CN110243590A - A Rotor System Fault Diagnosis Method Based on Principal Component Analysis and Width Learning - Google Patents

Abstract

The invention discloses a rotor system fault diagnosis method based on principal component analysis and width learning, which uses principal component analysis to reduce the dimensionality of the feature matrix formed after feature extraction, reduces the linear correlation between data, and eliminates redundancy Attributes, obtain a low-dimensional matrix that can retain its essential characteristics, and then input the matrix into the width learning system for fault identification, and complete the task of rotor system fault classification. The invention introduces the principal component analysis and width learning system into the fault diagnosis and identification of the rotor system. This method can effectively reduce the complexity of fault classification, greatly shorten the data modeling time, and improve the efficiency of fault identification of the rotor system. Complete the fault diagnosis task of the rotor system, it has good practicability and is worthy of popularization.

Description

A Rotor System Fault Diagnosis Method Based on Principal Component Analysis and Width Learning

technical field

The invention belongs to the technical field of fault detection of mechanical parts, and in particular relates to a fault diagnosis method of a rotor system based on principal component analysis and width learning.

Background technique

As the core component of rotating machinery, the rotor system plays an irreplaceable role in various related fields. The rotor system is widely used in rotating machinery. The failure of the rotating machinery in the working process will cause major economic losses, a large part of which is caused by the failure of the rotor system. The failure hazards include noise, rotor instability, serious It may even damage the mechanical structure and cause major safety accidents. Therefore, it has very important scientific significance and application value to effectively analyze and accurately diagnose the initial faults of the rotor system.

At present, the widely used methods for rotor fault diagnosis are window Fourier transform, empirical mode decomposition, wavelet analysis and other methods. However, after the feature extraction of the fault signal by the above method, the formed feature matrix has problems such as complex structure, high feature correlation, and high degree of redundancy, which will greatly increase the complexity of fault classification and reduce the accuracy of fault identification. Rate.

Contents of the invention

In view of this, the present invention provides a rotor system fault diagnosis method based on principal component analysis and width learning, the method first uses principal component analysis (PCA) to reduce the dimension of the feature matrix formed after feature extraction, reducing the Linear correlation between data, eliminate redundant attributes, obtain a low-dimensional matrix that can retain its essential features, and then input the matrix into the Broad Learning System (BLS for short) for fault identification, the Broad Learning System (Broad Learning System , referred to as BLS) can efficiently complete the rotor system fault classification task, so as to solve the deficiencies in the prior art.

Technical scheme of the present invention is:

A rotor system fault diagnosis method based on principal component analysis and width learning, comprising the following steps:

Step 1: Collect fault data T(n) in time domain;

Step 2: Carry out Fourier transform according to formula (1), transform the collected fault data T(n) in time domain into fault data X in frequency domain,

in,

In the above formula (1) and formula (2), n=0,1,...,N-1, k=0,1,...,N-1, N is the length of time domain fault data, j is a complex symbol, X is frequency domain fault data, including training samples and test samples, X={x ₁ , x ₂ ,..., _xi ,...x _m }, i=1,...,m , T(n) is the fault data in time domain;

Step 3: Obtain the covariance matrix C of the fault data X in the frequency domain;

Step 4: Determine the correlation between fault data X in different frequency domains;

Step 5: Decompose the eigenvalues of the covariance matrix C of the fault data X in the frequency domain according to formula (3), so as to obtain the eigenvector matrix Q and the eigenvalue matrix Σ, the eigenvalue matrix of the covariance matrix C of the fault data X in the frequency domain ∑ is expressed by formula (4), and the eigenvector matrix Q is expressed by formula (5),

C＝Q·∑·Q ^T (3)

in,

∑＝diag(λ ₁ ,λ ₂ ,...,λ _i ,...,λ _n ) (4)

Q＝[q ₁ ,q ₂ ,...,q _i ,...,q _n ] (5)

In the above formula (3), formula (4) and formula (5), C is the covariance matrix of the frequency domain fault data, Q is the eigenvector matrix, Σ is the eigenvalue matrix, λ ₁ ≥ λ ₂ ≥...≥ λ _i ≥...,≥λ _n , i=1,...,n, Q ^T is the transpose matrix of eigenvector matrix, n is the length of fault data in frequency domain, the number of all eigenvalues=all eigenvalues The number of vectors = the length of the fault data in the frequency domain = n, the eigenvector q _i and the eigenvalue λ _i are in a one-to-one correspondence;

Step 6: Perform principal component analysis on the frequency-domain fault data set X to obtain dimensionality-reduced frequency-domain fault data set X _k ;

Step 7: Divide the dimensionality-reduced frequency-domain fault data set X _k into a frequency-domain fault data set X _k1 for training and a frequency-domain fault data set X _k2 for testing;

Step 8: Construct a width learning system model using the trained frequency domain fault data set X _k1 ;

Step 9: Substituting the target weight β obtained in the process of building the breadth learning system model into the breadth learning system model to obtain the breadth learning system classification model;

Step 10: Substitute the tested frequency-domain fault data set X _k2 into the classification model of the wide learning system to obtain fault diagnosis results, and complete the test of the validity of the classification model of the wide learning system.

Preferably, obtaining the covariance matrix C of the fault data in the frequency domain in the step 3 includes the following steps:

S21. Since the frequency-domain fault data X has symmetry, the length of the frequency-domain fault data X can be intercepted according to formula (6),

n=N/2 (6)

In the above formula (6), n is the length after the interception of the length of the frequency domain fault data X, and N is the length of the time domain fault data;

S22. Calculate the sample mean value α of the fault data X in the frequency domain according to formula (7),

Among them, frequency domain fault data set X={x ₁ , x ₂ ,..., _xi ,...x _m }, i=1,...,m, m is the total number of samples, α is The sample mean value of frequency domain fault data X, x _i is the ith frequency domain fault data;

S23, obtain the covariance matrix C of the fault data in the frequency domain according to formula (8),

Among them, i=1,...,m, m is the total number of samples, C is the covariance matrix of the frequency domain fault data X, x _i is the i-th frequency domain fault data, α is the frequency domain fault data X The sample mean of .

