CN112067296B - 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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CN112067296B
CN112067296B CN202010936754.3A CN202010936754A CN112067296B CN 112067296 B CN112067296 B CN 112067296B CN 202010936754 A CN202010936754 A CN 202010936754A CN 112067296 B CN112067296 B CN 112067296B
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fault
rolling bearing
empirical mode
mode decomposition
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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

The invention discloses a rolling bearing fault diagnosis method based on empirical mode decomposition and nuclear correlation. The method comprises the steps of firstly decomposing an acquired single-channel signal into a virtual multi-channel signal by adopting an empirical mode decomposition method, then selecting the multi-channel signal by adopting a Bayesian information criterion, then extracting a fault signal of the rolling bearing based on nuclear correlation maximization, and finally performing fault diagnosis on the extracted signal by adopting an envelope analysis method. The invention further analyzes the influence of the change of the kernel width on the extraction effect of the fault signal. In order to verify the effectiveness and the advancement of the proposed method, the method is verified by using wheel set bearing signals, and a good experimental result is obtained.

Description

Rolling bearing fault diagnosis method based on empirical mode decomposition and nuclear correlation
Technical Field
The invention belongs to the field of mechanical engineering. The invention relates to a rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation.
Background
The rolling bearing has wide application in the field of mechanical engineering, and has high failure rate under the working conditions of high strength and high density. Therefore, it is important to monitor the state of the rolling bearing by a fault diagnosis method and replace the faulty bearing in real time to ensure the normal operation of the mechanical equipment.
The blind source separation algorithm is one of the branches of many classical fault diagnosis algorithms for separating the different components of a mixed signal. But since both the source signal and the mixing matrix are unknown, the order of the separated signals cannot be determined. In field practice, important information in a mixed signal is carried by one signal source, other multi-bit interfering or noisy signals. Therefore, a blind source extraction algorithm is provided, and the algorithm only extracts specific signal components in the mixed signal, so that the large calculation amount brought by the blind source separation algorithm is avoided.
A prerequisite for blind source extraction and blind source separation algorithms is to acquire multi-channel source signals at different monitoring locations. However, due to the influence of actual industrial production conditions, it is difficult to acquire a multi-channel source signal, compared with the method, a single-channel signal is easier to acquire, and blind source extraction based on the single-channel signal is more suitable for the actual situation of field application.
Disclosure of Invention
The invention aims to monitor the state of a rolling bearing, and distinguish and diagnose faults of an inner ring, an outer ring or a rolling body of the bearing according to characteristic frequencies of different fault types of the bearing. The invention can accurately distinguish the fault types of the rolling bearing under the condition that the rolling bearing signal is interfered by impact noise. The invention specifically adopts the following technical scheme:
a rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation comprises the following steps:
1) acquiring experimental data: respectively collecting vibration acceleration data of a rolling bearing in different fault states, wherein the different fault states comprise a rolling body fault, an inner ring fault and an outer ring fault, and calculating the fault frequency of the bearing according to technical parameters of the bearing;
2) decomposing an original signal into a multi-channel signal by an empirical mode decomposition method;
3) acquiring a covariance matrix of a multi-channel signal, and performing singular value decomposition;
4) acquiring the number of source signals based on a Bayesian information criterion, and determining channel signals for extracting fault signals;
5) preprocessing the acquired channel signals, wherein the preprocessing method comprises mean value removal by a zero-averaging method and correlation characteristic removal by a principal component analysis method;
6) determining time delay parameters and the size of the kernel width, acquiring an extraction vector based on the kernel correlation maximization, and extracting a rolling bearing fault signal;
7) and acquiring an envelope spectrogram of the extracted wheel set bearing fault signal and determining the type of the wheel set bearing fault.
Preferably, the specific way of calculating the failure frequency of the bearing according to the technical parameters of the bearing in the step 1) is as follows:
determining outer ring fault frequency:
Figure GDA0003244739050000021
determining the failure frequency of the inner ring:
Figure GDA0003244739050000022
determining the fault frequency of the rolling body:
Figure GDA0003244739050000023
wherein f isrThe rotating frequency of the rotating shaft is shown, n is the number of rolling elements of the bearing, phi is the included angle of a load radial surface, D is the diameter of the rolling elements, and D is the inner diameter of the bearing.
