CN112067296A - Rolling bearing fault diagnosis method based on empirical mode decomposition and nuclear correlation - Google Patents

Rolling bearing fault diagnosis method based on empirical mode decomposition and nuclear correlation Download PDF

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CN112067296A
CN112067296A CN202010936754.3A CN202010936754A CN112067296A CN 112067296 A CN112067296 A CN 112067296A CN 202010936754 A CN202010936754 A CN 202010936754A CN 112067296 A CN112067296 A CN 112067296A
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empirical mode
mode decomposition
bearing
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秦勇
赵雪军
刘志亮
冯志鹏
贾利民
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Beijing Jiaotong University
CRRC Qingdao Sifang Co Ltd
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Abstract

本发明公开了一种基于经验模态分解和核相关的滚动轴承故障诊断方法。该方法首先采用经验模态分解方法将获取到的单通道信号分解为虚拟的多通道信号,然后采用贝叶斯信息准则对多通道信号进行选择,接着基于核相关最大化提取滚动轴承故障信号,最后采用包络分析方法对提取的信号进行故障诊断。本发明还进一步分析了核宽度的变化对故障信号提取效果的影响。为了验证提出方法的有效性和先进性,本发明使用轮对轴承信号对方法进行了验证,取得了良好的实验结果。

Figure 202010936754

The invention discloses a fault diagnosis method for rolling bearings based on empirical mode decomposition and kernel correlation. The method first uses the empirical mode decomposition method to decompose the acquired single-channel signal into virtual multi-channel signals, then uses the Bayesian information criterion to select the multi-channel signals, and then extracts the rolling bearing fault signal based on kernel correlation maximization. The fault diagnosis of the extracted signal is carried out by using the envelope analysis method. The invention further analyzes the influence of the variation of the kernel width on the extraction effect of the fault signal. In order to verify the effectiveness and advancement of the proposed method, the present invention uses the wheelset bearing signal to verify the method, and obtains good experimental results.

Figure 202010936754

Description

基于经验模态分解和核相关的滚动轴承故障诊断方法Fault Diagnosis Method of Rolling Bearing Based on Empirical Mode Decomposition and Kernel Correlation

技术领域technical field

本发明属于机械工程领域。本发明涉及一种基于经验模态分解和核相关的滚动轴承故障信号提取方法。The invention belongs to the field of mechanical engineering. The invention relates to a method for extracting fault signals of rolling bearings based on empirical mode decomposition and kernel correlation.

背景技术Background technique

滚动轴承在机械工程领域内应用十分广泛,在高强度和高密度的工作条件下,滚动轴承具有很高的故障率。因此,通过故障诊断方法对滚动轴承的状态进行监测,实时更换故障轴承以保证机械设备的正常运转就显得尤为重要。Rolling bearings are widely used in the field of mechanical engineering. Under high-strength and high-density working conditions, rolling bearings have a high failure rate. Therefore, it is particularly important to monitor the state of rolling bearings through fault diagnosis methods and replace faulty bearings in real time to ensure the normal operation of mechanical equipment.

盲源分离算法是众多经典故障诊断算法的分支之一,用于将混合信号的不同组成成分分开。但由于源信号和混合矩阵都是未知的,所以分离出来的信号顺序无法确定。在现场实践中,混合信号中的重要信息是由一个信号源承载的,其他多位干扰信号或噪声信号。因此,盲源提取算法被提了出来,该算法只提取混合信号中的特定信号成分,避免了盲源分离算法带来的大计算量。Blind source separation algorithm is one of the branches of many classical fault diagnosis algorithms, which is used to separate different components of mixed signals. But since both the source signal and the mixing matrix are unknown, the sequence of the separated signals cannot be determined. In field practice, important information in a mixed signal is carried by one signal source, with other multi-bit interfering signals or noise signals. Therefore, a blind source extraction algorithm is proposed, which only extracts specific signal components in the mixed signal, avoiding the large amount of computation brought by the blind source separation algorithm.

