CN109582003A - Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis - Google Patents

Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis Download PDF

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CN109582003A
CN109582003A CN201811462243.1A CN201811462243A CN109582003A CN 109582003 A CN109582003 A CN 109582003A CN 201811462243 A CN201811462243 A CN 201811462243A CN 109582003 A CN109582003 A CN 109582003A
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陶新民
任超
姜述杰
郭文杰
李青
刘锐
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00Testing or monitoring of control systems or parts thereof
    • G05B23/02Electric testing or monitoring
    • G05B23/0205Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0259Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
    • G05B23/0262Confirmation of fault detection, e.g. extra checks to confirm that a failure has indeed occurred
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    • G01M13/00Testing of machine parts
    • G01M13/04Bearings
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    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, it is characterised in that: method includes the following steps: (1) collects the segmented rear composing training sample of vibration signal under bearing difference work shape;(2) feature extraction is carried out to the training sample that (1) obtains;(3) feature normalization of (2) is handled;(4) cluster labels collection is acquired using density peaks cluster to all characteristic sets of (3);(5) divergence and the interior divergence regularization term of cluster between using the cluster pseudo label of (4) to construct Local Clustering, and combined with divergence in the class scatter and class for having exemplar in FDA, determine final projection vector;(6) projection vector of (5) is utilized to seek projection set of the label characteristics collection in dimension reduction space;(7) the projection set training extreme learning machine of (6) is utilized;(8) vibration signal of collection is input in model after (2), (3) and (5) processing and determines operating condition.The present patent application is applied to the fault identification problem of bearing apparatus.

Description

Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis
Technical field:
The present application relates to a kind of bearing apparatus fault diagnosis fields, more particularly to one kind to be based on pseudo label semi-supervised kernel Local Fei Sheer discriminant analysis bearing failure diagnosis.
Background technique:
In industrial circle, in order to increase the reliability of equipment performance, reduction is caused under yield due to mechanical disorder The monitoring of the probability of drop, state of runtime machine is increasingly valued by people.Rotating machinery is in industrial department using the most Extensive one kind mechanical equipment, many machinery such as steam turbine, compressor, blower and milling train belong to this kind.However, its core Component bearing usually influences its normal work due to various various forms of failures, can even cause sometimes due to certain failure serious Disastrous accident, and result in significant economic losses, therefore the research for carrying out fault diagnosis has highly important reality Meaning.
Mechanical fault diagnosis is exactly to utilize signal processing and analyzing technology to the signal containing fault message measured, It finds out characteristic parameter related with failure and is differentiated using real-time technique state of these characteristic parameters to equipment.Here it relates to And to two aspect the problem of, first is that utilize signal processing technology carry out feature extraction;Second is that being carried out using mode identification technology Fault diagnosis.In terms of signal characteristic abstraction, be broadly divided into: the mean value of the temporal signatures of signal such as signal, mean-square value, peak value, Kurtosis and flexure etc.;Frequency domain character of signal such as energy spectrum, AR power spectrum etc.;And the time-frequency characteristics of signal such as wavelet analysis, Hilbert transformation and Short Time Fourier Transform etc..In order to fully characterize different classes of failure and then improve discrimination, just A variety of different characteristics are needed to be merged, this causes computation complexity to improve same but also the dimension of feature vector greatly increases When also extend time of fault diagnosis.Therefore how to be able to achieve reasonable Data Dimensionality Reduction is just particularly important.Principal component point The classic algorithm of (Principal Components Analysis, PCA) as Data Dimensionality Reduction is analysed, because feature can be effectively removed Between linearly related keep the main information of primitive character simultaneously and be widely used in fault diagnosis field.Locality