Preferably, the determination condition adopted in the step 4 to determine the correlation between different frequency domain fault data is:

If the covariance between the corresponding two features in the covariance matrix is a positive number, there is a positive correlation between the two features; if the covariance between the corresponding two features in the covariance matrix is negative, the two features show a negative correlation covariance If the covariance between the corresponding two features in the matrix is 0, it means that the two features are not correlated.

Preferably, the method for performing principal component analysis and dimensionality reduction on the frequency-domain fault data set X in step 6 includes the following steps:

S41. Select the first k eigenvalues λ _i in the eigenvalue matrix Σ, and calculate the cumulative contribution rate θ of the principal component variance according to formula (9),

Among them, θ is the cumulative contribution rate of the main component variance, λ _i and λ _j are the i-th and j-th eigenvalues respectively, k is the number of selected eigenvalues, n is the number of all eigenvalues, i=1, ...,k,j=1,...,n,k<n;

S42. Obtain the corresponding eigenvectors q _i corresponding to the first k eigenvalues λ _i according to formula (10),

Q _k ＝[q ₁ ,q ₂ ,...,q _i ,...,q _k ] (10)

Among them, i=1,...,k, k<n, k is the number of selected eigenvalues, n is the number of all eigenvalues, Q _k is the corresponding eigenvector corresponding to the first k eigenvalues λ _i The eigenvector matrix formed by q _i ;

S43, carry out principal component analysis dimensionality reduction to eigenvector matrix Q _k according to formula (11),

X _k ＝Q _k ·X (11)

Among them, Q _k corresponds to the eigenvector matrix formed by the corresponding eigenvectors q _i of the first k eigenvalues λ _i , X is the fault data set in the frequency domain, and X _k is the fault data set in the frequency domain after principal component analysis.

Preferably, the method for constructing the width learning system model in the described step 8 includes the following steps:

S51. Perform feature mapping on the trained frequency-domain fault data set X _k1 according to formula (12) to form a feature node Z _i ,

Among them, _Wei and is the randomly selected feature node coefficient, i=1,...,t, t is the total number of feature nodes, Z _i is the i-th feature node, X _k1 is the frequency domain fault data set for training;

S52. Denote the combination of all feature nodes Z _i as Z ^t according to formula (13),

Z ^t ≡[Z ₁ ,...,Z _i ,...,Z _t ] (13)

Among them, Z _i is the i-th feature node, Z ^t is the combination of all feature nodes Z _i , t is the number of all feature nodes, i=1,...,t;

S53. Perform nonlinear function transformation on the combination Z ^t of all feature nodes Z _i according to formula (14) to generate an enhanced node H _j ,

where H _j is the jth enhanced node, Z ^t is the combination of all feature nodes Z _i , and is the randomly selected enhancement node coefficient, j=1,...,c, c is the total number of enhancement nodes;

S54. According to formula (15), denote the combination of all enhanced nodes H _j as H ^c ,

H ^c ≡ [H ₁ ,...,H _j ,...,H _c ] (15)

Wherein, c is the total number of enhanced nodes, j=1,...,c, 0≤j≤m, H ^c is the combination of all enhanced nodes H _j , and H _j is the jth enhanced node;

S55. Merge all nodes into an extended matrix G according to formula (16),

G≡[Z ^t |H ^c ] (16)

Among them, G is the expansion matrix, Z ^t is the combination of all feature nodes Z _i , H ^c is the combination of all enhanced nodes H _j ;

S56. Construct the objective function F _min (β) of the target weight β of the width learning system according to formula (17),

Among them, β is the target weight, F _min (β) is the objective function to solve the target weight β, V is a constant, Y={y ₁ ,...,y _l ,...,y _k1 }, y _l is the first The labels corresponding to l training samples, Y is a label matrix formed by all training sample labels, l=1,..., k1, k1 is the total number of training samples, and G is an expansion matrix;

S57, using the gradient descent method to solve the F _min (β) function in the formula (17), the formula (18) can be obtained to solve the target weight β,

Among them, Y={y ₁ ,...,y _l ,...,y _k1 }, y _l is the label corresponding to the lth training sample, Y is the label matrix composed of all training sample labels, l=1, ..., k1, k1 is the total number of training samples, β is the target weight, G is the expansion matrix, G ^T is the transposition of the expansion matrix, I _nh is the identity matrix with dimension nh, and nh is the width learning system The total number of model feature nodes and enhanced nodes, namely nh=c+t, V is a constant;

S58. The width learning system model is constructed.

Compared with the prior art, the present invention introduces Principal Component Analysis (PCA) and Broad Learning System (BLS for short) into the fault diagnosis and identification of the rotor system, and proposes a rotor system based on Principal Component Analysis and Broad Learning Fault diagnosis method, this method uses principal component analysis (PCA) to carry out dimensionality reduction processing on the fault data transformed by FFT, and forms feature vectors representing different faults, and then inputs the data after dimensionality reduction into BLS for classification, and its beneficial effects are:

1. The present invention can effectively reduce the complexity of fault classification;

2. The present invention can greatly shorten the data modeling time, improve the efficiency of rotor system fault identification, and thus efficiently complete the task of rotor system fault diagnosis;

3. The present invention has good practicability and is worth popularizing.

Description of drawings

Fig. 1 is a flow chart of a rotor system fault diagnosis method based on principal component analysis and width learning of the present invention;

Fig. 2 is the structural representation of the breadth learning system BLS of the present invention;

Fig. 3 is a schematic diagram of the experimental bench structure of the present invention;

Fig. 4 is the impact figure of cumulative variance contribution rate of the present invention on test accuracy;

Fig. 5 is a graph showing the influence of the cumulative variance contribution rate on the training time in the present invention.

