CN110243590A - A kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width - Google Patents
A kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width Download PDFInfo
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Abstract
The invention discloses a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width, Dimensionality Reduction is carried out to the eigenmatrix formed after feature extraction using principal component analysis, reduce the linear dependence between data, eliminate redundant attributes, obtain the low-dimensional matrix that can retain its substantive characteristics, then the Input matrix width learning system is subjected to fault identification, completes rotor-support-foundation system failure modes task.Principal component analysis and width learning system are introduced into Fault Diagnosis for Rotor System identification by the present invention, this method can effectively reduce the complexity of failure modes, and it can substantially shorten the data modeling time, promote the efficiency of rotor-support-foundation system fault identification, to be efficiently completed Fault Diagnosis for Rotor System task, practicability is good, is worthy to be popularized.
Description
Technical Field
The invention belongs to the technical field of fault detection of mechanical parts, and particularly relates to a rotor system fault diagnosis method based on principal component analysis and width learning.
Background
The rotor system plays an irreplaceable role in various related fields as a core component of a rotary machine. The rotor system is applied to a plurality of rotating machines, and faults of the rotating machines in the working process can cause great economic loss, wherein a great part of faults are caused by the faults of the rotor system, and the fault damage comprises noise generation, rotor instability, serious damage even mechanical structure damage, and great safety accidents. Therefore, the method has very important scientific significance and application value for effectively analyzing and accurately diagnosing the initial fault of the rotor system.
At present, the methods widely applied to rotor fault diagnosis are window Fourier transform, empirical mode decomposition, wavelet analysis and the like. However, after the method extracts the features of the fault signal, the formed feature matrix has the problems of complex structure, large feature correlation, high redundancy degree and the like, and the problems can greatly increase the complexity of fault classification and reduce the accuracy of fault identification.
Disclosure of Invention
In view of the above, the present invention provides a rotor System fault diagnosis method based on principal component analysis and width Learning, the method first performs dimensionality reduction on a feature matrix formed after feature extraction by using Principal Component Analysis (PCA), reduces linear correlation between data, eliminates redundant attributes, obtains a low-dimensional matrix capable of retaining its essential features, and then inputs the matrix into a width Learning System (BLS) for fault identification, so that the width Learning System (BLS) can efficiently complete a rotor System fault classification task, so as to solve the defects in the prior art.
The technical scheme of the invention is as follows:
a rotor system fault diagnosis method based on principal component analysis and width learning comprises 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,...,xi,...xm1, 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·∑·QT (3)
wherein,
∑＝diag(λ1,λ2,...,λi,...,λn) (4)
Q＝[q1,q2,...,qi,...,qn] (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≥...≥λi≥...,≥λn，i＝1,...,n，QTThe 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 dataiAnd a characteristic value lambdaiIn a one-to-one correspondence;
step 6: carrying out principal component analysis and dimensionality reduction on the frequency domain fault data set X to obtain the frequency domain fault data set X subjected to dimensionality reductionk；
And 7: the frequency domain fault data set X after dimension reductionkFrequency domain fault data set X divided into trainingk1And tested frequency domain fault data set Xk2；
And 8: utilizing a trained frequency domain fault data set Xk1Constructing 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 testedk2Substituting the obtained fault diagnosis result into the classification model of the width learning system to complete the width learningAnd (5) testing the validity of the system classification model.
Preferably, the acquiring the covariance matrix C of the frequency domain fault data in 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 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,...,xi,...xmWhere m is the total number of samples, α is the mean of the samples of the frequency-domain fault data X, XiThe 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 XiFor the ith frequency domain fault data, α is the sample mean of the frequency domain fault data X.
Preferably, the determination conditions for determining the correlation between the fault data in different frequency domains in step 4 are as follows:
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.