preserving projections (Locality Preserving Projections, LPP) is the linear approximation of nonlinear method LaplacianEigenmap, As a kind of new subspace analysis method, initial data non-linearity manifold office is difficult to keep because can solve principal component analytical method The problem of portion's structure and be used widely.However, PCA and LPP belong to unsupervised dimension-reduction algorithm, in dimensionality reduction learning process It fails to using known classification information to make the feature after dimensionality reduction be unfavorable for the differentiation between classification.Fisher discriminant analysis is made There is supervision dimension reduction method for one, because by maximization class scatter and divergence in class can be minimized using existing classification information Method optimizing reduced order subspace so that the feature after dimensionality reduction is conducive to the differentiation between classification and then is widely used in various classification Field.Although the feature after FDA algorithm dimensionality reduction is conducive to improve the classification performance of algorithm, there is supervision dimensionality reduction since it belongs to Method, therefore need a large amount of label informations that could obtain preferable Generalization Capability in advance.However in practical application, especially event Hinder diagnostic field, being limited to obtain by various conditions largely has the sample of label very difficult, therefore usually occurs only a small amount of The situation of a large amount of unlabeled exemplars residues with the presence of exemplar.Enough there are exemplar, FDA and its improvement due to lacking Algorithm usually will appear over-fitting and then lead to Generalization Capability degradation.Therefore, how to utilize these largely without mark This guidance of signed-off sample has supervision dimensionality reduction study to become the emphasis that scholars pay close attention to.In consideration of it, in order to using largely without label sample This raising algorithm differentiates that performance, the present invention carry out clustering to sample using the clustering algorithm based on density peaks first and obtain Then pseudo label keeps unlabeled exemplars by divergence in increase standardization item to the class of part FDA algorithm and class scatter Cluster structural integrity, finally by with maintain exemplar class scatter maximize and class in divergence minimum part FDA algorithm objective function solves best projection vector together.Through proposed by the present invention based on pseudo label semi-supervised kernel part Coefficient vector after Fisher discriminant analysis method dimensionality reduction has better separating capacity and then is conducive to sentencing for subsequent classifier Not, so that performance of fault diagnosis is greatly improved.
In terms of mode identification method, neural network and algorithm of support vector machine (SVM) are because of its good non-linear differentiation Ability has been widely applied to fault diagnosis field.But the above method need training parameter it is more, cause the time longer and It is easily ensnared into locally optimal solution.Extreme learning machine (extreme learning machine) ELM as it is a kind of it is easy to use, Effective single hidden layer feedforward neural network learning algorithm, do not need the input weight for adjusting network during the execution of the algorithm and The biasing of hidden member, and unique optimal solution can be generated, therefore have the advantages that pace of learning is fast and Generalization Capability is good, it is very suitable Together in the very high fault diagnosis field of the classification problem under big data era, especially requirement of real-time.For this purpose, the present invention plans It is combined based on the Fisher discriminant analysis of pseudo label semi-supervised kernel part and extreme learning machine to realize the fast of bearing apparatus failure Speed diagnosis can realize Data Dimensionality Reduction from signal processing angle, when improving diagnosis while keeping different classes of separating capacity Effect;Slave pattern identifies angle again can realize the quick diagnosis of fault category by extreme learning machine, reduce runing time.
Summary of the invention:
1, it is based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, it is characterised in that: this method The following steps are included:
(1) it is collected using the vibration acceleration sensor being mounted on the spring bearing upper end casing of induction conductivity output shaft Vibration signal of the bearing under different work shapes, if there are four types of work shapes altogether: normal condition, inner ring malfunction, outer ring failure shape State and rolling element malfunction, when being respectively then that 1024 segment processings obtain entire to the signal progress length under various operating conditions Domain signal set Sm∈R1024×m, wherein m indicates the number of entire time-domain signal training sample set, Sn∈R1024×nTo there is label Time-domain signal sample set, wherein n indicates the number n < < m of label time-domain signal training sample set;
