CN108414226A - Fault Diagnosis of Roller Bearings under the variable working condition of feature based transfer learning - Google Patents

Fault Diagnosis of Roller Bearings under the variable working condition of feature based transfer learning Download PDF

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CN108414226A
CN108414226A CN201711428476.5A CN201711428476A CN108414226A CN 108414226 A CN108414226 A CN 108414226A CN 201711428476 A CN201711428476 A CN 201711428476A CN 108414226 A CN108414226 A CN 108414226A
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formula
feature
rolling bearing
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matrix
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CN108414226B (en
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康守强
胡明武
王玉静
谢金宝
王庆岩
邹佳悦
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Harbin University of Science and Technology
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    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

Fault Diagnosis of Roller Bearings under the variable working condition of feature based 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, and multiple features collection is constructed 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 mode 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

Fault Diagnosis of Roller Bearings under the variable working condition of feature based transfer learning
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 technology
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 mode is often to change.In recent years, to the axis of rolling under variable working condition The research of fault diagnosis is held by the extensive concern of scholar.
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 being 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；Binary system differential evolution is combined by document [5] with k nearest neighbor classification algorithm, is realized 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 rolled under variable working condition to a certain extent The failure modes of bearing, but traditional machine learning method is distributed training and test data when having differences, point established Class model generalization ability is poor, or even not applicable[7]。
In order to break conventional machines study limitation, in recent years transfer learning be widely used it is general[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 caused 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 for 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；A kind of least square method supporting vector machine (Support vector machine, SVM) of document [11] proposition Transfer learning method, carried model 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, seem particularly insufficient for the larger problem of data variance[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 relatively low.
Invention content
The present invention, which is directed under the conditions of rolling bearing especially variable working condition, to be difficult or can not obtain the vibration numbers of a large amount of tape labels 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 of feature based transfer learning therefore Hinder diagnostic method.
The present invention adopts the technical scheme that solve above-mentioned technical problem：
The realization process of Fault Diagnosis of Roller Bearings under the variable working condition of feature based transfer learning of the present invention For：
(1) feature extraction：
It is (normal, interior under different rotating speeds and different loads operating mode to known operating mode and unknown operating mode rolling bearing multimode Ring different faults degree, outer shroud different faults degree, rolling element different faults degree) vibration signal progress VMD operations, with observation Method determines the IMF number decomposed, and matrix is built 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 is built：
It is total in conjunction with singular value, singular value entropy by the time domain of known operating mode bearing vibration signal, frequency domain character in (1) With structure source domain training characteristics sample set；Similarly, the bearing vibration feature construction aiming field test feature sample of unknown operating mode This collection；
(3) the semi-supervised migration constituent analysis of multinuclear (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 spaces Hilbert, use within this space MMDE methods measurement source domain training characteristics sample and aiming field test feature sample it Between Largest Mean distance；
Known operating mode rolling bearing multimode vibration signal, selection can be reselected by the Largest Mean Distance Judgment Suitable known operating mode rolling bearing multimode vibration signal (source domain vibration signal data) assists unknown operating mode rolling bearing more State vibration signal (aiming field vibration signal data) learns, and improves 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 algorithms (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 operations is carried out to the vibration signal, the IMF decomposed is determined with observation Number builds matrix to IMF, and carries out SVD and obtain singular value, while seeking singular value entropy；Its detailed process is：
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-estimates 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 For：
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 ensures that the reconstruction accuracy of signal, Lagrangian make constraints 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；In iteration in order to keep calculating easy, 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, it is { u to obtain its real partk(t)}；
In formula, superscript n indicates update times；
Indicate that time domain vibration signal f (t) transforms to frequency domain vibration signal, subscript ^ expressions are approximately equal to； Indicate Time-Domain Modal component uk(t) state simulation of frequency region component is transformed to, subscript ^ expressions are approximately equal to.
Further, in step (3), the Reproducing Kernel Hilbert Space uses multinuclear Kernel, process For：
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 weights a of kernel functionm>=0, and a1+a2+…+aM=1；
It is weighted again with the gaussian radial basis function for meeting local characteristics using the Polynomial kernel function with global property Summation constructs multinuclear kernel function
Ki,j=aKpoly+(1-a)Krbf (11)
Wherein, a is multinuclear 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 multinuclear is：
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 representations 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 complexities, 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 indicates to be defined on source domain, aiming field and cross-domain nuclear matrix respectively；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)
For the relevance for improving in class label and Reproducing Kernel Hilbert Space between feature samples, SSTCA methods use Hilbert Schmidt separate standards (Hilbert-Schmidt Independence Criterion, HSIC) are weighed, 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 xjThe distance minimization after being converted through Feature Mapping, feature samples constraint function For
Wherein, x*iWithIt is x respectivelyiAnd xjFeature samples after Feature Mapping；Laplacian Matrix L=D-M, works as input Feature samples xiWith xjMeet within the scope of k neighbours, M=[mij], 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 object function of multinuclear SSTCA are
In formula, tab indexes matrix K* yy=γ Kyy+ (1- γ) I, γ are characterized sample class tab indexes parameter, trace (WTW it is) regularization term, μ is regularization parameter, and λ is to keep the tradeoff coefficient of data local characteristics, and λ >=0；
Seek the object function of formula (22), you can obtain optimum mapping nuclear matrix W.