盲源提取和盲源分离算法的一个前提条件是要获取不同监测位置的多通道源信号。然而,由于实际工业生产条件的影响,很难获取多通道的源信号,与之相比,单通道信号更易获取,基于单通道信号进行盲源提取更符合现场应用的实际情况。A prerequisite for the blind source extraction and blind source separation algorithms is to obtain multi-channel source signals at different monitoring locations. However, due to the influence of actual industrial production conditions, it is difficult to obtain multi-channel source signals. Compared with single-channel signals, it is easier to obtain single-channel signals. Blind source extraction based on single-channel signals is more in line with the actual situation of field applications.

发明内容SUMMARY OF THE INVENTION

本发明的目的是对滚动轴承的状态监测,根据不同轴承故障类型所具有的特征频率对轴承的内圈,外圈或滚动体故障进行区分和诊断。本发明可以在滚动轴承信号被冲击噪声干扰的条件下,准确地对滚动轴承的故障类型进行区分。本发明具体采用如下技术方案:The purpose of the present invention is to monitor the condition of the rolling bearing, and to distinguish and diagnose the faults of the inner ring, the outer ring or the rolling elements of the bearing according to the characteristic frequencies of different bearing fault types. The invention can accurately distinguish the fault types of the rolling bearing under the condition that the rolling bearing signal is disturbed by the impact noise. The present invention specifically adopts following technical scheme:

一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,包括以下步骤:A method for extracting fault signals of rolling bearings based on empirical mode decomposition and kernel correlation, comprising the following steps:

1)获取实验数据:分别采集滚动轴承处于不同故障状态下的振动加速度数据,所述不同故障状态包括滚动体故障,内圈故障,外圈故障,根据轴承的技术参数计算轴承的故障频率;1) Obtaining experimental data: separately collecting vibration acceleration data of the rolling bearing under different fault states, the different fault states include rolling element fault, inner ring fault, and outer ring fault, and calculating the fault frequency of the bearing according to the technical parameters of the bearing;

2)原始信号通过经验模态分解的方法分解为多通道信号;2) The original signal is decomposed into multi-channel signals by the method of empirical mode decomposition;

3)获取多通道信号的协方差矩阵,进行奇异值分解;3) Obtain the covariance matrix of the multi-channel signal, and perform singular value decomposition;

4)基于贝叶斯信息准则获取源信号数目,确定用于故障信号提取的通道信号;4) Obtain the number of source signals based on the Bayesian information criterion, and determine the channel signal used for fault signal extraction;

5)对获取到的通道信号进行预处理,预处理方法包括零均值化方法去除均值和主成分分析法去除相关性特征;5) Preprocessing the acquired channel signal, and the preprocessing method includes the zero-average method to remove the mean value and the principal component analysis method to remove the correlation feature;

6)确定时延参数和核宽度的大小,基于核相关最大化获取提取向量,再提取滚动轴承故障信号;6) Determine the size of the delay parameter and the kernel width, obtain the extraction vector based on the kernel correlation maximization, and then extract the rolling bearing fault signal;

7)获取提取轮对轴承故障信号的包络谱图并确定轮对轴承故障类型。7) Obtain and extract the envelope spectrum of the wheelset bearing fault signal and determine the wheelset bearing fault type.

优选地,所述步骤1)中根据轴承的技术参数计算轴承的故障频率的具体方式为:Preferably, the specific method for calculating the fault frequency of the bearing according to the technical parameters of the bearing in the step 1) is:

确定外圈故障频率:To determine the outer ring fault frequency:

Figure BDA0002672214220000021
Figure BDA0002672214220000021

确定内圈故障频率:To determine the inner ring fault frequency:

Figure BDA0002672214220000022
Figure BDA0002672214220000022

确定滚动体故障频率:To determine the frequency of rolling element failures:

Figure BDA0002672214220000023
Figure BDA0002672214220000023

其中,fr表示转轴的旋转频率,n表示轴承的滚动体数目,φ表示载荷径向面夹角,d表示滚动体的直径,D表示轴承内径。Among them, f r represents the rotation frequency of the rotating shaft, n represents the number of rolling elements of the bearing, φ represents the angle between the radial surfaces of the load, d represents the diameter of the rolling elements, and D represents the inner diameter of the bearing.

