CN110686897A - Variable working condition rolling bearing fault diagnosis method based on subspace alignment - Google Patents
Variable working condition rolling bearing fault diagnosis method based on subspace alignment Download PDFInfo
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Abstract
A variable working condition rolling bearing fault diagnosis method based on subspace alignment belongs to the field of mechanical fault diagnosis. Placing vibration signals of the bearing under different working conditions into a source field and a target field and generating corresponding subspaces, converting a sample into a subspace constructed by d-dimensional characteristic vectors, and calculating a conversion matrix M by minimizing Bregman divergence so as to align a subspace Z of the source fieldA＝ZSM and target Domain subspace ZTAnd (5) aligning coordinates so as to eliminate the difference of data distribution among the fields, and finally performing fault diagnosis on the samples in the projected target field sample set by using the trained classification model. The method can eliminate the influence of working conditions and obtain the information only reflecting the fault or performance degradation of the rolling bearing, so that the diagnosis of the fault of the rolling bearing is more accurate, and the method has extremely high popularization value.
Description
Technical Field
The invention relates to a rolling bearing fault diagnosis method, in particular to a variable working condition rolling bearing fault diagnosis method based on subspace alignment, and belongs to the field of mechanical fault diagnosis.
Background
Rolling bearings are the most widely used mechanical parts in the electrical, petrochemical, metallurgical, mechanical, aerospace and some military industrial sectors, and are among the most vulnerable parts. The novel lubricating oil pump has the advantages of high efficiency, small frictional resistance, convenience in assembly, easiness in lubrication and the like, is very common to rotary machinery, and plays a key role. Many faults of rotating mechanical equipment are closely related to rolling bearings. According to statistics, 70% of mechanical failures are vibration failures, and 30% of vibration failures are caused by rolling bearings. This is because the rolling bearing plays a role in bearing and transmitting load in mechanical equipment, and the operating conditions are relatively severe, and the rolling bearing is easily damaged and fails when continuously operated under high load and high rotation speed for a long time. The direct consequence of a rolling bearing failure is that, on the one hand, some of the functions of the system are reduced and lost, and, on the other hand, serious and even catastrophic accidents occur. Therefore, the fault diagnosis method of the rolling bearing is one of the key developed technologies in mechanical fault diagnosis, and has important social and economic significance.
Rolling bearings in mechanical devices often have variable operating conditions (load, rotational speed, etc. vary continuously or intermittently). The acquired sensing signals have direct correlation with working conditions. When the system operates under a variable working condition, new data continuously emerge, and originally available labeled sensing data and test samples under the new working condition generate distribution difference. The existing training samples are not enough to train to obtain a reliable fault diagnosis model. Meanwhile, the re-labeling of a batch of fault samples under a new working condition is time-consuming, labor-consuming and expensive.
Due to the vibration signals of the bearing under different working conditions and the distribution difference between the source field and the target field, the fault classifier trained by the source field cannot be directly used for fault classification in the target field, which causes an important problem of fault diagnosis of the rolling bearing, namely, how to utilize a small amount of labeled training samples or source field data under the condition of variable working conditions to establish a reliable model to predict new working conditions or target field data, wherein the source field data and the target field data can not have the same data distribution.
Disclosure of Invention
The invention aims to solve the technical problems of overcoming the difference of sensing data distribution under the condition of variable working conditions, and provides a method for eliminating the influence of the working conditions, acquiring information only reflecting the faults or performance degradation of a rolling bearing and accurately judging the faults of the rolling bearing.
