CN115046766A - Small sample bearing fault diagnosis method based on two-dimensional gray image self-adaptive subspace - Google Patents

Small sample bearing fault diagnosis method based on two-dimensional gray image self-adaptive subspace Download PDF

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CN115046766A
CN115046766A CN202210673986.3A CN202210673986A CN115046766A CN 115046766 A CN115046766 A CN 115046766A CN 202210673986 A CN202210673986 A CN 202210673986A CN 115046766 A CN115046766 A CN 115046766A
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bearing
subspace
fault
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赵志宏
窦广鉴
周晓宁
杨绍普
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Shijiazhuang Tiedao University
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Abstract

The invention discloses a small sample bearing fault diagnosis method based on a two-dimensional gray image adaptive subspace, which comprises the following steps of: acquiring n bearing vibration signals of different fault types through a sensor; the vibration signal of the bearing is processed according to the length,
Figure DEST_PATH_IMAGE002
sampling the step length, and converting the step length into a two-dimensional gray image to form a data set; selecting k samples from each fault type of the data set to form a support set S, and selecting h samples to form a query set Q; constructing a self-adaptive subspace network model for bearing fault diagnosis; inputting the support set S and the query set Q into a self-adaptive subspace network model, and obtaining a dynamic classifier through training; and testing by using the trained dynamic classifier network model to obtain a classification result. The method is more beneficial to representation and extraction of the features, can better classify and has better generalization performance.

