CN111665050B - Rolling bearing fault diagnosis method based on clustering K-SVD algorithm - Google Patents

Rolling bearing fault diagnosis method based on clustering K-SVD algorithm Download PDF

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CN111665050B
CN111665050B CN202010501122.4A CN202010501122A CN111665050B CN 111665050 B CN111665050 B CN 111665050B CN 202010501122 A CN202010501122 A CN 202010501122A CN 111665050 B CN111665050 B CN 111665050B
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李继猛
于青文
黎芷昕
吴浩
张金凤
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Abstract

The invention discloses a rolling bearing fault diagnosis method based on a clustering K-SVD algorithm, which mainly comprises the following steps: firstly, a time-varying filtering empirical mode decomposition algorithm based on particle swarm optimization is utilized to carry out self-adaptive decomposition on an original signal to obtain each eigenmode component, and correlation kurtosis indexes (K) of each component are calculatedcr) A value; then, the maximum K is selectedcrThe eigen-mode component of the index value is used as an input sample of the clustering K-SVD algorithm to carry out dictionary learning to obtain an ultra-complete dictionary DNew(ii) a Finally, using the overcomplete dictionary DNewAnd sparse feature extraction is carried out on the original signals of the rolling bearing by combining an orthogonal matching tracking algorithm, and envelope spectrum analysis is carried out on sparse representation results to extract the fault frequency features of the rolling bearing. The method effectively solves the problems that the learning precision of the fault impact characteristics of the rolling bearing is low by the classical K-SVD algorithm, and the like, and has important significance for realizing weak fault diagnosis of the rolling bearing.

Description

Rolling bearing fault diagnosis method based on clustering K-SVD algorithm
Technical Field
The invention relates to the technical field of equipment maintenance, in particular to a rolling bearing fault diagnosis method based on a clustering K-SVD algorithm.
Background
The rolling bearing is used as an important supporting part and widely applied to rotary machinery, but various damages inevitably happen to the rolling bearing due to severe operating environment and complex and changeable operating conditions, so that the safe and reliable operation of the whole machine is influenced. However, due to the influences of factors such as the installation position of the sensor, other rotating parts, a noisy working environment, electromagnetic interference and the like, the vibration signal acquired by the vibration sensor not only contains periodic pulse components caused by faults, but also has a large amount of noise and harmonic interference, so that effective characteristic information is submerged, and the difficulty in fault diagnosis of the rolling bearing is increased. Therefore, the research on the rolling bearing fault diagnosis technology is developed, the effective extraction of the rolling bearing fault characteristics in strong background noise is realized, the health state of the rolling bearing is accurately identified in time, and the method has important significance for guaranteeing the safe and reliable operation of equipment.
K-singular value decomposition (K-SVD for short) is a completely new non-stationary signal processing method proposed by Elad equal to 2006. The method is a classic dictionary learning algorithm, only one atom is updated in each iteration process, so that the method is more convergent, and the method trains and learns the overcomplete dictionary containing the impact components, so that the defect of poor adaptability of the fixed dictionary structure is overcome. And (4) alternately performing sparse representation of the constraint problem and a singular value decomposition updating algorithm to finally obtain the self-adaptive super-complete dictionary. The algorithm has a complete theoretical basis, and is widely applied to fault diagnosis with strong adaptability and high efficiency.
However, the vibration signal of the rolling bearing not only contains periodic impact components, but also contains a large amount of harmonic components and noise interference, so that the learned dictionary inevitably contains atoms similar to the noise or harmonic components, thereby reducing effective extraction of the impact characteristics of the rolling bearing fault and leading to failure in diagnosing the rolling bearing fault.
Disclosure of Invention
The invention aims to provide a rolling bearing fault diagnosis method based on a clustering K-SVD algorithm, which improves the extraction precision of rolling bearing fault characteristics by realizing the self-adaptive effective extraction of the impact characteristics in vibration signals and weakening the influence of noise and harmonic interference on the sparse representation of the rolling bearing fault impact characteristics.
The technical scheme adopted by the invention is as follows:
the invention provides a rolling bearing fault diagnosis method based on a clustering K-SVD algorithm, which comprises the following steps: s1, acquiring a vibration signal of the rolling bearing; s2, carrying out self-adaptive decomposition on the collected rolling bearing vibration signals by adopting a time-varying filtering empirical mode decomposition algorithm based on particle swarm optimization to obtain a plurality of eigenmode components; s3, calculating correlation kurtosis index (K) of each eigenmode componentcr) (ii) a S4, adopting clustering K-SVD algorithm to carry out correlation kurtosis index KcrPerforming dictionary learning on the largest eigenmode component to obtain an ultra-complete dictionary D containing obvious impact characteristic atomsNew(ii) a S5, adopting orthogonal matching pursuit algorithm and overcomplete dictionary DNewSparse representation is carried out on the vibration signals of the rolling bearing; s6, demodulating and analyzing the sparse representation result by using a Teager energy operator to obtain a demodulation envelope spectrum; and S7, identifying the fault frequency characteristics of the rolling bearing by utilizing the demodulation envelope spectrum, and diagnosing the fault of the rolling bearing.