In order to solve the technical problem, the invention discloses a variable working condition rolling bearing fault diagnosis method based on subspace alignment, which is characterized by comprising the following steps of:
firstly, collecting vibration signals of a plurality of rolling bearings in operation as samples, labeling fault types of partial samples as training data, and putting the training data into a source field, and putting partial samples as test data into a target field;
generation of subspace, Z, of source domain using principal component analysisS∈RD×dAnd subspace Z of the target domainT∈RD×d，ZSIs a PCA eigenvector matrix, Z, of the source domainTIs a PCA characteristic vector matrix of the target field;
converting the sample into a subspace constructed by the d-dimensional feature vector;
then, by minimizing Bregman divergence
Computing a transformation matrix M such that the post-source-domain subspace Z is alignedA＝ZSM and target Domain subspace ZTThe coordinates are aligned, so that the difference of data distribution among the fields is eliminated, and the aligned vibration signals only reflect the information of rolling bearing faults or performance degradation;
aligning the source domain sample set with the fault label to obtain a source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set, inputting the projected sample set into a standard SVM classification model for training, and finally obtaining a trained SVM classification model;
and finally, carrying out fault diagnosis on the samples in the projected target field sample set by using the trained SVM classification model, and judging the fault type of each sample.
The specific steps for generating the subspace are as follows:
firstly, acquiring vibration signals X belonging to X of a bearing under different working conditions in a plurality of running processes by using a vibration sensor, taking all vibration signals as a sample set, marking fault types of partial samples as labels, then putting the labels into a source field as training data, taking the fault type labels Y belonging to {1,2, …, K }, and putting partial samples into a target field as test data;
then, respectively extracting frequency domain characteristics with the length of D of each sample in the source field and the target field by using Fast Fourier Transform (FFT), namely a D-dimensional amplitude coefficient corresponding to each sample vibration signal;
after z-normalized normalization processing is carried out on D-dimensional amplitude coefficients of all samples in the source field and the target field, covariance matrixes of the samples in the source field and the target field are respectively calculated on the matrixes obtained after the normalization processing, then characteristic value decomposition is carried out on the covariance matrixes of the samples in the source field and the target field by using Principal Component Analysis (PCA), and characteristic vectors corresponding to the first D characteristic values are all taken to form basis vectors of subspace of the source field and the target field, namely,and
thus, the samples are converted into a subspace constructed by d-dimensional feature vectors, wherein: zSIs a PCA eigenvector matrix of the source domain, representing a source domain subspace, ZTIs a PCA eigenvector matrix of the target domain, representing the target domain subspace,
a matrix of real numbers representing D rows and D columns.
The specific steps for eliminating the difference of data distribution among the fields through subspace alignment are as follows: transforming the source-domain subspace Z using a transformation matrix MSTo the target domainSpace ZTCoordinate alignment, source domain subspace ZSObtaining aligned source domain subspace notation Z after M changesA＝ZSM，
Specifically, the method comprises the following steps:
utilizing aligned back source domain subspace ZAAnd target domain subspace ZTBregman divergence of
For determining transformed source-domain subspace ZAAnd target domain subspace ZTWhether the coordinates tend to be consistent or not is judged, if the Bregman divergence of the two samples tends to be consistent, the source field sample and the target field sample are projected to the aligned source field subspace ZAAnd a target domain subspace ZTThen, aligning the data coordinates;
accordingly, by minimizing the aligned back-source-domain subspace ZAAnd target domain subspace ZTBregman divergence of
Calculating an optimal transformation matrix M, i.e. M*＝argminM(δAT))，
Due to ZSAnd ZTAre all orthogonal matrices and the F matrix norm in Bregman divergence has orthogonal invariance, so Bregman divergence is:
in the formula (I), the compound is shown in the specification,
is ZSThe transposed matrix of (2);
to sum up, the optimal transformation matrix can be obtained
The specific steps of training the classifier are as follows:
first, a source domain sample with a fault label is collected
Aligned post-source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set
Wherein N represents the number of source domain samples;
the projected sample set is then used
And inputting a standard SVM classification model for training to finally obtain the trained SVM classification model.
The fault diagnosis comprises the following specific steps:
firstly, collecting target domain samples without labels
Projection into target subspace ZTObtaining a set of target domain samplesM represents the number of target field samples, and then the trained SVM classification model is used for collecting the projected target field samples
The samples in (1) are subjected to fault diagnosis, and the fault type of each sample is judged.