Preferably, the method for performing principal component analysis dimension reduction on the frequency domain fault data set X in step 6 includes the following steps:
s41, selecting the first k eigenvalues lambda from the eigenvalue matrix sigmaiCalculating 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, lambdaiAnd λjI and j are the ith and jth eigenvalues, k is the number of the selected eigenvalues, n is the number of all eigenvalues, i is 1<n；
S42, obtaining corresponding first k characteristic values lambda according to the formula (10)iCorresponding feature vector q ofi，
Qk＝[q1,q2,...,qi,...,qk] (10)
Wherein, i is 1<n, k is the number of the selected eigenvalues, n is the number of all eigenvalues, QkFor the first k eigenvalues λiCorresponding feature vector q ofiForming a feature vector matrix;
s43, feature vector matrix Q according to equation (11)kThe principal component analysis and the dimensionality reduction are carried out,
Xk＝Qk·X (11)
wherein Q iskCorresponding to the first k eigenvalues lambdaiCorresponding feature vector q ofiForming a feature vector matrix, wherein X is a frequency domain fault data set and XkThe frequency domain fault data set is subjected to principal component analysis and dimension reduction.
Preferably, the method for constructing the width learning system model in step 8 includes the following steps:
s51 frequency domain fault data set X trained according to equation (12)k1Feature mapping to form feature node Zi，
Wherein, WeiAndis a randomly selected characteristic node coefficient, i is 1iIs the ith characteristic node, Xk1Is 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 Zt，
Zt≡[Z1,...,Zi,...,Zt] (13)
Wherein Z isiIs the ith characteristic node, ZtIs all characteristic nodes ZiT is the number of all feature nodes, i is 1.
S53, all characteristic nodes Z according to the formula (14)iCombination Z oftGenerating enhanced node H by nonlinear function transformationj，
Wherein HjIs the jth enhanced node, ZtIs all characteristic nodes ZiIn 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 Hc，
Hc≡[H1,...,Hj,...,Hc] (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 HcFor all enhanced nodes HjCombination of (1), HjIs the jth enhanced node;
s55, combining all nodes into an expansion matrix G according to the formula (16),
G≡[Zt|Hc] (16)
where G is the spreading matrix, ZtIs all characteristic nodes ZiCombination of (1), HcFor all enhanced nodes HjA 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, Fmin(β) an objective function for solving the objective weight β, V is a constant, and Y is { Y ═ Y }1,...,yl,...,yk1}，ylThe 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,...,yl,...,yk1}，ylA 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, andTfor transposing of spreading matrices, InhThe 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.
Compared with the prior art, the invention introduces Principal Component Analysis (PCA) and a width learning system (BLS for short) into the rotor system fault diagnosis and identification, and provides a rotor system fault diagnosis method based on principal component analysis and width learning, the method adopts Principal Component Analysis (PCA) to perform dimension reduction processing on fault data subjected to FFT (fast Fourier transform) to form feature vectors for representing different faults, and then inputs the data subjected to dimension reduction into the BLS for classification, and the rotor system fault diagnosis method has the advantages that:
1. the invention can effectively reduce the complexity of fault classification;
2. the method can greatly shorten the data modeling time and improve the efficiency of rotor system fault identification, thereby efficiently completing the fault diagnosis task of the rotor system;
3. the invention has good practicability and is worth popularizing.
Drawings
FIG. 1 is a flow chart of a method for rotor system fault diagnosis based on principal component analysis and width learning in accordance with the present invention;
FIG. 2 is a block diagram of a width learning system BLS according to the present invention;
FIG. 3 is a schematic diagram of the experimental bench structure of the present invention;
FIG. 4 is a graph of the effect of cumulative variance contribution rate on test accuracy for the present invention;
FIG. 5 is a graph of the cumulative variance contribution rate versus training time for the present invention.
Description of reference numerals:
1. a data transmission cable; 2. an acceleration sensor; 3. a bearing to be tested; 4. a flywheel; 5. a coupling; 6. an AC motor; 7. a data acquisition card; 8. a PC machine; 9. and a frequency converter.
