CN108414226B - Fault Diagnosis of Roller Bearings under variable working condition based on feature transfer learning - Google Patents
Fault Diagnosis of Roller Bearings under variable working condition based on feature transfer learning Download PDFInfo
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Abstract
Fault Diagnosis of Roller Bearings under variable working condition based on feature transfer learning, is related to fault diagnosis field, is proposed for the low problem of accuracy rate of diagnosis under the conditions of rolling bearing especially variable working condition.This method decomposes each state vibration signal of rolling bearing using VMD, obtains a series of intrinsic mode functions, and the matrix constituted to it carries out singular value decomposition and asks singular value and singular value entropy, constructs multiple features collection in conjunction with the time domain of vibration signal, frequency domain character.It introduces semi-supervised migration component analyzing method simultaneously, and multi-core configuration is carried out to its kernel function, by different operating condition sample characteristics co-maps to a shared Reproducing Kernel Hilbert Space, and then improve in data class distinction between compactedness and class.It selects more effective data as source domain using Largest Mean difference embedding inlay technique, source domain feature samples input SVM is trained, the target domain characterization sample after test mapping.There is higher accuracy rate in the classification of rolling bearing multimode under variable working condition.
Description
Technical field
The present invention relates to Fault Diagnosis of Roller Bearings under a kind of variable working condition, are related to fault diagnosis technology field.
Background technique
Critical component one of of the rolling bearing as large rotating machinery equipment, carries out fault diagnosis to it and is conducive to prevent
Equipment breakdown occurs[1].For rolling bearing in actual work, operating condition is often to change.In recent years, to the axis of rolling under variable working condition
Hold extensive concern of the research by scholar of fault diagnosis.
Document [2] combine Hilbert-Huang transform and singular value decomposition (Singular value decomposition,
SVD feature extraction) is carried out to bearing vibration signal, recurrent neural network is recycled to realize variable working condition lower bearing failure point
Class；Document [3] proposes that a kind of local mean value decomposes the method combined with SVD, the feelings shorter to the rolling bearing variable working condition time
Condition can effectively identify fault category；Document [4] is realized using Envelope Analysis combination multi-scale entropy and empirical mode decomposition method
Rolling bearing fault diagnosis under variable speed；Document [5] combines binary system differential evolution with k nearest neighbor classification algorithm, realizes
Rolling bearing fault diagnosis under variable working condition；Document [6] utilizes improved Method Using Relevance Vector Machine and adaptive features select method, establishes
The failure modes model of varying load lower bearing.Above-mentioned document the method, realizes roll under variable working condition to a certain extent
The failure modes of bearing, but traditional machine learning method is distributed trained and test data when having differences, point established
Class model generalization ability is poor, or even not applicable[7]。
In order to break the limitation of conventional machines study, transfer learning is very widely used in recent years[8].Transfer learning
Method is not required to make same distributional assumption as conventional machines study requirement training data and test data, and it can avoid conventional machines
In study the data of acquisition are re-scaled with the consuming of human and material resources brought by label[9].The main thought of transfer learning is
It acquires from existing source domain, then by these knowledge migrations to aiming field, to complete the classification of aiming field.It is rolled under variable working condition
When bearing failure diagnosis, data distribution is exactly unsatisfactory for same distribution occasion, while being labeled to the floor data newly obtained and be
It is very difficult.Transfer learning method is very suitable to rolling bearing data under processing variable working condition, has in terms of fault diagnosis
A small amount of research.Document [10] proposes that the feature extracting method based on autocorrelation matrix SVD is combined with transfer learning, realizes electricity
The fault diagnosis of machine；Document [11] proposes a kind of least square method supporting vector machine (Support vector machine, SVM)
Transfer learning method, institute's climbing form type promote bearing diagnosis performance.Document [12] constructs improvement Bayesian neural network
Transfer learning algorithm, be applied to classification of remote-sensing images, obtain better effects.The above method is all made of the migration of Case-based Reasoning
Learning method diagnoses failure, but these methods are when solving classification problem, it is desirable that the otherness between same area to the greatest extent may not be used
Can be small, the problem larger for data variance seems especially insufficient[13]。
Can be seen that by analyzing above, under the conditions of rolling bearing especially variable working condition utilize failure in the prior art
Diagnostic method is difficult or can not obtain the vibration data of a large amount of tape labels, causes accuracy rate of diagnosis lower.
Summary of the invention
The present invention is for the vibration number that is difficult or can not obtain a large amount of tape labels under the conditions of rolling bearing especially variable working condition
According to so that the problem that accuracy rate of diagnosis is low, and then provide rolling bearing under a kind of variable working condition based on feature transfer learning therefore
Hinder diagnostic method.
