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 failures of mechanical parts detection technique fields, and in particular to one kind is based on principal component analysis and width
The Fault Diagnosis Approach For Rotor Systems of habit.
Background technique
Core component of the rotor-support-foundation system as rotating machinery, plays the effect that can not be substituted in each related fields.Turn
For subsystem using numerous on rotating machinery, the failure that rotating machinery occurs during the work time will cause great economic damage
It loses, wherein being caused since rotor-support-foundation system breaks down, fault harm includes generating noise, and rotor loses
Surely, serious or even mechanical structure can be made to damage, cause great safety accident.Therefore, rotor-support-foundation system incipient failure is carried out
It effectively analyzes and accurately diagnoses, there is scientific meaning and application value crucially.
Currently, method widely used for Rotor Fault Diagnosis is window Fourier transform, empirical mode decomposition,
The methods of wavelet analysis.However, there are structures to answer for the eigenmatrix of formation after the above method carries out feature extraction to fault-signal
It is miscellaneous, the problems such as feature correlation is big, and degree of redundancy is high, and these problems can greatly increase the complexity of failure modes, reduce
The accuracy rate of fault identification.
Summary of the invention
In view of this, the present invention provides a kind of Fault Diagnosis for Rotor System sides learnt based on principal component analysis and width
Method, this method carry out Dimensionality Reduction, drop to the eigenmatrix formed after feature extraction first with principal component analysis (PCA)
Linear dependence between low data eliminates redundant attributes, the low-dimensional matrix that can retain its substantive characteristics is obtained, then by the matrix
It inputs width learning system (Broad Learning System, abbreviation BLS) and carries out fault identification, width learning system
(Broad Learning System, abbreviation BLS) can be efficiently completed rotor-support-foundation system failure modes task, existing to solve
There is the deficiency in technology.
The technical scheme is that
A kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width, comprising the following steps:
Step 1: acquisition time domain fault data T (n)；
Step 2: Fourier transformation being carried out according to formula (1), time domain fault data T (n) collected is transformed to frequency domain event
Hinder data X,
Wherein,
In above-mentioned formula (1) and formula (2), n=0,1 ..., N-1, k=0,1 ..., N-1, N be time domain fault data length
Degree, j are complex symbol, and X is frequency domain fault data, including training sample and test sample, X={ x1, x2,...,xi,...xm,
I=1 ..., m, T (n) are time domain fault data；
Step 3: obtaining the covariance matrix C of frequency domain fault data X；
Step 4: determining the correlation between different frequency domain fault data X；
Step 5: Eigenvalues Decomposition being carried out according to covariance matrix C of the formula (3) to frequency domain fault data X, to obtain frequency
The eigenvectors matrix Q and eigenvalue matrix ∑ of the covariance matrix C of domain fault data X, eigenvalue matrix ∑ formula (4) table
Showing, eigenvectors matrix Q is indicated with formula (5),
C=Q ∑ QT (3)
Wherein,
∑=diag (λ1,λ2,...,λi,...,λn) (4)
Q=[q1,q2,...,qi,...,qn] (5)
In above-mentioned formula (3), formula (4) and formula (5), C is the covariance matrix of frequency domain fault data, and Q is characterized vector matrix,
∑ is characterized value matrix, λ1≥λ2≥...≥λi≥...,≥λn, i=1 ..., n, QTIt is characterized the transposed matrix of vector matrix,
N is the length of frequency domain fault data, number=all feature vectors number=frequency domain fault data length of all characteristic values
Degree=n, feature vector qiWith eigenvalue λiIn one-to-one relationship；
Step 6: the frequency domain fault data collection after principal component analysis dimensionality reduction obtains dimensionality reduction is carried out to frequency domain fault data collection X
Xk；
Step 7: by the frequency domain fault data collection X after dimensionality reductionkIt is divided into trained frequency domain fault data collection Xk1With the frequency of test
Domain fault data collection Xk2；
Step 8: utilizing the frequency domain fault data collection X of trainingk1Construct width model of learning system；
Step 9: the target weight β solved during width model of learning system will be constructed and substitute into width learning system mould
Width learning system disaggregated model is obtained in type；
Step 10: by the frequency domain fault data collection X of testk2It substitutes into width learning system disaggregated model and obtains fault diagnosis
As a result, completing the test to width learning system disaggregated model validity.
Preferably, the covariance matrix C of frequency domain fault data is obtained in the step 3 including the following steps:
S21, there is symmetry due to frequency domain fault data X, thus can according to formula (6) to the length of frequency domain fault data X into
Row interception,
N=N/2 (6)
In above-mentioned formula (6), n is the length after intercepting to the length of frequency domain fault data X, and N is time domain fault data
Length；
S22, the sample average α that frequency domain fault data X is sought according to formula (7),
Wherein, frequency domain fault data collection X={ x1, x2,...,xi,...xm, i=1 ..., m, m are the total number of sample,
α is the sample average of frequency domain fault data X, xiFor i-th of frequency domain fault data；
S23, the covariance matrix C that frequency domain fault data is sought according to formula (8),
Wherein, i=1 ..., m, m are the total number of sample, and C is the covariance matrix of frequency domain fault data X, xiIt is i-th
A frequency domain fault data, α are the sample averages of frequency domain fault data X.
Preferably, the decision condition for determining that the correlation between different frequency domain fault datas is taken in the step 4 is:
If the covariance in covariance matrix between corresponding two features is positive number, positive correlation is presented between two features, if
Covariance in covariance matrix between corresponding two features is negative, then it is right in negative correlativing relation covariance matrix to present between two features
Answering the covariance between two features is 0, then uncorrelated between two features of explanation.