Description

Small sample bearing fault diagnosis method based on two-dimensional gray image self-adaptive subspace
Technical Field
The invention relates to the technical field of bearing fault diagnosis methods, in particular to a small-sample bearing fault diagnosis method based on a two-dimensional gray scale image self-adaptive subspace.
Background
The rolling bearing is one of the vital parts in the mechanical equipment, and is also one of the parts which are easy to malfunction in the mechanical equipment. The occurrence of bearing failure causes a certain economic loss and time loss, and more seriously, may be life threatening. It is therefore important to diagnose the bearing vibration signal.
In recent years, a failure diagnosis technique based on deep learning has attracted much attention because it avoids excessive dependence on people and improves the efficiency of failure diagnosis. Most of these techniques require a large amount of training data. In practical engineering applications, however, it is difficult and expensive to collect a large number of signal samples for each type of fault. The small sample learning can learn the fault diagnosis knowledge from limited fault samples, does not need a large number of samples for training, and has strong diagnosis capability and generalization capability.
The adaptive subspace method is a small sample learning method based on metric learning. The method is different from the methods such as prototype classification of small sample learning and the like in classification in a unified feature space. The subspace classification method is to establish a subspace for each fault type and classify in the subspaces of a plurality of fault types. Compared with a unified feature space, the subspace can establish a more accurate model for each fault type, and therefore a better fault diagnosis result is obtained.
Disclosure of Invention
The invention aims to provide a small sample bearing fault diagnosis method which is more favorable for representing and extracting characteristics, can better classify and has better generalization performance.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a small sample bearing fault diagnosis method based on two-dimensional gray scale image adaptive subspace is characterized by comprising the following steps:
acquiring n bearing vibration signals of different fault types through a sensor;
sampling a bearing vibration signal according to the length b and the length b by taking the square of a natural number and the step length w, and converting the sampled bearing vibration signal into a two-dimensional gray image to form a data set;
selecting k samples from each fault type of the data set to form a support set S, and selecting h samples to form a query set Q;
constructing a self-adaptive subspace network model for bearing fault diagnosis;
inputting the support set S and the query set Q into a self-adaptive subspace network model, and obtaining a dynamic classifier through training;
and testing by using the trained dynamic classifier network model to obtain a classification result.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the method converts the one-dimensional vibration signal into the two-dimensional gray scale image as input, thereby better retaining the original information of the data; the gray-scale map is used as input, the representation and extraction of features are facilitated better, the bearing fault types are classified by adopting a dynamic subspace method based on measurement, the classification precision is better, and the generalization performance is better.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a sample graph of a gray scale image converted using a bearing vibration signal in accordance with an embodiment of the present invention;
FIG. 3 is a diagram of an adaptive subspace network model architecture used in accordance with an embodiment of the present invention;
FIG. 4 is a graph of loss during training according to an embodiment of the present invention;
FIG. 5 is a graph of accuracy during training according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
As shown in fig. 1, an embodiment of the present invention discloses a method for diagnosing a fault of a small sample bearing based on a two-dimensional gray scale image adaptive subspace, which specifically includes the following steps:
step 1): acquiring bearing vibration signals of n different fault types through a sensor;
step 2): sampling the bearing vibration signals according to the step length w of the length b (b is the square of a natural number, and b is L multiplied by L), and converting the step length w into a two-dimensional gray image to form a bearing fault data set, wherein a gray image of the bearing vibration signals of 4 different fault categories is shown in FIG. 2;
specifically, the method for converting the vibration signal into the two-dimensional gray image comprises the following steps:
firstly, a one-dimensional bearing vibration signal sample with the length of b is converted into an L multiplied by L two-dimensional matrix A, and the formula is as follows:
A(e，f)＝G(L×(e-1)+f)
in the formula: g () is a two-dimensional matrix conversion function, and A (e, f) (e, f e (0, L)) is the value of the element at the row e and column f in the converted matrix.
Then converting the two-dimensional matrix A into a gray image D, and specifically operating to normalize the two-dimensional matrix, namely compressing the value of the two-dimensional matrix to be within the interval of 0 to 1; and multiplying by 255 to convert into pixel values of the two-dimensional gray image, wherein the formula is as follows:
Figure BDA0003695671380000031
in the formula: d (e, f) (e, f epsilon (0, L)) is the pixel value of the ith row and the ftth column in the gray scale image matrix of the bearing vibration signal, max (A) is the maximum value of the elements in the matrix A, and min (A) is the minimum value of the elements in the matrix A.
Step 3): selecting k samples from each fault type of the data set to form a support set S, and selecting h samples to form a query set Q;
step 4): constructing a self-adaptive subspace network model for bearing fault diagnosis, wherein the model consists of two parts, namely a feature extractor f θ And a classifier, as shown in FIG. 3;