The technical solution adopted by the present invention to solve the above technical problem is:
The realization process of Fault Diagnosis of Roller Bearings under variable working condition of the present invention based on feature transfer learning
Are as follows:
(1) feature extraction:
It is (normal, interior under different rotating speeds and different loads operating condition to known operating condition and unknown operating condition rolling bearing multimode
Ring different faults degree, outer ring different faults degree, rolling element different faults degree) vibration signal progress VMD operation, with observation
Method determines the IMF number decomposed, constructs matrix to IMF, and carries out SVD and obtain singular value, while seeking singular value entropy；It extracts again
Time domain, the frequency domain character index of vibration signal；
(2) feature samples collection constructs:
It is total in conjunction with singular value, singular value entropy by the time domain of operating condition bearing vibration signal known in (1), frequency domain character
With building source domain training characteristics sample set；Similarly, the bearing vibration feature construction aiming field test feature sample of unknown operating condition
This collection；
(3) the semi-supervised migration constituent analysis of multicore (semi-supervised migration constituent analysis, abbreviation SSTCA):
Source domain training characteristics sample set in (2) and aiming field test feature sample set common trait are mapped to reproducing kernel
In the space Hilbert, within this space with MMDE method measurement source domain training characteristics sample and aiming field test feature sample it
Between Largest Mean distance；
Known operating condition rolling bearing multimode vibration signal, selection can be reselected by the Largest Mean Distance Judgment
Known operating condition rolling bearing multimode vibration signal (source domain vibration signal data) assists unknown operating condition rolling bearing multimode vibration
Dynamic signal (aiming field vibration signal data) study, is improved to aiming field vibration signal data classification recognition capability；
(4) rolling bearing fault diagnosis under variable working condition:
Source domain training characteristics sample set after mapping in (3) is inputted in SVM, while right with GA algorithm (genetic algorithm)
The penalty factor of SVM and radial base nuclear parameter carry out optimizing, finally obtain the training mould of rolling bearing fault diagnosis under variable working condition
Type；Aiming field test feature sample after mapping is input in the training pattern, rolling bearing fault under variable working condition is obtained
Diagnostic result.
Further, in step (1), VMD operation is carried out to the vibration signal, the IMF decomposed is determined with observation
Number constructs matrix to IMF, and carries out SVD and obtain singular value, while seeking singular value entropy；Its detailed process are as follows:
Variation mode decomposition process is divided into the construction of variational problem and solves two parts:
1) construction of variational problem
Assuming that k modal components u can be obtained in rolling bearing multimode original vibration signal fk(t), it is converted through Hilbert
Obtain each modal components uk(t) analytic signal, and obtain uk(t) unilateral frequency spectrum
uk(t) unilateral frequency spectrum=(δ (t)+j/ π t) * uk(t) (1)
In formula, δ (t) is impulse function；T in above formula indicates the time；
Centre frequency e is mixed-estimated for each analytic signal-jωkt, by the spectrum modulation to Base Band of each mode,
It obtains
In formula, ωkIndicate the centre frequency of k-th of modal components；
Calculate square L of (2) formula gradient2Norm, estimates the bandwidth of each mode signals, and controlled variational problem indicates
Are as follows:
In formula,To seek partial derivative to t, { uk} :={ u1,u2,…,uK, { ωk} :={ ω1,ω2,…,ωK}；{uk}
It is each modal components uk(t) set；
2) solution of variational problem
In order to which variational problem is become non-binding by binding character, introduces secondary penalty factor α and Lagrange multiplier is calculated
Sub- λ (t)；Secondary penalty factor guarantees that the reconstruction accuracy of signal, Lagrangian make constraint condition keep stringency；Extension
Lagrangian formulation is
In formula, { λ } indicates the set of λ (t)；
Using multiplication operator alternating direction method, u is updated by iterationk n+1、ωk n+1And λn+1Seek Lagrange extension expression
" saddle point " of formula, the as optimal solution of variational problem；It is easy in order to make to calculate in iteration, by uk n+1、ωk n+1Frequency domain is transformed to,
Seek uk n+1The renewal process of (ω)
Centre frequency renewal process
Composite type (5), (6) are rightInverse Fourier transform is carried out, obtaining its real part is { uk(t)}；
In formula, superscript n indicates update times；
Indicate that time domain vibration signal f (t) transforms to frequency domain vibration signal, subscript ^ expression is approximately equal to；Indicate Time-Domain Modal component uk(t) state simulation of frequency region component is transformed to, subscript ^ expression is approximately equal to.
Further, in step (3), the Reproducing Kernel Hilbert Space uses multicore Kernel, process
Are as follows:
Convex combination is carried out using a variety of basic kernel functions and reaches best features mapping purpose, and expression formula is
In formula, M is the number of kernel function, the weight a of kernel functionm>=0, and a1+a2+…+aM=1；
Again using the Polynomial kernel function with global property and the gaussian radial basis function for meeting local characteristics weighting
Summation constructs multicore kernel function
Ki,j=aKpoly+(1-a)Krbf (11)
Wherein, a is multicore coefficient, and 0≤a≤1, KpolyIt is Polynomial kernel function, KrbfIt is gaussian radial basis function.