Detailed Description
The invention provides a rotor system fault diagnosis method based on principal component analysis and width learning, and the invention is described below with reference to a flow diagram of fig. 1.
As shown in fig. 1, the technical solution of the present invention is:
a rotor system fault diagnosis method based on principal component analysis and width learning comprises 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,...,xi,...xm1, 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·∑·QT (3)
wherein,
∑＝diag(λ1,λ2,...,λi,...,λn) (4)
Q＝[q1,q2,...,qi,...,qn] (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≥...≥λi≥...,≥λn，i＝1,...,n，QTThe 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 dataiAnd a characteristic value lambdaiIn a one-to-one correspondence;
step 6: carrying out principal component analysis and dimensionality reduction on the frequency domain fault data set X to obtain the frequency domain fault data set X subjected to dimensionality reductionk；
And 7: the frequency domain fault data set X after dimension reductionkFrequency domain fault data set X divided into trainingk1And tested frequency domain fault data set Xk2；
And 8: utilizing a trained frequency domain fault data set Xk1Constructing 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 testedk2And 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.
Further, the acquiring the covariance matrix C of the frequency domain fault data in 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 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,...,xi,...xmWhere m is the total number of samples, α is the mean of the samples of the frequency-domain fault data X, XiThe 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 XiFor the ith frequency domain fault data, α is the sample mean of the frequency domain fault data X.
Further, the judgment conditions for judging the correlation between the fault data in different frequency domains in the step 4 are as follows:
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.
Further, the method for performing principal component analysis and dimension reduction on the frequency domain fault data set X in step 6 includes the following steps:
s41, selecting the first k eigenvalues lambda from the eigenvalue matrix sigmaiCalculating 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, lambdaiAnd λjI and j are the ith and jth eigenvalues, k is the number of the selected eigenvalues, n is the number of all eigenvalues, i is 1<n；
S42, obtaining corresponding first k characteristic values lambda according to the formula (10)iCorresponding feature vector q ofi，
Qk＝[q1,q2,...,qi,...,qk] (10)
Wherein, i is 1<n, k is the number of the selected eigenvalues, n is the number of all eigenvalues, QkFor the first k eigenvalues λiCorresponding feature vector q ofiForming a feature vector matrix;
s43, feature vector matrix Q according to equation (11)kThe principal component analysis and the dimensionality reduction are carried out,
Xk＝Qk·X (11)
wherein Q iskCorresponding to the first k eigenvalues lambdaiCorresponding feature vector q ofiForming a feature vector matrix, wherein X is a frequency domain fault data set and XkThe frequency domain fault data set is subjected to principal component analysis and dimension reduction.
Further, the method for constructing the width learning system model in step 8 includes the following steps:
s51, according toEquation (12) for the trained frequency domain fault data set Xk1Feature mapping to form feature node Zi，
Wherein, WeiAndis a randomly selected characteristic node coefficient, i is 1iIs the ith characteristic node, Xk1Is 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 Zt，
Zt≡[Z1,...,Zi,...,Zt] (13)
Wherein Z isiIs the ith characteristic node, ZtIs all characteristic nodes ZiT is the number of all feature nodes, i is 1.
S53, all characteristic nodes Z according to the formula (14)iCombination Z oftGenerating enhanced node H by nonlinear function transformationj，
Wherein HjIs the jth enhanced node, ZtIs all characteristic nodes ZiIn 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 Hc，
Hc≡[H1,...,Hj,...,Hc] (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 HcFor all enhanced nodes HjCombination of (1), HjIs the jth enhanced node;
s55, combining all nodes into an expansion matrix G according to the formula (16),
G≡[Zt|Hc] (16)
where G is the spreading matrix, ZtIs all characteristic nodes ZiCombination of (1), HcFor all enhanced nodes HjA 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, Fmin(β) an objective function for solving the objective weight β, V is a constant, and Y is { Y ═ Y }1,...,yl,...,yk1}，ylThe 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) the function is solved, and equation (18) is used to solve the objectiveThe weight is scaled β so that the weight,
wherein Y is { Y ═ Y1,...,yl,...,yk1}，ylA 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, andTfor transposing of spreading matrices, InhThe 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.
