CN112257747B - Diagnostic method based on compressed data and supervised global-local/non-local analysis - Google Patents
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Abstract
The invention discloses a diagnosis method based on compressed data and supervised global-local/non-local analysis, which is a three-stage bearing fault diagnosis method based on compressed data and supervised global-local/non-local discriminant analysis. In a first stage, compressed data is obtained based on a compressed sensing framework; in the second stage, a new manifold learning algorithm is proposed: monitoring global-local/non-local discriminant analysis, mapping compressed data to a low-dimensional space by using the algorithm, and reserving global and local/non-local information of the compressed data; in the third stage, the low-dimensional features are classified as inputs to the SVM.
Description
Technical Field
The invention belongs to the technical field of compressed sensing, manifold learning and fault diagnosis, and relates to a three-stage bearing fault diagnosis method based on compressed data and supervised global-local/non-local discriminant analysis
Background
Rolling bearing is one of important components of rotary machinery, and a shutdown caused by faults of the rolling bearing brings great economic loss, so that the condition detection and fault diagnosis of the rolling bearing are particularly important. Vibration signals generated by the rotary machine contain rich characteristic information and are often collected as the basis of fault diagnosis and analysis. The well-known nyquist sampling law states that the sampling frequency must be greater than 2 times the highest frequency in the signal under test when the signal is acquired, but as mechanical fabrication continues to advance toward intelligence and refinement, the application of this sampling law will produce a vast amount of vibration data, which presents a significant challenge for data storage, transmission and processing. The proposal of the compressed sensing theory provides a new idea for breaking the bottleneck. There have been many studies currently showing the advantages of compressed sensing in fault diagnosis: the redundant data volume is reduced, and the diagnosis efficiency is further improved. However, the information in the compressed data is not most favorable for classification although it is favorable for recovering the original signal, so that further extraction of the discrimination information of the compressed signal is of great significance for improving the diagnosis accuracy and shortening the diagnosis time.
At present, the research of further extracting low-dimensional features from compressed data is relatively few, the common methods comprise Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), and the PCA is an unsupervised dimension reduction method capable of retaining original information to the greatest extent; LDA is a supervised dimension reduction method that maximizes the distance between heterogeneous samples. However, the above methods are based on global projection techniques, which do not detect their local intrinsic structures well, and these local structures can represent authentication information embedded in different categories of neighboring data. Local manifold learning algorithms such as local hold projection (LPP) and Local Linear Embedding (LLE) can extract the local intrinsic structure of the data, but easily ignore the global information. Therefore, in recent years, feature fusion algorithms based on global and local structures have received a great deal of attention in the field of fault diagnosis. Most of the feature fusion algorithms integrate objective functions for extracting global features and local features to form a final objective function, and projection dimension reduction is carried out through a solved projection matrix. Most of the algorithms are used for feature selection, feature sets are required to be extracted in advance based on priori knowledge, and meanwhile, label information of various samples with guiding significance for classification is not fully considered.
Disclosure of Invention
The invention aims to provide a three-stage bearing fault diagnosis method based on compressed data and supervised global-local/non-local discriminant analysis, which can reduce storage burden and ensure diagnosis precision.
In order to achieve the above purpose, the technical scheme adopted by the invention is a three-stage bearing fault diagnosis method based on compressed data and supervised global-local/non-local discriminant analysis, wherein in the first stage, compressed data is obtained based on a compressed sensing frame to reduce storage burden; in the second stage (feature extraction link of compressed data), a new manifold learning algorithm is proposed: monitoring global-local/non-local discriminant analysis, mapping compressed data to a low-dimensional space by using the algorithm, and reserving global and local/non-local information of the compressed data; in the third stage, the low-dimensional features are classified as inputs to the SVM.
S1 obtaining compressed data based on compressed sensing framework
Compressed Sensing (CS) is a new sampling technique that is not limited by signal bandwidth, can sample at a sampling rate below nyquist, and the sampling process discards a large amount of redundant information in the vibration data. The basic idea of CS is: as long as the signal is sparse in some transform domain, the signal can be projected into a low-dimensional space by a measurement matrix that is incoherent with the transform basis (sparse basis), and the original signal can be reconstructed with a small number of data features in the low-dimensional space that are sufficient to represent the original signal. The method uses the compressed signal projected into the low dimensional space as input for subsequent fault diagnosis.