wherein, the feature extractor f θ Consists of a multi-layer convolutional neural network (which can be 3, 4, 5.. 10 layers). By means of a feature extractor f θ Mapping the gray level image D to a feature space to obtain a corresponding feature vector f θ (D) And differencing with the average value of the feature vectors of each type of bearing fault.
Specifically, the ith gray level image sample x of the bearing fault class C is taken c，i Using a feature extractor f θ Extracting a sample x c，i To obtain a feature vector f θ (x c，i ). And then with the feature vector mean value mu of the bearing fault class C c Make a difference to obtain a set
Figure BDA0003695671380000041
The formula is as follows:
Figure BDA0003695671380000042
Figure BDA0003695671380000043
in the formula: mu.s c Mean value of feature vectors, f, for bearing fault class C θ () A function is extracted for the feature.
Will be assembled
Figure BDA0003695671380000044
Construction of subspace P of bearing fault class C by means of truncation of singular value decomposition matrix c (c∈[1，n]) Here, theSpace P c (c∈[1，n]) Generated by the support set samples of the fault class C, the obtained subspace P is different from the support set samples c Are also different, so the subspace P generated c Referred to as the adaptation subspace.
In particular, the set to be derived from the bearing fault class C
Figure BDA0003695671380000045
Singular value decomposition is performed, and the formula is as follows:
Figure BDA0003695671380000046
in the formula, U and V are k multiplied by k dimensional matrixes formed by k eigenvectors, and sigma is a k multiplied by k dimensional matrix with k eigenvalues as main diagonal lines;
then, the first z dimensions in the U are selected to obtain a truncation matrix P of the bearing fault category C c Due to P c Has orthogonality, so P c As a subspace for the bearing fault category C.
Step 5): optimizing the subspace by utilizing the query sample set Q to ensure that the subspaces P of different fault types c (c∈[1，n]) The distance between the sub-classifiers is maximized, and the distinguishing capability of the sub-spaces is better, so that the fault classifier with higher robustness is obtained.
The optimization method of the subspace comprises the following steps:
(1) inputting samples Q in a query set Q into a feature extractor f θ Obtain the feature vector f θ (q) calculating f θ (q) to each fault category subspace P c (c∈[1，n]) A distance d between i (q) calculating the probability that the query sample q belongs to each bearing fault category through a softmax () function; calculating every two fault classification subspaces P by projection F-norm c (c∈[1，n]) The distance between them; calculating a loss function L t And make every two fault classification subspaces P by back propagation c (c∈[1，n]) Maximizes the distance between and updates the feature extractor network parameters. Finally, a dynamic classifier is obtained through training, and the dynamic classifier canNew classes can be identified and classified by a small number of samples.
Specifically, a feature vector f of a query sample q is calculated θ (q) to bearing failure class C subspace P c (c∈[1，n]) A distance d between c (q) the formula is as follows:
d c (q)＝-||(I-M c )(f θ (q)-μ c )|| 2
in the formula: m c ＝P c P c T 。
Calculating the probability that the query sample q belongs to each bearing fault category through a softmax () function, wherein the formula is as follows:
Figure BDA0003695671380000051
the distance between each two bearing class subspaces is calculated using the projected F-norm. The formula is as follows:
Figure BDA0003695671380000052
in the formula: p l And P j Given the basis of the two bearing fault classification subspaces, z is the dimension of the subspace.
(2) To make the obtained fault classification subspace P c (c∈[1n]) With better separability and improved identification of faulty bearing types, by maximizing the fault classification subspace P c (c∈[1，n]) Is achieved, i.e. minimized, by the distance between
Figure BDA0003695671380000053
In particular by minimizing the following L t To obtain:
Figure BDA0003695671380000054
in the formula: the first term is the classification loss, n is the number of fault classesK is the number of samples per fault category; the second term is that each fault class subspace P c (c∈[1，n]) The distance between the two is maximized, and lambda is a self-defined parameter.
Minimizing the loss function L t The values are obtained by a method of back propagation training. Parameters of the adaptive subspace classification model are updated. Through training the model, a classifier is obtained, which can classify the bearing fault classes through a small number of samples.
Step 6): inputting the test sample into the tested adaptive network model to obtain a classification result;
specifically, a test sample t is transmitted to a feature extractor f θ To obtain a feature vector f θ (t) of (d). Then f is calculated θ (t) to each fault category subspace P c (c∈[1，n]) A distance d therebetween c (t); and calculating the probability that the test sample t belongs to each bearing fault category through a softmax () function, wherein the category with the maximum probability is defined as the fault category of the test sample.
The bearing vibration data of the university of Kesselski is used in the embodiment, 4 types of bearing vibration data are selected in the experiment, wherein the 4 types of bearing vibration data comprise 1 normal data and 3 data of different fault types, each data is divided by length of 1024 step length 100 and sampled, and the data is converted into a two-dimensional gray image with the scale of 32 multiplied by 32 to form a data set. In the training process, 5 samples are randomly extracted from each class in the training set to form a support set in each round, and 15 samples are randomly extracted from each class in the verification set to form a query set. The support set and the query set are transmitted to the model for training, in this example, the training times are set to 100 times, and the learning rate is set to 0.001. The loss curve saved during training is shown in fig. 4 and the accuracy curve is shown in fig. 5. The trained model is tested by using the test set, and the accuracy reaches 99.83 percent.