The invention aims to eliminate the redundancy of a characteristic matrix and solve the classification problem of more fault data, adopts a principal component analysis method to carry out attribute reduction, can achieve the aim of simplifying the characteristic matrix on the premise of losing information as little as possible, and simultaneously introduces a width learning system to the field of fault diagnosis for realizing the rapid identification between a characteristic vector and a fault type of the characteristic vector after the principal component analysis dimensionality reduction.
In order to eliminate redundant information of a feature matrix, reduce linear correlation among data and improve the efficiency of rotor system fault identification, a simple and efficient dimension reduction method needs to be selected, and Principal Component Analysis (PCA) is a classical dimension reduction method. The method is simple and easy to understand, and the using process is completely free of parameter limitation, so that the method is widely applied to various fields such as images, voice, communication and the like. In addition, the method can reveal a simple structure hidden behind complex data, reduce the linear correlation among the data and obtain the best description of the fault state. More importantly, the PCA can reduce the redundancy of fault data on the premise of losing information as little as possible, thereby achieving the purpose of reducing the dimension of the data. Therefore, PCA is used herein to perform dimensional reduction on the fault signature matrix subjected to the fast Fourier transform.
In order to realize rapid identification between the fault characteristic vector and the type thereof after PCA dimension reduction, a width learning system (BLS) is adopted for fault diagnosis. In BLS, the original input is transferred and placed as a mapping feature in the feature node and is widely spread in the enhancement node, which may preserve the validity of the system on the data. Furthermore, all mapped features and enhancement nodes are directly connected to the output, and the corresponding output coefficients can be found by the Pseudo-inverse (Pseudo).
The invention provides a rotor system fault diagnosis method based on PCA and BLS, which is characterized in that the PCA is adopted to perform dimension reduction processing on fault data subjected to FFT conversion to form characteristic vectors representing different faults, and then the data subjected to dimension reduction is input into the BLS to be classified.
There are two basic methods employed in the present invention:
1. principal component analysis
Principal Component Analysis (PCA), also known as Karhunen-Loeve Transform, is a technique for data dimensionality reduction that essentially reduces the dimensionality of training samples on the basis of as little information as possible loss, the main idea being to map n-dimensional features onto k-dimensions, which are completely new orthogonal features, also known as principal components, and k-dimensional features (k ≦ n) reconstructed on the basis of the original n-dimensional features.
The PCA works by sequentially finding a set of mutually orthogonal coordinate axes from the original space, and selecting new coordinate axes which are closely related to the data itself, wherein the 1 st new coordinate axis is selected to be the direction with the largest variance in the original data, the 2 nd new coordinate axis is selected to be the plane orthogonal to the 1 st coordinate axis so that the variance is the largest, and the 3 rd axis is the plane orthogonal to the 1 st and 2 nd axes and has the largest variance. By analogy, n such coordinate axes can be obtained. From these newly obtained axes, most of the variances are contained in the preceding k axes, and the variance contained in the following axes is almost 0. Thus, for the axes with variance of almost 0, the user can consider ignoring, thus keeping the first k axes with the most variance. In fact, this is equivalent to only retaining the dimension features that contain most of the variance, ignoring the feature dimensions that contain variance almost 0, and thus achieving a reduction in the dimension of the data features.