It preferably, include following to the frequency domain fault data collection X method for carrying out principal component analysis dimensionality reduction in the step 6
Several steps:
S41, preceding k eigenvalue λ is chosen in eigenvalue matrix ∑i, pivot variance, which is calculated, according to formula (9) accumulates contribution rate
θ,
Wherein, θ is that pivot variance accumulates contribution rate, λiAnd λjRespectively ith and jth characteristic value, k are selected spy
Value indicative number, n are the number of all characteristic values, i=1 ..., k, j=1 ..., n, k < n；
S42, corresponding preceding k eigenvalue λ is obtained according to formula (10)iCharacter pair vector qi,
Qk=[q1,q2,...,qi,...,qk] (10)
Wherein, i=1 ..., k, k < n, k are selected characteristic value number, and n is the number of all characteristic values, QkIt is right
K eigenvalue λ before answeringiCharacter pair vector qiThe eigenvectors matrix of composition；
S43, according to formula (11) to eigenvectors matrix QkPrincipal component analysis dimensionality reduction is carried out,
Xk=Qk·X (11)
Wherein, QkK eigenvalue λ before correspondingiCharacter pair vector qiThe eigenvectors matrix of composition, X are frequency domain failure
Data set, XkFor the frequency domain fault data collection after principal component analysis dimensionality reduction.
Preferably, the method for width model of learning system is constructed in the step 8 including the following steps:
S51, according to formula (12) to trained frequency domain fault data collection Xk1Feature Mapping is carried out to form characteristic node Zi,
Wherein, WeiWithIt is the characteristic node coefficient randomly selected, i=1 ..., t, t are characterized node total number, ZiIt is
Ith feature node, Xk1For trained frequency domain fault data collection；
S52, according to formula (13) by all characteristic node ZiCombination be denoted as Zt,
Zt≡[Z1,...,Zi,...,Zt] (13)
Wherein, ZiIt is ith feature node, ZtIt is all characteristic node ZiCombination, t be all characteristic nodes
Number, i=1 ..., t；
S53, according to formula (14) to all characteristic node ZiCombination ZtIt carries out non-linear function transformation and generates enhancing node
Hj,
Wherein, HjIt is j-th of enhancing node, ZtIt is all characteristic node ZiCombination,WithIt is the increasing randomly selected
Strong node coefficient, j=1 ..., c, c are the total number for enhancing node；
S54, according to formula (15) by all enhancing node HjCombination be denoted as Hc,
Hc≡[H1,...,Hj,...,Hc] (15)
Wherein, c is the sum for enhancing node, j=1 ..., c, 0≤j≤m, HcFor all enhancing node HjCombination,
HjIt is j-th of enhancing node；
S55, all nodes are merged by extended matrix G according to formula (16),
G≡[Zt|Hc] (16)
Wherein, G is extended matrix, ZtIt is all characteristic node ZiCombination, HcFor all enhancing node HjCombination；
S56, according to formula (17) construct width learning system target weight β objective function Fmin(β),
Wherein, β is target weight, Fmin(β) is the objective function for solving target weight β, and V is constant, Y={ y1,...,
yl,...,yk1, ylFor the corresponding label of first of training sample, Y is the label matrix that all training sample labels are constituted, l=
1 ..., k1, k1 are the total number of training sample, and G is extended matrix；
S57, using gradient descent method to the F in formula (17)min(β) function is solved, and can obtain formula (18) to solve mesh
Weight beta is marked,
Wherein, Y={ y1,...,yl,...,yk1, ylFor the corresponding label of first of training sample, Y is all training samples
The label matrix that label is constituted, l=1 ..., k1, k1 are the total number of training sample, and β is target weight, and G is extended matrix,
GTFor the transposition of extended matrix, InhIt is the unit matrix that dimension is nh, nh is width model of learning system characteristic node and enhancing
The sum of node, i.e. nh=c+t, V are constant；
S58, the building of width model of learning system finish.
Compared with prior art, the present invention is by principal component analysis (PCA) and width learning system (Broad Learning
System, abbreviation BLS) it is introduced into Fault Diagnosis for Rotor System identification, it proposes a kind of based on principal component analysis and width
The Fault Diagnosis Approach For Rotor Systems of habit, this method carry out the fault data Jing Guo FFT transform using principal component analysis (PCA)
Dimension-reduction treatment forms the feature vector of characterization different faults, and then the data input BLS after dimensionality reduction classifies, beneficial
Effect is:
1, the present invention can effectively reduce the complexity of failure modes；
2, the present invention can substantially shorten the data modeling time, the efficiency of rotor-support-foundation system fault identification be promoted, thus efficiently
Completion Fault Diagnosis for Rotor System task；
3, practicability of the present invention is good, is worthy to be popularized.
Detailed description of the invention
Fig. 1 is a kind of process of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width of the invention
Figure；
Fig. 2 is the structural schematic diagram of width learning system BLS of the invention；
Fig. 3 is experimental bench structural schematic diagram of the invention；
Fig. 4 is the influence diagram of cumulative proportion in ANOVA of the invention to measuring accuracy；
Fig. 5 is cumulative proportion in ANOVA of the invention to training time influence diagram.
Description of symbols:
1, data cable；2, acceleration transducer；3, bearing to be tested；4, flywheel；5, shaft coupling；6, AC electrical
Machine；7, data collecting card；8, PC machine；9, frequency converter.
Specific embodiment
The present invention provides a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width, tie below
The flow diagram of Fig. 1 is closed, the present invention will be described.