Preferably, the step 2) specifically adopts the following mode:
decomposing a source signal into a plurality of eigenmode functions IMFs ═ sc1,sc2...scp-1,rp]TThe original signal is combined with its IMFs to form a new multi-channel signal
xnew(t)＝[x,sc1,sc2...scp-1,rp]T
In the formula, sciRepresenting signal components of different frequency bands, rpRepresenting the signal margin, xnewRepresenting the newly composed multi-channel signal.
Preferably, the step 3) specifically adopts the following steps:
the covariance matrix calculation method comprises
xnew＝E[xnew(t)xnew T(t)]
Singular value pass of covariance matrix
Figure GDA0003244739050000031
To obtain asIs the n principal eigenvalues, Λs＝diag{λ1≥λ2…≥λn}，ΛeIs the M-p noise eigenvalues, Λe＝diag{λn+1≥λn+2…≥λMM denotes the signal xnew(t) a dimension; vsAnd VeIs a unitary matrix of the first phase,
Figure GDA0003244739050000032
Figure GDA0003244739050000033
Figure GDA0003244739050000034
preferably, the step 4) specifically adopts the following steps:
and selecting a Bayesian information criterion for source number estimation, wherein a Bayesian selection model objective function is shown as the following formula:
Figure GDA0003244739050000035
in the formula (I), the compound is shown in the specification,
Figure GDA0003244739050000036
n represents the data length for calculating the covariance matrix, k represents the number of estimated signal sources, l is the number of non-zero eigenvalues, pkThe model objective function can be estimated by Bayesian information criterion for the probability that the signal source number is k, sigma is noise power, and d is data dimension
Figure GDA0003244739050000037
Preferably, the step 5) specifically adopts the following steps:
preprocessing by using zero-averaging method and pre-whitening method
Z＝WX
In the formula, W represents a pre-whitening matrix, X represents an observed signal matrix, and Z represents a pre-whitening signal matrix.
Preferably, the step 6) specifically adopts the following steps:
establishing an objective function
Figure GDA0003244739050000038
Where K (t, i) denotes a gray matrix of observed signals, and c ═ c1,..,cm]TM represents a time variable;
the reciprocal of the variable c of the objective function J (c) is obtained by the following formula
Figure GDA0003244739050000039
Lagrange operator is introduced to define system differential equation
Figure GDA0003244739050000041
Where beta represents the lagrangian operator,
c is made equal to the reciprocal of the objective function and normalized
Figure GDA0003244739050000042
c by passing through
Figure GDA0003244739050000043
Obtaining the characteristic vector of the maximum characteristic value corresponding to the determined fixed point
Figure GDA0003244739050000044
In the formula, eig (-) determines the feature vector corresponding to the maximum feature value, and the extracted signal is calculated by the following formula
y(t)＝<ω,ε(t)>H＝K(t,:)c
Where y (t) represents the extracted feature signal, ω is the extraction vector, and ∈ (t) — [ epsilon [ ]1(t),ε2(t)…,εk(t)]TAre k signal time series.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 shows the outer lane fault selected channel signal.
Fig. 3 extracts an outer ring fault signal and an envelope spectrum thereof.
Fig. 4 shows the outer ring fault signal extracted when the kernel width is 0.5 and the envelope spectrum analysis result thereof.
Fig. 5 shows the outer ring fault signal extracted when the kernel width is 1 and the envelope spectrum analysis result thereof.
Detailed Description
The following detailed description of the implementation of the present invention is made with reference to the accompanying drawings, in which the algorithm steps are shown in fig. 1:
acquiring data and fault characteristics, respectively acquiring vibration acceleration data of the rolling bearing in different fault states, including a rolling body fault, an inner ring fault and an outer ring fault, calculating the fault frequency of the bearing according to technical parameters of the bearing, wherein the calculation method is shown in the formulas (1) to (3), and the selected local fault of the faulty bearing is the outer ring fault.
Outer ring fault frequency:
Figure GDA0003244739050000051
inner ring failure frequency:
Figure GDA0003244739050000052
frequency of rolling element failure:
Figure GDA0003244739050000053
fr represents the rotation frequency of the rotating shaft, n represents the number of rolling elements of the bearing, phi represents the included angle of a load radial surface, D represents the diameter of the rolling elements, and D represents the inner diameter of the bearing;
2) decomposing a source signal into a plurality of intrinsic mode functions IMFs (intrinsic mode functions) through an EMD (empirical mode decomposition) algorithm, wherein the IMFs is sc1,sc2...scp-1,rp]TThe original signal is combined with its IMFs to form a new multi-channel signal xnew(t)＝[x,sc1,sc2...scp-1,rp]TAs shown in fig. 2.