Further, the step S2 specifically includes:
(1) setting the search ranges of a bandwidth threshold epsilon and a B spline order n in a time-varying filtering empirical mode decomposition algorithm as [ 0.11 ] and [ 530 ], and enabling the two parameters to jointly form a position coordinate of the particle;
(2) carrying out self-adaptive decomposition on the vibration signal by using different particle position information and adopting a time-varying filtering empirical mode decomposition algorithm to obtain a plurality of eigenmode components, and calculating the envelope entropy E of all eigenmode components corresponding to each particle position informationpAnd taking the minimum value of the envelope entropy as the fitness value of the particle;
envelope entropy E of signal x (i) (1, 2, …, N)PThe calculation formula is as follows:
Figure BDA0002524846880000021
where p (i) is the envelope of the analytic signal obtained by Hilbert transform of signal x (i), and N is the signal length.
(3) Updating the individual local extremum and the overall local extremum by utilizing the fitness value of each particle, and further updating the position information and the speed information of the particle swarm;
(4) when the iteration times reach the maximum set value or the error is smaller than the set threshold value, outputting the optimal fitness value and the corresponding particle position information;
(5) substituting the obtained optimal particle position information, namely the bandwidth threshold epsilon and the B spline order n into a time-varying filtering empirical mode decomposition algorithm to obtain a final decomposition result u ═ u { for the vibration signal of the rolling bearing1，u2，…uKIn which ukDenotes the kth eigenmode component, and K denotes the number of eigenmode components.
Further, the step S3 specifically includes: for the K eigenmode components obtained in step S2, each eigenmode component u is calculatedkRelated kurtosis index KcrThe calculation formula is as follows:
Figure BDA0002524846880000031
where x represents the original signal and x represents the original signal,
Figure BDA0002524846880000032
and
Figure BDA0002524846880000033
respectively, the original signal x and the k-th eigenmode component ukN is the signal length.
Further, the step S4 specifically includes:
(1) by calculating the correlation kurtosis indexes K of K eigenmode componentscrSelecting the eigenmode component u with the maximum correlation kurtosis indexmAs input to the clustering K-SVD algorithm;
(2) setting K-SVD algorithm parameters, and adopting K-SVD algorithm to carry out eigenmode component umPerforming dictionary learning to obtain an ultra-complete dictionary D;
(3) and analyzing the overcomplete dictionary D by adopting a K-means clustering algorithm.
Further, the analyzing the overcomplete dictionary D by using the K-means clustering algorithm specifically includes:
(1) calculating each atom D in the overcomplete dictionary Dj(J ═ 1,2, …, J denotes the number of atoms in dictionary D) is used as a kurtosis index
Figure BDA0002524846880000034
Index of sum margin
Figure BDA0002524846880000035
As characterizing atom djFeature vector of
Figure BDA0002524846880000036
(2) Constructing a sample set Λ ═ v by using feature vectors of all atoms1,ν2,…,νJThe method is used as the input of a K-means clustering algorithm, the clustering number is set to be 2, and 2 samples are randomly selected from Lambda to serve as an initial mean vector (mu)1，μ2}；
(3) Calculating v of each input samplejAnd each mean vector mul(l is 1, 2) distance
Figure BDA0002524846880000041
Determining v according to the nearest mean vectorjSo that all samples are divided into two classes C1And C2;
(4) updating the mean vector of the corresponding category with all samples in each category; if the mean vector does not change before and after updating, stopping clustering and outputting a clustering result C ═ C1，C2}; otherwise, returning to execute the step (3);
(5) selecting one kind of atoms with larger characteristic vectors from the clustering result to reconstruct the dictionary, and obtaining an overcomplete dictionary D containing the atoms with obvious impact characteristicsNew。
Further, the step S5 specifically includes:
using overcomplete dictionaries DNewSparse representation is carried out on the vibration signal x of the rolling bearing:
Figure BDA0002524846880000042
wherein d iskRepresenting an overcomplete dictionary DNewα represents a sparse representation coefficient, and r represents a residual. The problem of solving the sparse representation coefficient alpha is reduced to a problem based on l0Solving the problem of the coefficients of the norm:
(l0):min||α||0subject to x＝Dα+r
solving the l by using an orthogonal matching pursuit algorithm with the sparsity of 10And solving the problem by the norm coefficient to obtain a sparse representation result of the vibration signal of the rolling bearing.