Has the advantages that:
the invention aligns the sample in the source field with the subspace Z of the source fieldAAligning the data coordinates, and aligning the target field sample with the target field subspace ZTThe data coordinate alignment mode overcomes the difference of sensing data distribution under the condition of variable working conditions, and provides a method which can eliminate the influence of the working conditions and obtain the information only reflecting the fault or performance degradation of the rolling bearing;
according to the invention, aiming at the difference of fault sensing data distribution under different working conditions, Bregman divergence is used for describing the distribution difference between the source field and the target field, and the source field subspace Z is obtained by introducing a conversion matrix MSAlignment to target Domain subspace ZTPost-minimization of Bregman divergence between domains such that the transformed source domain subspace ZAAnd target domain subspace ZTThe approaches are consistent, and after the spaces are similar, the distribution difference between the training data (source field) and the test data (target field) is reduced, so that the model trained in the source field can be used for diagnosis in the target field;
the invention overcomes the difference of the distribution of the sensing data under the condition of variable working conditions, and provides a method which can eliminate the influence of the working conditions and obtain the information only reflecting the fault or the performance degradation of the rolling bearing, thereby ensuring that the diagnosis of the fault of the rolling bearing is more accurate and having extremely high popularization value.
Drawings
FIG. 1 is a schematic diagram of a variable working condition rolling bearing fault diagnosis method based on subspace alignment.
FIG. 2 is a schematic diagram of coordinate alignment of the variable working condition rolling bearing fault diagnosis method based on subspace alignment.
FIG. 3 is a schematic flow chart of the variable working condition rolling bearing fault diagnosis method based on subspace alignment.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in FIG. 1, the invention relates to a fault diagnosis method for a variable working condition rolling bearing based on subspace alignment,
firstly, collecting vibration signals of a plurality of rolling bearings in operation as samples, labeling fault types of partial samples as training data, and putting the training data into a source field, and putting partial samples as test data into a target field;
generation of subspace, Z, of source domain using principal component analysisS∈RD×dAnd subspace Z of the target domainT∈RD×d，ZSIs a PCA eigenvector matrix, Z, of the source domainTIs a PCA characteristic vector matrix of the target field;
converting the sample into a subspace constructed by the d-dimensional feature vector;
and then by minimizing Bregman divergence
Computing a transformation matrix M such that the post-source-domain subspace Z is alignedA＝ZSM and target Domain subspace ZTThe coordinates are aligned, so that the difference of data distribution among the fields is eliminated, and the aligned vibration signals only reflect the information of rolling bearing faults or performance degradation;
aligning the source domain sample set with the fault label to obtain a source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set, inputting the projected sample set into a standard SVM classification model for training, and finally obtaining a trained SVM classification model;
and finally, carrying out fault diagnosis on the samples in the projected target field sample set by using the trained SVM classification model, and judging the fault type of each sample.
As shown in fig. 3, a method for diagnosing a fault of a rolling bearing under variable working conditions based on subspace alignment specifically comprises the following steps:
step one, generating a subspace:
firstly, acquiring vibration signals X belonging to X of a bearing under different working conditions in a plurality of running processes by using a vibration sensor, taking all vibration signals as a sample set, marking fault types of partial samples as labels, then putting the labels into a source field as training data, taking the fault type labels Y belonging to {1,2, …, K }, and putting partial samples into a target field as test data;
then, respectively extracting frequency domain characteristics with the length of D of each sample in the source field and the target field by using Fast Fourier Transform (FFT), namely a D-dimensional amplitude coefficient corresponding to each sample vibration signal;
z-processing D-dimensional amplitude coefficients of all samples in the source field and the target fieldAfter normalized normalization, covariance matrices of source and target field samples are respectively calculated for the matrices obtained after normalization, then Principal Component Analysis (PCA) is used to perform eigenvalue decomposition on the covariance matrices of the source and target field samples, eigenvectors corresponding to the first d eigenvalues are all taken to form basis vectors of subspace of the source and target fields, that is,
and
thus, the samples are converted into a subspace constructed by d-dimensional feature vectors, wherein: zSIs a PCA eigenvector matrix of the source domain, representing a source domain subspace, ZTIs a PCA eigenvector matrix of the target domain, representing the target domain subspace,
a matrix of real numbers representing D rows and D columns.