Further, the known operating mode and unknown operating mode rolling bearing multimode include：Different rotating speeds and different loads Normal, inner ring different faults degree, outer shroud different faults degree, rolling element different faults degree under operating mode.
The beneficial effects of the invention are as follows：For being difficult under the conditions of rolling bearing especially variable working condition or can not obtain a large amount of bands 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 is combined of transfer learning.It should Method decomposes each state vibration signal of rolling bearing using VMD, obtains a series of intrinsic mode functions, is constituted to it Matrix carries out singular value decomposition and asks singular value and singular value entropy, and multiple features are constructed 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 mode sample characteristics co-maps to a shared reproducing kernel The spaces 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 It tests and shows put forward multinuclear SSTCA-SVM methods compared with other methods, have in the classification of rolling bearing multimode under variable working condition There is higher accuracy.
The transfer learning method of feature based 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 the semi-supervised migration component analyzing method in transfer learning method is special to the vibration of rolling bearing under variable working condition Sign is migrated, and its kernel function is configured to multinuclear 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 to avoid " negative transfer " further combined with SVM Status fault is classified.
Description of the drawings
Fig. 1 is field adaptation method schematic diagram；Fig. 2 is Fault Diagnosis of Roller Bearings stream under the variable working condition of the present 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 results 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 after mapping is closed with accuracy rate System's figure (AC/BD)；Fig. 7 is the intrinsic dimensionality and accuracy rate relational graph (ACD/B) after mapping.
Specific implementation mode
As shown in Fig. 1 to 7, present embodiment provide rolling bearing under the variable working condition of the feature based transfer learning therefore Barrier diagnostic method (Fault Diagnosis of Roller Bearings under feature based multinuclear SSTCA-SVM variable working condition) realization process be：
(1) feature extraction：
It is (normal, interior under different rotating speeds and different loads operating mode to known operating mode and unknown operating mode rolling bearing multimode Ring different faults degree, outer shroud different faults degree, rolling element different faults degree) vibration signal progress VMD operations, with observation Method determines the IMF number decomposed, and matrix is built 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 is built：
It is total in conjunction with singular value, singular value entropy by the time domain of known operating mode bearing vibration signal, frequency domain character in (1) With structure source domain training characteristics sample set；Similarly, the bearing vibration feature construction aiming field test feature sample of unknown operating mode This collection；
(3) the semi-supervised migration constituent analysis of multinuclear (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 spaces Hilbert, use within this space MMDE methods measurement source domain training characteristics sample and aiming field test feature sample it Between Largest Mean distance；
Known operating mode rolling bearing multimode vibration signal, selection can be reselected by the Largest Mean Distance Judgment Suitable known operating mode rolling bearing multimode vibration signal (source domain vibration signal data) assists unknown operating mode rolling bearing more State vibration signal (aiming field vibration signal data) learns, and improves 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 algorithms (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 variable working condition of above-mentioned feature based transfer learning, carry out 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-estimates to each analytic signal-jωkt, 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 ensures that the reconstruction accuracy of signal, Lagrangian make constraints 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.In iteration in order to keep calculating easy, 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, it is { u to obtain its real partk(t)}。
2, singular value and singular value entropy
SVD itself has preferable stability and invariance[16].Assuming that X is the matrix (m of m × n>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 the different faults feature of vibration signal, for this variation of quantitative description, is asked with information entropy theory Go out singular value entropy[17].Each intrinsic mode function (Intrinsic mode function, IMF) has different frequency contents, and Singular value after decomposition is also different, is normalized 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, the transfer learning of feature based
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, and mapping relations, as Xs ∪ X are indicated 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, to shared subspace, makes full use of feature samples are transportable to know with target domain characterization sample set Feature Mapping Know, improves cross-cutting learning ability.
The semi-supervised migration constituent analysis of 3.2 multinuclears
3.2.1 multinuclear 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 multinuclear expression formula of different Kernels is
In formula, M is the number of kernel function, the weights a of kernel functionm>=0, and a1+a2+…+aM=1.
According to Mercer theorems 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 multinuclear kernel function
Ki,j=aKpoly+(1-a)Krbf (11)
Wherein, a is multinuclear 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 representations are
In formula, nsIt is source domain feature samples number, nTIt is target domain characterization number of samples.