Compared with the prior art, the invention has the following beneficial effects:
the diagnosis method provided by the invention adopts the time-varying filtering empirical mode decomposition algorithm based on particle swarm optimization to carry out self-adaptive decomposition on the vibration of the rolling bearing, so that the self-adaptive selection of algorithm parameters is realized, and the problem of mode aliasing is solved; meanwhile, the relevant kurtosis indexes are used for selecting the mode components containing rich fault information as the input of a K-SVD algorithm, dictionary learning is carried out, and the learning precision of atoms with impact morphological characteristics is improved; meanwhile, the dictionary is further analyzed by adopting a K-means clustering algorithm, atoms irrelevant to the impact form can be eliminated, the influence of noise and harmonic components on the fault feature extraction precision of the rolling bearing is avoided, and the fault diagnosis accuracy of the rolling bearing can be effectively improved.
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FIG. 1 is a schematic flow chart of a rolling bearing fault diagnosis method based on a clustering K-SVD algorithm, which is provided by the invention;
FIG. 2 is a schematic time domain waveform of a vibration signal of a rolling bearing;
FIG. 3 is a schematic diagram of a demodulated envelope spectrum of a vibration signal of a rolling bearing;
FIG. 4 is a diagram illustrating empirical mode decomposition results of time-varying filtering based on particle swarm optimization;
FIG. 5 is a schematic diagram of atomic clustering;
FIG. 6 is DNewSchematic diagram of atomic waveforms in (1);
FIG. 7 is a schematic diagram of a time domain waveform obtained by the present method;
fig. 8 is a schematic diagram of a demodulation envelope spectrum obtained by the method.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
The invention provides a rolling bearing fault diagnosis method based on a clustering K-SVD algorithm, as shown in figure 1, the diagnosis method specifically comprises the following steps:
s1, acquiring a vibration signal of the rolling bearing;
the method specifically comprises the following steps: the rolling bearing of the locomotive with the outer ring peeling fault is arranged on a vibration test bench to be tested to acquire a vibration signal, in the embodiment, the frequency conversion is set to be fr6.33Hz, with the sampling frequency set to fs12.8kHz, data length set to 8000; the time domain waveform of the vibration signal of the rolling bearing and the demodulation envelope spectrum thereof are shown in fig. 2 and 3.
S2, carrying out self-adaptive decomposition on the collected rolling bearing vibration signals by using a time-varying filtering empirical mode decomposition algorithm optimized by particle swarm to obtain a plurality of eigenmode components;
the method specifically comprises the following steps: firstly, setting initial parameters of a particle swarm algorithm, in this embodiment, the population number is set to 50, the maximum evolution algebra is set to 2000, the solving precision is set to 1e-5, and the search ranges of a bandwidth threshold epsilon and a B spline order n in the time-varying filtering empirical mode decomposition algorithm are respectively [ 0.11 []And [ 530 ]]And combining the two parametersTogether constitute the position coordinates of the particles; secondly, carrying out self-adaptive decomposition on the vibration signal by using different particle position information and adopting a time-varying filtering empirical mode decomposition algorithm to obtain a plurality of eigenmode components, and calculating the envelope entropy E of all eigenmode components corresponding to each particle position informationpWherein, in the step (A),
Figure BDA0002524846880000061
p (i) is the envelope of the analytic signal obtained by Hilbert transform of a signal x (i), N is the signal length, and the minimum value of the envelope entropy is taken as the fitness value of the particle; thirdly, updating the individual local extremum and the overall local extremum by utilizing the fitness value of each particle, and further updating the position information and the speed information of the particle swarm; then, when the iteration times reach the maximum set value or the error is smaller than the set threshold value, outputting the optimal fitness value and the corresponding particle position information; and finally, substituting the obtained optimal particle position information, namely the bandwidth threshold epsilon is 0.43 and the B spline order n is 30 into a time-varying filtering empirical mode decomposition algorithm to obtain a final decomposition result u ═ { u } of the vibration signal of the rolling bearing1，u2，…，u11As shown in fig. 4.
S3, calculating correlation kurtosis index (K) of each eigenmode componentcr)；
The method specifically comprises the following steps: using formulas
Figure BDA0002524846880000062
Where x represents the original signal and x represents the original signal,
Figure BDA0002524846880000063
and
Figure BDA0002524846880000064
respectively, the original signal x and the k-th eigenmode component ukN is the signal length, calculating the phase of each eigenmode componentThe kurtosis index, the results obtained are shown in fig. 4.