Further, in step (3), the detailed process of the semi-supervised migration constituent analysis of multicore are as follows:
Assuming that Φ (Xs) and Φ (XT) be source domain training characteristics sample set after Reproducing Kernel Hilbert Space maps with
Aiming field test feature sample set, MMDE method measurement representation are
In formula, nsIt is source domain training characteristics number of samples, nTIt is aiming field test feature number of samples；
To reduce MMDE computational complexity, indicate that MMDE is using matrixing
Dist(Φ(XS),Φ(XT))=trace (KL) (13)
In formula (13), trace indicates to seek the mark of matrix；Nuclear matrix K is
In formula (13), L is
In formula (14), KS,S, KT,T, KS,T, KT,SIt respectively indicates and is defined on source domain, aiming field and cross-domain nuclear matrix；Nuclear moment
Element in battle array is Ki,j=Φ (xi)TΦ(xj), Ki,jIndicate kernel function；Indicate nuclear space；
It is expressed as after nuclear matrix K transformation
K=(KK-1/2)(K-1/2K) (16)
Use matrixBy (m≤n on nuclear mapping to m-dimensional spaces+nT), nuclear matrix K is transformed to
In formula,
Formula (13) is transformed into according to formula (17)
To improve the relevance in class label and Reproducing Kernel Hilbert Space between feature samples, SSTCA method is used
Hilbert Schmidt separate standards (Hilbert-Schmidt Independence Criterion, HSIC) are measured,
Its expression formula is
HSIC (X, Y)=(1/ (nS+nT-1)2)trace(HKHKyy) (19)
In formula, X is feature samples in nuclear space, and Y is the corresponding class label of source domain feature samples；Center matrix1 is the column vector for being all 1, and I is unit matrix；KyyIt is defined on source domain feature samples
Nuclear matrix；
To realize input feature vector sample xiWith xjIn the distance minimization after Feature Mapping converts, feature samples constraint function
For
Wherein, x* iAnd x* jIt is x respectivelyiAnd xjFeature samples after Feature Mapping；Laplacian MatrixWork as input
Feature samples xiWith xjMeet the M=[m within the scope of k neighbourij], mij=exp (- d2 ij/2σ2), dijFor input feature vector sample
Between Euclidean distance, σ is parameter；D is diagonal matrix, is configured to
In conclusion convolution (18), (19) and (20), the objective function of multicore SSTCA are
In formula, tab indexes matrix K* yy=γ Kyy+ (1- γ) I, γ are characterized sample class tab indexes parameter, trace
(WTIt W) is regularization term, μ is regularization parameter, and λ is the tradeoff coefficient for keeping data local characteristics, and λ >=0；
Optimum mapping nuclear matrix W can be obtained in the objective function for seeking formula (22).
Further, the known operating condition and unknown operating condition rolling bearing multimode include: different rotating speeds and different loads
Operating condition lower inner ring different faults degree, outer ring different faults degree, rolling element different faults degree.
The beneficial effects of the present invention are: for being difficult or can not obtain a large amount of bands under the conditions of rolling bearing especially variable working condition
The vibration data of label, so that the problem that accuracy rate of diagnosis is low, proposes a kind of based on variation mode decomposition (Variational
Mode decomposition, VMD) and multiple features construction and the Fault Diagnosis of Roller Bearings that combines of transfer learning.It should
Method decomposes each state vibration signal of rolling bearing using VMD, obtains a series of intrinsic mode functions, constitutes to it
Matrix carries out singular value decomposition and asks singular value and singular value entropy, constructs multiple features in conjunction with the time domain of vibration signal, frequency domain character
Collection.Simultaneously introduce semi-supervised migration component analyzing method (Semisupervised transfer component analysis,
SSTCA multi-core configuration), and to its kernel function is carried out, by different operating condition sample characteristics co-maps to a shared reproducing kernel
The space Hilbert, and then improve distinction between compactedness and class in data class.More had using the selection of Largest Mean difference embedding inlay technique
Source domain feature samples input SVM is trained, the target domain characterization sample after test mapping by the data of effect as source domain.It is real
Test show mentioned multicore SSTCA-SVM method be compared with other methods compared with, under variable working condition rolling bearing multimode classification in have
There is higher accuracy.
Transfer learning method based on feature can be converted when data difference is larger by sample characteristics reduces source domain and mesh
Mark the data distribution difference between domain[13].Especially semi-supervised migration component analyzing method (Semisupervised
Transfer component analysis, SSTCA) to the transfer learning significant effect of different sample characteristics[14], this method
Different characteristic sample is mapped to shared Reproducing Kernel Hilbert Space, source domain training characteristics sample is made full use of in this nuclear space
Ben Ji and its label information, the relevance after raising eigentransformation in nuclear space between feature samples classification and feature samples.Cause
This, present invention introduces vibration of the semi-supervised migration component analyzing method in transfer learning method to rolling bearing under variable working condition is special
Sign is migrated, and its kernel function is configured to multicore kernel function, and the mapping effect of reproducing kernel space is further increased with this.Together
When, using Largest Mean difference embedding grammar (Maximum mean discrepancy embedding, MMDE), measure source domain
The transportable property of data to target numeric field data realizes that rolling bearing is more under variable working condition further combined with SVM to avoid " negative transfer "
Status fault classification.
Detailed description of the invention
Fig. 1 is field adaptation method schematic diagram；Fig. 2 is Fault Diagnosis of Roller Bearings stream under variable working condition of the invention
Cheng Tu；Fig. 3 is the corresponding central frequency distribution figure of different N values (N takes 2,3,4 and 5 respectively)；Fig. 4 is VMD result and each component frequency
Spectrogram；Fig. 5 is the intrinsic dimensionality and accuracy rate relational graph (C/B) after mapping；Fig. 6 is that the intrinsic dimensionality and accuracy rate after mapping close
System's figure (AC/BD)；Fig. 7 is the intrinsic dimensionality and accuracy rate relational graph (ACD/B) after mapping.