2. Width learning system
The width Learning System (BLS) proposed by professor c.l. philip Chen (handsfree) is constructed in a flat manner, and the BLS is designed based on the idea of inputting mapping features as RVFLLNN. The BLS can establish feature nodes and enhanced nodes to perform feature extraction and dimension reduction on big data and maintain the effectiveness of a system on the data. In addition, all the mapped features and the enhancement nodes are directly connected to the output end, and the corresponding output coefficients can be solved through Pseudo-inverse (Pseudo), so that the defect of long training time is effectively eliminated. More importantly, BLS also enables the extension of the network structure through fast incremental learning without the need for full network retraining. Meanwhile, after the network is built, the 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 fig. 2, and the building process of the BLS structure is as follows:
step 1: forming characteristic nodes of the network by utilizing input data through linear transformation;
step 2: randomly generating enhanced nodes by the mapped characteristics through nonlinear transformation;
and step 3: all mapping features and enhancement nodes are directly connected to the output;
and 4, solving the corresponding output weight through a fast Pseudo-inverse (Pseudo), and completing model building after the output weight is solved.
In order to verify the advantages of the invention, a comparison verification test is carried out, the verification test of the invention adopts a QPZZ-II type rotating machinery vibration analysis and fault diagnosis test bed, the test bed can simulate various states and vibrations of the rotating machinery, can carry out comparison analysis and diagnosis of various states, can simulate fault characteristics under different speed conditions at variable speed, the variable speed range is 75-1450 r/min, the test bed is shown as figure 3, the whole test bed comprises a data transmission cable 1, an acceleration sensor 2, a bearing 3 to be tested, a flywheel 4, a coupler 5, an alternating current motor 6, a data acquisition card 7, a PC machine 8 and a frequency converter 9, the alternating current motor 6 is provided with the frequency converter 9, an output shaft of the alternating current motor 6 is connected with a driving rotating shaft of the bearing 3 to be tested through the coupler 5, the bearing 3 to be tested is sleeved and fixed on the driving rotating shaft and a bearing base, the flywheel 4 is respectively sleeved and fixed on the driving rotating shaft and the output shaft of the alternating current motor 6, the acceleration sensor 2 is arranged on the bearing 3 to be tested, the acceleration sensor 2 is electrically connected with the data acquisition card 7 through the data transmission cable 1, and the data acquisition card 7 is electrically connected with the PC 8 through the data transmission cable 1.
The operating environment in which the experiments of the present invention were carried out is shown below:
the method is completed under a computer with an Intel (R) Xeon (R) Bronze 3104 CPU @1.70GHz and 16GB memory under an MATLAB 2018b software platform.
The invention adopts a USB-4431 data acquisition card produced by American NI company to combine with LabVIEW to carry out signal acquisition, sets the sampling frequency to be 12kHz, sets the sampling time to be 100s, respectively sets the rotating speed of a motor to be 1000r/min, 1250r/min and 1500r/min, acquires 9 fault data and 1 normal data under the load of 0, has the data interception length of 1024, and has the fault types shown in Table 1:
TABLE 1- -Fault type Specification Table
| Type of failure | Name of | Fault classification |
| Inner ring | IR | 1 |
| Outer ring | OR | 2 |
| Rolling body | Ball | 3 |
| Outer ring and rolling body | OUTB | 4 |
| Rotor unbalance | ROTOR | 5 |
| Unbalanced rotor + inner ring | ROIN | 6 |
| Unbalanced rotor + outer ring | ROOUT | 7 |
| Rotor unbalance + rolling body | ROB | 8 |
| Rotor unbalance + outer ring + rolling body | ROOB | 9 |
| Is normal | normal | 10 |
The experimental data at different rotation speeds are divided equally, i.e. 936 sets are used as model training samples and 234 sets are used as test samples, wherein each set of experiment includes all the data in table 1.
And performing Fast Fourier Transform (FFT) on the obtained rotor system experimental data, transforming the rotor system experimental data from a time domain to a frequency domain for analysis, and changing the data length from 1024 dimensions to 512 dimensions after the FFT.
In order to test the effectiveness of the Principal Component Analysis (PCA) method, experiments were performed to compare the Principal Component Analysis (PCA) method with other dimensionality reduction methods, including Linear Local Tangent Space Arrangement (LLTSA), nonlinear manifold learning Local Tangent Space Arrangement (LTSA), and Local Linear Embedding (LLE), and the dimensionality of the data was maintained at 150 dimensions after dimensionality reduction by different methods.