Claims (5)

1. A small sample bearing fault diagnosis method based on two-dimensional gray scale image adaptive subspace is characterized by comprising the following steps:
acquiring n bearing vibration signals of different fault types through a sensor;
sampling a bearing vibration signal according to the length b and the length b by taking the square of a natural number and the step length w, and converting the sampled signal into a two-dimensional gray image to form a data set;
selecting k samples from each fault type of the data set to form a support set S, and selecting h samples to form a query set Q;
constructing a self-adaptive subspace network model for bearing fault diagnosis;
inputting the support set S and the query set Q into a self-adaptive subspace network model, and obtaining a dynamic classifier through training;
and testing by using the trained dynamic classifier network model to obtain a classification result.
2. The method for diagnosing the fault of the bearing with the small sample based on the two-dimensional gray scale image adaptive subspace as recited in claim 1, wherein the method for converting the vibration signal of the bearing into the gray scale image comprises the following steps:
firstly, a one-dimensional bearing vibration signal sample with the length of b is converted into an L multiplied by L two-dimensional matrix A, then the two-dimensional matrix A is converted into a gray image D, and the specific operation is to normalize the two-dimensional matrix, namely compress the value of the two-dimensional matrix to the interval of 0 to 1, and multiply the value by 255 to convert the two-dimensional matrix into the pixel value of the two-dimensional gray image.
3. The method for diagnosing the fault of the bearing with the small sample based on the two-dimensional gray scale image adaptive subspace as recited in claim 1, wherein the bearing vibration signal is converted into a gray scale image formula as follows:
A(e，f)＝G(L×(e-1)+f)
Figure RE-FDA0003739624810000011
in the formula: g () is a two-dimensional matrix conversion function, A (E, f) (E, f epsilon (0, L)) is the value of the element in the ith row and the fth column in the converted matrix, D (E, f) (E, f epsilon (0, L)) is the pixel value in the ith row and the fth column in the gray scale image matrix of the vibration signal of the bearing, max (A) is the maximum value of the element in the matrix A, and min (A) is the minimum value of E in the element in the matrix A.
4. The small-sample bearing fault diagnosis method based on the two-dimensional gray scale image adaptive subspace as claimed in claim 1, wherein the method for constructing the adaptive subspace network model for bearing fault diagnosis and training the model comprises the following steps:
the self-adaptive subspace network model for bearing fault diagnosis consists of two parts, namely a feature extractor f θ And a dynamic classifier;
feature extractor f θ Composed of multiple layers of convolutional neural networks, by a feature extractor f θ Mapping the gray level image D to a feature space to obtain a corresponding feature vector f θ (D) And making a difference with the average value of the feature vectors of each type of bearing faults;
will be assembled
Figure RE-FDA0003739624810000021
Construction of the adaptive subspace P of the fault class C by means of truncation of the singular value decomposition matrix c (c∈[1，n])；
Inputting the support set S and the query set Q into a self-adaptive subspace network model, and obtaining a dynamic classifier through training; passing the query sample q through a feature extractor f θ Obtain the feature vector f θ (q) calculating f θ (q) to bearing failure class C subspace P c (c∈[1，n]) A distance d between c (q)；
Calculating the probability between the query sample and each category through a softmax () function;
computing a projection metric using the projected F-norm to maximize the distance between each bearing class subspace;
and performing back propagation training by minimizing the loss function value to update parameters of the self-adaptive subspace classification model, and obtaining a dynamic classifier by training the model, wherein the dynamic classifier can classify new classes by a small amount of samples.
5. The method for diagnosing the bearing fault of the small sample based on the two-dimensional gray scale image adaptive subspace as claimed in claim 4, wherein the formula for making the difference between the image feature vector and the average value of the feature vectors of each type of bearing fault is as follows:
Figure RE-FDA0003739624810000022
Figure RE-FDA0003739624810000023
in the formula: mu.s c Mean value of feature vectors, f, for bearing fault class C θ () Extracting a function for the feature;
the singular value decomposition formula is as follows:
Figure RE-FDA0003739624810000024
in the formula, U and V are k multiplied by k dimensional matrixes formed by k eigenvectors, and sigma is a k multiplied by k dimensional matrix with k eigenvalues as main diagonals;
the calculation f θ (q) to failure class C subspace P c (c∈[1，n]) A distance d between c (q) the formula is as follows:
d c (q)＝-||(I-M c )(f θ (q)-μ c )|| 2
in the formula: m c ＝P c P c T ；
The softmax () function formula is as follows:
Figure RE-FDA0003739624810000031
the projection F-norm formula and the loss function formula are as follows:
Figure RE-FDA0003739624810000032
in the formula: p l And P j Given the basis of two bearing fault classification subspaces, z is the dimension of the subspace;
the loss function is as follows:
Figure RE-FDA0003739624810000033
in the formula: the first term is the classification loss, n is the number of fault classes, and k is the number of samples of each fault class; the second term is to make the fault class subspace P c (c∈[1，n]) The distance between the two is maximized, and lambda is a self-defined parameter.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116051911A (en) * 2023-03-29 2023-05-02 北京大学 Small sample bearing vibration image data fault diagnosis method based on uncertainty learning
CN117197073A (en) * 2023-09-07 2023-12-08 石家庄铁道大学 Rectangular object automatic counting method based on machine vision

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116051911A (en) * 2023-03-29 2023-05-02 北京大学 Small sample bearing vibration image data fault diagnosis method based on uncertainty learning
CN116051911B (en) * 2023-03-29 2023-07-07 北京大学 Small sample bearing vibration image data fault diagnosis method based on uncertainty learning
CN117197073A (en) * 2023-09-07 2023-12-08 石家庄铁道大学 Rectangular object automatic counting method based on machine vision
CN117197073B (en) * 2023-09-07 2024-03-05 石家庄铁道大学 Rectangular object automatic counting method based on machine vision

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