As shown in Figure 1, the technical scheme is that
A kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width, comprising the following steps:
Step 1: acquisition time domain fault data T (n)；
Step 2: Fourier transformation being carried out according to formula (1), time domain fault data T (n) collected is transformed to frequency domain event
Hinder data X,
Wherein,
In above-mentioned formula (1) and formula (2), n=0,1 ..., N-1, k=0,1 ..., N-1, N be time domain fault data length
Degree, j are complex symbol, and X is frequency domain fault data, including training sample and test sample, X={ x1, x2,...,xi,...xm,
I=1 ..., m, T (n) are time domain fault data；
Step 3: obtaining the covariance matrix C of frequency domain fault data X；
Step 4: determining the correlation between different frequency domain fault data X；
Step 5: Eigenvalues Decomposition being carried out according to covariance matrix C of the formula (3) to frequency domain fault data X, to obtain frequency
The eigenvectors matrix Q and eigenvalue matrix ∑ of the covariance matrix C of domain fault data X, eigenvalue matrix ∑ formula (4) table
Showing, eigenvectors matrix Q is indicated with formula (5),
C=Q ∑ QT (3)
Wherein,
∑=diag (λ1,λ2,...,λi,...,λn) (4)
Q=[q1,q2,...,qi,...,qn] (5)
In above-mentioned formula (3), formula (4) and formula (5), C is the covariance matrix of frequency domain fault data, and Q is characterized vector matrix,
∑ is characterized value matrix, λ1≥λ2≥...≥λi≥...,≥λn, i=1 ..., n, QTIt is characterized the transposed matrix of vector matrix,
N is the length of frequency domain fault data, number=all feature vectors number=frequency domain fault data length of all characteristic values
Degree=n, feature vector qiWith eigenvalue λiIn one-to-one relationship；
Step 6: the frequency domain fault data collection after principal component analysis dimensionality reduction obtains dimensionality reduction is carried out to frequency domain fault data collection X
Xk；
Step 7: by the frequency domain fault data collection X after dimensionality reductionkIt is divided into trained frequency domain fault data collection Xk1With the frequency of test
Domain fault data collection Xk2；
Step 8: utilizing the frequency domain fault data collection X of trainingk1Construct width model of learning system；
Step 9: the target weight β solved during width model of learning system will be constructed and substitute into width learning system mould
Width learning system disaggregated model is obtained in type；
Step 10: by the frequency domain fault data collection X of testk2It substitutes into width learning system disaggregated model and obtains fault diagnosis
As a result, completing the test to width learning system disaggregated model validity.
Further, the covariance matrix C of frequency domain fault data is obtained in the step 3 including the following steps:
S21, there is symmetry due to frequency domain fault data X, thus can according to formula (6) to the length of frequency domain fault data X into
Row interception,
N=N/2 (6)
In above-mentioned formula (6), n is the length after intercepting to the length of frequency domain fault data X, and N is time domain fault data
Length；
S22, the sample average α that frequency domain fault data X is sought according to formula (7),
Wherein, frequency domain fault data collection X={ x1, x2,...,xi,...xm, i=1 ..., m, m are the total number of sample,
α is the sample average of frequency domain fault data X, xiFor i-th of frequency domain fault data；
S23, the covariance matrix C that frequency domain fault data is sought according to formula (8),
Wherein, i=1 ..., m, m are the total number of sample, and C is the covariance matrix of frequency domain fault data X, xiIt is i-th
A frequency domain fault data, α are the sample averages of frequency domain fault data X.
Further, the decision condition that the correlation between different frequency domain fault datas is taken is determined in the step 4
It is:
If the covariance in covariance matrix between corresponding two features is positive number, positive correlation is presented between two features, if
Covariance in covariance matrix between corresponding two features is negative, then it is right in negative correlativing relation covariance matrix to present between two features
Answering the covariance between two features is 0, then uncorrelated between two features of explanation.
Further, in the step 6 to frequency domain fault data collection X carry out principal component analysis dimensionality reduction method include with
Under several steps:
S41, preceding k eigenvalue λ is chosen in eigenvalue matrix ∑i, pivot variance, which is calculated, according to formula (9) accumulates contribution rate
θ,
Wherein, θ is that pivot variance accumulates contribution rate, λiAnd λjRespectively ith and jth characteristic value, k are selected spy
Value indicative number, n are the number of all characteristic values, i=1 ..., k, j=1 ..., n, k < n；
S42, corresponding preceding k eigenvalue λ is obtained according to formula (10)iCharacter pair vector qi,
Qk=[q1,q2,...,qi,...,qk] (10)
Wherein, i=1 ..., k, k < n, k are selected characteristic value number, and n is the number of all characteristic values, QkIt is right
K eigenvalue λ before answeringiCharacter pair vector qiThe eigenvectors matrix of composition；
S43, according to formula (11) to eigenvectors matrix QkPrincipal component analysis dimensionality reduction is carried out,
Xk=Qk·X (11)
Wherein, QkK eigenvalue λ before correspondingiCharacter pair vector qiThe eigenvectors matrix of composition, X are frequency domain failure
Data set, XkFor the frequency domain fault data collection after principal component analysis dimensionality reduction.