In addition, the classification models adopted by the data after dimension reduction are all BLS, the structures of the classification models are all 500-fold, and in addition, the following experiment results are all obtained by obtaining the average values after the data set runs for 10 times.
The data collected at 1000r/min, 1250r/min, 1500r/min are shown in tables 2, 3 and 4, respectively:
TABLE 2- -Performance comparison of the respective dimensionality reduction methods on the data set (1000r/min)
As can be seen from Table 2, all the dimension-reduced data can effectively reduce the training time and testing time of the model compared with the non-dimension-reduced data. After the data is processed by a Principal Component Analysis (PCA) method, the testing precision of the data on the BLS reaches 99.95%, and the data can also keep extremely high stability, which is superior to other dimension reduction methods. This shows that under the data set, the data after Principal Component Analysis (PCA) dimension reduction can show better performance on the BLS.
TABLE 3- -comparison of Performance of the respective dimensionality reduction methods on the data set (1250r/min)
As shown in Table 3, although the data can effectively improve the training time of the model after LTSA dimension reduction, the test precision is reduced by 15% compared with the original test precision, which indicates that the dimension reduction effect of the method is not ideal. After the fault data is subjected to Principal Component Analysis (PCA) dimensionality reduction, the testing precision and the training precision of the fault data on the BLS reach 100%, which are superior to 99.93% and 99.87% of LLTSA. Meanwhile, the method can also accelerate the training time and the testing time of the model. Compared with non-dimensionality-reduced data, the data subjected to Principal Component Analysis (PCA) dimensionality reduction can effectively reduce model training and testing time, improve the testing accuracy of the model and improve the stability of the model, and meanwhile, the Principal Component Analysis (PCA) is competitive in any situation.
TABLE 4- -Performance comparison of the various dimensionality reduction methods on the data set (1500r/min)
As can be seen from Table 4, the test accuracy obtained after the data were processed by Principal Component Analysis (PCA) was at least 0.35% higher than that obtained by the other methods. In addition, the stability of the obtained testing precision is better than that of other methods. Compared with the data without dimension reduction, the data processed by the Principal Component Analysis (PCA) can effectively reduce the training time and the testing time of the model, and improve the testing precision and the stability of the model, so that the validity of the Principal Component Analysis (PCA) method is proved.
In conclusion, no matter which dimension reduction method is used for processing the data, the task of reducing the model modeling time and the test time can be completed, but it is not difficult to find that the test precision and the stability of the model can be effectively improved only through the data subjected to dimension reduction through Principal Component Analysis (PCA), which shows that the Principal Component Analysis (PCA) can well remove the data redundancy, and therefore the effectiveness of the data is reserved. In addition, performing Principal Component Analysis (PCA) processing on the data can also improve the execution efficiency of BLS.
In order to investigate the influence of the cumulative variance contribution ratio on the classification effect, in the experiment, the classifier used by the data is BLS, and the structures are all set to 500-. The initial cumulative variance contribution rate was set to 0.95, with each increment of 0.005 up to 0.995. The experimental comparison aspects comprise the testing precision and the model training time, and meanwhile, the following experimental results are obtained after 10 times of operation.
The experimental results are shown in fig. 4 and 5, as shown in fig. 4, within a certain range, the test accuracy of the data at different rotation speeds shows a trend that the data increases first and then becomes stable along with the superposition of the cumulative variance contribution rates, which indicates that the redundancy of the data at different rotation speeds can be reduced by Principal Component Analysis (PCA), the cumulative variance contribution rate of the data reaching the stable point of the test accuracy at 1250r/min is 0.965, and the other two are 0.98.
It can be easily seen from fig. 5 that the training time for all data is significantly increased as the cumulative variance contribution rate is increased. This is because the higher the cumulative variance contribution rate, the less Principal Component Analysis (PCA) reduces the data dimension and the longer the BLS can train on the data.