Specific embodiment
As shown in Fig. 1 to 7, present embodiment provides rolling bearing event under the variable working condition based on feature transfer learning
Hinder the realization process of diagnostic method (based on Fault Diagnosis of Roller Bearings under the SSTCA-SVM variable working condition of feature multicore) are as follows:
(1) feature extraction:
It is (normal, interior under different rotating speeds and different loads operating condition to known operating condition and unknown operating condition rolling bearing multimode
Ring different faults degree, outer ring different faults degree, rolling element different faults degree) vibration signal progress VMD operation, with observation
Method determines the IMF number decomposed, constructs matrix to IMF, and carries out SVD and obtain singular value, while seeking singular value entropy；It extracts again
Time domain, the frequency domain character index of vibration signal；
(2) feature samples collection constructs:
It is total in conjunction with singular value, singular value entropy by the time domain of operating condition bearing vibration signal known in (1), frequency domain character
With building source domain training characteristics sample set；Similarly, the bearing vibration feature construction aiming field test feature sample of unknown operating condition
This collection；
(3) the semi-supervised migration constituent analysis of multicore (semi-supervised migration constituent analysis, abbreviation SSTCA):
Source domain training characteristics sample set in (2) and aiming field test feature sample set common trait are mapped to reproducing kernel
In the space Hilbert, within this space with MMDE method measurement source domain training characteristics sample and aiming field test feature sample it
Between Largest Mean distance；
Known operating condition rolling bearing multimode vibration signal, selection can be reselected by the Largest Mean Distance Judgment
Suitable known operating condition rolling bearing multimode vibration signal (source domain vibration signal data) assists unknown operating condition rolling bearing more
State vibration signal (aiming field vibration signal data) study, is improved to aiming field vibration signal data classification recognition capability；
(4) rolling bearing fault diagnosis under variable working condition:
Source domain training characteristics sample set after mapping in (3) is inputted in SVM, while right with GA algorithm (genetic algorithm)
The penalty factor of SVM and radial base nuclear parameter carry out optimizing, finally obtain the training mould of rolling bearing fault diagnosis under variable working condition
Type；Aiming field test feature sample after mapping is input in the training pattern, rolling bearing fault under variable working condition is obtained
Diagnostic result.
The method, flow chart are as shown in Figure 2.
For the specific implementation of Fault Diagnosis of Roller Bearings under the above-mentioned variable working condition based on feature transfer learning, carry out
It is detailed further below:
1, variation mode decomposition principle
Variation mode decomposition (Variational mode decomposition, VMD) process is divided into the structure of variational problem
Make and solve two parts[15]。
1) construction of variational problem
Assuming that k modal components u can be obtained in original signal fk(t), each modal components u is obtained through Hilbert transformationk(t)
Analytic signal, and obtain uk(t) unilateral frequency spectrum
(δ(t)+j/πt)*uk(t) (1)
In formula, δ (t) is impulse function.
Centre frequency e is mixed-estimated to each analytic signal-jω k t, by the spectrum modulation to Base Band of each mode, obtain
It arrives
In formula, ωkIndicate the centre frequency of k-th of modal components.
Calculate square L of (2) formula gradient2Norm, estimates the bandwidth of each mode signals, and controlled variational problem indicates
For
In formula,To seek partial derivative to t, { uk} :={ u1,u2,…,uK, { ωk} :={ ω1,ω2,…,ωK}。
2) solution of variational problem
In order to which variational problem is become non-binding by binding character, introduces secondary penalty factor α and Lagrange multiplier is calculated
Sub- λ (t).Secondary penalty factor guarantees that the reconstruction accuracy of signal, Lagrangian make constraint condition keep stringency.Extension
Lagrangian formulation is
It solves (4) variational problem and u is updated by iteration using multiplication operator alternating direction methodk n+1、ωk n+1And λn+1Seek
" saddle point " of Lagrange extension expression formula, the as optimal solution of variational problem.It is easy in order to make to calculate in iteration, by uk n +1、ωk n+1Frequency domain is transformed to, u is soughtk n+1The renewal process of (ω)
Centre frequency renewal process
Composite type (5), (6) are rightInverse Fourier transform is carried out, obtaining its real part is { uk(t)}。
2, singular value and singular value entropy
SVD itself has preferable stability and invariance[16].Assuming that X is the matrix (m > n) of m × n, order be r (r≤
N), the orthogonal matrix V of the orthogonal matrix U and n × n of existing m × m, so that
UTXV=Λ (7)
Wherein, Λ is the non-negative diagonal matrix of m × n
Wherein, S=diag (e1,e2,…,er),e1,e2,…,erThe referred to as singular value of X.
Singular value includes that the different faults feature of vibration signal is asked for this variation of quantitative description with information entropy theory
Singular value entropy out[17].Each intrinsic mode function (Intrinsic mode function, IMF) has different frequency contents, and
Singular value after decomposition is also different, normalizes to each component, obtains Ti=ei 2/ E, wherein E=E1+E2+…+En, Ei=ei 2, i=
1,2,…,n.The singular value entropy for obtaining each modal components is
Wherein, pi=Ti/ T,
3, based on the transfer learning of feature
3.1 field adaptation methods
Assuming that source domain is Ds={ Xs, Ys }, Xs is source domain feature samples collection, and Ys is Label space.Aiming field is DT=
{XT, XTIt is target domain characterization sample set, the label of target domain characterization sample is unknown.Field adaptation method Feature Mapping process
Schematic diagram is as shown in Figure 1.