Explanation of reference signs:

1. Data transmission cable; 2. Acceleration sensor; 3. Bearing to be tested; 4. Flywheel; 5. Coupling; 6. AC motor; 7. Data acquisition card; 8. PC; 9. Inverter.

Detailed ways

The present invention provides a rotor system fault diagnosis method based on principal component analysis and width learning. The present invention will be described below in conjunction with the schematic flow chart in FIG. 1 .

As shown in Figure 1, technical scheme of the present invention is:

A rotor system fault diagnosis method based on principal component analysis and width learning, comprising the following steps:

Step 1: Collect fault data T(n) in time domain;

Step 2: Carry out Fourier transform according to formula (1), transform the collected fault data T(n) in time domain into fault data X in frequency domain,

in,

In the above formula (1) and formula (2), n=0,1,...,N-1, k=0,1,...,N-1, N is the length of time domain fault data, j is a complex symbol, X is frequency domain fault data, including training samples and test samples, X={x ₁ , x ₂ ,..., _xi ,...x _m }, i=1,...,m , T(n) is the fault data in time domain;

Step 3: Obtain the covariance matrix C of the fault data X in the frequency domain;

Step 4: Determine the correlation between fault data X in different frequency domains;

Step 5: Decompose the eigenvalues of the covariance matrix C of the fault data X in the frequency domain according to formula (3), so as to obtain the eigenvector matrix Q and the eigenvalue matrix Σ, the eigenvalue matrix of the covariance matrix C of the fault data X in the frequency domain ∑ is expressed by formula (4), and the eigenvector matrix Q is expressed by formula (5),

C＝Q·∑·Q ^T (3)

in,

∑＝diag(λ ₁ ,λ ₂ ,...,λ _i ,...,λ _n ) (4)

Q＝[q ₁ ,q ₂ ,...,q _i ,...,q _n ] (5)

In the above formula (3), formula (4) and formula (5), C is the covariance matrix of the frequency domain fault data, Q is the eigenvector matrix, Σ is the eigenvalue matrix, λ ₁ ≥ λ ₂ ≥...≥ λ _i ≥...,≥λ _n , i=1,...,n, Q ^T is the transpose matrix of eigenvector matrix, n is the length of fault data in frequency domain, the number of all eigenvalues=all eigenvalues The number of vectors = the length of the fault data in the frequency domain = n, the eigenvector q _i and the eigenvalue λ _i are in a one-to-one correspondence;

Step 6: Perform principal component analysis on the frequency-domain fault data set X to obtain dimensionality-reduced frequency-domain fault data set X _k ;

Step 7: Divide the dimensionality-reduced frequency-domain fault data set X _k into a frequency-domain fault data set X _k1 for training and a frequency-domain fault data set X _k2 for testing;

Step 8: Construct a width learning system model using the trained frequency domain fault data set X _k1 ;

Step 9: Substituting the target weight β obtained in the process of building the breadth learning system model into the breadth learning system model to obtain the breadth learning system classification model;

Step 10: Substitute the tested frequency-domain fault data set X _k2 into the classification model of the wide learning system to obtain fault diagnosis results, and complete the test of the validity of the classification model of the wide learning system.

Further, obtaining the covariance matrix C of the fault data in the frequency domain in the step 3 includes the following steps:

S21. Since the frequency-domain fault data X has symmetry, the length of the frequency-domain fault data X can be intercepted according to formula (6),

n=N/2 (6)

In the above formula (6), n is the length after the interception of the length of the frequency domain fault data X, and N is the length of the time domain fault data;

S22. Calculate the sample mean value α of the fault data X in the frequency domain according to formula (7),

Among them, frequency domain fault data set X={x ₁ , x ₂ ,..., _xi ,...x _m }, i=1,...,m, m is the total number of samples, α is The sample mean value of frequency domain fault data X, x _i is the ith frequency domain fault data;

S23, obtain the covariance matrix C of the fault data in the frequency domain according to formula (8),

Among them, i=1,...,m, m is the total number of samples, C is the covariance matrix of the frequency domain fault data X, x _i is the i-th frequency domain fault data, α is the frequency domain fault data X The sample mean of .

Further, the determination condition adopted for determining the correlation between different frequency domain fault data in the step 4 is:

If the covariance between the corresponding two features in the covariance matrix is a positive number, there is a positive correlation between the two features; if the covariance between the corresponding two features in the covariance matrix is negative, the two features show a negative correlation covariance If the covariance between the corresponding two features in the matrix is 0, it means that the two features are not correlated.

Further, the method for performing principal component analysis and dimensionality reduction on the fault data set X in the frequency domain in step 6 includes the following steps:

S41. Select the first k eigenvalues λ _i in the eigenvalue matrix Σ, and calculate the cumulative contribution rate θ of the principal component variance according to formula (9),

Among them, θ is the cumulative contribution rate of the main component variance, λ _i and λ _j are the i-th and j-th eigenvalues respectively, k is the number of selected eigenvalues, n is the number of all eigenvalues, i=1, ...,k,j=1,...,n,k<n;

S42. Obtain the corresponding eigenvectors q _i corresponding to the first k eigenvalues λ _i according to formula (10),

Q _k ＝[q ₁ ,q ₂ ,...,q _i ,...,q _k ] (10)

Among them, i=1,...,k, k<n, k is the number of selected eigenvalues, n is the number of all eigenvalues, Q _k is the corresponding eigenvector corresponding to the first k eigenvalues λ _i The eigenvector matrix formed by q _i ;

S43, carry out principal component analysis dimensionality reduction to eigenvector matrix Q _k according to formula (11),

X _k ＝Q _k ·X (11)

Among them, Q _k corresponds to the eigenvector matrix formed by the corresponding eigenvectors q _i of the first k eigenvalues λ _i , X is the fault data set in the frequency domain, and X _k is the fault data set in the frequency domain after principal component analysis.