优选地,所述步骤2)具体采用如下方式:Preferably, the step 2) is specifically adopted as follows:

将源信号分解成多个本征模态函数IMFs,IMFs=[sc1,sc2...scp-1,rp]T,原始信号与其IMFs组合形成新的多通道信号The source signal is decomposed into multiple eigenmode functions IMFs, IMFs=[sc 1 ,sc 2 ...sc p-1 ,r p ] T , the original signal and its IMFs are combined to form a new multi-channel signal

xnew(t)=[x,sc1,sc2...scp-1,rp]T x new (t)=[x,sc 1 ,sc 2 ...sc p-1 ,r p ] T

式中,sci表示不同频段的信号分量,rp表示信号余量,xnew表示新组成的多通道信号。In the formula, sc i represents the signal components of different frequency bands, r p represents the signal margin, and x new represents the newly composed multi-channel signal.

优选地,所述步骤3)具体采用如下步骤:Preferably, the step 3) specifically adopts the following steps:

协方差矩阵计算方法为The covariance matrix is calculated as

xnew=E[xnew(t)xnew T(t)]x new = E[x new (t)x new T (t)]

协方差矩阵的奇异值通过

Figure BDA0002672214220000031
得到,Λs是n个主特征值,Λs=diag{λ1≥λ2…≥λn},Λe是M-p个噪声特征值,Λe=diag{λn+1≥λn+2…≥λM},M表示信号xnew(t)的维数;Vs和Ve为酉矩阵,
Figure BDA0002672214220000032
Figure BDA0002672214220000033
The singular values of the covariance matrix are passed through
Figure BDA0002672214220000031
Obtained, Λ s is the n main eigenvalues, Λ s =diag{λ 1 ≥λ 2 ... ≥λ n }, Λ e is the Mp noise eigenvalues, Λ e =diag{λ n+1 ≥λ n+2 ...≥λ M }, M represents the dimension of the signal x new (t); V s and V e are unitary matrices,
Figure BDA0002672214220000032
Figure BDA0002672214220000033

优选地,所述步骤4)具体采用如下步骤:Preferably, the step 4) specifically adopts the following steps:

选择贝叶斯信息准则进行源数估计,贝叶斯选择模型目标函数如下式所示:The Bayesian information criterion is selected for source number estimation, and the objective function of the Bayesian selection model is as follows:

Figure BDA0002672214220000034
Figure BDA0002672214220000034

式中,

Figure BDA0002672214220000035
N代表用于计算协方差矩阵的数据长度,k代表估计的信号源数,l为非零特征值的个数,pk为信号源数为k的概率,σ为噪声功率,d为数据维度,该模型目标函数可以通过贝叶斯信息准则估计得到In the formula,
Figure BDA0002672214220000035
N is the data length used to calculate the covariance matrix, k is the estimated number of signal sources, l is the number of non-zero eigenvalues, p k is the probability that the number of signal sources is k, σ is the noise power, and d is the data dimension , the model objective function can be estimated by the Bayesian information criterion

Figure BDA0002672214220000036
Figure BDA0002672214220000036

优选地,所述步骤5)具体采用如下步骤:Preferably, the step 5) specifically adopts the following steps:

采用零均值化方法和预白化方法进行预处理Preprocessing with zero-meaning method and pre-whitening method

Z=WXZ=WX

式中,W表示预白化矩阵,X表示观测信号矩阵,Z表示预白化信号矩阵。In the formula, W represents the pre-whitening matrix, X represents the observation signal matrix, and Z represents the pre-whitening signal matrix.