Field adaptation method can reduce the distributional difference between source domain data and target numeric field data, by source domain feature samples
Collection and target domain characterization sample set carry out Feature Mapping jointly, indicate mapping relations, as Xs ∪ X with ΦT→Φ(Xs∪XT)。
Before common trait mapping, marginal probability distribution difference P (Xs) ≠ P of source domain feature samples collection and target domain characterization sample set
(XT).After Feature Mapping, Φ (Xs) and Φ (XT) marginal probability distribution P (Φ (Xs)) ≈ P (Φ (X as similar as possibleT)).Source
Characteristic of field sample set and target domain characterization sample set Feature Mapping make full use of feature samples are transportable to know to shared subspace
Know, improves cross-cutting learning ability.
The semi-supervised migration constituent analysis of 3.2 multicores
3.2.1 multicore Kernel
When being unevenly distributed weighing apparatus data using the processing of single kernel function, effect is usually not ideal enough[18].For under variable working condition
Bearing vibration signal data, there is also the unbalanced situations of different conditions data distribution.In order to change at single kernel function
The deficiency for managing rolling bearing data under variable working condition carries out convex combination using a variety of basic kernel functions, to reach best features mapping
Purpose.The multicore expression formula of different Kernels is
In formula, M is the number of kernel function, the weight a of kernel functionm>=0, and a1+a2+…+aM=1.
According to Mercer theorem and rolling bearing data distribution characteristic, using with global property Polynomial kernel function and
Meet the gaussian radial basis function weighted sum of local characteristics, constructs multicore kernel function
Ki,j=aKpoly+(1-a)Krbf (11)
Wherein, a is multicore coefficient, and 0≤a≤1, KpolyIt is Polynomial kernel function, KrbfIt is gaussian radial basis function.
3.2.2 semi-supervised migration constituent analysis (SSTCA)
Assuming that Φ (Xs) and Φ (XT) it is source domain feature samples collection and target after Reproducing Kernel Hilbert Space maps
Characteristic of field sample set, MMDE measurement representation are
In formula, nsIt is source domain feature samples number, nTIt is target domain characterization number of samples.
To reduce MMDE computational complexity, indicate that MMDE is using matrixing
Dist(Φ(XS),Φ(XT))=trace (KL) (13)
In formula (13), trace indicates to seek the mark of matrix.Nuclear matrix K is
In formula (13), L is
In formula (14), KS,S, KT,T, KS,T, KT,SIt respectively indicates and is defined on source domain, aiming field and cross-domain nuclear matrix.Nuclear moment
Element in battle array is Ki,j=Φ (xi)TΦ(xj), Ki,jIndicate kernel function.Nuclear matrix K is expressed as
K=(KK-1/2)(K-1/2K) (16)
Use matrixBy (m≤n on nuclear mapping to m-dimensional spaces+nT), nuclear matrix K is transformed to
In formula,
Formula (13) is transformed into according to formula (17)
To improve the relevance in class label and Reproducing Kernel Hilbert Space between feature samples, SSTCA method is used
Hilbert Schmidt separate standards (Hilbert-Schmidt Independence Criterion, HSIC)[19]It weighs
Amount, expression formula are
HSIC (X, Y)=(1/ (nS+nT-1)2)trace(HKHKyy) (19)
In formula, X is feature samples in nuclear space, and Y is the corresponding class label of source domain feature samples.Center matrix1 is the column vector for being all 1, and I is unit matrix.KyyIt is defined on source domain feature samples
Nuclear matrix.
To realize input feature vector sample xiWith xjIn the distance minimization after Feature Mapping converts, feature samples constraint function
For
Wherein, x* iAnd x* jIt is x respectivelyiAnd xjFeature samples after Feature Mapping.Laplacian MatrixWork as input
Feature samples xiWith xjMeet the M=[m within the scope of k neighbourij], mij=exp (- d2 ij/2σ2), dijFor input feature vector sample
Between Euclidean distance, σ is parameter.D is diagonal matrix, is configured to
In conclusion convolution (18), (19) and (20), multicore SSTCA method objective function are
In formula, tab indexes matrix K* yy=γ Kyy+ (1- γ) I, γ are characterized sample class tab indexes parameter, trace
(WTIt W) is regularization term, μ is regularization parameter, and λ is the tradeoff coefficient for keeping data local characteristics, and λ >=0.
Optimum mapping nuclear matrix W can be obtained in the objective function for seeking formula (22).
The application and analysis of the method for the present invention
1, experiment condition and parameter
Experimental data comes from U.S.'s Case Western Reserve University electrical engineering laboratory rolling bearing data center.Test macro packet
Driving motor and load and control circuit are included, data are collected by the data logger in 16 channels, and sample frequency includes
12kHz and 48kHz.
Motor drive terminal deep-groove ball rolling bearing is selected in this experiment, and model SKF6205, sample frequency 48kHz test number
According to.Rolling bearing inner ring lesion diameter is respectively 0.1778mm, 0.3556mm and 0.5334mm, while different lesion diameters include
Different loads, different rotating speeds variable working condition under bearing vibration signal data.It is as shown in table 1 that inner ring malfunction is divided into 3 classes.
Similarly, rolling bearing outer ring, rolling element malfunction respectively have 3 classes, and separately plus normal condition one is divided into 10 classes.