Further, the method for constructing the width learning system model in step 8 includes the following steps:

S51. Perform feature mapping on the trained frequency-domain fault data set X _k1 according to formula (12) to form a feature node Z _i ,

Among them, _Wei and is the randomly selected feature node coefficient, i=1,...,t, t is the total number of feature nodes, Z _i is the i-th feature node, X _k1 is the frequency domain fault data set for training;

S52. Denote the combination of all feature nodes Z _i as Z ^t according to formula (13),

Z ^t ≡[Z ₁ ,...,Z _i ,...,Z _t ] (13)

Among them, Z _i is the i-th feature node, Z ^t is the combination of all feature nodes Z _i , t is the number of all feature nodes, i=1,...,t;

S53. Perform nonlinear function transformation on the combination Z ^t of all feature nodes Z _i according to formula (14) to generate an enhanced node H _j ,

where H _j is the jth enhanced node, Z ^t is the combination of all feature nodes Z _i , and is the randomly selected enhancement node coefficient, j=1,...,c, c is the total number of enhancement nodes;

S54. According to formula (15), denote the combination of all enhanced nodes H _j as H ^c ,

H ^c ≡ [H ₁ ,...,H _j ,...,H _c ] (15)

Wherein, c is the total number of enhanced nodes, j=1,...,c, 0≤j≤m, H ^c is the combination of all enhanced nodes H _j , and H _j is the jth enhanced node;

S55. Merge all nodes into an extended matrix G according to formula (16),

G≡[Z ^t |H ^c ] (16)

Among them, G is the expansion matrix, Z ^t is the combination of all feature nodes Z _i , H ^c is the combination of all enhanced nodes H _j ;

S56. Construct the objective function F _min (β) of the target weight β of the width learning system according to formula (17),

Among them, β is the target weight, F _min (β) is the objective function to solve the target weight β, V is a constant, Y={y ₁ ,...,y _l ,...,y _k1 }, y _l is the first The labels corresponding to l training samples, Y is a label matrix formed by all training sample labels, l=1,..., k1, k1 is the total number of training samples, and G is an expansion matrix;

S57, using the gradient descent method to solve the F _min (β) function in the formula (17), the formula (18) can be obtained to solve the target weight β,

Among them, Y={y ₁ ,...,y _l ,...,y _k1 }, y _l is the label corresponding to the lth training sample, Y is the label matrix composed of all training sample labels, l=1, ..., k1, k1 is the total number of training samples, β is the target weight, G is the expansion matrix, G ^T is the transposition of the expansion matrix, I _nh is the identity matrix with dimension nh, and nh is the width learning system The total number of model feature nodes and enhanced nodes, namely nh=c+t, V is a constant;

S58. The width learning system model is constructed.

In order to eliminate the redundancy of the feature matrix, the present invention adopts the principal component analysis method to reduce the attributes for the classification problem with a lot of fault data, which can achieve the purpose of simplifying the feature matrix on the premise of losing as little information as possible, and at the same time provide Realize the rapid identification between feature vectors and fault types after principal component analysis dimension reduction, and introduce the width learning system to the field of fault diagnosis. In the width learning system, feature nodes and enhancement nodes can realize feature extraction and dimension reduction of data. The model All nodes are directly connected to the output terminal, and the corresponding output coefficients can be obtained by pseudo-inverse (Pseudo).

In order to eliminate the redundant information of the feature matrix, reduce the linear correlation between data, and improve the efficiency of rotor system fault identification, it is necessary to select a simple and efficient dimensionality reduction method. Principal component analysis (PCA) is a classic reduction method. dimension method. Because it is easy to understand and has no parameter restrictions in the use process, it has been widely used in various fields, such as image, voice, communication, etc. Its essence is to calculate the covariance matrix of the process data set, and then use the eigenvector of the matrix to determine The direction of the dimensionality reduction projection. In addition, the method can reveal the simple structure hidden behind the complex data, reduce the linear correlation among the data, and obtain the best description of the fault state. More importantly, PCA can reduce the redundancy of faulty data on the premise of losing as little information as possible, so as to achieve the purpose of data dimensionality reduction. Therefore, PCA is used in this paper to reduce the dimension of the fault feature matrix after fast Fourier transform.

In order to realize the rapid identification between fault feature vectors and their types after PCA dimension reduction, a Breadth Learning System (BLS) is used for fault diagnosis. In BLS, the original input is transferred and placed as mapped features in feature nodes, and extensively expanded in augmentation nodes, which can keep the system effective on data. In addition, all mapped feature and enhancement nodes are directly connected to the output, and the corresponding output coefficients can be obtained by pseudo-inverse (Pseudo).

The invention proposes a rotor system fault diagnosis method based on PCA and BLS. PCA is used to perform dimension reduction processing on fault data transformed by FFT to form feature vectors representing different faults, and then the dimension-reduced data is input into BLS for classification.

There are two basic methods adopted in the present invention:

1. Principal component analysis

Principal Component Analysis (PCA), also known as Karhunen-Loeve Transform (Karhunen-Loeve Transform), is a technique for data dimensionality reduction, the essence of which is to reduce the number of training samples on the basis of losing as little information as possible. The dimensionality, the main idea is to map n-dimensional features to k-dimensional, this k-dimensional is a new orthogonal feature also known as principal component, which is a k-dimensional feature reconstructed on the basis of the original n-dimensional features (k≤n).