3) Covariance matrix calculation with xnew＝E[xnew(t)xnew T(t)]。
4) And (5) singular value decomposition. The singular values of the covariance matrix may be calculated by
Figure GDA0003244739050000054
Obtained with a singular value of Λs＝{λ1,λ2,...,λn}。
5) And estimating the source number. The invention selects Bayesian information criterion to estimate the source number.
The Bayesian selection model objective function is shown as equation (4):
Figure GDA0003244739050000055
in the formula, N represents the data length for calculating the covariance matrix, k represents the number of estimated signal sources, and the model objective function can be estimated by Bayesian information criterion, as shown in formula (5)
Figure GDA0003244739050000056
6) In order to eliminate the interference of direct current components and different characteristic correlations, the IMFs are preprocessed by a zero-averaging method and a pre-whitening method, as shown in formula (6):
Z＝WX (6)
in the formula, W represents a pre-whitening matrix, X represents an observed signal matrix, and Z represents a pre-whitening signal matrix.
7) And (4) selecting parameters. Selecting a time delay parameter and a kernel width of a kernel function, obtaining an extraction vector according to a kernel correlation maximization method, and extracting a target signal for early fault diagnosis.
The time delay parameter tau reflects the periodic characteristics of the wheel set bearing fault signals and can be obtained through calculation of the bearing rotating speed and the structural parameters, the tau in the experiment is 57, and the kernel width of the kernel function is set to be 5.
By maximizing the autocorrelation function of the time delay signal and the original signal, a target signal meeting the conditions can be extracted. The objective function can be obtained by equation (7) according to the autocorrelation function maximization criterion
Figure GDA0003244739050000061
Where K (t, i) denotes a gray matrix of observed signals, and c ═ c1,..,cm]TAnd m represents a time variable.
The reciprocal of the objective function J (c) with respect to the variable c can be obtained by the following equation (8)
Figure GDA0003244739050000062
Lagrange operators are introduced to define a system differential equation as shown in a formula (9)
Figure GDA0003244739050000063
Where β represents the lagrangian operator.
Equation (9) can be obtained by a two-step fixed-point algorithm iteration rule. Let c equal the inverse of the objective function and perform a normalization process so that 2 β m in (10) is omitted due to the normalization step, as shown in equation (10).
Figure GDA0003244739050000064
The iteration rule in equation (10) can be determined by
Figure GDA0003244739050000065
And obtaining the characteristic vector of the maximum characteristic value corresponding to the determined fixed point. Thus, c can be obtained by (11)
Figure GDA0003244739050000066
In the formula, eig (·) determines the feature vector corresponding to the maximum feature value, the extracted signal can be obtained by calculating the formula (12), and the extracted signal is as shown in fig. 3(a)
y(t)＝<ω,ε(t)>H＝K(t,:)c (12)
8) And acquiring an envelope spectrogram of the extracted wheel set bearing fault signal and determining the type of the wheel set bearing fault, as shown in fig. 3 (b).
9) The method further analyzes the influence of the kernel width on the fault signal extraction result, and selects the optimal kernel width by an enumeration method under different scales. For example, the core width values of 0.1, 0.5, 1.5, 10 are used to extract the fault signal. The results of the fault signal extraction using the core widths of 0.1 and 1 are shown in fig. 4 and 5. It can be known from the figure that the fault signal extraction effect when the kernel width is 0.1 is obviously better than that when the kernel width is 1, and the combination of the experimental result when the kernel width is 5 shows that the kernel width has a significant influence 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 by comprising the following steps:
1) acquiring experimental data: respectively collecting vibration acceleration data of a rolling bearing in different fault states, wherein the different fault states comprise a rolling body fault, an inner ring fault and an outer ring fault, and calculating the fault frequency of the bearing according to technical parameters of the bearing;
2) decomposing an original signal into a multi-channel signal by an empirical mode decomposition method;
3) acquiring a covariance matrix of a multi-channel signal, and performing singular value decomposition;
4) acquiring the number of source signals based on a Bayesian information criterion, and determining channel signals for extracting fault signals;
5) preprocessing the acquired channel signals, wherein the preprocessing method comprises mean value removal by a zero-averaging method and correlation characteristic removal by a principal component analysis method;
6) determining time delay parameters and the size of the kernel width, acquiring an extraction vector based on the kernel correlation maximization, and extracting a rolling bearing fault signal;
7) and acquiring an envelope spectrogram of the extracted wheel set bearing fault signal and determining the type of the wheel set bearing fault.