Further, the method for width model of learning system is constructed in the step 8 including the following steps:
S51, according to formula (12) to trained frequency domain fault data collection Xk1Feature Mapping is carried out to form characteristic node Zi,
Wherein, WeiWithIt is the characteristic node coefficient randomly selected, i=1 ..., t, t are characterized node total number, ZiIt is
Ith feature node, Xk1For trained frequency domain fault data collection；
S52, according to formula (13) by all characteristic node ZiCombination be denoted as Zt,
Zt≡[Z1,...,Zi,...,Zt] (13)
Wherein, ZiIt is ith feature node, ZtIt is all characteristic node ZiCombination, t be all characteristic nodes
Number, i=1 ..., t；
S53, according to formula (14) to all characteristic node ZiCombination ZtIt carries out non-linear function transformation and generates enhancing node
Hj,
Wherein, HjIt is j-th of enhancing node, ZtIt is all characteristic node ZiCombination,WithIt is the increasing randomly selected
Strong node coefficient, j=1 ..., c, c are the total number for enhancing node；
S54, according to formula (15) by all enhancing node HjCombination be denoted as Hc,
Hc≡[H1,...,Hj,...,Hc] (15)
Wherein, c is the sum for enhancing node, j=1 ..., c, 0≤j≤m, HcFor all enhancing node HjCombination,
HjIt is j-th of enhancing node；
S55, all nodes are merged by extended matrix G according to formula (16),
G≡[Zt|Hc] (16)
Wherein, G is extended matrix, ZtIt is all characteristic node ZiCombination, HcFor all enhancing node HjCombination；
S56, according to formula (17) construct width learning system target weight β objective function Fmin(β),
Wherein, β is target weight, Fmin(β) is the objective function for solving target weight β, and V is constant, Y={ y1,...,
yl,...,yk1, ylFor the corresponding label of first of training sample, Y is the label matrix that all training sample labels are constituted, l=
1 ..., k1, k1 are the total number of training sample, and G is extended matrix；
S57, using gradient descent method to the F in formula (17)min(β) function is solved, and can obtain formula (18) to solve mesh
Weight beta is marked,
Wherein, Y={ y1,...,yl,...,yk1, ylFor the corresponding label of first of training sample, Y is all training samples
The label matrix that label is constituted, l=1 ..., k1, k1 are the total number of training sample, and β is target weight, and G is extended matrix,
GTFor the transposition of extended matrix, InhIt is the unit matrix that dimension is nh, nh is width model of learning system characteristic node and enhancing
The sum of node, i.e. nh=c+t, V are constant；
S58, the building of width model of learning system finish.
The present invention is to eliminate the redundancy of eigenmatrix, for the classification problem more than fault data, using principal component analysis
Method carries out attribute reduction, can achieve the purpose that simplify eigenmatrix, simultaneously under the premise of losing information less as far as possible
For the quick identification after realization principal component analysis dimensionality reduction between feature vector and its fault type, width learning system is introduced to failure
Diagnostic field, in width learning system, characteristic node and enhancing node can be realized feature extraction and dimensionality reduction to data, should
All nodes of model are directly connected to output end, and corresponding output factor can be found out by pseudoinverse (Pseudo).
For the redundancy for eliminating eigenmatrix, the linear dependence between data is reduced, promotes rotor-support-foundation system fault identification
Efficiency, need to select a kind of simple, efficient dimension reduction method, principal component analysis (PCA) is a kind of dimension reduction method of classics.By
It is easily understood and use process complete printenv limitation in it, has been widely used in every field, such as image, voice,
Communication etc., essence are to recycle the feature vector of matrix to determine that dimensionality reduction is thrown by the covariance matrix of calculating process data set
The direction of shadow.In addition, this method can disclose the simple structure for being hidden in complex data behind, the linear correlation between data is reduced
Property, obtain the best description to malfunction.Importantly, PCA can reduce event under the premise of losing information less as far as possible
The redundancy for hindering data, to achieve the purpose that Data Dimensionality Reduction.Therefore, herein using PCA to by Fast Fourier Transform (FFT)
Fault signature matrix carry out Dimensionality Reduction.
After realizing PCA dimensionality reduction, quick identification between fault feature vector and its type, using width learning system
(BLS) fault diagnosis is carried out.In BLS, it is originally inputted and is transferred and is placed as the mappings characteristics in characteristic node, and
Wide spread is carried out in enhancing node, this can keep system to the validity of data.In addition, the feature and enhancing of all mappings
Node is directly connected to output end, and corresponding output factor can be found out by pseudoinverse (Pseudo).
The invention proposes the Fault Diagnosis Approach For Rotor Systems based on PCA and BLS, using PCA to by FFT transform
Fault data carries out dimension-reduction treatment, forms the feature vector of characterization different faults, then carries out the data input BLS after dimensionality reduction
Classification.
There are two types of the basic skills used in the present invention:
1, principal component analysis
Principal component analysis (PCA), also referred to as karr Hu Ning-Loew convert (Karhunen-Loeve Transform), are
A technique for it is substantially to reduce the dimension of training sample on the basis of losing information less as far as possible for Data Dimensionality Reduction,
Main thought is that n dimensional feature is mapped in k dimension, and it is in original n that this k dimension, which is that completely new orthogonal characteristic is also referred to as principal component,
The k dimensional feature (k≤n) for reconfiguring out on the basis of dimensional feature.
The work of PCA is exactly that one group of mutually orthogonal reference axis is sequentially looked for from original space, new reference axis
Selection and data are closely related in itself, wherein the 1st new reference axis selection is the maximum side of variance in initial data
To, the 2nd new reference axis selection is to make variance maximum in the plane orthogonal with the 1st reference axis, the 3rd axis be with the 1st,
Variance is maximum in the orthogonal plane of 2 axis.And so on, available n such reference axis.From these new seats obtained
It can be obtained in parameter, most of variance is included in the reference axis of front k, and variance contained by subsequent reference axis is almost 0.In
Being is almost 0 reference axis for variance, and user, which can be considered, to be ignored, to retain front k containing most variances
Reference axis.In fact, this, which is equivalent to, only retains the dimensional characteristics comprising most variances, ignoring comprising variance is almost 0
Characteristic dimension, and then realize to the Dimensionality Reduction of data characteristics.
