstruct the signal
- Step 5 Perform modulation bispectral analysis on the frequency band of the reconstructed signal to obtain the fault characteristic frequency of the rolling bearing.
- Step 1 Let U j,k be a vector space, and then divide this vector space into two mutually orthogonal subspaces as shown in Equation 1:
- j represents the level of the tree
- j and k are integers
- h(k) denotes a low-pass filter
- g(k) denotes a high-pass filter
- the expression is as follows:
- Step 6 Calculate each wavelet packet coefficient The energy, the expression is as follows:
- Step 7 Calculate each wavelet packet coefficient
- the eigenvector T the expression is as follows:
- Step 8 When the energy is large, E j,k is usually a large value, which brings some inconvenience in data analysis; therefore, the feature vector T needs to be normalized to obtain the formula 10:
- step 5 The specific steps of the step 5 are as follows:
- Step 1 In the frequency domain, the modulation bispectrum analysis of the signal y(t) in the form of a discrete Fourier transform Y(f) is defined as Equation 12:
- y(t) denotes the signal for reconstructing the energy concentration band in the feature vector R
- B MS (f c , f x ) denotes the bispectrum of the reconstructed signal y(t);
- E ⁇ > denotes the expectation;
- c is the carrier frequency;
- f x is the modulation frequency;
- (f c +f x ) and (f c -f x ) are the upper sideband frequency and the lower sideband frequency, respectively;
- Step 2 In order to more accurately quantize the sideband amplitude, the modulation bispectrum analysis modifies the carrier frequency f c component by eliminating the substantial influence; to distinguish the improved modulation bispectrum analysis from the normal modulation bispectrum analysis, the modulation is represented by MSB-SE Bispectral analysis sidebands are defined as follows:
- Step 3 To obtain the f c slice, calculate by modulating the average of the bispectrum analysis in the incremental direction of f x :
- ⁇ f represents the resolution of f x
- B(f c ) represents the slice of improved modulation bispectrum analysis, and m represents the number of f x resolutions
- Step 4 In order to obtain more robust results, the average of the slices based on several optimal modulation bispectrum analysis is expressed as:
- v is the number of selected f c slices;
- B(f x ) represents the detector for modulation bispectrum analysis.
- a rolling bearing fault diagnosis method based on wavelet packet energy spectrum and modulation bispectrum analysis characterized in that the method comprises the following steps:
- Step 1 measuring the vibration signal of the detected rolling bearing by the vibration sensor;
- the original signal x(t) in the embodiment is the vibration signal of the outer ring of the rolling bearing, the sampling frequency of the signal is 71.5 Hz, the sampling length is point 285715, outside the bearing
- the loop fault frequency is 88.5 Hz.
- the waveform of the original signal is shown in Figure 1. It can be seen that there is a lot of noise.
- Step 2 performing wavelet packet decomposition (WPT) on the original signal to obtain each frequency band of the wavelet packet;
- WPT wavelet packet decomposition
- Step 3 Find the wavelet packet energy spectrum (WPE) of each frequency band and normalize it, and obtain the normalized frequency bands as shown in FIG. 2;
- WPE wavelet packet energy spectrum
- Step 4 Selecting an energy concentration band from each of the normalized frequency bands for signal reconstruction as shown in FIG. 3;
- Step 5 Perform modulation bispectral analysis (MSB) on the frequency band of the reconstructed signal to separate the modulation components, and extract the fault characteristic frequency of the rolling bearing as shown in Fig. 4.
- the main frequencies are multiple frequencies such as 88.5 Hz, 177 Hz, 265.5 Hz, etc.
- the characteristic frequency of the outer ring fault is consistent, and the fault characteristic information of the outer ring of the rolling bearing is accurately extracted.