(2) feature extraction is carried out to the training samples information that step (1) obtains, obtains to shake under the various operating conditions of effecting reaction Dynamic signal characteristic set, if sharing d feature, then entire training sample characteristic set X* m∈Rd×m;There is exemplar feature set Close X* n∈Rd×n
(3) the feature training sample set obtained to step (2) is standardized, and makes the numerical value of each characteristic index Range determines that in mean value be 0, in the standardized normal distribution section that variance is 1;Entire training sample characteristic set after then normalizing Xm∈Rd×m;There is exemplar characteristic set X after normalizationn∈Rd×n
(4) the entire training sample characteristic set X after the normalization obtained to step (3)mIt is clustered and is calculated using density peaks Method acquires cluster labels setAnd whether be boundary point identification sets platform
(5) the cluster labels set obtained using step (4)With identification sets platformBetween construction Local Clustering Divergence SulbWith divergence S in Local ClusteringulwRegularization term, and have exemplar X in the Fisher discriminant analysis of partnInstitute is right The local class scatter S answeredlbDivergence S in drawn game categorylwIt optimizes together, determines final projection vector Tss-KLFDA∈ Rm×r, wherein dimensionality reduction dimension is r < < d;
(6) projection vector T obtained in step (5) is utilizedss-KLFDASolve XmProjection vector in r dimension reduced order subspace Set Zm∈Rr×mAnd XnProjection vector set Zn∈Rr×n
(7) projection vector set Z after the dimensionality reduction acquired in step (6) is utilizedn∈Rr×nTraining extreme learning machine model Melm
(8) it is collected by the vibration acceleration sensor being mounted on the spring bearing upper end casing of induction conductivity output shaft The vibration signal of the bearing is 1024 segment processings according to the method for step (2) calculating feature vector through length X is obtained after method normalization by step (3)new∈Rd×1, the projection vector T that is obtained using step (5)ss-KLFDASolve Xnew? R ties up the projection vector set Z in reduced order subspacenew∈Rr×1It is then input to trained model MelmThe middle current bearing of determination Final working condition.
2, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that be to extract vibration signal time-domain snapshots 12 statistics to method used by the feature extraction in step (2) Feature, including average value, root mean square, variance, standard deviation, rectified mean value, peak-to-peak value, kurtosis value, peak factor, wave The shape factor, the kurtosis factor, the pulse factor, the nargin factor carry out 5 layers of small wavelength-division to vibration signal time-domain snapshots using DB4 small echo The energy spectrum and energy spectrum entropy totally 12 dimension fault signatures of 5 details coefficients and 1 approximation component are solved and extracted, and vibration is believed Number time-domain snapshots carry out 5 floor empirical mode decomposition and extract the energy spectrum and energy spectrum entropy of 5 Intrinsic mode functions and 1 remainder Totally 12 dimension fault signature, amounts to d=32 dimensional feature after combination.
3, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that method used by being standardized in step (3) to each index value is z-score method, tool Steps are as follows for body: settingTo any indexIt is standardized place Method used by managing is as follows:
μ is recorded simultaneouslyi, σi, the standardization of i=1 ..., d in case of new samples.
4, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that acquisition cluster labels Ji Tai in step (3)And whether be boundary point identification sets platformUsed method is utilized based on density peaks clustering algorithm to all sample set XmClustering is carried out, Specific step is as follows: data-oriented collection Xm={ x1, x2..., xi..., xm}∈Rd×m, wherein xi∈RdRepresent i-th of sample to Amount, for each sample point xiIts local density values ρ is quantitatively calculated firstiWith Distance Density higher sample point away from From δi, embody are as follows:
dijFor xiAnd xjEuclidean distance, dcFor distance is truncated, it is arranged so that the average distance number of each data point is The 2% of data point sum, further setsIt indicatesThe lower sequence of descending arrangement, i.e. satisfaction:Then