The precondition for compressed sensing is the sparse nature of the signal. Equation (1) describes the sparse representation process of x: an N-dimensional original vibration signal x in the transform domainThe above is sparse representation, and the sparse coefficient is s (k non-zero coefficients are in s, and k is less than N).
According to CS theory, a sparse signal x is projected to a low-dimensional space through a measurement matrix phi (phi epsilon R (M×N)) to obtain a compressed signal y in M dimensions, and meanwhile, the sampling and the compression of the signal are completed, and the process can be expressed as:
The projection matrix Φ must meet the finite constraint equidistant property (RIP), and a typical gaussian random matrix, a bernoulli matrix, a partial hadamard matrix, and other random matrices can meet the condition. Finally, the last link of compressed sensing is as follows: the original signal x (x epsilon R N) is recovered from the compressed signal y (y epsilon R M), which is an underdetermined equation with an unknown number greater than the number of equations, and typically has numerous solutions, so that an optimal solution is required to be determined, and the optimal solution can be performed by using an orthogonal matching pursuit algorithm (OMP) commonly used at present.
S2, new manifold learning algorithm-supervision global-local/non-local discriminant analysis (SGLNDA)
S2.1 Linear Discriminant Analysis (LDA)
LDA is a supervised dimension reduction method based on the optimal classification effect, namely, the distance between projected different types of samples is as far as possible, and the projection points of the same type of samples are as close as possible. The R M-dimensional sample composition dataset x= { X 1,x2,...,xR } contains k categories { C 1,C2,...,Ck }, maximizes the objective function of LDA in equation (3), and can yield the projection matrix W.
Wherein S b is an inter-class divergence matrix, and S w is an intra-class divergence matrix:
n j samples are included in the j-th class, Represents the mean of the j-th class,/>The overall mean of the R samples is represented. One obvious disadvantage of LDA is that the local structure of the data is ignored.
S2.2 supervision of local/non-local differential analysis (SLNDA)
When the local/non-local relation possibly existing between any point a and surrounding points is considered, label information of each point is introduced, namely a and a 1,a2 belong to A class, and B 1 and B 2 belong to B class. There may be 4 relationships of point a to surrounding points: a and a 1; a and a 2; a and b 1; non-homogeneous non-neighbor relationship between a and b 2. The purpose of supervising the local/non-local projection is to find a mapping matrix W so that the samples of the same class of neighbors can be mapped to subspaces that are still mutually adjacent; and similar non-neighbor samples are mapped to subspaces so that the similar non-neighbor samples can be adjacent to each other; non-homogeneous non-neighbor samples are mapped to subspaces far apart from each other; whereas samples of non-homogeneous neighbors are mapped to subspaces that can be distant from each other. Features obtained by dimension reduction using such a projection matrix will have discrimination information most suitable for classification.
Assuming that a group of data x= { X 1,x2,...,xN }, dividing the data into K classes, defining a weight matrix S i to describe the data of the similar neighbors; the weight matrix S n describes non-homogeneous non-neighbor data. S (x i,xj) is the distance between the two samples x i and x j (the present method uses euclidean distance), N k(xj represents the k-nearest neighbor of x j, pi i and pi j represent class labels of x i and x j, respectively. In the objective function shown in equation (8), y i＝WTxi,yi is the projection of x i in the low-dimensional space, D l is the diagonal matrix, and the elements on the diagonal are the sum of the column vectors of S l. When the objective function (8) is minimized, the larger the distance weight coefficient of two similar neighbor samples is, the smaller the distance between the two sample projection points obtained by minimizing the objective function is, and a projection matrix W which is still as close as possible after the similar neighbor samples are projected into a low-dimensional space is obtained. Similarly, a projection matrix can be obtained by maximizing the objective function shown in the formula (9), and the non-similar non-neighboring samples are projected to the positions far away from each other in the low-dimensional space, wherein the element on the diagonal of the diagonal matrix of D n is the sum of the column vectors of S n.