1 rolling bearing variable working condition lower inner ring malfunction of table
Set of data samples under experimental setup rolling bearing 10 class state, 4 kinds of working conditions: 1) operating condition A is 0hp, 1797r/
Min set of data samples；2) operating condition B is 1hp, 1772r/min set of data samples；3) operating condition C is 2hp, 1750r/min data sample
Collection；4) operating condition D is 3hp, 1730r/min set of data samples.Set of data samples composition is as shown in table 2, wherein " more/either simplex condition " table
Show in 10 class state of rolling bearing under various working feature samples collection as source domain data, single operating condition as target numeric field data,
Other and so on.
The different operating condition rolling bearing set of data samples of table 2 are constituted
2, multiple features construct
Firstly, obtaining several IMF using VMD, mode number N is determined by centre frequency using observation, with 1hp,
For the rolling bearing inner ring fault vibration signal of 1772r/min operating condition carries out VMD operation, each sample takes vibration signal 4096
Point.It is as shown in Figure 3 that decomposition obtains centre frequency result corresponding to different modalities number N.
As seen from Figure 3, when mode number N is greater than 4, there is overlapping phenomenon in different center frequency line, illustrates to generate decomposition,
When mode number N is less than 4, different center frequency line occurs decomposing not exclusively, that is, owes decomposing phenomenon, therefore determines that mode number is 4.Mould
After state number is determined, VMD result and each component spectrogram are as shown in Figure 4.
VMD is carried out to bearing vibration signal under variable working condition using same method and obtains IMF, and forms matrix, is asked
Take singular value and singular value entropy.Because the IMF number that different divided oscillation signal solutions obtain may be different, for convenient for subsequent processing, IMF
The few supplement null vector of number keeps the intrinsic dimensionality extracted consistent.Meanwhile extract bearing vibration signal 7 time domains and
17 frequency domain character indexs are detailed in bibliography [20].
To sum up, singular value, singular value entropy and the time domain rolling bearing fault vibration signal extracted, frequency domain are special
It levies index and constructs multiple features collection, and to eliminate the dimension impact of different characteristic data, multiple features collection is normalized.
3, transportable property judgement
According to statistical theory, MMDE method in Reproducing Kernel Hilbert Space, with source domain data and target numeric field data it
Between the difference of overall Largest Mean show the distributional difference between two fields.Rolling bearing source domain feature sample under experiment variable working condition
This collection A, B, C, D make Largest Mean difference measurement with target domain characterization sample set A, B, C, D respectively, obtain Largest Mean difference system
Evaluation is as shown in table 3.Largest Mean difference in table between source domain feature samples collection and target domain characterization sample set is smaller, illustrates source
The transportable property of domain to aiming field is stronger, this is conducive to selection and the high source domain data auxiliary mark domain of aiming field data similarity
Data classification.
3 Largest Mean Variant statistical value table of table
4, multicore SSTCA experimental result
1) multicore experimental contrast analysis
Using SVM as classifier, the SSTCA of multicore is compared into experiment from the SSTCA method of different monokaryon kernel functions.
Source domain feature samples collection and target domain characterization sample set choose either simplex condition or multi-state data set, by taking C/B as an example, multicore in experiment
In SSTCA, gaussian radial basis function and polynomial kernel parameter are 10, and multicore coefficient a is 0.9, and regularization μ is that 1, k neighbour value is
200, standardization local parameter λ is 120, and label classification parameter γ is 1000.Different kernel functions and different working condition experimentings are accurate
Rate is as shown in table 4.
Rolling bearing fault recognition accuracy under the different kernel function SSTCA variable working condition of table 4
By table 4 as it can be seen that no matter either simplex condition or multi-state data set are as source domain or aiming field, the multicore side SSTCA-SVM
The equal highest of the fault recognition rate of method.Its very big reason is that multicore kernel function is unbalanced in processing source domain data and target numeric field data
When have preferable advantage.
2) multicore SSTCA and other algorithm comparative analyses
(1) based on bearing vibration feature under variable working condition, multicore SSTCA and KPCA, PCA Feature Mapping method are carried out
Comparison.
A) either simplex condition/either simplex condition (C/B) data are tested, source domain uses the feature set of operating condition C, and aiming field uses work
The feature set of condition B obtains that test results are shown in figure 5 after different characteristic mapping method and SVM training pattern.
B) multi-state/multi-state (AC/BD) data are tested, test results are shown in figure 6.
C) multi-state/either simplex condition (ACD/B) data are tested, test results are shown in figure 7.
Can be seen that by Fig. 5, Fig. 6 and Fig. 7, training characteristics sample set and test feature sample set dimension from 1 increase to 12 when,
Multicore SSTCA and KPCA, PCA are continuously improved respectively in connection with three kinds of method accuracys rate of SVM.After dimension is more than 12, KPCA and
Two methods of the fault diagnosis accuracy rate of PCA is not high and has fluctuation, and the accuracy rate of diagnosis of multicore SSTCA method totally keeps flat
Steady and slightly raising, and it is above two methods of KPCA and PCA.
(2) multicore SSTCA-SVM and TSVM, LapSVM non-migrating learning method compare, test result accuracy rate such as 5 institute of table
Show.