Abstract
一种基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法，包括如下步骤：步骤一，测量被检测的滚动轴承的振动信号；步骤二，对振动信号进行小波包分解，得到小波包的各频段；步骤三，求出各频段的小波包能量谱并进行归一化，得到归一化后的各频段；步骤四，从归一化后的各频段中选择能量集中的频段进行信号的重构；步骤五，对重构信号的频段进行调制双谱分析，得到滚动轴承的故障特征频率。将WPE的瞬态特性和MSB的周期特性相结合，有效提升了轴承故障诊断的效果，能够准确地提取故障特征频率而且信噪比高，并且在旋转机械故障诊断领域具有良好的应用前景。
Description
本发明涉及机械设备状态监测和故障诊断领域，具体是基于小波包和调制双谱分析的滚动轴承故障诊断方法。
滚动轴承是各种旋转机械中应用最广泛的通用零部件之一，它的运行状态往往直接影响整机的性能，因此滚动轴承的故障诊断具有重要的研究和应用价值。
小波包能量谱是一种时频分析方法，可通过对振动信号进行小波包能量谱分析，得到每一频带内振动信号的变化规律，提取出能够反映轴承故障信息的特征信号，进而较为准确有效的诊断和识别机械设备的早期故障。近年来，一些学者对小波包变换开展了大量的研究工作。唐贵基等(唐贵基,蔡伟.应用小波包和包络分析的滚动轴承故障诊断[J].振动、测试与诊断,2009,29(2):201-204.)提出了小波包能量谱和包络分析相结合的方法，将其应用于滚动轴承的故障检测中。Nikolaou等(Nikolaou N G,Antoniadis I A.Rolling element bearing fault diagnosis using waveletpackets[J].Coal Mine Machinery,2009,35(3):197-205.)提出了利用小波包能量谱作为系统工具分析局部缺陷轴承振动信号的方法。王冬云等(王冬云,张文志.基于小波包变换的滚动轴承故障诊断[J].2012,23(3):295-298.)针对故障轴承振动信号能量集中的特点，应用小波包能量谱分析进行特征提取，同时提出了故障特征参数自动提取方法。Hemmati等(Hemmati F,Orfali W,Gadala M S.Roller bearing acoustic signature extraction by wavelet packet transform,applications in fault detection and size estimation[J].Applied Acoustics,2016,104:101-118.)提出利用小波包能量谱来检测和诊断初始缺陷的大小和位置。但在上述文章只考虑小波包用来分析信号的瞬态特性，并没有考虑信号的周期性，使得故障特征频率不够明显，难以准确有效的提取故 障特征，影响故障诊断精度。
发明内容
针对现有技术的不足，本发明拟解决的技术问题是，提供一种基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法。
本发明解决所述技术问题的技术方案是，提供一种基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法，其特征在于该方法包括如下步骤：
步骤一：测量被检测的滚动轴承的振动信号；
步骤二：对振动信号进行小波包分解，得到小波包的各频段；
步骤三：求出各频段的小波包能量谱并进行归一化，得到归一化后的各频段；
步骤四：从归一化后的各频段中选择能量集中的频段进行信号的重构；
步骤五：对重构信号的频段进行调制双谱分析，得到滚动轴承的故障特征频率。
与现有技术相比，本发明有益效果在于：
(1)小波包能量谱能够有效地提取瞬态信号，但是提取故障特征频率效果并不好。本方法将WPE的瞬态特性和MSB的周期特性相结合，有效地提升了轴承故障诊断的效果，能够准确地提取故障特征频率而且信噪比高，并且在旋转机械故障诊断领域具有良好的应用前景。
(2)针对故障轴承能量集中的特点，小波包能量谱分析能够有效的提取强背景噪声中有故障轴承的微弱特征信息，能够有效地筛选出最有效的小波包系数用于信号的重构，有利于发现轴承的早期故障。