The most undesirable situation for pattern recognition is non-neighbor distribution of homogeneous samples and neighbor distribution of non-homogeneous samples. The weight matrix Q constructed with '1' as a penalty factor is used to describe data of heterogeneous neighbors, with the projection points being alienated from each other by maximizing the objective function (12). Wherein D q is a diagonal matrix whose diagonal sums the column vectors with a value of Q; similarly, the weight matrix H is used for describing the similar non-adjacent data, and projection points are mutually close by minimizing an objective function (13). Where D h is the diagonal matrix, which is the sum of the column vectors with values H on the diagonal.
According to the above analysis, local/non-local discrimination information of sample data can be captured by combining the objective functions of the formulas (8), (9), (12) and (13).
S2.3 Supervisory Global-local/non-local discriminant analysis (SGLNDA)
SGLNDA is formed by combining the objective function of mining local/non-local discrimination information in S2.2 described above with the objective function of LDA in S2.1 for mining global discrimination information, as shown in equation (14). SGLNDA by minimizing the objective function, the defect that the LDA algorithm in S2.1 ignores the local structural characteristics of the data can be overcome, and global discrimination information can be supplemented for monitoring local/non-local projection in S2.2, so that the global information and the local/non-local discrimination information of sample data can be extracted simultaneously.
Wherein ,Slh＝XLlXT+XLhXT,Snq＝XLnXT+XLqXT, ultimately converts the minimization problem of (14) into a problem of deriving the eigenvalues of the following equation.
(Sb+Slh)W＝λ(SW+Snq)W (15)
N ordered eigenvalues lambda 1≤λ2≤λ3≤…λN and their corresponding eigenvectors w 1,w1,w1,…wN are obtained by solving equation (15). The first D eigenvectors are retained to form a new projection matrix w D (D < N), which is finally converted into a D-dimensional signal Y D by equation (16):
S3 SVM classifier identifies faults
And (5) carrying out state identification by using the SVM. The low-dimensional features extracted in the previous stage are input into a classifier for training. The basic idea of SVM is to find an optimal classification hyperplane so that there is a maximum separation between the points of different classes closer to the hyperplane.
Compared with the prior art, the invention has the following beneficial effects:
According to the invention, the compressed projection data obtained based on the compressed sensing frame is adopted to carry out fault diagnosis of the rolling bearing, identification information of a compressed signal is further extracted in a feature extraction link, but most of low-dimensional feature extraction methods based on the compressed data only extract single global features for fault diagnosis, the extracted manifold learning algorithm supplements local/non-local internal structural features for the compressed projection data, tag information of various samples with guiding significance is fully considered, and global-local/non-local identification information is extracted for subsequent fault diagnosis. The invention makes a brand new exploration in the feature extraction link of the compressed data, which has important significance for improving the diagnosis precision and shortening the diagnosis time.
Drawings
Fig. 1 is a schematic diagram of the distribution of a point a and surrounding points, a and a 1,a2 belong to the class a, and B 1 and B 2 belong to the class B.
Fig. 2 is a flow diagram of the proposed diagnostic model.
Fig. 3 is a rolling bearing failure simulation experiment table of the university of western storage in united states.
Fig. 4 is a graph of low dimensional feature size versus classification accuracy after projection of different compressed signals. Different compression signals corresponding to the compression rate alpha= 0.1,0.09,0.08,0.07,0.06,0.05,0.04,0.03 are projected to low-dimensional spaces with different dimensions, and the corresponding classification precision is obtained.
FIG. 5 is a graph comparing performance of diagnostics based on independent features and combined features. For different compressed signals, LDA, SLNDA and SGLNDA are used for respectively extracting independent global information, independent local/non-local information and combined global-local/non-local information in a feature extraction link, and the diagnosis result obtained based on the three types of information is shown in figure 5.