Step two, eliminating the difference of data distribution among the fields through subspace alignment:
as shown in FIG. 2, the source-domain subspace Z is transformed using a transformation matrix MSTo a target domain subspace ZTCoordinate alignment, source domain subspace ZSObtaining aligned source domain subspace notation Z after M changesA＝ZSM，
Specifically, the method comprises the following steps:
utilizing aligned back source domain subspace ZAAnd target domain subspace ZTBregman divergence of
For determining transformed source-domain subspace ZAAnd target domain subspace ZTWhether the coordinates tend to be consistent or not, and if the Bregman divergence of the coordinates and the Bregman divergence tend to be consistent, judging that the source field sample and the target field sample are consistentProjection of domain samples into aligned post-source domain subspace ZAAnd a target domain subspace ZTThen, aligning the data coordinates;
accordingly, by minimizing the aligned back-source-domain subspace ZAAnd target domain subspace ZTBregman divergence of
Calculating an optimal transformation matrix M, i.e. M*＝argminM(δAT))，
Due to ZSAnd ZTAre all orthogonal matrices and the F matrix norm in Bregman divergence has orthogonal invariance, so Bregman divergence is:
in the formula (I), the compound is shown in the specification,
is ZSThe transposed matrix of (2);
to sum up, the optimal transformation matrix can be obtained
Step three, training a classifier:
first, a source domain sample with a fault label is collected
Aligned post-source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set
Wherein N represents the number of source domain samples;
the projected sample set is then used
And inputting a standard SVM classification model for training to finally obtain the trained SVM classification model.
Step four, fault diagnosis:
firstly, collecting target domain samples without labels
Projection into target subspace ZTObtaining a set of target domain samples
M represents the number of target field samples, and then the trained SVM classification model is used for collecting the projected target field samplesThe samples in (1) are subjected to fault diagnosis, and the fault type of each sample is judged.
To measure the similarity between the source domain samples and the target domain samples, the method defines the following similarity function Sim (X)S,XT) I.e. Sim (X)S,XT)＝XSZAZ′TX′T。
The similarity function Sim (X)S,XT) The result of (2) can be directly used for a K-nearest neighbor classification algorithm, but cannot be directly used for training an SVM classification model. When LIBSVM software is used, the method uses Sim (X)S,XT) And training the SVM classification model by using the kernel matrix. In order to prevent the over-fitting problem, the method uses a cross-validation method to find the optimal model parameters.
Claims (5)
1. A variable working condition rolling bearing fault diagnosis method based on subspace alignment is characterized by comprising the following steps:
firstly, collecting vibration signals of a plurality of rolling bearings in operation as samples, labeling fault types of partial samples as training data, and putting the training data into a source field, and putting partial samples as test data into a target field;
generation of subspace, Z, of source domain using principal component analysisS∈RD×dAnd subspace Z of the target domainT∈RD×d，ZSIs a PCA eigenvector matrix, Z, of the source domainTIs a PCA characteristic vector matrix of the target field;
converting the sample into a subspace constructed by the d-dimensional feature vector;
then, by minimizing Bregman divergence
Computing a transformation matrix M such that the post-source-domain subspace Z is alignedA＝ZSM and target Domain subspace ZTThe coordinates are aligned, so that the difference of data distribution among the fields is eliminated, and the aligned vibration signals only reflect the information of rolling bearing faults or performance degradation;
aligning the source domain sample set with the fault label to obtain a source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set, inputting the projected sample set into a standard SVM classification model for training, and finally obtaining a trained SVM classification model;
and finally, carrying out fault diagnosis on the samples in the projected target field sample set by using the trained SVM classification model, and judging the fault type of each sample.