2, width learning system
C.L.Philip Chen (Chen Junlong) professor propose width learning system (Broad Learning System,
Abbreviation BLS) it is to be constructed in a manner of flat, BLS is based on designing mappings characteristics as the RVFLLNN thought inputted.BLS
It can establish characteristic node and enhancing node to keep system to the effective of data the carry out feature extraction of big data and dimensionality reduction
Property.In addition, the feature of all mappings and enhancing node are directly connected to output end, corresponding output factor can pass through pseudoinverse
(Pseudo) it finds out, this has effectively eliminated training time long disadvantage.Importantly, BLS can also be by without complete
The fast Incremental Learning of network retraining realizes the extension of network structure.Meanwhile after the completion of network foundation, BLS can be with
Low-rank approximation combines to simplify system, and the structural redundancy of model is avoided with this.
BLS structure as shown in Fig. 2, BLS structure to build process as described below:
Step 1: forming the characteristic node of network by linear transformation using input data；
Step 2: the feature of mapping generates enhancing node by nonlinear transformation at random；
Step 3: all mappings characteristics and enhancing node are directly connected to output end；
Step 4: corresponding output weight can be found out by quick pseudoinverse (Pseudo), after output weight acquires, model
Build completion.
In order to verify advantages of the present invention, contrast verification test is done, confirmatory experiment of the invention is revolved using II type of QPZZ-
Turn machinery vibration analysis and fault diagnostic test platform, the experiment porch analog rotating machinery various states and vibration can carry out
The comparative analysis and diagnosis of various states, variable-ratio simulate fault signature under the conditions of friction speed, and slewing range is 75-
1450r/min, experimental bench is as shown in figure 3, entire experimental bench includes data cable 1, acceleration transducer 2, axis to be tested
3, flywheel 4, shaft coupling 5, ac motor 6, data collecting card 7, PC machine 8 and frequency converter 9 are held, is provided on ac motor 6
The output shaft of frequency converter 9, ac motor 6 is connect by shaft coupling 5 with the drive shaft of bearing 3 to be tested, bearing 3 to be tested
Suit is fixed in drive shaft and bearing base, is set with and is fixed on the output shaft of drive shaft and ac motor 6
Flywheel 4 is provided with acceleration transducer 2 on bearing 3 to be tested, and acceleration transducer 2 is adopted by data cable 1 with data
Truck 7 is electrically connected, and data collecting card 7 is electrically connected by data cable 1 with PC machine 8.
The running environment that the present invention is tested is for example shown below:
3104 [email protected] of Intel (R) Xeon (R) Bronze is equipped under MATLAB 2018b software platform,
It is completed under the computer of 16GB memory.
The present invention carries out signal acquisition using the USB-4431 data collecting card combination LabVIEW of U.S. NI company production,
Sample frequency is set as 12kHz, sampling time 100s, give respectively motor speed be 1000r/min, 1250r/min and
1500r/min, 9 kinds of fault datas and a kind of normal data under 0 load of acquisition, data cutout length is 1024, fault type
It is as shown in table 1:
Table 1--- fault type illustrates table
| Fault type | Name | Failure modes |
| Inner ring | IR | 1 |
| Outer ring | OR | 2 |
| Rolling element | Ball | 3 |
| Outer ring+rolling element | OUTB | 4 |
| Rotor unbalance | ROTOR | 5 |
| Rotor unbalance+inner ring | ROIN | 6 |
| Rotor unbalance+outer ring | ROOUT | 7 |
| Rotor unbalance+rolling element | ROB | 8 |
| Rotor unbalance+outer ring+rolling element | ROOB | 9 |
| Normally | normal | 10 |
Experimental data under different rotating speeds is all made of identical division, i.e., makees model training sample using 936 groups, and 234 groups
Do test sample, wherein every group of experiment all includes all data in table 1.
Fast Fourier Transform (FFT) (FFT) is carried out to rotor-support-foundation system experimental data obtained, is transformed from the time domain to frequency
Domain is analyzed, and after FFT transform, data length becomes 512 dimensions from 1024 dimensions.
It is following to test principal component analysis (PCA) method and its in order to test the validity of principal component analysis (PCA) method
Its dimension reduction method compares, including linear local tangent space alignment (LLTSA), non-linearity manifold study local tangent space row
It arranges (LTSA), is locally linear embedding into (LLE), data dimension after distinct methods dimensionality reduction is held in 150 dimensions.
In addition, disaggregated model used by data is BLS after dimensionality reduction and its structure is 500-500, in addition, following realities
Testing result all is acquired average value gained after data set is run 10 times.
Data experiment result collected is respectively such as 2,3 and 4 institute of table under 1000r/min, 1250r/min, 1500r/min
Show:
Performance of each dimension reduction method of table 2--- on data set compares (1000r/min)
As known from Table 2, compared with the data of non-dimensionality reduction, the data after all dimensionality reductions can effectively reduce the training of model
Time and testing time.After the processing of principal component analysis (PCA) method, measuring accuracy of the data on BLS reaches
99.95%, and high stability can also be kept, this will be better than other dimension reduction methods.This explanation under the data set,
Data after principal component analysis (PCA) dimensionality reduction can show more good performance on BLS.