优选地,所述步骤6)具体采用如下步骤:Preferably, the step 6) specifically adopts the following steps:

建立目标函数Create an objective function

Figure BDA0002672214220000037
Figure BDA0002672214220000037

式中,K(t,i)表示观测信号的格莱姆矩阵,c=[c1,..,cm]T,m表示时间变量;In the formula, K(t,i) represents the Gramma matrix of the observed signal, c=[c 1 ,..,cm ] T , m represents the time variable;

目标函数J(c)关于变量c的倒数通过下式求得The reciprocal of the objective function J(c) with respect to the variable c is obtained by the following formula

Figure BDA0002672214220000038
Figure BDA0002672214220000038

引入拉格朗日算子定义系统微分方程Introducing Lagrangian Operator to Define System Differential Equations

Figure BDA0002672214220000041
Figure BDA0002672214220000041

式中β表示拉格朗日算子,where β represents the Lagrange operator,

使c等于目标函数的倒数,并进行归一化处理Make c equal to the inverse of the objective function and normalize it

Figure BDA0002672214220000042
Figure BDA0002672214220000042

c通过由

Figure BDA0002672214220000043
确定的固定点所对应的最大特征值的特征向量得到c by
Figure BDA0002672214220000043
The eigenvector of the largest eigenvalue corresponding to the determined fixed point is obtained

Figure BDA0002672214220000044
Figure BDA0002672214220000044

式中,eig(·)确定最大特征值所对应的特征向量,则提取的信号通过下式计算得到In the formula, eig( ) determines the eigenvector corresponding to the largest eigenvalue, then the extracted signal is calculated by the following formula

y(t)=<ω,ε(t)>H=K(t,:)cy(t)=<ω,ε(t)> H = K(t,:)c

其中,y(t)表示提取的特征信号,w为提取向量,ε(t)=[ε1(t),ε2(t)…,εk(t)]T为k个信号时间序列。Among them, y(t) represents the extracted feature signal, w is the extraction vector, ε(t)=[ε 1 (t),ε 2 (t)...,ε k (t)] T is the k signal time series.

附图说明Description of drawings

图1本发明方法流程图。Fig. 1 is a flow chart of the method of the present invention.

图2外圈故障选定的通道信号。Figure 2. Outer ring fault selected channel signal.

图3提取到的外圈故障信号及其包络谱。Figure 3. The extracted outer ring fault signal and its envelope spectrum.

图4核宽度取0.5时提取的外圈故障信号及其包络谱分析结果。Figure 4. The outer ring fault signal and its envelope spectrum analysis results when the core width is 0.5.

图5核宽度取1时提取的外圈故障信号及其包络谱分析结果。Figure 5. The outer ring fault signal and its envelope spectrum analysis results extracted when the core width is 1.

具体实施方式Detailed ways

下面结合附图对本发明的实施具体说明,算法步骤如图1所示:Below in conjunction with the accompanying drawings, the implementation of the present invention will be specifically described, and the algorithm steps are shown in Figure 1:

获取数据及故障特征,分别采集滚动轴承处于不同故障状态下的振动加速度数据,包括滚动体故障,内圈故障,外圈故障,根据轴承的技术参数计算轴承的故障频率,计算方法如式(1)-(3)所示,选取的故障轴承的局部故障为外圈故障。Acquire data and fault characteristics, respectively collect the vibration acceleration data of the rolling bearing under different fault states, including rolling element fault, inner ring fault, and outer ring fault, and calculate the fault frequency of the bearing according to the technical parameters of the bearing. The calculation method is as formula (1) As shown in -(3), the partial fault of the selected faulty bearing is the outer ring fault.

外圈故障频率:Outer ring fault frequency:

Figure BDA0002672214220000051
Figure BDA0002672214220000051

内圈故障频率:Inner ring fault frequency:

Figure BDA0002672214220000052
Figure BDA0002672214220000052

滚动体故障频率:Rolling element failure frequency:

Figure BDA0002672214220000053
Figure BDA0002672214220000053

fr表示转轴的旋转频率,n表示轴承的滚动体数目,φ表示载荷径向面夹角,d表示滚动体的直径,D表示轴承内径;fr represents the rotation frequency of the rotating shaft, n represents the number of rolling elements of the bearing, φ represents the angle between the radial surfaces of the load, d represents the diameter of the rolling elements, and D represents the inner diameter of the bearing;

2)将源信号通过EMD算法分解成多个本征模态函数IMFs,IMFs=[sc1,sc2...scp-1,rp]T,原始信号与其IMFs组合形成新的多通道信号xnew(t)=[x,sc1,sc2...scp-1,rp]T,如图2所示。2) Decompose the source signal into multiple eigenmode function IMFs by EMD algorithm, IMFs=[sc 1 ,sc 2 ...sc p-1 ,r p ] T , the original signal and its IMFs are combined to form a new multi-channel The signal x new (t)=[x, sc 1 , sc 2 . . . sc p-1 , r p ] T , as shown in FIG. 2 .