图1为本发明基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法实施例1的时域波形图；
图2为本发明基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法实施例1的小波包能量谱图；
图3为本发明基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法 实施例1的重构信号的波形图；
图4为本发明基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法实施例1的MSB的结果图；
下面给出本发明的具体实施例。具体实施例仅用于进一步详细说明本发明，不限制本申请权利要求的保护范围。
本发明提供了一种基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法(简称方法)，其特征在于该方法包括如下步骤：
步骤一：通过振动传感器测量被检测的滚动轴承的振动信号；
步骤二：对振动信号进行小波包分解，得到小波包的各频段；
步骤三：求出各频段的小波包能量谱并进行归一化，得到归一化后的各频段；
步骤四：从归一化后的各频段中选择能量集中的频段进行信号的重构；
步骤五：对重构信号的频段进行调制双谱分析，得到滚动轴承的故障特征频率。
所述步骤三的具体步骤如下：
步骤1：设U
j,k是一个向量空间，然后将此向量空间分割为两个相互正交的子空间如式1所示：
式中j表示树的级别，k(k＝0,…,2
j-1)表示级别j中的节点索引；j和k均为整数；
重复分裂U
j,k直到j达到其最大分解级J(J表示无穷大)时，产生2
J个相互正交的子空间；
步骤2：小波包函数
(n＝0,1,2,3,…,)表达式如下：
式中n表示振荡参数，t表示时间；
步骤3：当j＝k＝0时，n＝0得到小波包函数的尺度函数Φ(t)如式3所示，n＝1得到小波包函数的小波母函数Ψ(t)如式4所示：
步骤4：当小波包函数
(n＝2,3,…,)时，其表达式如式5和6所示：
式中
h(k)表示低通滤波器，g(k)表示高通滤波器；h(k)和g(k)之间的正交关系为g(k)＝(-1)
kh(1-k)；<·，·>表示内积运算；
步骤5：由信号x(t)和小波包函数
(n＝0,1,2,3,…,)进行内积运算得到小波包系数
表达式如下：
步骤6：计算每个小波包系数
的能量，表达式如下：
步骤7：计算每个小波包系数
的特征向量T，表达式如下：
步骤8：当能量较大时，E
j,k通常是一个较大的数值，在数据分析上会带来一些不方便；因此，需要对特征向量T进行归一化处理，得到式10：
则进行归一化处理后的特征向量R为：
所述步骤五的具体如下步骤：
步骤1：在频域中，以离散傅立叶变换Y(f)的形式表示信号y(t)的调制双谱分析定义为式12：
B
MS(f
c,f
x)＝E<Y(f
c+f
x)Y(f
c-f
x)Y
*(f
c)Y
*(f
c)> (12)
式中y(t)表示选取特征向量R中能量集中的频段进行重构的信号；B
MS(f
c,f
x)表示重构信号y(t)的双谱；E<>表示期望；f
c为载波频率；f
x为调制频率；(f
c+f
x)和(f
c-f
x)分别为上边带频率和下边带频率；
步骤2：为了更精确地量化边带幅度，调制双谱分析通过消除实质影响来修改载波频率f
c分量；为了区分改善的调制双谱分析与正常的调制双谱分析，用MSB-SE表示调制双谱分析边带，定义如下：
式中
表示重构信号y(t)的改善双谱；B
MS(f
c,0)表示f
x＝0时的平方功率谱；
步骤3：为了得到f
c切片，通过在f
x增量方向上调制双谱分析的平均值来计算：
式中Δf表示f
x的分辨率；B(f
c)表示改善调制双谱分析的切片，m表示f
x分辨率的个数；
步骤4：为了获得更稳健的结果，基于若干个最优的调制双谱分析切片的平均值表示为：
式中v是选定的f
c切片的个数；B(f
x)表示调制双谱分析的检测器。
实施例1
一种基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法，其特征在于该方法包括如下步骤：