Performance of each dimension reduction method of table 3--- on data set compares (1250r/min)
As shown in table 3, although the training time of the effective lift scheme of data energy after LTSA dimensionality reduction, its measuring accuracy
15% is reduced than originally, this illustrates the dimensionality reduction of this method, and the effect is unsatisfactory.Fault data is tieed up by principal component analysis (PCA)
After number reduction, measuring accuracy and training precision on BLS have all reached 100%, this will be better than the 99.93% of LLTSA
With 99.87%.Meanwhile this method can also accelerate the training time and testing time of model.Compared with non-dimensionality reduction data, by master
Data after constituent analysis (PCA) dimensionality reduction can effectively reduce model training and testing time, improve the measuring accuracy of model, mention
The stability of rising mould type, while this also illustrates, principal component analysis (PCA) all has competitiveness in above-mentioned any situation.
Performance of each dimension reduction method of table 4--- on data set compares (1500r/min)
It can be obtained by table 4, resulting measuring accuracy is at least than other sides after principal component analysis (PCA) handles data
The resulting measuring accuracy of method is high by 0.35%.In addition, the stability of its gained measuring accuracy is also better than other several methods.With nothing
The data of dimensionality reduction are compared, and treated for principal component analysis (PCA) when data can effectively reduce training time and the test of model
Between, lift scheme measuring accuracy and its stability, therefore, this also demonstrates the validity of principal component analysis (PCA) method.
In conclusion either treated that data can complete cuts down model modeling time and survey for which kind of dimension reduction method
The task of examination time, but it is seen that, the data only after principal component analysis (PCA) dimensionality reduction could effective lift scheme
Measuring accuracy and its stability, this illustrate principal component analysis (PCA) can be good at remove data redundancy, thus encumbrance
According to validity.In addition, the execution efficiency of BLS can also be improved by carrying out principal component analysis (PCA) processing to data.
It must be influenced to inquire into cumulative proportion in ANOVA to classifying quality, in this experiment, classification used by data
Device is BLS, and structure is disposed as 500-500.Initial build variance contribution ratio is set as 0.95, increases by 0.005 every time, until
0.995.Testing the aspect that compares includes measuring accuracy and model training time, meanwhile, following experimental results are operation 10 times
Gained afterwards.
Experimental result is as shown in Figures 4 and 5, as shown in figure 4, in a certain range, the measuring accuracy of data under different rotating speeds
Stable trend after first increasing will be showed with the superposition of cumulative proportion in ANOVA, this illustrates that principal component analysis (PCA) is right
Data under different rotating speeds can reduce its redundancy, and data reach the accumulation side of measuring accuracy stable point at 1250r/min
Poor contribution rate is 0.965, and for 0.98., this shows that under equal conditions principal component analysis (PCA) is to the data set to both remaining
Dimensionality reduction effect is better than the data set under other two kinds of revolving speeds.
It is not difficult to find that the training time of all data all can be obvious with the increase of cumulative proportion in ANOVA from Fig. 5
Promotion.This is because cumulative proportion in ANOVA is higher, principal component analysis (PCA) is fewer to the reduction of data dimension, BLS pairs
The time that data are trained is also longer.
As it can be seen that the measuring accuracy of three kinds of data can all be shown flat after first increasing with the increase of cumulative proportion in ANOVA
Trend, but the time needed for their modelings shows the phenomenon that continuing to increase, and this three kinds of data of explanation can all pass through principal component
Analysis (PCA) method reduces the modeling required time while data characteristics is effectively ensured, data reach under 1250r/min revolving speed
The cumulative proportion in ANOVA of optimal measuring accuracy is lower by 0.15 than the data under other two kinds of revolving speeds, this explanation is in face of different
Cumulative proportion in ANOVA can be flexibly chosen when data according to specific circumstances, reasonable feature extraction is carried out to it.
Influence for more different models to experiment, the disaggregated model that this experiment uses includes extreme learning machine (ELM),
Multilayer extreme learning machine (HELM), regularization extreme learning machine (RELM), width learning system (BLS).
Wherein, it is 100-100-1000, the section of RELM that the number of hidden nodes of ELM, which is set as the structure setting of 1000, HELM,
The number of nodes that points are set as 1000, BLS is set as 500-500.
Activation primitive all selects Sigmoid function in the hidden layer of ELM, HELM, RELM, and on the enhancement layer of SS-BLS
Activation primitive selection is also Sigmoid function.Meanwhile in BLS characteristic node layer and enhance node layer weight and biasing all
It is to be uniformly distributed extraction from the standard on section [- 1,1], in addition, data dimension after principal component analysis (PCA) dimensionality reduction is equal
150 dimensions are maintained at, following all experimental results are all average value acquired after running 10 times on respective model.
Data experiment result collected is respectively such as table 5 under 1000r/min, 1250r/min, 1500r/min, shown in 6,7:
Performance of the data set on each model compares (1000r/min) after table 5--- principal component analysis (PCA) dimensionality reduction
It is not difficult to find that ELM shows extremely strong stability, but its training time and survey during the test from table 5
Other disaggregated models will be much higher than by trying the time, and BLS will be better than other classifiers in training precision and measuring accuracy.Meanwhile
The modeling time of BLS only needs 1.19s, this is also better than ELM, and the training time of RELM, HELM, this illustrates that the model can be more preferable
Completion fault diagnosis task.