The job of PCA is to sequentially find a set of mutually orthogonal coordinate axes from the original space. The selection of new coordinate axes is closely related to the data itself. Among them, the selection of the first new coordinate axis is the variance in the original data. The largest direction, the selection of the second new coordinate axis is the plane that is orthogonal to the first coordinate axis so that the variance is the largest, and the third axis is the largest variance in the plane that is orthogonal to the first and second axes. By analogy, n such coordinate axes can be obtained. From these newly obtained coordinate axes, most of the variance is contained in the first k coordinate axes, and the variance contained in the latter coordinate axes is almost zero. Therefore, for the coordinate axes whose variance is almost 0, the user can consider ignoring them, so as to retain the first k coordinate axes containing most of the variance. In fact, this is equivalent to only retaining the dimensional features that contain most of the variance, ignoring the feature dimensions that contain almost zero variance, and then realizing the dimensionality reduction of the data features.

2. Wide Learning System

The Broad Learning System (BLS for short) proposed by Professor C.L.Philip Chen is built in a flat manner. BLS is designed based on the idea of using mapping features as input to RVFLLNN. BLS can establish feature nodes and enhancement nodes to perform feature extraction and dimensionality reduction on big data, and maintain the validity of the system for data. In addition, all mapped feature and enhancement nodes are directly connected to the output, and the corresponding output coefficients can be obtained by pseudo-inverse (Pseudo), which effectively eliminates the shortcoming of long training time. More importantly, BLS also enables network structure expansion through fast incremental learning without full network retraining. At the same time, when the network is established, BLS can be combined with low-rank approximation to simplify the system, so as to avoid the structural redundancy of the model.

The BLS structure is shown in Figure 2, and the construction process of the BLS structure is as follows:

Step 1: Use the input data to form the characteristic nodes of the network through linear transformation;

Step 2: The mapped features randomly generate enhanced nodes through nonlinear transformation;

Step 3: All mapped features and augmentation nodes are directly connected to the output;

Step 4: The corresponding output weight can be obtained by fast pseudo-inverse (Pseudo). After the output weight is obtained, the model is built.

In order to verify the advantages of the present invention, a comparative verification test has been done. The verification experiment of the present invention adopts the QPZZ-II rotating machinery vibration analysis and fault diagnosis test bench. This experimental platform can simulate various states and vibrations of rotating machinery, and can carry out various The comparative analysis and diagnosis of the state, variable speed simulation of fault characteristics under different speed conditions, the variable speed range is 75-1450r/min, the test bench is shown in Figure 3, the whole test bench includes data transmission cable 1, acceleration sensor 2, waiting Test bearing 3, flywheel 4, coupling 5, AC motor 6, data acquisition card 7, PC 8 and frequency converter 9, AC motor 6 is provided with frequency converter 9, and the output shaft of AC motor 6 passes through coupling 5 It is connected with the drive shaft of the bearing to be tested 3, the bearing to be tested 3 is set and fixed on the drive shaft and the bearing base, the drive shaft and the output shaft of the AC motor 6 are respectively fitted with a flywheel 4, and the bearing to be tested 3 is provided with an acceleration The sensor 2 and the acceleration sensor 2 are electrically connected to the data acquisition card 7 through the data transmission cable 1, and the data acquisition card 7 is electrically connected to the PC 8 through the data transmission cable 1.

The present invention carries out the operating environment of experiment as follows:

It was completed under the computer equipped with Intel(R) Xeon(R) Bronze 3104 CPU@1.70GHz and 16GB memory under the MATLAB 2018b software platform.

The present invention adopts the USB-4431 data acquisition card produced by U.S. NI Company to carry out signal acquisition in conjunction with LabVIEW, and the setting sampling frequency is 12kHz, the sampling time is 100s, and the given motor speed is 1000r/min, 1250r/min and 1500r/min respectively, Collect 9 types of fault data and 1 type of normal data under 0 load, the data interception length is 1024, and the fault types are shown in Table 1:

Table 1---Description table of fault types

Fault type name Fault classification Inner circle IR 1 Outer ring OR 2 rolling element ball 3 Outer ring + rolling element OUTB 4 rotor unbalance ROTOR 5 Unbalanced rotor + inner ring ROIN 6 Rotor unbalance + outer ring ROOUT 7 Rotor unbalance + rolling elements ROB 8 Unbalanced rotor + outer ring + rolling elements ROOB 9 normal normal 10

The experimental data at different speeds are all divided in the same way, that is, 936 groups are used as model training samples, and 234 groups are used as test samples. Each group of experiments contains all the data in Table 1.

Fast Fourier transform (FFT) is performed on the obtained rotor system experimental data, and it is transformed from time domain to frequency domain for analysis. After FFT transformation, the data length changes from 1024 dimensions to 512 dimensions.

In order to test the effectiveness of the principal component analysis (PCA) method, the following experiments compare the principal component analysis (PCA) method with other dimensionality reduction methods, including linear local tangent space arrangement (LLTSA), nonlinear manifold learning local cut Spatial arrangement (LTSA), local linear embedding (LLE), the dimensionality of the data is kept at 150 dimensions after different methods of dimensionality reduction.

In addition, the classification models used for the data after dimensionality reduction are all BLS and their structures are all 500-500. In addition, the following experimental results are obtained from the average value obtained after running the data set 10 times.