2. The variable working condition rolling bearing fault diagnosis method based on subspace alignment as claimed in claim 1, wherein the specific steps of generating the subspace are as follows:
firstly, acquiring vibration signals X belonging to X of a bearing under different working conditions in a plurality of running processes by using a vibration sensor, taking all vibration signals as a sample set, marking fault types of partial samples as labels, then putting the labels into a source field as training data, taking the fault type labels Y belonging to {1,2, …, K }, and putting partial samples into a target field as test data;
then, respectively extracting frequency domain characteristics with the length of D of each sample in the source field and the target field by using Fast Fourier Transform (FFT), namely a D-dimensional amplitude coefficient corresponding to each sample vibration signal;
for source domain and target domainAfter Z-normalized normalization processing is carried out on the D-dimensional amplitude coefficients of all samples, covariance matrixes of the source field samples and the target field samples are respectively calculated on the matrixes obtained after the normalization processing, then characteristic value decomposition is carried out on the covariance matrixes of the source field samples and the target field samples by using Principal Component Analysis (PCA), characteristic vectors corresponding to the first D characteristic values are all taken to form base vectors of subspace of the source field samples and the target field samples, namely,
and
thus, the samples are converted into a subspace constructed by d-dimensional feature vectors, wherein: zSIs a PCA eigenvector matrix of the source domain, representing a source domain subspace, ZTIs a PCA eigenvector matrix of the target domain, representing the target domain subspace,
a matrix of real numbers representing D rows and D columns.
3. The variable working condition rolling bearing fault diagnosis method based on subspace alignment according to claim 1, wherein the specific step of eliminating the difference of data distribution among the fields through subspace alignment is as follows: transforming the source-domain subspace Z using a transformation matrix MSTo a target domain subspace ZTCoordinate alignment, source domain subspace ZSObtaining aligned source domain subspace notation Z after M changesA＝ZSM，
Specifically, the method comprises the following steps:
utilizing aligned back source domain subspace ZAAnd target domain subspace ZTBregman divergence of
For determining transformed source-domain subspace ZAAnd target domain subspace ZTWhether the coordinates tend to be consistent or not is judged, if the Bregman divergence of the two samples tends to be consistent, the source field sample and the target field sample are projected to the aligned source field subspace ZAAnd a target domain subspace ZTThen, aligning the data coordinates;
accordingly, by minimizing the aligned back-source-domain subspace ZAAnd target domain subspace ZTBregman divergence of
Calculating an optimal transformation matrix M, i.e. M*＝argminM(δAT))，
Due to ZSAnd ZTAre all orthogonal matrices and the F matrix norm in Bregman divergence has orthogonal invariance, so Bregman divergence is:
in the formula (I), the compound is shown in the specification,
is ZSThe transposed matrix of (2);
to sum up, the optimal transformation matrix can be obtained
4. The subspace alignment-based variable working condition rolling bearing fault diagnosis method according to claim 1, characterized in that the training classifier comprises the following specific steps:
first, a source domain sample with a fault label is collected
Aligned post-source domain subspace ZAProjection into target subspace ZTObtaining a projected sample set
Wherein N represents the number of source domain samples;
the projected sample set is then used
And inputting a standard SVM classification model for training to finally obtain the trained SVM classification model.
5. The variable working condition rolling bearing fault diagnosis method based on subspace alignment according to claim 1 or 4, characterized in that the fault diagnosis comprises the following specific steps:
firstly, collecting target domain samples without labels
Projection into target subspace ZTObtaining a set of target domain samples
M represents the number of target field samples, and then the trained SVM classification model is used for collecting the projected target field samples
The samples in (1) are subjected to fault diagnosis, and the fault type of each sample is judged.
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