Performance of the data set on each model compares (1250r/min) after table 6--- principal component analysis (PCA) dimensionality reduction
As shown in Table 6, after principal component analysis (PCA) carries out dimensionality reduction, all disaggregated models can obtain optimal instruction
Practice precision and measuring accuracy, and measuring accuracy all keeps high stability, this also demonstrates principal component analysis (PCA) simultaneously
Dimension reduction method has extremely strong stability, and from the angle of training time, the training time of BLS only needs 1.33s, this is better than
The training time of other models.This illustrates that BLS has competitiveness compared with other disaggregated models.
Performance of the data set on each model compares (1500r/min) after table 7--- principal component analysis (PCA) dimensionality reduction
As shown in table 7, under the fault data collection of 1500r/min acquisition, HELM, RELM can be with faster modeling speeds
The fault diagnosis task under the data set is completed, and this two kinds of models are also able to maintain fabulous stability.BLS is applied to the event
Classification task is done on barrier data set, resulting training precision and measuring accuracy will be better than other several models.From the modeling time
It is seen in angle, the time needed for BLS is most short, and only ELM models the 1/10 of time, this illustrates that the node of BLS can be efficient complete
The feature extraction of paired data collection and dimensionality reduction.
As it can be seen that the modeling time of model and testing time will be better than other revolving speed drags under 1500r/min revolving speed
Required training and testing time, this shows that motor speed is faster, and model time needed for data set collected is shorter.
For fault data collected under different rotating speeds, compared to other several models, BLS can be with most fast modeling speed, most
Excellent measuring accuracy completes the classification task under different faults data set, in addition, BLS can also ensure that high stability, this
Illustrate that BLS has extremely strong adaptability.
A kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width of the invention, use it is main at
Analysis (PCA) dimension reduction method can effectively eliminate the correlation of feature vector in eigenmatrix, realize to eigenmatrix
Dimensionality Reduction, to achieve the purpose that reduce eigenmatrix redundancy.In practical applications, principal component analysis (PCA) can be directed to
Particular problem chooses cumulative proportion in ANOVA and carries out reasonable dimensionality reduction to eigenmatrix, this embodies principal component analysis (PCA) side
The flexibility of method, meanwhile, by the way that BLS is introduced fault diagnosis field, its applicability has been widened, compared with other disaggregated models,
BLS can be efficiently completed fault diagnosis task, this embodies the model with good superiority.
A kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width proposed by the present invention, by it is main at
Analysis (PCA) and width learning system (Broad Learning System, abbreviation BLS) are introduced into rotor-support-foundation system failure and examine
In disconnected identification, this method carries out dimension-reduction treatment to the fault data Jing Guo FFT transform using principal component analysis (PCA), forms table
The feature vector of different faults is levied, then the data input BLS after dimensionality reduction classifies, failure modes can be effectively reduced
Complexity, and can substantially shorten the data modeling time, the efficiency of rotor-support-foundation system fault identification be promoted, to be efficiently completed
Fault Diagnosis for Rotor System task, practicability is good, is worthy to be popularized.
Disclosed above is only preferable specific embodiment of the invention, and still, the embodiment of the present invention is not limited to this,
What anyone skilled in the art can be thought variation should all fall into protection scope of the present invention.
Claims (5)
1. a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width, which is characterized in that including following
Step:
Step 1: acquisition time domain fault data T (n)；
Step 2: Fourier transformation being carried out according to formula (1), time domain fault data T (n) collected is transformed to frequency domain number of faults
According to X,
Wherein,
In above-mentioned formula (1) and formula (2), n=0,1 ..., N-1, k=0,1 ..., N-1, N be time domain fault data length, j
For complex symbol, X is frequency domain fault data, including training sample and test sample, X={ x1, x2,...,xi,...xm, i=
1 ..., m, T (n) are time domain fault data；
Step 3: obtaining the covariance matrix C of frequency domain fault data X；
Step 4: determining the correlation between different frequency domain fault data X；
Step 5: Eigenvalues Decomposition being carried out according to covariance matrix C of the formula (3) to frequency domain fault data X, to obtain frequency domain event
Hinder the eigenvectors matrix Q and eigenvalue matrix ∑ of the covariance matrix C of data X, eigenvalue matrix ∑ is indicated with formula (4), special
Levy vector matrix Q is indicated with formula (5),
C=Q ∑ QT (3)
Wherein,
∑=diag (λ1,λ2,...,λi,...,λn) (4)
Q=[q1,q2,...,qi,...,qn] (5)
In above-mentioned formula (3), formula (4) and formula (5), C is the covariance matrix of frequency domain fault data, and Q is characterized vector matrix, and ∑ is
Eigenvalue matrix, λ1≥λ2≥...≥λi≥...,≥λn, i=1 ..., n, QTIt is characterized the transposed matrix of vector matrix, n is
The length of frequency domain fault data, number=all feature vectors number=frequency domain fault data length of all characteristic values=
N, feature vector qiWith eigenvalue λiIn one-to-one relationship；
Step 6: the frequency domain fault data collection X after principal component analysis dimensionality reduction obtains dimensionality reduction is carried out to frequency domain fault data collection Xk；
Step 7: by the frequency domain fault data collection X after dimensionality reductionkIt is divided into trained frequency domain fault data collection Xk1With the frequency domain event of test
Hinder data set Xk2；
Step 8: utilizing the frequency domain fault data collection X of trainingk1Construct width model of learning system；
Step 9: the target weight β solved during width model of learning system will be constructed and substituted into width model of learning system
Obtain width learning system disaggregated model；
Step 10: by the frequency domain fault data collection X of testk2It substitutes into and obtains fault diagnosis knot in width learning system disaggregated model
Fruit completes the test to width learning system disaggregated model validity.