3)协方差矩阵计算,协方差矩阵计算方法为xnew=E[xnew(t)xnew T(t)]。3) Covariance matrix calculation, the covariance matrix calculation method is x new =E[x new (t)x new T (t)].

4)奇异值分解。协方差矩阵的奇异值可以通过

Figure BDA0002672214220000054
得到,其奇异值为Λs={λ12,...,λn}。4) Singular value decomposition. The singular values of the covariance matrix can be obtained by
Figure BDA0002672214220000054
Obtained, its singular value is Λ s ={λ 12 ,...,λ n }.

5)源数估计。本发明选择贝叶斯信息准则进行源数估计。5) Source number estimation. The invention selects the Bayesian information criterion to estimate the number of sources.

贝叶斯选择模型目标函数如式(4)所示:The objective function of Bayesian selection model is shown in formula (4):

Figure BDA0002672214220000055
Figure BDA0002672214220000055

式中,N代表用于计算协方差矩阵的数据长度,k代表估计的信号源数,该模型目标函数可以通过贝叶斯信息准则估计得到,如式(5)所示In the formula, N represents the data length used to calculate the covariance matrix, and k represents the estimated number of signal sources. The objective function of the model can be estimated by the Bayesian information criterion, as shown in equation (5)

Figure BDA0002672214220000056
Figure BDA0002672214220000056

6)为了消除直流成分和不同特征相关性的干扰,采用零均值化方法和预白化方法对IMFs进行预处理,如式(6)所示:6) In order to eliminate the interference of the DC component and the correlation of different features, the zero-average method and the pre-whitening method are used to preprocess the IMFs, as shown in formula (6):

Z=WX (6)Z=WX (6)

式中,W表示预白化矩阵,X表示观测信号矩阵,Z表示预白化信号矩阵。In the formula, W represents the pre-whitening matrix, X represents the observation signal matrix, and Z represents the pre-whitening signal matrix.

7)参数选定。选定时延参数及核函数核宽度,根据核相关最大化方法获取提取向量,并提取目标信号用于早期故障诊断。7) Parameter selection. The delay parameters and the kernel width of the kernel function are selected, the extraction vector is obtained according to the kernel correlation maximization method, and the target signal is extracted for early fault diagnosis.

时延参数τ反应了轮对轴承故障信号的周期特性,可通过轴承转速和结构参数计算得到,本次实验τ为57,核函数核宽度设置为5。The delay parameter τ reflects the periodic characteristics of the wheelset bearing fault signal, which can be calculated from the bearing speed and structural parameters. In this experiment, τ is 57, and the kernel width of the kernel function is set to 5.

通过最大化时延信号与原信号的自相关函数,能够提取到满足条件的目标信号。根据自相关函数最大化准则,目标函数能够通过式(7)获得By maximizing the autocorrelation function between the delayed signal and the original signal, the target signal that meets the conditions can be extracted. According to the maximization criterion of the autocorrelation function, the objective function can be obtained by formula (7)

Figure BDA0002672214220000061
Figure BDA0002672214220000061

式中,K(t,i)表示观测信号的格莱姆矩阵,c=[c1,..,cm]T,m表示时间变量。In the formula, K(t,i) represents the Gramma matrix of the observed signal, c=[c 1 ,..,cm ] T , and m represents the time variable.