It can be seen that the test accuracy of the three data shows a trend of increasing first and then flattening along with the increase of the cumulative variance contribution rate, but the time required for modeling shows a phenomenon of continuously increasing, which indicates that the three data can effectively ensure the data characteristics through a Principal Component Analysis (PCA) method and simultaneously reduce the time required for modeling, and the cumulative variance contribution rate of the data reaching the optimal test accuracy at the rotation speed of 1250r/min is 0.15 lower than that of the data at the other two rotation speeds, which indicates that the cumulative variance contribution rate can be flexibly selected according to specific conditions to reasonably extract the characteristics of the data when different data are faced.
In order to compare the influence of different models on the experiment, the classification models adopted by the experiment comprise an Extreme Learning Machine (ELM), a multi-layer extreme learning machine (HELM), a Regularized Extreme Learning Machine (RELM) and a width learning system (BLS).
Wherein, the hidden node number of ELM is set to 1000, the structure of HELM is set to 100-.
The Sigmoid function is selected for the activation functions on the hidden layer of ELM, HELM, and RELM, and the Sigmoid function is selected for the activation functions on the enhancement layer of SS-BLS. Meanwhile, the weights and biases of the characteristic node layer and the enhanced node layer in the BLS are extracted from the standard uniform distribution on the interval [ -1, 1], in addition, the dimensionality of the data is kept at 150 dimensions after the dimension reduction through Principal Component Analysis (PCA), and all the following experimental results are average values obtained after 10 times of operation on respective models.
The experimental results of the data collected at 1000r/min, 1250r/min and 1500r/min are shown in tables 5, 6 and 7 respectively:
TABLE 5- -comparison of Performance of Principal Component Analysis (PCA) reduced data sets on models (1000r/min)
As can be easily found from table 5, the ELM exhibits very strong stability during the testing process, but the training time and the testing time are much higher than those of other classification models, and the BLS is better than other classifiers in both training accuracy and testing accuracy. Meanwhile, the modeling time of the BLS is only 1.19s, which is also superior to the training time of ELM, RELM and HELM, and thus the model can better complete the task of fault diagnosis.
TABLE 6- -comparison of Performance of Principal Component Analysis (PCA) reduced data sets on models (1250r/min)
As can be seen from table 6, after the Principal Component Analysis (PCA) is performed to perform dimension reduction, all classification models can obtain optimal training precision and testing precision, and the testing precision keeps extremely high stability, which also proves that the Principal Component Analysis (PCA) dimension reduction method has extremely high stability, and from the perspective of training time, the training time of the BLS is only 1.33s, which is superior to the training time of other models. This indicates that BLS is competitive with other classification models.
TABLE 7- -comparison of Performance of Principal Component Analysis (PCA) reduced data sets on models (1500r/min)
As shown in Table 7, under the fault data set collected at 1500r/min, the HELM and the RELM can complete the fault diagnosis task under the data set at a higher modeling speed, and the two models can also keep excellent stability. The BLS is applied to the fault data set to perform classification tasks, and the obtained training precision and testing precision are superior to those of other models. From the modeling time perspective, the time required by the BLS is the shortest, which is 1/10 of the ELM modeling time, which indicates that the nodes of the BLS can efficiently complete feature extraction and dimension reduction on the data set.
It can be seen that at the rotation speed of 1500r/min, the modeling time and the testing time of the model are both better than the training and testing time required by models at other rotation speeds, which indicates that the faster the motor rotation speed is, the shorter the model time required by the acquired data set is. Compared with other models, the BLS can finish classification tasks under different fault data sets at the fastest modeling speed and the optimal testing precision aiming at fault data collected under different rotating speeds, and in addition, the BLS can also ensure the extremely high stability, which shows that the BLS has extremely strong adaptability.