The local density values ρ of all sample points is obtainediWith the distance δ of the higher sample point of Distance DensityiAfterwards, with part Density piFor horizontal axis, distance δiDraw X-Y scheme for the longitudinal axis, be called decision diagram, choose those with higher local density and The point of relatively high distance is as cluster centre, it is determined that after cluster centre, remaining each point is attributed to apart from it most Close density is higher than cluster belonging to its point, if XmInclude ncA cluster,For the corresponding data point of each cluster centre Number, i.e. mjA sample is the cluster centre of j-th of cluster,For the cluster labels set of all data points, i.e., ciIndicate data set XmIn i-th of data point xiBelong to ciA cluster, its initialization definitions are as follows:
dcPoint set, then the highest point of density in its borderline region is found for each cluster, and with the close of the point Degree is used as valve primaryChang screens the noise spot of the cluster, i.e., only retains the point that density in cluster is greater than or equal to the threshold values, enableNormal point and boundary point identification are represented, if hi=1 is expressed as boundary point, otherwise hi=0 is expressed as normal point,
4, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that T in step (5)ss-KLFDACalculation method is as described below:
Divergence S between construction Local ClusteringulbS is expressed as with matrix formulb=XmLulbXm T, wherein Lulb=Dulb-Wulb∈ Rm×m, Dulb∈Rm×mIt is a diagonal matrix, its i-th of diagonal entry isLikewise, office Portion clusters interior divergence SulwS can also be expressed as with matrix formulw=XmLulwXm T, wherein Lulw=Dulw-Wulw∈Rm×m, Dulw ∈Rm×mIt is a diagonal matrix, its i-th of diagonal entry is
Here Wulb, WulwIt is the matrix of m × m, and
WhereinRepresentative belongs to cluster ciSample size,σi=| | xi-xi (k)| |, xi (k)It is xiKth=7 neighbours, | | | | indicate Euclidean distance;
Construct local class scatter matrix SlbScatter Matrix S in drawn game categorylw, SlbIt can also be expressed as with matrix form Slb=XnLlbXn T.Wherein, Llb=Dlb-Wlb∈Rn×n, Dlb∈Rn×nIt is a diagonal matrix, its i-th of diagonal entry isLikewise, SlwS can also be expressed as with matrix formlw=XnLlwXn T.Wherein, Llw=Dlw-Wlw∈ Rn×n, Dlw∈Rn×nIt is a diagonal matrix, its i-th of diagonal entry isHere Wlb, WlwIt is n The matrix of × n, and
It indicates in class yiThere is the quantity of exemplar in ∈ { 1,2 ..., c }, c classification number is 4 here,
By LlbAnd LlwIt is extended to m m matrix by zero-padding, is embodied as follows:
Thenβ=0.5,
Construction feature equation KLsslbKa=λ KLsslwKa, above formula can regard generalized eigenvalue λ as1≥λ2>=..., >=λm Generalized eigenvector corresponding with itsGeneralized-grads Theory.K represents nuclear matrix, wherein Kij=κ (xi, xj), κ (xi, xj) it is gaussian kernel function: κ (xi, xj)=exp (- | | xi-xj||22), σ represents core width, here σ= 0.5;Therefore, final projection vector Tss-KLFDA∈Rm×rIt is expressed asφ(Xm) represent XmIn nuclear space Projection vector.
5, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that the method for solving of projection vector of the step (6) in r dimension reduced order subspace is as follows: for new samples x, The feature representation of reduced order subspace is as follows:
X → z=TT ss-KLFDAφ (x)=(a1, a2..., ar)Tφ(Xm)Tφ(x)
=(a1, a2..., ar)TK (:, x)
Enable Ta ss-KLFDA=(a1, a2..., ar), then above formula can be further expressed asHere K (:, x)=[κ (x1, x), κ (x2, x) ..., κ (xm, x)]T
6, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that M in step (7)elmModel is trained by following method: hidden layer number L is determined first, output layer Number is classification number c, is set as 4, as 4 kinds of operating conditions, random initializtion input weight and bias matrix here, is set as defeated Enter weight PInput∈RL×r, hidden neuron biasing Binput∈RL×1, extend BinputFor B ∈ RL×(n), calculate hidden layer output matrix H ∈RL×(n):
Construct data category matrix of consequence T ∈ R(n)×c, tij=1, work as xijWhen ∈ j class, other are -1, acquire output weight Matrix β ∈ RL×c, β=H+T, H+For the Moore-Penrose generalized inverse matrix of H, extreme learning machine mould after training is finally obtained Type: Melm={ Pinput, Binput, β };
7, according to claim 1 to be examined based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing fault It is disconnected, which is characterized in that the feature vector, X of new samples in step (8)newDetermination using the feature extraction side in step (2) Method, that standardization processing method utilizes is the μ of step (3) storagei, σi, i=1,2 ... d carry out z-score standardization, utilize step Suddenly the T that (5) obtainss-KLFDACalculate XnewProjection vector Z in r dimension reduced order subspacenew∈Rr×1, the determination of end-state by MelmModel is determining,
Ttest=Htest T×β
Take max (Htest) corresponding to subscript be current bearing equipment working condition output.