5 multicore SSTCA-SVM of table and non-migrating learning method contrast test accuracy rate
Since TSVM, LapSVM non-migrating learning method directly use source domain data training pattern, aiming field data test mould
Type cannot excavate the common characteristic information between domain, and multicore SSTCA-SVM method migration source domain data have knowledge to target
Domain, auxiliary mark numeric field data classification, by table 5 as it can be seen that the test accuracy rate highest of this method.
(3) multicore SSTCA and the field MIDA, SA, ITL, GFK, SSA and TCA adaptation method[21]Comparison.Recruitment respectively
Condition C, AC, ACD use operating condition B, BD, B as target numeric field data, through each field adaptation method and svm classifier as source domain data
Obtain that the results are shown in Table 6 after device.
6 different field adaptation method of table compares accuracy rate
By table 6 as it can be seen that other than ITL method can obtain preferable test result in operating condition C/B, ACD/B, other fields
Adaptation method is not strong to rolling bearing data adaptability under variable working condition, and accuracy rate is not high.Wherein, the survey of TCA-SVM method
Examination accuracy rate is also far below multicore SSTCA-SVM method.Its reason is that multicore SSTCA-SVM improves feature using HSIC method
Sample and sample class label relevance, this is conducive to the classification of target numeric field data.On the other hand, multicore SSTCA-SVM method
Multicore kernel function the unbalanced feature samples mapping transformation effect of rolling bearing under variable working condition is got well than other methods, this is advantageous
Distributional difference between reduction source domain and target numeric field data.
The method of the present invention is concluded that by above-mentioned application
(1) propose combine VMD and SVD to bearing vibration signal carry out singular value features extraction, then with singular value entropy,
The method that vibration signal time domain, frequency domain character cooperatively construct rolling bearing multi-domain characteristics collection, so that rolling can more be characterized by obtaining
The feature of dynamic bearing state.
(2) introducing SSTCA method completes the transfer learning task between not same area, and constructs the side SSTCA of multicore kernel function
Method improves bearing vibration Feature Mapping ability under variable working condition, and then reduces feature samples distributional difference between domain.
(3) source domain feature samples and the similar journey between target domain characterization sample are measured using Largest Mean difference embedding grammar
Degree, and propose to select source domain data using Largest Mean Variant statistical value, improve the recognition accuracy to target numeric field data.
(4) multicore SSTCA method and other Feature Mapping methods, field adaptation method, non-migrating learning method compare.
Experiment shows multicore SSTCA-SVM method to rolling bearing unknown state recognition effect under variable working condition more preferably.
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Claims (5)
1. Fault Diagnosis of Roller Bearings under the variable working condition based on feature transfer learning, which is characterized in that the reality of the method
Existing process are as follows:
(1) feature extraction:
VMD operation is carried out to known operating condition and unknown operating condition rolling bearing multimode vibration signal, determines decomposition with observation
IMF number constructs matrix to IMF, and carries out SVD and obtain singular value, while seeking singular value entropy；Extract again vibration signal when
Domain, frequency domain character index；
(2) feature samples collection constructs:
By the time domain of operating condition bearing vibration signal known in (1), frequency domain character, in conjunction with singular value, the common structure of singular value entropy
Build source domain training characteristics sample set；Similarly, the bearing vibration feature construction aiming field test feature sample set of unknown operating condition；
(3) the semi-supervised migration constituent analysis of multicore:
Source domain training characteristics sample set in (2) and aiming field test feature sample set common trait are mapped to reproducing kernel
In the space Hilbert, within this space with MMDE method measurement source domain training characteristics sample and aiming field test feature sample it
Between Largest Mean distance；
Known operating condition rolling bearing multimode vibration signal can be reselected by the Largest Mean Distance Judgment, known to selection
Operating condition rolling bearing multimode vibration signal assists unknown operating condition rolling bearing multimode vibration signal study, improves to aiming field
Vibration signal data classification recognition capability；
(4) rolling bearing fault diagnosis under variable working condition:
By in the source domain training characteristics sample set input SVM in (3) after mapping, at the same with GA algorithm to the penalty factor of SVM with
Radial base nuclear parameter carries out optimizing, finally obtains the training pattern of rolling bearing fault diagnosis under variable working condition；By the mesh after mapping
Mark domain test feature samples are input in the training pattern, obtain rolling bearing fault diagnosis result under variable working condition.