目标函数J(c)关于变量c的倒数可通过式(8)求得The reciprocal of the objective function J(c) about the variable c can be obtained by formula (8)

Figure BDA0002672214220000062
Figure BDA0002672214220000062

引入拉格朗日算子定义系统微分方程,如式(9)所示The Lagrangian operator is introduced to define the system differential equation, as shown in equation (9)

Figure BDA0002672214220000063
Figure BDA0002672214220000063

式中β表示拉格朗日算子。where β represents the Lagrangian operator.

式(9)可以通过两步固定点算法迭代规则求得。使c等于目标函数的倒数,并进行归一化处理以,如式(10)所示,(10)中的2βm由于归一化步骤省略。Equation (9) can be obtained by the iterative rule of the two-step fixed-point algorithm. Make c equal to the inverse of the objective function, and perform normalization processing to, as shown in equation (10), 2βm in (10) is omitted due to the normalization step.

Figure BDA0002672214220000064
Figure BDA0002672214220000064

式(10)中的迭代规则可以通过由

Figure BDA0002672214220000065
确定的固定点所对应的最大特征值的特征向量得到。因此,c能够通过(11)获得The iterative rule in Eq. (10) can be determined by
Figure BDA0002672214220000065
The eigenvector of the largest eigenvalue corresponding to the determined fixed point is obtained. Therefore, c can be obtained by (11)

Figure BDA0002672214220000066
Figure BDA0002672214220000066

式中,eig(·)确定最大特征值所对应的特征向量,则提取的信号可通过式(12)计算得到,提取到的信号如图3(a)所示In the formula, eig( ) determines the eigenvector corresponding to the maximum eigenvalue, then the extracted signal can be calculated by formula (12), and the extracted signal is shown in Figure 3(a)

y(t)=<ω,ε(t)>H=K(t,:)c (12)y(t)=<ω,ε(t)> H = K(t,:)c (12)

8)获取提取轮对轴承故障信号的包络谱图并确定轮对轴承故障类型,如图3(b)所示。8) Obtain and extract the envelope spectrum of the wheelset bearing fault signal and determine the wheelset bearing fault type, as shown in Figure 3(b).

9)本发明进一步分析了核宽度的大小对故障信号提取结果的影响,本发明通过不同尺度下的枚举方法来选择最优核宽度。例如,采用核宽度值为0.1、0.5、1.5、10来提取故障信号。采用核宽度为0.1和1的故障信号提取结果如图4和图5所示。由图可知核宽度取0.1时的故障信号提取效果要明显优于核宽度取1时的故障信号提取效果,结合核宽度取5时的实验结果表明,核宽度对于算法性能影响显著。9) The present invention further analyzes the influence of the size of the kernel width on the extraction result of the fault signal, and the present invention selects the optimal kernel width through enumeration methods under different scales. For example, kernel width values of 0.1, 0.5, 1.5, 10 are used to extract fault signals. The extraction results of fault signals with kernel widths of 0.1 and 1 are shown in Fig. 4 and Fig. 5. It can be seen from the figure that the extraction effect of the fault signal when the kernel width is 0.1 is significantly better than that when the kernel width is 1. Combined with the experimental results when the kernel width is 5, it shows that the kernel width has a significant impact on the performance of the algorithm.

Claims (7)