FIG. 6 is a result of three methods of extracting a different number of low-dimensional features for classification recognition. The low-dimensional feature size of the feature extraction link can affect the final classification accuracy, so in order to more reasonably compare the classification performances of the CS-PCA-SVM, the CS-LPP-SVM and the method, the classification results obtained after the three methods extract the low-dimensional features with different sizes in the feature extraction link are required to be compared. The part extracts different numbers of low-dimensional features from the compression vibration data with alpha=0.06 by adopting the three methods respectively for classification and identification.
Detailed Description
The invention is further described below with reference to the drawings and the detailed description.
(1) Label information for each sample is introduced in a new manifold learning algorithm to account for local/non-local structures. When the possible relation between any point a and surrounding points is considered, the label information of each point is introduced, namely a and a 1,a2 belong to A class, and B 1 and B 2 belong to B class. Fig. 1 shows 4 possible relationships of point a with surrounding points: a and a 1; a and a 2; a and b 1; non-homogeneous non-neighbor relationship between a and b 2. The purpose of supervising the local/non-local projection is to find a mapping matrix W so that the samples of the same class of neighbors can be mapped to subspaces that are still mutually adjacent; and the similar non-adjacent samples are mapped to subspaces so as to enable the samples to be adjacent to each other; non-homogeneous non-neighbor samples are mapped to subspaces far apart from each other; and the samples of non-similar neighbors are mapped to subspaces and can be far away from each other, so that the characteristics obtained after dimension reduction are most suitable for classification.
(2) The effectiveness of the proposed method was investigated. Take as an example experimental data of a drive-end rolling bearing failure disclosed in the university of western storage in united states. On the laboratory bench shown in fig. 3, the bearings were tested in 4 states (normal, outer ring failure, inner ring failure and rolling body failure) formed by machining of electric sparks at the corresponding portions, and the damage diameter was 0.18mm. The vibration signal was collected at a sampling frequency of 12kHz under 4 conditions of (1797 rpm,0 hp), (1772 rpm,1 hp), (1775 rpm,2 hp), (1730 rpm,3 hp) for each state of the bearing. Taking 1200 as the sample length, 100 samples are selected in each vibration signal without overlapping, namely 400 samples are used for each state, and 1600 samples are used for each state. The low-dimensional feature size of the feature extraction link of the method can influence the final classification precision, and the classification precision of compressed data obtained by different compression ratios under different projection dimensions is experimentally researched, and the result is shown in fig. 4. In order to study the superiority of the proposed method in classifying by using global-local/non-local fusion features in the feature extraction link, for different compressed signals, separate global information, separate local/non-local information and combined global-local/non-local information are respectively extracted by using LDA, SLNDA and the proposed SGLNDA in the feature extraction link, and the diagnosis result obtained based on the three types of information is shown in figure 5.
(3) In order to more reasonably compare the superiority of the proposed method, taking experimental data of the rolling bearing fault at the driving end disclosed by the university of Western storage as an example, the low-dimensional feature size of the feature extraction link is considered to influence the final classification accuracy, and the classification results obtained after the CS-PCA-SVM, the CS-LPP-SVM and the proposed method extract the low-dimensional features with different sizes in the feature extraction link are required to be compared. The part extracts different numbers of low-dimensional features from the compression vibration data with alpha=0.06 by adopting the three methods to carry out classification recognition, and the classification result is shown in fig. 6.