According to the rotor system fault diagnosis method based on principal component analysis and width learning, the Principal Component Analysis (PCA) dimension reduction method can effectively eliminate the correlation of the eigenvectors in the characteristic matrix, and realize the dimension reduction of the characteristic matrix, so that the aim of reducing the redundancy of the characteristic matrix is fulfilled. In practical application, the Principal Component Analysis (PCA) can select the cumulative variance contribution rate to reasonably reduce the dimension of the feature matrix aiming at specific problems, the flexibility of the Principal Component Analysis (PCA) method is reflected, meanwhile, the applicability of the BLS is widened by introducing the BLS into the field of fault diagnosis, compared with other classification models, the BLS can efficiently complete a fault diagnosis task, and the model has good superiority.
According to the rotor System fault diagnosis method based on principal component analysis and width Learning, Principal Component Analysis (PCA) and a width Learning System (BLS for short) are introduced into rotor System fault diagnosis and recognition, the Principal Component Analysis (PCA) is adopted to perform dimensionality reduction processing on fault data subjected to FFT (fast Fourier transform) conversion to form feature vectors representing different faults, then the dimensionality reduced data is input into the BLS to be classified, the complexity of fault classification can be effectively reduced, data modeling time can be greatly shortened, the efficiency of rotor System fault recognition is improved, and therefore a rotor System fault diagnosis task is efficiently completed.
The above disclosure is only for the preferred embodiments of the present invention, but the embodiments of the present invention are not limited thereto, and any variations that can be made by those skilled in the art are intended to fall within the 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,...,xi,...xm1, 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·∑·QT (3)
wherein,
∑＝diag(λ1,λ2,...,λi,...,λn) (4)
Q＝[q1,q2,...,qi,...,qn] (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≥...≥λi≥...,≥λn，i＝1,...,n，QTThe 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 dataiAnd a characteristic value lambdaiIn 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 Xk；
And 7: the frequency domain fault data set X after dimension reductionkFrequency domain fault data set X divided into trainingk1And tested frequency domain fault data set Xk2；
And 8: utilizing a trained frequency domain fault data set Xk1Constructing 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 testedk2And 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,...,xi,...xmWhere m is the total number of samples, α is the mean of the samples of the frequency-domain fault data X, XiFor 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 XiFor 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 sigmaiCalculating 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, lambdaiAnd λjRespectively 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 ofi，
Qk＝[q1,q2,...,qi,...,qk] (10)
Wherein, i is 1<n, k is the number of the selected eigenvalues, n is the number of all eigenvalues, QkFor the first k eigenvalues λiCorresponding feature vector q ofiForming a feature vector matrix;
s43, feature vector matrix Q according to equation (11)kThe principal component analysis and the dimensionality reduction are carried out,
Xk＝Qk·X (11)
wherein Q iskCorresponding to the first k eigenvalues lambdaiCorresponding feature vector q ofiForming a feature vector matrix, wherein X is a frequency domain fault data set and XkThe 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 Zi，
Wherein, WeiAndis a randomly selected characteristic node coefficient, i is 1iIs the ith characteristic node, Xk1Is 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 Zt，
Zt≡[Z1,...,Zi,...,Zt] (13)
Wherein Z isiIs the ith characteristic node, ZtIs all characteristic nodes ZiT is the number of all feature nodes, i is 1.
S53, all characteristic nodes Z according to the formula (14)iCombination Z oftGenerating enhanced node H by nonlinear function transformationj，
Wherein HjIs the jth enhanced node, ZtIs all characteristic nodes ZiIn 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 Hc，
Hc≡[H1,...,Hj,...,Hc] (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 HcFor all enhanced nodes HjCombination of (1), HjIs the jth enhanced node;
s55, combining all nodes into an expansion matrix G according to the formula (16),
G≡[Zt|Hc] (16)
where G is the spreading matrix, ZtIs all characteristic nodes ZiCombination of (1), HcFor all enhanced nodes HjA 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, Fmin(β) an objective function for solving the objective weight β, V is a constant, and Y is { Y ═ Y }1,...,yl,...,yk1}，ylThe 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,...,yl,...,yk1}，ylA 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, andTfor transposing of spreading matrices, InhThe 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.
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