1.一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,包括以下步骤:1. a rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation, is characterized in that, comprises the following steps: 1)获取实验数据:分别采集滚动轴承处于不同故障状态下的振动加速度数据,所述不同故障状态包括滚动体故障,内圈故障,外圈故障,根据轴承的技术参数计算轴承的故障频率;1) Obtaining experimental data: separately collecting vibration acceleration data of the rolling bearing under different fault states, the different fault states include rolling element fault, inner ring fault, and outer ring fault, and calculating the fault frequency of the bearing according to the technical parameters of the bearing; 2)原始信号通过经验模态分解的方法分解为多通道信号;2) The original signal is decomposed into multi-channel signals by the method of empirical mode decomposition; 3)获取多通道信号的协方差矩阵,进行奇异值分解;3) Obtain the covariance matrix of the multi-channel signal, and perform singular value decomposition; 4)基于贝叶斯信息准则获取源信号数目,确定用于故障信号提取的通道信号;4) Obtain the number of source signals based on the Bayesian information criterion, and determine the channel signal used for fault signal extraction; 5)对获取到的通道信号进行预处理,预处理方法包括零均值化方法去除均值和主成分分析法去除相关性特征;5) Preprocessing the acquired channel signal, and the preprocessing method includes the zero-average method to remove the mean value and the principal component analysis method to remove the correlation feature; 6)确定时延参数和核宽度的大小,基于核相关最大化获取提取向量,再提取滚动轴承故障信号;6) Determine the size of the delay parameter and the kernel width, obtain the extraction vector based on the kernel correlation maximization, and then extract the rolling bearing fault signal; 7)获取提取轮对轴承故障信号的包络谱图并确定轮对轴承故障类型。7) Obtain and extract the envelope spectrum of the wheelset bearing fault signal and determine the wheelset bearing fault type. 2.如权利要求1所述的一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,所述步骤1)中根据轴承的技术参数计算轴承的故障频率的具体方式为:2. A method for extracting fault signals of rolling bearings based on empirical mode decomposition and nuclear correlation as claimed in claim 1, wherein the specific method for calculating the fault frequency of the bearing according to the technical parameters of the bearing in the step 1) is as follows: : 确定外圈故障频率:To determine the outer ring fault frequency:
Figure FDA0002672214210000011
Figure FDA0002672214210000011
确定内圈故障频率:To determine the inner ring fault frequency:
Figure FDA0002672214210000012
Figure FDA0002672214210000012
确定滚动体故障频率:To determine the frequency of rolling element failures:
Figure FDA0002672214210000013
Figure FDA0002672214210000013
其中,fr表示转轴的旋转频率,n表示轴承的滚动体数目,φ表示载荷径向面夹角,d表示滚动体的直径,D表示轴承内径。Among them, f r represents the rotation frequency of the rotating shaft, n represents the number of rolling elements of the bearing, φ represents the angle between the radial surfaces of the load, d represents the diameter of the rolling elements, and D represents the inner diameter of the bearing.
3.如权利要求1所述的一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,所述步骤2)具体采用如下方式:3. A kind of rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation as claimed in claim 1, is characterized in that, described step 2) specifically adopts the following way: 将源信号分解成多个本征模态函数IMFs,IMFs=[sc1,sc2...scp-1,rp]T,原始信号与其IMFs组合形成新的多通道信号The source signal is decomposed into multiple eigenmode functions IMFs, IMFs=[sc 1 , sc 2 ... sc p-1 , r p ] T , the original signal and its IMFs are combined to form a new multi-channel signal xnew(t)=[x,sc1,sc2...scp-1,rp]T x new (t)=[x, sc 1 , sc 2 . . . sc p-1 , r p ] T 式中,sci表示不同频段的信号分量,rp表示信号余量,xnew表示新组成的多通道信号。In the formula, sc i represents the signal components of different frequency bands, r p represents the signal margin, and x new represents the newly composed multi-channel signal. 4.如权利要求1所述的一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,所述步骤3)具体采用如下步骤:4. a kind of rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation as claimed in claim 1, is characterized in that, described step 3) specifically adopts following steps: 协方差矩阵计算方法为The covariance matrix is calculated as xnew=E[xnew(t)xnew T(t)]x new = E[x new (t)x new T (t)] 协方差矩阵的奇异值通过
