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

Abstract

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.

Description

Fault Diagnosis Method of Rolling Bearing Based on Empirical Mode Decomposition and Kernel Correlation

technical field

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.

Background technique

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.

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.

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.

SUMMARY OF THE INVENTION

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:

A method for extracting fault signals of rolling bearings based on empirical mode decomposition and kernel correlation, comprising the following steps:

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) The original signal is decomposed into multi-channel signals by the method of empirical mode decomposition;

3) Obtain the covariance matrix of the multi-channel signal, and perform singular value decomposition;

4) Obtain the number of source signals based on the Bayesian information criterion, and determine the channel signal used for fault signal extraction;

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) 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) Obtain and extract the envelope spectrum of the wheelset bearing fault signal and determine the wheelset bearing fault type.

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:

To determine the outer ring fault frequency:

To determine the inner ring fault frequency:

To determine the frequency of rolling element failures:

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.

Preferably, the step 2) is specifically adopted as follows:

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

x _new (t)=[x,sc ₁ ,sc ₂ ...sc _p-1 ,r _p ] ^T

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.

Preferably, the step 3) specifically adopts the following steps:

The covariance matrix is calculated as

x _new = E[x _new (t)x _new ^T (t)]

得到，Λ_s是n个主特征值，Λ_s＝diag{λ₁≥λ₂…≥λ_n}，Λ_e是M-p个噪声特征值，Λ_e＝diag{λ_n+1≥λ_n+2…≥λ_M}，M表示信号x_new(t)的维数；V_s和V_e为酉矩阵，

The singular values of the covariance matrix are passed through

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,

Preferably, the step 4) specifically adopts the following steps:

The Bayesian information criterion is selected for source number estimation, and the objective function of the Bayesian selection model is as follows:

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，p_k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,

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

Preferably, the step 5) specifically adopts the following steps:

Preprocessing with zero-meaning method and pre-whitening method

Z=WX

In the formula, W represents the pre-whitening matrix, X represents the observation signal matrix, and Z represents the pre-whitening signal matrix.

Preferably, the step 6) specifically adopts the following steps:

Create an objective function

In the formula, K(t,i) represents the Gramma matrix of the observed signal, c=[c ₁ ,..,cm ] ^T , _m represents the time variable;

The reciprocal of the objective function J(c) with respect to the variable c is obtained by the following formula

Introducing Lagrangian Operator to Define System Differential Equations

where β represents the Lagrange operator,

Make c equal to the inverse of the objective function and normalize it

确定的固定点所对应的最大特征值的特征向量得到c by

The eigenvector of the largest eigenvalue corresponding to the determined fixed point is obtained

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,:)c

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.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Figure 2. Outer ring fault selected channel signal.

Figure 3. The extracted outer ring fault signal and its envelope spectrum.

Figure 4. The outer ring fault signal and its envelope spectrum analysis results when the core width is 0.5.

Figure 5. The outer ring fault signal and its envelope spectrum analysis results extracted when the core width is 1.

Detailed ways

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:

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.

Outer ring fault frequency:

Inner ring fault frequency:

Rolling element failure frequency:

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) 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) Covariance matrix calculation, the covariance matrix calculation method is x _new =E[x _new (t)x _new ^T (t)].

得到，其奇异值为Λ_s＝{λ₁,λ₂,...,λ_n}。4) Singular value decomposition. The singular values of the covariance matrix can be obtained by

Obtained, its singular value is Λ _s ={λ ₁ ,λ ₂ ,...,λ _n }.

5) Source number estimation. The invention selects the Bayesian information criterion to estimate the number of sources.

The objective function of Bayesian selection model is shown in formula (4):

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)

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)

In the formula, W represents the pre-whitening matrix, X represents the observation signal matrix, and Z represents the pre-whitening signal matrix.

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.

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.

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)

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.

The reciprocal of the objective function J(c) about the variable c can be obtained by formula (8)

The Lagrangian operator is introduced to define the system differential equation, as shown in equation (9)

where β represents the Lagrangian operator.

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.

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

The eigenvector of the largest eigenvalue corresponding to the determined fixed point is obtained. Therefore, c can be obtained by (11)

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)

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) 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. a rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation, is characterized in that, comprises the following steps: 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) The original signal is decomposed into multi-channel signals by the method of empirical mode decomposition; 3) Obtain the covariance matrix of the multi-channel signal, and perform singular value decomposition; 4) Obtain the number of source signals based on the Bayesian information criterion, and determine the channel signal used for fault signal extraction; 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) 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) Obtain and extract the envelope spectrum of the wheelset bearing fault signal and determine the wheelset bearing fault type. 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: : To determine the outer ring fault frequency:

To determine the inner ring fault frequency:

To determine the frequency of rolling element failures:

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. 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: 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 x _new (t)=[x, sc ₁ , sc ₂ . . . sc _p-1 , r _p ] ^T 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. 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: The covariance matrix is calculated as x _new = E[x _new (t)x _new ^T (t)] The singular values of the covariance matrix are passed through

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,

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: The Bayesian information criterion is selected for source number estimation, and the objective function of the Bayesian selection model is as follows:

In the formula,

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

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: Preprocessing with zero-meaning method and pre-whitening method Z=WX In the formula, W represents the pre-whitening matrix, X represents the observation signal matrix, and Z represents the pre-whitening signal matrix. 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: Create an objective function

In the formula, K(t, i) represents the Gramma matrix of the observed signal, c=[c ₁ , .., cm ] ^T , _m represents the time variable; The reciprocal of the objective function J(c) with respect to the variable c is obtained by the following formula

Introducing Lagrangian Operator to Define System Differential Equations

where β represents the Lagrange operator, Make c equal to the inverse of the objective function and normalize it

c by

The eigenvector of the largest eigenvalue corresponding to the determined fixed point is obtained

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,:)c 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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