2. The rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation according to claim 1, wherein the specific way of calculating the fault frequency of the bearing according to the technical parameters of the bearing in the step 1) is as follows:
determining outer ring fault frequency:
Figure FDA0003187557910000011
determining the failure frequency of the inner ring:
Figure FDA0003187557910000012
determining the fault frequency of the rolling body:
Figure FDA0003187557910000013
wherein f isrThe rotating frequency of the rotating shaft is shown, n is the number of rolling elements of the bearing, phi is the included angle of a load radial surface, D is the diameter of the rolling elements, and D is the inner diameter of the bearing.
3. The rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation according to claim 1, characterized in that the step 2) specifically adopts the following mode:
decomposing a source signal into a plurality of eigenmode functions IMFs ═ sc1,sc2...scp-1,rp]TThe original signal is combined with its IMFs to form a new multi-channel signal
xnew(t)＝[x,sc1,sc2...scp-1,rp]T
In the formula, sciRepresenting signal components of different frequency bands, rpRepresenting the signal margin, xnewRepresenting the newly composed multi-channel signal.
4. The rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation according to claim 1, wherein the step 3) specifically adopts the following steps:
the covariance matrix calculation method comprises
xnew＝E[xnew(t)xnew T(t)]
Singular value pass of covariance matrix
Figure FDA0003187557910000024
To obtain asIs the n principal eigenvalues, Λs=diag{λ1≥λ2…≥λn}，ΛeIs the M-p noise eigenvalues, Λe=diag{λn+1≥λn+2…≥λMM denotes the signal xnew(t) a dimension; vsAnd VeIs a unitary matrix of the first phase,
Figure FDA0003187557910000025
Figure FDA0003187557910000026
5. the rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation according to claim 1, wherein the step 4) specifically adopts the following steps:
and selecting a Bayesian information criterion for source number estimation, wherein a Bayesian selection model objective function is shown as the following formula:
Figure FDA0003187557910000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003187557910000022
n represents the data length for calculating the covariance matrix, k represents the number of estimated signal sources, l is the number of non-zero eigenvalues, pkThe model objective function can be estimated by Bayesian information criterion for the probability that the signal source number is k, sigma is noise power, and d is data dimension
Figure FDA0003187557910000023
6. The rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation according to claim 1, wherein the step 5) specifically adopts the following steps:
preprocessing by using zero-averaging method and pre-whitening method
Z＝WX
In the formula, W represents a pre-whitening matrix, X represents an observed signal matrix, and Z represents a pre-whitening signal matrix.
7. The rolling bearing fault signal extraction method based on empirical mode decomposition and nuclear correlation according to claim 1, wherein the step 6) specifically adopts the following steps:
establishing an objective function
Figure FDA0003187557910000031
Where K (t, i) denotes a gray matrix of observed signals, and c ═ c1,..,cm]TM represents a time variable;
the reciprocal of the variable c of the objective function J (c) is obtained by the following formula
Figure FDA0003187557910000032
Lagrange operator is introduced to define system differential equation
Figure FDA0003187557910000033
Where beta represents the lagrangian operator,
c is made equal to the reciprocal of the objective function and normalized
Figure FDA0003187557910000034
c by passing through
Figure FDA0003187557910000035
Obtaining the characteristic vector of the maximum characteristic value corresponding to the determined fixed point
Figure FDA0003187557910000036
In the formula, eig (-) determines the feature vector corresponding to the maximum feature value, and the extracted signal is calculated by the following formula
y(t)＝<ω,ε(t)>H＝K(t,:)c
Where y (t) represents the extracted feature signal, ω is the extraction vector, [ epsilon ] (t) = [ epsilon ], [1(t),ε2(t)…,εk(t)]TAre k signal time series.
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CN104655425A (en) * 2015-03-06 2015-05-27 重庆大学 Bearing fault classification diagnosis method based on sparse representation and LDM (large margin distribution machine)
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