To reduce MMDE computational complexities, 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 indicates to be defined on source domain, aiming field and cross-domain nuclear matrix respectively.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)
For the relevance for improving in class label and Reproducing Kernel Hilbert Space between feature samples, SSTCA methods use 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 xjThe distance minimization after being converted through Feature Mapping, feature samples constraint function For
Wherein, x* iAnd x* jIt is x respectivelyiAnd xjFeature samples after Feature Mapping.Laplacian Matrix L=D-M, works as input Feature samples xiWith xjMeet within the scope of k neighbours, M=[mij], 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), multinuclear SSTCA method object functions are
In formula, tab indexes matrix K* yy=γ Kyy+ (1- γ) I, γ are characterized sample class tab indexes parameter, trace (WTW it is) regularization term, μ is regularization parameter, and λ is to keep the tradeoff coefficient of data local characteristics, and λ >=0.
Seek the object function of formula (22), you can obtain optimum mapping nuclear matrix W.
The application of the method for the present invention and analysis
1, experiment condition and parameter
Experimental data comes from U.S. Case Western Reserve University electrical engineering laboratory rolling bearing data center.Test system 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.
This experiment selects motor drive terminal deep-groove ball rolling bearing, model SKF6205, sample frequency 48kHz to 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 shroud, 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 mode A is 0hp, 1797r/ Min set of data samples；2) operating mode B is 1hp, 1772r/min set of data samples；3) operating mode C is 2hp, 1750r/min data sample Collection；4) operating mode 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 mode as target numeric field data, Other and so on.
The different operating mode rolling bearing set of data samples of table 2 are constituted
2, multiple features construct
First, several IMF are obtained using VMD, mode number N are determined by centre frequency using observation, with 1hp, For the rolling bearing inner ring fault vibration signal of 1772r/min operating modes carries out VMD operations, each sample takes vibration signal 4096 Point.Decomposition obtains the centre frequency corresponding to different modalities number N, and the results are shown in Figure 3.
As seen from Figure 3, when mode number N is more 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 incomplete, that is, owes decomposing phenomenon, therefore determines that mode number is 4.Mould After state number is determined, VMD results 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 ease of subsequent processing, IMF The few supplement null vector of number, keeps the intrinsic dimensionality of extraction consistent.Meanwhile extract bearing vibration signal 7 time domains and 17 frequency domain character indexs refer to 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 judges
According to statistical theory, MMDE methods 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 are classified.
3 Largest Mean Variant statistical value table of table
4, multinuclear SSTCA experimental results
1) multinuclear experimental contrast analysis
Using SVM as grader, the SSTCA of multinuclear is subjected to contrast experiment from the SSTCA methods of different monokaryon kernel functions. Source domain feature samples collection chooses either simplex condition or multi-state data set, by taking C/B as an example, multinuclear with target domain characterization sample set in experiment In SSTCA, gaussian radial basis function and polynomial kernel parameter are 10, and multinuclear coefficient a is 0.9, and regularization μ is that 1, k neighbour's values are 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 multinuclear side SSTCA-SVM The equal highest of fault recognition rate of method.Its very big reason is that multinuclear kernel function is unbalanced in processing source domain data and target numeric field data When have preferable advantage.
2) multinuclear SSTCA and other algorithm comparative analyses
(1) it is based on bearing vibration feature under variable working condition, multinuclear 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 mode C, aiming field to use work The feature set of condition B obtains that test results are shown in figure 5 after different characteristic mapping method and SVM training patterns.
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, Multinuclear SSTCA is continuously improved with KPCA, PCA 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 multinuclear SSTCA methods totally keeps flat Steady and slightly raising, and it is above two methods of KPCA and PCA.
(2) multinuclear SSTCA-SVM is compared with TSVM, LapSVM non-migrating learning method, test result accuracy rate such as 5 institute of table Show.
5 multinuclear 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 multinuclear SSTCA-SVM methods 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) multinuclear SSTCA and the field MIDA, SA, ITL, GFK, SSA and TCA adaptation method[21]Comparison.Recruitment respectively Condition C, AC, ACD use operating mode 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 methods can obtain preferable test result in operating mode 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 methods It tries accuracy rate and is also far below multinuclear SSTCA-SVM methods.Its reason is that multinuclear SSTCA-SVM improves feature using HSIC methods Sample and sample class label relevance, this is conducive to the classification of target numeric field data.On the other hand, multinuclear SSTCA-SVM methods Multinuclear 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 drawn the following conclusions by above 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 build rolling bearing multi-domain characteristics collection can more characterize rolling to obtain The feature of dynamic bearing state.
(2) introducing SSTCA methods complete the transfer learning task between not same area, and construct the side SSTCA of multinuclear kernel function Method improves bearing vibration Feature Mapping ability under variable working condition, and then reduces feature samples distributional difference between domain.