2. a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width according to claim 1,
It is characterized in that, obtaining the covariance matrix C of frequency domain fault data in the step 3 including the following steps:
S21, since frequency domain fault data X has symmetry, therefore can be cut according to length of the formula (6) to frequency domain fault data X
It takes,
N=N/2 (6)
In above-mentioned formula (6), n is the length after intercepting to the length of frequency domain fault data X, and N is the length of time domain fault data
Degree；
S22, the sample average α that frequency domain fault data X is sought according to formula (7),
Wherein, frequency domain fault data collection X={ x1, x2,...,xi,...xm, i=1 ..., m, m are the total number of sample, and α is frequency
The sample average of domain fault data X, xiFor i-th of frequency domain fault data；
S23, the covariance matrix C that frequency domain fault data is sought according to formula (8),
Wherein, i=1 ..., m, m are the total number of sample, and C is the covariance matrix of frequency domain fault data X, xiFor i-th of frequency domain
Fault data, α are the sample averages of frequency domain fault data X.
3. a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width according to claim 1,
It is characterized in that, the decision condition for determining that the correlation between different frequency domain fault datas is taken in the step 4 is:
If the covariance in covariance matrix between corresponding two features is positive number, positive correlation is presented between two features, if association side
Covariance in poor matrix between corresponding two features is negative, then presents between two features corresponding two in negative correlativing relation covariance matrix
Covariance between feature is 0, then uncorrelated between two features of explanation.
4. a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width according to claim 1,
It is characterized in that, including following to the frequency domain fault data collection X method for carrying out principal component analysis dimensionality reduction in the step 6
Step:
S41, preceding k eigenvalue λ is chosen in eigenvalue matrix ∑i, pivot variance, which is calculated, according to formula (9) accumulates contribution rate θ,
Wherein, θ is that pivot variance accumulates contribution rate, λiAnd λjRespectively ith and jth characteristic value, k are selected characteristic value
Number, n are the number of all characteristic values, i=1 ..., k, j=1 ..., n, k < n；
S42, corresponding preceding k eigenvalue λ is obtained according to formula (10)iCharacter pair vector qi,
Qk=[q1,q2,...,qi,...,qk] (10)
Wherein, i=1 ..., k, k < n, k are selected characteristic value number, and n is the number of all characteristic values, QkIt is corresponding preceding k
A eigenvalue λiCharacter pair vector qiThe eigenvectors matrix of composition；
S43, according to formula (11) to eigenvectors matrix QkPrincipal component analysis dimensionality reduction is carried out,
Xk=Qk·X (11)
Wherein, QkK eigenvalue λ before correspondingiCharacter pair vector qiThe eigenvectors matrix of composition, X are frequency domain fault data
Collection, XkFor the frequency domain fault data collection after principal component analysis dimensionality reduction.
5. a kind of Fault Diagnosis Approach For Rotor Systems learnt based on principal component analysis and width according to claim 1,
It is characterized in that, the method for constructing width model of learning system in the step 8 including the following steps:
S51, according to formula (12) to trained frequency domain fault data collection Xk1Feature Mapping is carried out to form characteristic node Zi,
Wherein, WeiWithIt is the characteristic node coefficient randomly selected, i=1 ..., t, t are characterized node total number, ZiIt is i-th
A characteristic node, Xk1For trained frequency domain fault data collection；
S52, according to formula (13) by all characteristic node ZiCombination be denoted as Zt,
Zt≡[Z1,...,Zi,...,Zt] (13)
Wherein, ZiIt is ith feature node, ZtIt is all characteristic node ZiCombination, t be all characteristic nodes number, i
=1 ..., t；
S53, according to formula (14) to all characteristic node ZiCombination ZtIt carries out non-linear function transformation and generates enhancing node Hj,
Wherein, HjIt is j-th of enhancing node, ZtIt is all characteristic node ZiCombination,WithIt is the enhancing section randomly selected
Dot factor, j=1 ..., c, c are the total number for enhancing node；
S54, according to formula (15) by all enhancing node HjCombination be denoted as Hc,
Hc≡[H1,...,Hj,...,Hc] (15)
Wherein, c is the sum for enhancing node, j=1 ..., c, 0≤j≤m, HcFor all enhancing node HjCombination, HjIt is
J-th of enhancing node；
S55, all nodes are merged by extended matrix G according to formula (16),
G≡[Zt|Hc] (16)
Wherein, G is extended matrix, ZtIt is all characteristic node ZiCombination, HcFor all enhancing node HjCombination；
S56, according to formula (17) construct width learning system target weight β objective function Fmin(β),
Wherein, β is target weight, Fmin(β) is the objective function for solving target weight β, and V is constant, Y={ y1,...,
yl,...,yk1, ylFor the corresponding label of first of training sample, Y is the label matrix that all training sample labels are constituted, l=
1 ..., k1, k1 are the total number of training sample, and G is extended matrix；
S57, using gradient descent method to the F in formula (17)min(β) function is solved, and can obtain formula (18) to solve target power
Weight β,
Wherein, Y={ y1,...,yl,...,yk1, ylFor the corresponding label of first of training sample, Y is all training sample labels
The label matrix of composition, l=1 ..., k1, k1 are the total number of training sample, and β is target weight, and G is extended matrix, GTFor
The transposition of extended matrix, InhIt is the unit matrix that dimension is nh, nh is width model of learning system characteristic node and enhancing node
Sum, i.e. nh=c+t, V are constant；
S58, the building of width model of learning system finish.
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