The experimental results of data collected at 1000r/min, 1250r/min and 1500r/min are shown in Tables 2, 3 and 4 respectively:

Table 2---Performance comparison of various dimensionality reduction methods on data sets (1000r/min)

It can be seen from Table 2 that compared with the data without dimension reduction, all the data after dimension reduction can effectively reduce the training time and test time of the model. After being processed by the principal component analysis (PCA) method, the test accuracy of the data on the BLS reaches 99.95%, and it can also maintain extremely high stability, which is better than other dimensionality reduction methods. This shows that under this data set, the data after principal component analysis (PCA) dimensionality reduction can show better performance on BLS.

Table 3---Performance comparison of various dimensionality reduction methods on the data set (1250r/min)

As shown in Table 3, although the data dimensionality reduction by LTSA can effectively improve the training time of the model, its test accuracy is reduced by 15% compared with the original, which shows that the dimensionality reduction effect of this method is not ideal. After the fault data undergoes principal component analysis (PCA) dimension reduction, its test accuracy and training accuracy on BLS both reach 100%, which is better than LLTSA's 99.93% and 99.87%. At the same time, this method can also speed up the training time and testing time of the model. Compared with the unreduced data, the data after principal component analysis (PCA) dimensionality reduction can effectively reduce the model training and testing time, improve the test accuracy of the model, and improve the stability of the model. At the same time, this also shows that the principal component analysis ( PCA) is competitive in any of the above cases.

Table 4---Performance comparison of various dimensionality reduction methods on data sets (1500r/min)

It can be seen from Table 4 that the test accuracy obtained by principal component analysis (PCA) after processing the data is at least 0.35% higher than that obtained by other methods. In addition, the stability of the test accuracy obtained by it is also better than several other methods. Compared with the data without dimensionality reduction, the data processed by principal component analysis (PCA) can effectively reduce the training time and test time of the model, and improve the accuracy and stability of the model test. Therefore, this also proves that the principal component analysis (PCA) ) method is effective.

To sum up, no matter what kind of dimensionality reduction method, the data processed can complete the task of reducing model modeling time and testing time, but it is not difficult to find that only the dimensionality reduction by principal component analysis (PCA) Data can effectively improve the test accuracy and stability of the model, which shows that principal component analysis (PCA) can remove data redundancy very well, thereby retaining the validity of the data. In addition, performing principal component analysis (PCA) processing on the data can also improve the execution efficiency of BLS.

In order to explore the influence of the cumulative variance contribution rate on the classification effect, in this experiment, the classifier used in the data is BLS, and the structure is set to 500-500. The initial cumulative variance contribution rate is set to 0.95, increasing by 0.005 each time until 0.995. The aspects of experimental comparison include test accuracy and model training time. At the same time, the following experimental results are obtained after running 10 times.

The experimental results are shown in Figures 4 and 5. As shown in Figure 4, within a certain range, the test accuracy of the data at different speeds will show a trend of increasing first and then stabilizing with the superposition of the cumulative variance contribution rate, which shows that the principal component analysis (PCA) can reduce the redundancy of the data at different speeds. The cumulative variance contribution rate of the data reaching the stable point of test accuracy at 1250r/min is 0.965, and the other two are 0.98. This shows that under the same conditions, the main The dimension reduction effect of component analysis (PCA) on this data set is better than that of the other two rotational speed data sets.

It is not difficult to find from Figure 5 that the training time of all data will be significantly improved with the increase of the cumulative variance contribution rate. This is because the higher the cumulative variance contribution rate, the less reduction of the data dimension by PCA, and the longer the training time of BLS on the data.

It can be seen that the test accuracy of the three kinds of data will show a trend of first increasing and then flattening with the increase of the cumulative variance contribution rate, but the time required for their modeling shows a continuous increase, which shows that the three kinds of data can be passed The principal component analysis (PCA) method effectively ensures the data characteristics and reduces the time required for modeling. The cumulative variance contribution rate of the data at 1250r/min to achieve the best test accuracy is 0.15 lower than that of the data at the other two speeds. It shows that in the face of different data, the cumulative variance contribution rate can be flexibly selected according to the specific situation for reasonable feature extraction.

In order to compare the impact of different models on the experiment, the classification models used in this experiment include extreme learning machine (ELM), multilayer extreme learning machine (HELM), regularized extreme learning machine (RELM), and breadth learning system (BLS).

Among them, the number of hidden layer nodes of ELM is set to 1000, the structure of HELM is set to 100-100-1000, the number of nodes of RELM is set to 1000, and the number of nodes of BLS is set to 500-500.

The activation functions on the hidden layer of ELM, HELM, and RELM all select the Sigmoid function, and the activation function on the enhancement layer of SS-BLS also selects the Sigmoid function. At the same time, the weights and offsets of the feature node layer and the enhanced node layer in BLS are extracted from the standard uniform distribution on the interval [-1, 1]. In addition, the dimensions of the data are maintained after principal component analysis (PCA) In 150 dimensions, all the experimental results below are the average values obtained after running 10 times on the respective models.

The experimental results of data collected at 1000r/min, 1250r/min, and 1500r/min are shown in Tables 5, 6, and 7 respectively:

Table 5---Principal component analysis (PCA) performance comparison of data sets on each model after dimensionality reduction (1000r/min)

It is not difficult to find from Table 5 that ELM has shown strong stability during the test process, but its training time and test time are much higher than other classification models, and BLS is better than other classification models in terms of training accuracy and test accuracy. Classifier. At the same time, the modeling time of BLS is only 1.19s, which is also better than the training time of ELM, RELM, and HELM, which shows that the model can better complete the task of fault diagnosis.