(3) Largest Mean difference embedding grammar is used to weigh source domain feature samples and the similar journey between target domain characterization sample Degree, and propose to select source domain data using Largest Mean Variant statistical value, improve the recognition accuracy to target numeric field data.
(4) multinuclear SSTCA methods are compared with other Feature Mapping methods, field adaptation method, non-migrating learning method. Experiment shows multinuclear SSTCA-SVM methods 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 of feature based transfer learning, which is characterized in that the reality of the method Now process is：
(1) feature extraction：
VMD operations are carried out to known operating mode and unknown operating mode rolling bearing multimode vibration signal, decomposition is determined with observation IMF number builds 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 is built：
By the time domain of known operating mode bearing vibration signal, frequency domain character in (1), 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 mode；
(3) the semi-supervised migration constituent analysis of multinuclear：
Source domain training characteristics sample set in (2) and aiming field test feature sample set common trait are mapped to reproducing kernel In the spaces Hilbert, use within this space MMDE methods measurement source domain training characteristics sample and aiming field test feature sample it Between Largest Mean distance；
Known operating mode rolling bearing multimode vibration signal can be reselected by the Largest Mean Distance Judgment, selection is suitable Known operating mode rolling bearing multimode vibration signal assist the study of unknown operating mode rolling bearing multimode vibration signal, improve pair Aiming field vibration signal data classification recognition capability；
(4) rolling bearing fault diagnosis under variable working condition：
Will in the source domain training characteristics sample set input SVM in (3) after mapping, while with GA algorithms 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 of feature based transfer learning according to claim 1, special Sign is：
In step (1), VMD operations are carried out to the vibration signal, the IMF number decomposed is determined with observation, IMF is built Matrix, and carry out SVD and obtain singular value, while seeking singular value entropy；Its detailed process is：
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) (1)
In formula, δ (t) is impulse function；T in above formula indicates the time；
Centre frequency e is mixed-estimates 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 is expressed as：
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 ensures that the reconstruction accuracy of signal, Lagrangian make constraints keep stringency；The drawing of extension Ge Lang expression formulas are
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；In iteration in order to keep calculating easy, 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, it is { u to obtain its real partk(t)}；
In formula, superscript n indicates update times；
Indicate that time domain vibration signal f (t) transforms to frequency domain vibration signal, subscript ^ expressions are approximately equal to；
Indicate Time-Domain Modal component uk(t) state simulation of frequency region component is transformed to, subscript ^ expressions are approximately equal to.
3. Fault Diagnosis of Roller Bearings under the variable working condition of feature based transfer learning according to claim 2, special Sign is：
In step (3), the Reproducing Kernel Hilbert Space is using multinuclear Kernel, process：
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 weights a of kernel functionm>=0, and a1+a2+…+aM=1；
The Polynomial kernel function with global property is used again and meets the gaussian radial basis function weighted sum of local characteristics, Construct multinuclear kernel function
Ki,j=aKpoly+(1-a)Krbf (11)
Wherein, a is multinuclear 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 of feature based transfer learning according to claim 3, special Sign is：
In step (3), the detailed process of the semi-supervised migration constituent analysis of multinuclear is：
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 representations 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 complexities, 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 indicates to be defined on source domain, aiming field and cross-domain nuclear matrix respectively；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)
For the relevance for improving in class label and Reproducing Kernel Hilbert Space between feature samples, SSTCA methods use Xi Er Bert Schmidt's separate standards are weighed, 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 matrix1 is the column vector for being all 1, and I is unit matrix；KyyThe core being defined on source domain feature samples Matrix；
To realize input feature vector sample xiWith xjThe distance minimization after being converted through Feature Mapping, feature samples constraint function are
Wherein, x* iAnd x* jIt is x respectivelyiAnd xjFeature samples after Feature Mapping；Laplacian Matrix L=D-M, as the spy of input Levy sample xiWith xjMeet within the scope of k neighbours, M=[mij], 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 object function of multinuclear SSTCA are
In formula, tab indexes matrix K* yy=γ Kyy+ (1- γ) I, γ are characterized sample class tab indexes parameter, trace (WTW it is) regularization term, μ is regularization parameter, and λ is to keep the tradeoff coefficient of data local characteristics, and λ >=0；
Seek the object function of formula (22), you can obtain optimum mapping nuclear matrix W.
5. rolling bearing fault diagnosis side under the variable working condition of feature based transfer learning according to claim 1,2,3 or 4 Method, it is characterised in that：The known operating mode and unknown operating mode rolling bearing multimode include：Different rotating speeds and different loads operating mode Under normal, inner ring different faults degree, outer shroud different faults degree, rolling element different faults degree.
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