2. Fault Diagnosis of Roller Bearings under the variable working condition according to claim 1 based on feature transfer learning, special
Sign is:
In step (1), VMD operation is carried out to the vibration signal, the IMF number decomposed is determined with observation, IMF is constructed
Matrix, and carry out SVD and obtain singular value, while seeking singular value entropy；Its detailed process are as follows:
Variation mode decomposition process is divided into the construction of variational problem and solves two parts:
1) construction of variational problem
Assuming that k modal components u can be obtained in rolling bearing multimode original vibration signal fk(t), it converts and obtains through Hilbert
Each modal components uk(t) analytic signal, and obtain uk(t) unilateral frequency spectrum
uk(t) unilateral frequency spectrum=(δ (t)+j/ π t) * uk(t) in (1) formula, δ (t) is impulse function；The equal table of t in above formula
Show the time；
Centre frequency e is mixed-estimated for each analytic signal-jωkt, by the spectrum modulation to Base Band of each mode, obtain
In formula, ωkIndicate the centre frequency of k-th of modal components；
Calculate square L of (2) formula gradient2Norm, estimates the bandwidth of each mode signals, and controlled variational problem indicates are as follows:
In formula,To seek partial derivative to t, { uk} :={ u1,u2,…,uK, { ωk} :={ ω1,ω2,…,ωK}；{ukIt is each
Modal components uk(t) set；
2) solution of variational problem
In order to which variational problem is become non-binding by binding character, secondary penalty factor α and Lagrange multiplier operator λ are introduced
(t)；Secondary penalty factor guarantees that the reconstruction accuracy of signal, Lagrangian make constraint condition keep stringency；The drawing of extension
Ge Lang expression formula is
In formula, { λ } indicates the set of λ (t)；
Using multiplication operator alternating direction method, u is updated by iterationk n+1、ωk n+1And λn+1Seek Lagrange extension expression formula
" saddle point ", the as optimal solution of variational problem；It is easy in order to make to calculate in iteration, by uk n+1、ωk n+1Frequency domain is transformed to, is sought
uk n+1The renewal process of (ω)
Centre frequency renewal process
Composite type (5), (6) are rightInverse Fourier transform is carried out, obtaining its real part is { uk(t)}；
In formula, superscript n indicates update times；
Indicate that time domain vibration signal f (t) transforms to frequency domain vibration signal, subscript ^ expression is approximately equal to；
Indicate Time-Domain Modal component uk(t) state simulation of frequency region component is transformed to, subscript ^ expression is approximately equal to.
3. Fault Diagnosis of Roller Bearings under the variable working condition according to claim 2 based on feature transfer learning, special
Sign is:
In step (3), the Reproducing Kernel Hilbert Space uses multicore Kernel, process are as follows:
Convex combination is carried out using a variety of basic kernel functions and reaches best features mapping purpose, and expression formula is
In formula, M is the number of kernel function, the weight a of kernel functionm>=0, and a1+a2+…+aM=1；
The gaussian radial basis function weighted sum for using the Polynomial kernel function with global property again and meeting local characteristics,
Construct multicore kernel function
Ki,j=aKpoly+(1-a)Krbf (11)
Wherein, a is multicore coefficient, and 0≤a≤1, KpolyIt is Polynomial kernel function, KrbfIt is gaussian radial basis function.
4. Fault Diagnosis of Roller Bearings under the variable working condition according to claim 3 based on feature transfer learning, special
Sign is:
In step (3), the detailed process of the semi-supervised migration constituent analysis of multicore are as follows:
Assuming that Φ (Xs) and Φ (XT) it is source domain training characteristics sample set and target after Reproducing Kernel Hilbert Space maps
Domain test feature samples collection, MMDE method measurement representation are
In formula, nsIt is source domain training characteristics number of samples, nTIt is aiming field test feature number of samples；
To reduce MMDE computational complexity, indicate that MMDE is using matrixing
Dist(Φ(XS),Φ(XT))=trace (KL) (13)
In formula (13), trace indicates to seek the mark of matrix；Nuclear matrix K is
In formula (13), L is
In formula (14), KS,S, KT,T, KS,T, KT,SIt respectively indicates and is defined on source domain, aiming field and cross-domain nuclear matrix；In nuclear matrix
Element be Ki,j=Φ (xi)TΦ(xj), Ki,jIndicate kernel function；Indicate nuclear space；
It is expressed as after nuclear matrix K transformation
K=(KK-1/2)(K-1/2K) (16)
Use matrixBy (m≤n on nuclear mapping to m-dimensional spaces+ nT), nuclear matrix K is transformed to
In formula,
Formula (13) is transformed into according to formula (17)
To improve the relevance in class label and Reproducing Kernel Hilbert Space between feature samples, SSTCA method uses Xi Er
Bert Schmidt's separate standards are measured, and expression formula is
HSIC (X, Y)=(1/ (nS+nT-1)2)trace(HKHKyy) (19)
In formula, X is feature samples in nuclear space, and Y is the corresponding class label of source domain feature samples；Center matrix H=Ins+nT–
(1/(ns+nT))11T, 1 is the column vector for being all 1, and I is unit matrix；KyyThe nuclear matrix being defined on source domain feature samples；
To realize input feature vector sample xiWith xjIn the distance minimization after Feature Mapping converts, feature samples constraint function is
Wherein, x* iWithIt is x respectivelyiAnd xjFeature samples after Feature Mapping；Laplacian MatrixAs the spy of input
Levy sample xiWith xjMeet the M=[m within the scope of k neighbourij], mij=exp (- d2 ij/2σ2), dijBetween input feature vector sample
Euclidean distance, σ is parameter；D is diagonal matrix, is configured to
In conclusion convolution (18), (19) and (20), the objective function of multicore SSTCA are
In formula, tab indexes matrix K* yy=γ Kyy+ (1- γ) I, γ are characterized sample class tab indexes parameter, trace
(WTIt W) is regularization term, μ is regularization parameter, and λ is the tradeoff coefficient for keeping data local characteristics, and λ >=0；
Optimum mapping nuclear matrix W can be obtained in the objective function for seeking formula (22).
5. rolling bearing fault diagnosis side under the variable working condition according to claim 1,2,3 or 4 based on feature transfer learning
Method, it is characterised in that: operating condition and unknown operating condition rolling bearing multimode include: different rotating speeds and different loads operating condition known to described
Lower inner ring different faults degree, outer ring different faults degree, rolling element different faults degree.
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