Claims (1)
1. A diagnostic method based on compressed bearing vibration data and supervised global-local/non-local analysis, characterized by: in a first stage, obtaining compressed bearing vibration data based on a compressed sensing frame; in the second stage, a new manifold learning algorithm is proposed: monitoring global-local/non-local discriminant analysis, mapping the vibration data of the compression bearing to a low-dimensional space, and reserving global and local/non-local information of the vibration data; in the third stage, classifying the low-dimensional features as input of the SVM;
S1, obtaining compression bearing vibration data based on a compression sensing frame;
using the compressed signal projected into the low-dimensional space as an input for subsequent fault diagnosis; the premise of compressed sensing is the sparse characteristic of the signal; equation (1) describes the sparse representation process of x: an N-dimensional original vibration signal x in the transform domain The sparse representation can be realized, and the sparse coefficient is s; the s has k nonzero coefficients, k is less than N;
According to CS theory, a sparse signal x is projected to a low-dimensional space through a measurement matrix phi, phi epsilon R (M×N), a compressed signal y in M dimensions is obtained, and meanwhile, sampling and compression of the signal are completed, and the method is expressed as:
Wherein the projection matrix Φ must satisfy a finite constraint equidistant property RIP; recovering an original signal x from the compressed signal y, wherein x is R N,y∈RM, and an optimal solution is determined by carrying out optimal solution, and carrying out optimal solution by an orthogonal matching tracking algorithm;
s2, a new manifold learning algorithm-supervised global-local/non-local discriminant analysis;
S2.1, linear discriminant analysis;
LDA is a supervised dimension reduction method based on the best classification effect, namely: the distance between the projected samples of different types is as far as possible, and the projection points of the samples of the same type are as close as possible; r M-dimensional samples form a bearing vibration dataset X= { X 1,x2,...,xR } containing k categories { C 1,C2,...,Ck }, and the objective function of LDA in the formula (3) is maximized to obtain a projection matrix W;
wherein S b is an inter-class divergence matrix, and S w is an intra-class divergence matrix:
n j samples are included in the j-th class, Represents the mean of the j-th class,/>Representing the overall mean of the R samples;
s2.2, supervising local/non-local differential analysis;
Assuming that a group of bearing vibration data X= { X 1,x2,...,xN }, dividing the bearing vibration data into K classes, and defining a weight matrix S i to describe bearing vibration data of similar neighbors; the weight matrix S n describes non-homogeneous non-adjacent bearing vibration data; s (x i,xj) is the distance between the two samples x i and x j, N k(xj represents the k-nearest neighbor of x j, pi i and pi j represent class labels of x i and x j, respectively; in the objective function shown in formula (8), y i＝WTxi,yi is the projection of x i in a low-dimensional space, D l is a diagonal matrix, and the element on the diagonal is the sum of column vectors of S l; when the objective function (8) is minimized, the larger the distance weight coefficient of two similar neighbor samples is, the smaller the distance between the two sample projection points obtained by minimizing the objective function is, namely, a projection matrix W which enables the similar neighbor samples to be still as close as possible after being projected into a low-dimensional space is obtained; similarly, a projection matrix is obtained by maximizing an objective function shown in the formula (9), non-similar non-adjacent samples are projected to positions distant from each other in a low-dimensional space, and elements on the diagonal of the diagonal matrix D n are the sum of column vectors of S n;
The weight matrix Q constructed by taking '1' as a penalty factor is used for describing bearing vibration data of non-homogeneous neighbors, and projection points are mutually distant by maximizing an objective function (12); d q is a diagonal matrix whose sum of column vectors on the diagonal has a value Q; describing the vibration data of the similar non-adjacent bearings by using a weight matrix H, and enabling projection points to be close to each other by minimizing an objective function (13); wherein D h is a diagonal matrix whose sum of column vectors with values H on the diagonal;
According to the analysis, the local/non-local discrimination information of the vibration data of the sample bearing can be captured by combining the objective functions of the formulas (8), (9), (12) and (13);
s2.3, supervising global-local/non-local discriminant analysis;
Combining the objective function for mining local/non-local discrimination information in S2.2 with the objective function for mining global discrimination information of LDA in S2.1, as shown in formula (14);
Wherein ,Slh＝XLlXT+XLhXT,Snq＝XLnXT+XLqXT, finally converts the minimization problem of (14) into a problem of deriving a characteristic value of the following formula;
(Sb+Slh)W＝λ(SW+Snq)W (15)
Obtaining N ordered eigenvalues lambda 1≤λ2≤λ3≤…λN and corresponding eigenvectors w 1,w1,w1,…wN by solving the formula (15); the first D eigenvectors are reserved to form a new projection matrix w D, D < N, and finally the new projection matrix is converted into a D-dimensional signal Y D through a formula (16):
S3 SVM classifier identifies the fault;
Carrying out state identification by using an SVM; inputting the extracted low-dimensional features into a classifier for training; the SVM finds an optimal classification hyperplane so that there is a maximum separation between the different classes of points nearer to the hyperplane.
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