步骤一：通过振动传感器测量被检测的滚动轴承的振动信号；本实施例中的原始信号x(t)为滚动轴承外圈的振动信号，信号的采样频率为71.5Hz，采样长度为点285715，轴承外圈故障频率为88.5Hz。原始信号的波形图如图1所示，可以看出存在着大量的噪声。
步骤二：对原始信号进行小波包(WPT)分解，得到小波包的各频段；
步骤三：求出各频段的小波包能量谱(WPE)并进行归一化，得到归一化后的各频段如图2所示；
步骤四：从归一化后的各频段中选择能量集中频段进行信号的重构如图3所示；
步骤五：对重构信号的频段进行调制双谱分析(MSB)分离调制成分，提取滚动轴承的故障特征频率如图4所示，主要频率是88.5Hz、177Hz、265.5Hz等多倍频，与计算的外圈故障特征频率吻合，准确的提取了滚动轴承外圈故障特征信息。
本发明未述及之处适用于现有技术。
Claims (3)
- 一种基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法，其特征在于该方法包括如下步骤：步骤一：测量被检测的滚动轴承的振动信号；步骤二：对振动信号进行小波包分解，得到小波包的各频段；步骤三：求出各频段的小波包能量谱并进行归一化，得到归一化后的各频段；步骤四：从归一化后的各频段中选择能量集中的频段进行信号的重构；步骤五：对重构信号的频段进行调制双谱分析，得到滚动轴承的故障特征频率。
- 根据权利要求1所述的基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法，其特征在于所述步骤三的具体步骤如下：步骤1：设U j,k是一个向量空间，然后将此向量空间分割为两个相互正交的子空间如式1所示：
式中j表示树的级别，k表示级别j中的节点索引；j和k均为整数；k＝0,…,2 j-1；重复分裂U j,k直到j达到其最大分解级J时，产生2 J个相互正交的子空间；步骤2：小波包函数表达式如下：
式中n表示振荡参数，t表示时间；步骤3：当j＝k＝0时，n＝0得到小波包函数的尺度函数Φ(t)如式3所示，n＝1得到小波包函数的小波母函数Ψ(t)如式4所示：
步骤4：当小波包函数时，其表达式如式5和6所示：
式中h(k)表示低通滤波器，g(k)表示高通滤波器；h(k)和g(k)之间的正交关系为g(k)＝(-1) kh(1-k)；<·，·)表示内积运算；
步骤5：由信号x(t)和小波包函数进行内积运算得到小波包系数
表达式如下：
步骤6：计算每个小波包系数的能量，表达式如下：
步骤7：计算每个小波包系数的特征向量T，表达式如下：
步骤8：对特征向量T进行归一化处理，得到式10：
则进行归一化处理后的特征向量R为：
- 根据权利要求1所述的基于小波包能量谱和调制双谱分析的滚动轴承故障诊断方法，其特征在于所述步骤五的具体如下步骤：步骤1：在频域中，以离散傅立叶变换Y(f)的形式表示信号y(t)的调制双谱分析定义为式12：B MS(f c,f x)＝E<Y(f c+f x)Y(f c-f x)Y *(f c)Y *(f c)> (12)式中y(t)表示选取特征向量R中能量集中的频段进行重构的信号；B MS(f c,f x)表示重构信号y(t)的双谱；E<>表示期望；f c为载波频率；f x为调制频率；(f c+f x)和(f c-f x)分别为上边带频率和下边带频率；步骤2：为了更精确地量化边带幅度，调制双谱分析通过消除实质影响来修改载波频率f c分量；为了区分改善的调制双谱分析与正常的调制双谱分析，用MSB-SE表示调制双谱分析边带，定义如下：
式中表示重构信号y(t)的改善双谱；B MS(f c,0)表示f x＝0时的平方功率谱；
步骤3：为了得到f c切片，通过在f x增量方向上调制双谱分析的平均值来计算：
式中Δf表示f x的分辨率；B(f c)表示改善调制双谱分析的切片，m表示f x分辨率的个数；步骤4：为了获得更稳健的结果，基于若干个最优的调制双谱分析切片的平均值表示为：
式中v是选定的f c切片的个数；B(f x)表示调制双谱分析的检测器。
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