Beneficial effects of the present invention:
1. Method for Bearing Fault Diagnosis of the invention, feature extracting method is using can be conducive to improve classification performance Have a supervision dimension reduction method, while making full use of unlabeled exemplars information guiding to have label dimensionality reduction using semi-supervised learning mechanism It practises, the dimensionality reduction feature made has more distinction, and can effectively avoid FDA and its innovatory algorithm because receiving exemplar quantity Limit the over-fitting occurred.
2. Method for Bearing Fault Diagnosis of the invention carries out cluster point to sample using the clustering algorithm based on density peaks Analysis obtains pseudo label, and compared with K-means algorithm and spectral clustering, which does not need specified cluster number in advance and initial Cluster centre and the cluster that can recognize that various shape and size, therefore the pseudo label being very suitable under cluster number unknown situation Solve problems.In addition, the extreme learning machine that the present invention is also exceedingly fast using training speed is greatly improved as the method for pattern-recognition The timeliness of fault diagnosis.Therefore the present invention combines two kinds of algorithms, can improve diagnosis efficiency from signal processing angle, from Pattern-recognition angle can be reduced runing time again.
3. Method for Bearing Fault Diagnosis of the invention, by increasing divergence and class scatter in regularization term to class simultaneously Mode keeps unlabeled exemplars to cluster structural integrity, only considers that the global and local space structure of holding is consistent with PCA and LPP Property it is different, this method can greatly enhance separating capacity between the class of dimensionality reduction feature and have good robustness.
Detailed description of the invention:
Attached drawing 1 is that cluster labels determine schematic diagram in the embodiment of the present invention 2.
Attached drawing 2 is that boundary point label determines schematic diagram in the embodiment of the present invention 2.
Attached drawing 3 is rotating machinery simulation test experiment platform structure figure in the embodiment of the present invention 5.
Attached drawing 4 is the vibration signal time-domain snapshots figure in the embodiment of the present invention 5 under each operating condition.
Attached drawing 5 is the preceding bidimensional characteristic profile in the embodiment of the present invention 5 after PCA projects dimensionality reduction.
Attached drawing 6 is the preceding bidimensional characteristic profile in the embodiment of the present invention 5 after LPP projects dimensionality reduction.
Attached drawing 7 is the preceding bidimensional characteristic profile in the embodiment of the present invention 5 after FDA projects dimensionality reduction.
Attached drawing 8 be in the embodiment of the present invention 5 after the Fisher discriminant analysis dimensionality reduction of pseudo label semi-supervised kernel part before two Dimensional feature distribution map.
Attached drawing 9 is PCA, LPP, FDA and inventive algorithm classification performance comparison diagram in the embodiment of the present invention 5.
Attached drawing 10 is temporal signatures algorithms of different classification performance comparison diagram in the embodiment of the present invention 6.
Attached drawing 11 is wavelet field feature algorithms of different classification performance comparison diagram in the embodiment of the present invention 6.
Attached drawing 12 is EMD characteristics of decomposition algorithms of different classification performance comparison diagram in the embodiment of the present invention 6.
Attached drawing 13 is temporal signatures and the combination algorithms of different classification performance comparison of small echo characteristic of field in the embodiment of the present invention 6 Figure.
Attached drawing 14 is temporal signatures and EMD characteristic of field combination algorithms of different classification performance comparison diagram in the embodiment of the present invention 6.
Attached drawing 15 is wavelet field feature and the combination algorithms of different classification performance comparison of EMD characteristic of field in the embodiment of the present invention 6 Figure.
Attached drawing 16 is the performance comparison figure of algorithms of different under different dimensionality reduction dimension variations in the embodiment of the present invention 6.