Figure FDA0002672214210000024
得到,Λs是n个主特征值,Λs=diag{λ1≥λ2...≥λn},Λe是M-p个噪声特征值,Λe=diag{λn+1≥λn+2...≥λM},M表示信号xnew(t)的维数;Vs和Ve为酉矩阵,
Figure FDA0002672214210000025
Figure FDA0002672214210000026
The singular values of the covariance matrix are passed through
Figure FDA0002672214210000024
Obtained, Λ s is the n main eigenvalues, Λ s =diag{λ 1 ≥λ 2 ... ≥λ n }, Λ e is the Mp noise eigenvalues, Λ e =diag{λ n+1 ≥λ n +2 ...≥λ M }, M represents the dimension of the signal x new (t); V s and V e are unitary matrices,
Figure FDA0002672214210000025
Figure FDA0002672214210000026
5.如权利要求1所述的一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,所述步骤4)具体采用如下步骤:5. a kind of rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation as claimed in claim 1, is characterized in that, described step 4) specifically adopts following steps: 选择贝叶斯信息准则进行源数估计,贝叶斯选择模型目标函数如下式所示:The Bayesian information criterion is selected for source number estimation, and the objective function of the Bayesian selection model is as follows:
Figure FDA0002672214210000021
Figure FDA0002672214210000021
式中,
Figure FDA0002672214210000022
N代表用于计算协方差矩阵的数据长度,k代表估计的信号源数,I为非零特征值的个数,pk为信号源数为k的概率,σ为噪声功率,d为数据维度,该模型目标函数可以通过贝叶斯信息准则估计得到
In the formula,
Figure FDA0002672214210000022
N is the data length used to calculate the covariance matrix, k is the estimated number of signal sources, I is the number of non-zero eigenvalues, p k is the probability that the number of signal sources is k, σ is the noise power, and d is the data dimension , the model objective function can be estimated by the Bayesian information criterion
Figure FDA0002672214210000023
Figure FDA0002672214210000023
6.如权利要求1所述的一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,所述步骤5)具体采用如下步骤:6. A kind of rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation as claimed in claim 1, is characterized in that, described step 5) specifically adopts following steps: 采用零均值化方法和预白化方法进行预处理Preprocessing with zero-meaning method and pre-whitening method Z=WXZ=WX 式中,W表示预白化矩阵,X表示观测信号矩阵,Z表示预白化信号矩阵。In the formula, W represents the pre-whitening matrix, X represents the observation signal matrix, and Z represents the pre-whitening signal matrix. 7.如权利要求1所述的一种基于经验模态分解和核相关的滚动轴承故障信号提取方法,其特征在于,所述步骤6)具体采用如下步骤:7. A kind of rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation as claimed in claim 1, is characterized in that, described step 6) specifically adopts following steps: 建立目标函数Create an objective function
Figure FDA0002672214210000031
Figure FDA0002672214210000031
式中,K(t,i)表示观测信号的格莱姆矩阵,c=[c1,..,cm]T,m表示时间变量;In the formula, K(t, i) represents the Gramma matrix of the observed signal, c=[c 1 , .., cm ] T , m represents the time variable; 目标函数J(c)关于变量c的倒数通过下式求得The reciprocal of the objective function J(c) with respect to the variable c is obtained by the following formula
Figure FDA0002672214210000032
Figure FDA0002672214210000032
引入拉格朗日算子定义系统微分方程Introducing Lagrangian Operator to Define System Differential Equations
Figure FDA0002672214210000033
Figure FDA0002672214210000033
式中β表示拉格朗日算子,where β represents the Lagrange operator, 使c等于目标函数的倒数,并进行归一化处理Make c equal to the inverse of the objective function and normalize it
Figure FDA0002672214210000034
Figure FDA0002672214210000034
c通过由
Figure FDA0002672214210000035
确定的固定点所对应的最大特征值的特征向量得到
c by
Figure FDA0002672214210000035
The eigenvector of the largest eigenvalue corresponding to the determined fixed point is obtained
Figure FDA0002672214210000036
Figure FDA0002672214210000036
式中,eig(·)确定最大特征值所对应的特征向量,则提取的信号通过下式计算得到In the formula, eig( ) determines the eigenvector corresponding to the largest eigenvalue, then the extracted signal is calculated by the following formula y(t)=<ω,ε(t)>H=K(t,:)cy(t)=<ω,ε(t)> H =K(t,:)c 其中,y(t)表示提取的特征信号,w为提取向量,ε(t)=[ε1(t),ε2(t)...,εk(t)]T为k个信号时间序列。Among them, y(t) represents the extracted feature signal, w is the extraction vector, ε(t)=[ε 1 (t), ε 2 (t)...,ε k (t)] T is the k signal time sequence.
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