Table 6---Principal component analysis (PCA) performance comparison of data sets on each model after dimensionality reduction (1250r/min)

It can be seen from Table 6 that after dimensionality reduction by principal component analysis (PCA), all classification models can achieve optimal training accuracy and test accuracy, and the test accuracy remains extremely high stability, which also proves that the principal component Analysis (PCA) dimensionality reduction method has strong stability. From the perspective of training time, the training time of BLS only needs 1.33s, which is better than the training time of other models. This shows that BLS is competitive with other classification models.

Table 7---Principal component analysis (PCA) performance comparison of data sets on each model after dimensionality reduction (1500r/min)

As shown in Table 7, under the fault data set collected at 1500r/min, both HELM and RELM can complete the fault diagnosis task under the data set at a relatively fast modeling speed, and these two models can also maintain excellent stability. BLS is applied to the fault data set for classification tasks, and the training accuracy and test accuracy obtained are better than other models. From the perspective of modeling time, the time required by BLS is the shortest, only 1/10 of the modeling time of ELM, which shows that the nodes of BLS can efficiently complete the feature extraction and dimension reduction of the data set.

It can be seen that at the speed of 1500r/min, the modeling time and testing time of the model are better than the training and testing time of the model at other speeds, which shows that the faster the motor speed, the faster the model required for the collected data set. The shorter the time. For the fault data collected at different speeds, compared with other models, BLS can complete the classification tasks under different fault data sets with the fastest modeling speed and the best test accuracy. In addition, BLS can also guarantee Extremely high stability, which shows that BLS has strong adaptability.

A rotor system fault diagnosis method based on principal component analysis and width learning of the present invention, the principal component analysis (PCA) dimension reduction method adopted can effectively eliminate the correlation of the eigenvectors in the eigenmatrix, and realize the dimensionality of the eigenmatrix Reduction, so as to achieve the purpose of reducing the redundancy of the feature matrix. In practical applications, Principal Component Analysis (PCA) can select the cumulative variance contribution rate for specific problems to reduce the dimensionality of the feature matrix reasonably, which reflects the flexibility of the Principal Component Analysis (PCA) method. At the same time, by introducing BLS into the fault In the field of diagnosis, its applicability has been broadened. Compared with other classification models, BLS can efficiently complete fault diagnosis tasks, which reflects the superiority of this model.

A rotor system fault diagnosis method based on principal component analysis and breadth learning proposed by the present invention introduces Principal Component Analysis (PCA) and Broad Learning System (BLS for short) into rotor system fault diagnosis and identification. Principal component analysis (PCA) is used to reduce the dimensionality of the FFT-transformed fault data to form feature vectors representing different faults, and then input the dimensionally reduced data into BLS for classification, which can effectively reduce the complexity of fault classification, and It can greatly shorten the data modeling time, improve the efficiency of rotor system fault identification, and thus efficiently complete the task of rotor system fault diagnosis. It has good practicability and is worthy of promotion.

The above disclosures are only preferred specific embodiments of the present invention, however, the embodiments of the present invention are not limited thereto, and any changes conceivable by those skilled in the art shall fall within the protection scope of the present invention.

Claims (5)

1. A rotor system fault diagnosis method based on principal component analysis and width learning is characterized by comprising the following steps:

step 1: collecting time domain fault data T (n);

step 2: fourier transform is carried out according to the formula (1), the collected time domain fault data T (n) is transformed into frequency domain fault data X,

wherein,

in the above equations (1) and (2), N is 0,1,., N-1, k is 0,1,. N, N-1, N is the length of the time domain fault data, j is a complex symbol, X is frequency domain fault data, and includes training samples and test samples, and X is { X ═₁，x₂,...,x_i,...x_m1, 1., m, t (n) is time domain fault data;

and step 3: acquiring a covariance matrix C of frequency domain fault data X;

and 4, step 4: judging the correlation among the fault data X in different frequency domains;

and 5: performing eigenvalue decomposition on the covariance matrix C of the frequency domain fault data X according to the formula (3) to obtain an eigenvector matrix Q and an eigenvalue matrix Sigma of the covariance matrix C of the frequency domain fault data X, wherein the eigenvalue matrix Sigma is represented by the formula (4), the eigenvector matrix Q is represented by the formula (5),

C＝Q·∑·Q^T (3)

wherein,

∑＝diag(λ₁,λ₂,...,λ_i,...,λ_n) (4)

Q＝[q₁,q₂,...,q_i,...,q_n] (5)

in the above equations (3), (4) and (5), C is a covariance matrix of frequency domain fault data, Q is an eigenvector matrix, Σ is an eigenvalue matrix, λ₁≥λ₂≥...≥λ_i≥...,≥λ_n，i＝1,...,n，Q^TThe method is characterized in that the method is a transposed matrix of an eigenvector matrix, n is the length of frequency domain fault data, the number of all eigenvalues is equal to the number of all eigenvectors is equal to the length of the frequency domain fault data, and the eigenvector q is equal to the length of the frequency domain fault data_iAnd a characteristic value lambda_iIn a one-to-one correspondence;

step 6: for frequency domainCarrying out principal component analysis and dimensionality reduction on the fault data set X to obtain a dimensionality-reduced frequency domain fault data set X_k；

And 7: the frequency domain fault data set X after dimension reduction_kFrequency domain fault data set X divided into training_k1And tested frequency domain fault data set X_k2；

And 8: utilizing a trained frequency domain fault data set X_k1Constructing a width learning system model;

step 9, substituting the target weight β solved in the process of constructing the width learning system model into the width learning system model to obtain a width learning system classification model;

step 10: frequency domain fault data set X to be tested_k2And substituting the fault diagnosis result into the width learning system classification model to finish the test on the validity of the width learning system classification model.