S4, adopting clustering K-SVD algorithm to carry out correlation kurtosis index KcrPerforming dictionary learning on the largest eigenmode component to obtain an ultra-complete dictionary D containing obvious impact characteristic atomsNew；
The method specifically comprises the following steps: firstly, through comparative analysis of correlation kurtosis indexes of 11 eigenmode components, a 1 st eigenmode component u is selected1As input samples of the K-SVD algorithm, wherein the parameters of the K-SVD algorithm are set as: the sample/atom length is 280 data points, and the atom number is 650; modeling the component u using the K-SVD algorithm1Performing dictionary learning to obtain an ultra-complete dictionary D; then, analyzing the overcomplete dictionary D by using a K-means clustering algorithm, calculating the kurtosis index and the margin index of each atom in the dictionary D to form a characteristic vector representing the atom, taking the characteristic vectors of all the atoms as the input of the K-means clustering algorithm, automatically dividing the atoms in the dictionary D into two types, and selecting one type of atoms with larger characteristic vectors to reconstruct the dictionary to obtain the overcomplete dictionary D containing the obviously impacted characteristic atoms as shown in figure 5New. As shown in FIG. 6, a secondary dictionary D is providedNewThe time domain waveform of 4 randomly selected atoms in the cluster is shown in fig. 6, and the clustered atom form has obvious pulse characteristics.
S5, adopting orthogonal matching pursuit algorithm and overcomplete dictionary DNewSparse representation is carried out on the vibration signals of the rolling bearing;
the method specifically comprises the following steps: using overcomplete dictionaries DNewCarrying out sparse representation on the bearing vibration by adopting an orthogonal matching pursuit algorithm with the sparsity of 1, wherein the obtained result is shown in figure 7; compared with fig. 2, the time domain waveform shown in fig. 7 has significantly reduced noise and obvious periodic impact characteristics.
S6, demodulating and analyzing the sparse representation result by using a Teager energy operator to obtain a demodulation envelope spectrum, as shown in FIG. 8.
And S7, identifying the fault frequency characteristics of the rolling bearing by utilizing the demodulation envelope spectrum, and diagnosing the fault of the rolling bearing. In demodulating envelope spectrum, except for rolling bearing outer ring failureCharacteristic frequency foBesides, multiple harmonic component 2 xf of fault characteristic frequency can be foundo、3×fo、4×fo、5×foThe local damage of the outer ring of the rolling bearing is predicted; and the identification precision of the fault characteristic frequency is greatly improved.
The rolling bearing fault diagnosis method based on the clustering K-SVD algorithm successfully extracts the fault characteristic frequency of the bearing, compared with the classic K-SVD method, the method utilizes the time-varying filtering empirical mode decomposition algorithm of particle swarm optimization to carry out self-adaptive decomposition on the signal, and utilizes the relevant kurtosis indexes to select the mode components containing abundant fault information, thereby weakening the influence of noise and harmonic interference on the dictionary learning precision; meanwhile, atoms irrelevant to the impact form are further removed by utilizing a K-means clustering algorithm, so that the extraction precision of the fault impact characteristics of the rolling bearing is improved, and the method has important significance for realizing weak fault diagnosis of the rolling bearing.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.

Claims (5)

1. A rolling bearing fault diagnosis method based on a clustering K-SVD algorithm is characterized in that: the method comprises the following steps:
s1, acquiring a vibration signal of the rolling bearing;
s2, carrying out self-adaptive decomposition on the collected rolling bearing vibration signals by adopting a time-varying filtering empirical mode decomposition algorithm based on particle swarm optimization to obtain a plurality of eigenmode components;
s3, calculating correlation kurtosis index (K) of each eigenmode componentcr)；
S4, adopting clustering K-SVD algorithm to carry out correlation kurtosis index KcrPerforming dictionary learning on the largest eigenmode component to obtain the super-complete character containing the obvious impact characteristic atomsBackup dictionary DNew；
S5, adopting orthogonal matching pursuit algorithm and overcomplete dictionary DNewSparse representation is carried out on the vibration signals of the rolling bearing;
s6, demodulating and analyzing the sparse representation result by using a Teager energy operator to obtain a demodulation envelope spectrum;
s7, identifying the fault frequency characteristics of the rolling bearing by utilizing the demodulation envelope spectrum, and diagnosing the fault of the rolling bearing;
the step S2 specifically includes:
(1) setting the search ranges of a bandwidth threshold epsilon and a B spline order n in a time-varying filtering empirical mode decomposition algorithm as [ 0.11 ] and [ 530 ], and enabling the two parameters to jointly form a position coordinate of the particle;
(2) carrying out self-adaptive decomposition on the vibration signal by using different particle position information and adopting a time-varying filtering empirical mode decomposition algorithm to obtain a plurality of eigenmode components, and calculating the envelope entropy E of all eigenmode components corresponding to each particle position informationpAnd taking the minimum value of the envelope entropy as the fitness value of the particle;
envelope entropy E of signal x (i) (i =1,2, …, N)PThe calculation formula is as follows:
Figure DEST_PATH_IMAGE002
wherein p (i) is an envelope of an analytic signal obtained by Hilbert transform of a signal x (i), and N is a signal length;
(3) updating the individual local extremum and the overall local extremum by utilizing the fitness value of each particle, and further updating the position information and the speed information of the particle swarm;
(4) when the iteration times reach the maximum set value or the error is smaller than the set threshold value, outputting the optimal fitness value and the corresponding particle position information;
(5) substituting the obtained optimal particle position information, namely the bandwidth threshold epsilon and the B spline order n, into a time-varying filtering empirical mode decomposition algorithm to obtain a final decomposition result u = of the vibration signal of the rolling bearing{u1，u2，…uKIn which ukDenotes the kth eigenmode component, and K denotes the number of eigenmode components.