2. The method for diagnosing the rotor system fault based on the principal component analysis and the width learning as claimed in claim 1, wherein the step 3 of obtaining the covariance matrix C of the frequency domain fault data comprises the following steps:

s21, since the frequency domain fault data X has symmetry, the length of the frequency domain fault data X can be cut according to equation (6),

n＝N/2 (6)

in the above formula (6), N is a length obtained by intercepting the length of the frequency domain fault data X, and N is a length of the time domain fault data;

s22, calculating the sample mean value α of the frequency domain fault data X according to the formula (7),

wherein, the frequency domain fault data set X ═ { X ═ X₁，x₂,...,x_i,...x_mWhere m is the total number of samples, α is the mean of the samples of the frequency-domain fault data X, X_iFor the ith frequency domain fault data；

S23, obtaining the covariance matrix C of the frequency domain fault data according to the formula (8),

where, i is 1.. the m is the total number of samples, C is the covariance matrix of the frequency domain fault data X, and X_iFor the ith frequency domain fault data, α is the sample mean of the frequency domain fault data X.

3. The method for diagnosing the rotor system fault based on the principal component analysis and the width learning as claimed in claim 1, wherein the step 4 of determining the correlation between the fault data of different frequency domains is performed by taking the following conditions:

if the covariance between two corresponding features in the covariance matrix is positive, the two features present a positive correlation, and if the covariance between two corresponding features in the covariance matrix is negative, the covariance between two corresponding features in the covariance matrix presents a negative correlation is 0, which indicates that the two features are not correlated.

4. The method for diagnosing the rotor system fault based on the principal component analysis and the width learning of claim 1, wherein the method for performing the principal component analysis dimension reduction on the frequency domain fault data set X in the step 6 comprises the following steps:

s41, selecting the first k eigenvalues lambda from the eigenvalue matrix sigma_iCalculating a principal component variance cumulative contribution rate theta according to the equation (9),

wherein, theta is the accumulated contribution rate of the principal component variance, lambda_iAnd λ_jRespectively is the ith and jth eigenvalue, k is the number of the selected eigenvalues, n is allThe number of characteristic values, i 1., k, j 1., n, k<n；

S42, obtaining corresponding first k characteristic values lambda according to the formula (10)_iCorresponding feature vector q of_i，

Q_k＝[q₁,q₂,...,q_i,...,q_k] (10)

Wherein, i is 1<n, k is the number of the selected eigenvalues, n is the number of all eigenvalues, Q_kFor the first k eigenvalues λ_iCorresponding feature vector q of_iForming a feature vector matrix;

s43, feature vector matrix Q according to equation (11)_kThe principal component analysis and the dimensionality reduction are carried out,

X_k＝Q_k·X (11)

wherein Q is_kCorresponding to the first k eigenvalues lambda_iCorresponding feature vector q of_iForming a feature vector matrix, wherein X is a frequency domain fault data set and X_kThe frequency domain fault data set is subjected to principal component analysis and dimension reduction.

5. The method for diagnosing the rotor system fault based on the principal component analysis and the width learning as claimed in claim 1, wherein the method for constructing the width learning system model in the step 8 comprises the following steps:

s51 frequency domain fault data set X trained according to equation (12)_k1Feature mapping to form feature node Z_i，

Wherein, W_eiAndis a randomly selected characteristic node coefficient, i is 1_iIs the ith characteristic node, X_k1Is a trained frequency domain fault data set;

s52, dividing all the characteristic nodes Z according to the formula (13)_iThe combination of (A) is denoted as Z^t，

Z^t≡[Z₁,...,Z_i,...,Z_t] (13)

Wherein Z is_iIs the ith characteristic node, Z^tIs all characteristic nodes Z_iT is the number of all feature nodes, i is 1.

S53, all characteristic nodes Z according to the formula (14)_iCombination Z of^tGenerating enhanced node H by nonlinear function transformation_j，

Wherein H_jIs the jth enhanced node, Z^tIs all characteristic nodes Z_iIn the combination of (a) and (b),andthe method comprises the following steps that (1) randomly selected enhanced node coefficients are selected, wherein j is 1, and c is the total number of enhanced nodes;

s54, all the enhanced nodes H are connected according to the formula (15)_jThe combination of (A) is denoted as H^c，

H^c≡[H₁,...,H_j,...,H_c] (15)

Wherein c is the total number of the enhanced nodes, j is 1, c, j is more than or equal to 0 and less than or equal to m, and H^cFor all enhanced nodes H_jCombination of (1), H_jIs the jth enhanced node;

s55, combining all nodes into an expansion matrix G according to the formula (16),

G≡[Z^t|H^c] (16)

where G is the spreading matrix, Z^tIs all characteristic nodes Z_iCombination of (1), H^cFor all enhanced nodes H_jA combination of (1);

s56, constructing an objective function F of the target weight β of the width learning system according to the formula (17)_min(β)，

Wherein β is the target weight, F_min(β) an objective function for solving the objective weight β, V is a constant, and Y is { Y ═ Y }₁,...,y_l,...,y_k1}，y_lThe label corresponding to the ith training sample is Y, the label matrix formed by all the training sample labels is l ═ 1., k1, and k1 are the total number of the training samples, and G is an expansion matrix;

s57 gradient descent method for F in formula (17)_min(β) solving the function, equation (18) is obtained for solving the objective weights β,

wherein Y is { Y ═ Y₁,...,y_l,...,y_k1}，y_lA label corresponding to the ith training sample, Y is a label matrix formed by all training sample labels, i is 1., k1, k1 is the total number of training samples, β is a target weight, G is an expansion matrix, G is a linear expansion matrix, and^Tfor transposing of spreading matrices, I_nhThe method comprises the following steps of (1) obtaining a unit matrix with dimension nh, wherein nh is the total number of characteristic nodes and enhanced nodes of a width learning system model, namely nh is c + t, and V is a constant;

and S58, completing the construction of the width learning system model.