2. The rolling bearing failure diagnosis method according to claim 1, characterized in that: the step S3 specifically includes: for the K eigenmode components obtained in step S2, each eigenmode component u is calculatedkRelated kurtosis index KcrThe calculation formula is as follows:
Figure DEST_PATH_IMAGE004
where x represents the original signal and x represents the original signal,
Figure DEST_PATH_IMAGE006
and
Figure DEST_PATH_IMAGE008
respectively, the original signal x and the k-th eigenmode component ukN is the signal length.
3. The rolling bearing failure diagnosis method according to claim 2, characterized in that: the step S4 specifically includes:
(1) by calculating the correlation kurtosis indexes K of K eigenmode componentscrSelecting the eigenmode component u with the maximum correlation kurtosis indexmAs input to the clustering K-SVD algorithm;
(2) setting K-SVD algorithm parameters, and adopting K-SVD algorithm to carry out eigenmode component umPerforming dictionary learning to obtain an ultra-complete dictionary D;
(3) and analyzing the overcomplete dictionary D by adopting a K-means clustering algorithm.
4. The rolling bearing failure diagnosis method according to claim 3, characterized in that: the analyzing the overcomplete dictionary D by adopting the K-means clustering algorithm specifically comprises the following steps:
(1) calculating each atom D in the overcomplete dictionary Dj(J =1,2, …, J representing the number of atoms in dictionary D) is used as a kurtosis index
Figure DEST_PATH_IMAGE010
Index of sum margin
Figure DEST_PATH_IMAGE012
As characterizing atom djFeature vector of
Figure DEST_PATH_IMAGE014
；
(2) Constructing a sample set using feature vectors of all atoms
Figure DEST_PATH_IMAGE016
As an input of the K-means clustering algorithm, the clustering number is set to be 2, and 2 samples are randomly selected from Lambda to serve as an initial mean vector (mu)1，μ2}；
(3) Computing each input sample
Figure DEST_PATH_IMAGE018
And each mean vector mu l (lDistance of =1, 2)
Figure DEST_PATH_IMAGE020
Is determined from the nearest mean vector
Figure DEST_PATH_IMAGE018A
So that all samples are divided into two classes C1And C2；
(4) Updating the mean vector of the corresponding category with all samples in each category; stopping clustering if the mean vector does not change before and after updating, and outputting a clustering result C = { C = { C = }1, C2}; otherwise, returning to execute the step (3);
(5) selecting one kind of atoms with larger feature vectors from the clustering result to be used againConstructing a dictionary to obtain an overcomplete dictionary D containing atoms with obvious impact characteristicsNew。
5. The rolling bearing failure diagnosis method according to claim 4, characterized in that: the step S5 specifically includes:
using overcomplete dictionaries DNewSparse representation is carried out on the vibration signal x of the rolling bearing:
Figure DEST_PATH_IMAGE023
wherein d iskRepresenting an overcomplete dictionary DNewA represents a sparse representation coefficient, r represents a residual; the problem of solving the sparse representation coefficient alpha is reduced to a problem based onl 0Solving the problem of the coefficients of the norm:
Figure DEST_PATH_IMAGE025
solving the method by using an orthogonal matching pursuit algorithm with the sparsity of 1l 0And solving the problem by the norm coefficient to obtain a sparse representation result of the vibration signal of the rolling bearing.
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