Attached drawing 17 is the nicety of grading comparison in the embodiment of the present invention 6 after different dimension reduction methods and different classifications algorithm combination Figure.
Specific embodiment:
Embodiment 1:
Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, the local Fisher differentiates Parser comprises the following specific steps that:
Enable xi∈RdI-th of sample vector is represented, corresponding class label is yi∈ { 1,2 ..., c }, c are classification number.It enables Xn={ x1, x2..., xi..., xn}∈Rd×nRepresentative has exemplar data matrix, Xm={ x1, x2..., xi..., xm}∈Rd×m Population sample data matrix is represented, wherein m indicates the quantity of training sample, and n is the quantity for having exemplar, m > n.Enable Xm= {Xn, Xu, XuIt is the set of unmarked sample.Assuming that zi∈Rr(1≤r≤d) is by matrix T ∈ Rd×rConvert obtained low-dimensional The projective representation of subspace: zi=TTxi
Local Fisher Discrimination Analysis Algorithm (LFDA) can be stated with following optimization problem:
Here, Slb, Slw∈Rd×dRespectively indicate Scatter Matrix in local class scatter matrix drawn game category, definition difference Are as follows:
Here Wlb, WlwIt is the matrix of n × n, and
It indicates in class yiThere are the quantity of exemplar, A in ∈ { 1,2 ..., c }ijIt is heuristic based on local scaleization xiAnd xjBetween similarity measurement, AijIt is defined as
Parameter σiIndicate xiLocalization scale parameter, be defined as σi=| | xi-xi (k)||
Wherein, xi (k)It is xiKth neighbour, be usually arranged as 7, | | | | indicate Euclidean distance.
Above-mentioned optimization problem can be solved with following generalized eigenvalue problem:
Assuming that final generalized eigenvalue is ordered as λ by sequence of successively decreasing1≥λ2…≥λd
Wherein λi, i=1,2 ..., d are corresponding generalized eigenvectorsGeneralized eigenvalue, most Eventually, TLFDAIt can indicate are as follows:
The matrix of LFDA indicates
In order to facilitate our algorithm of description, we furthermore present the expression matrix form of LFDA.SlbIt can use down The pairs of form in face is expressed:
Equally, SlbS can also be expressed as with matrix formlb=XnLlbXn T
Wherein, Llb=Dlb-Wlb∈Rn×n, Dlb∈Rn×nIt is a diagonal matrix, its i-th of diagonal entry is
Likewise, SlwS can also be expressed as with matrix formlw=XnLlwXn T
Wherein, Llw=Dlw-Wlw∈Rn×n, Dlw∈Rn×nIt is a diagonal matrix, its i-th of diagonal entry is
Therefore, the objective function of LFDA can be further expressed as with matrix form
Embodiment 2:
Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, the pseudo label generation is made Density peaks clustering algorithm comprises the following specific steps that:
Data-oriented collection Xm={ x1, x2 ..., xi..., xm}∈Rd×m, wherein xi∈RdI-th of sample vector is represented, for Each sample point xiIts local density values ρ is quantitatively calculated firstiWith the distance δ of the higher sample point of Distance Densityi, it Be defined as follows:
Here parameter dcIt need to be specified in advance for truncation distance, dijRepresent xiAnd xjEuclidean distance.
Further setIt indicatesThe lower sequence of descending arrangement, i.e. satisfaction:
Obviously, from the equations above it is not difficult to find that be locally or globally for maximum sample point for density value, they δiIt can be than the δ of other sample pointsjIt is worth much bigger.Therefore, those δiThe very big sample point of value is probably cluster centre.
The local density values ρ of all sample points is obtainediWith the distance δ of the higher sample point of Distance DensityiAfterwards, with part Density piFor horizontal axis, distance δiX-Y scheme is drawn for the longitudinal axis, is called decision diagram.Choose those with higher local density and The point of relatively high distance is as cluster centre.After cluster centre has been determined, remaining each point is attributed to apart from it most Close density is higher than cluster belonging to its point.If XmInclude ncA cluster,For the corresponding data point of each cluster centre Number, i.e. mjData point is the cluster centre of j-th of cluster.For the cluster labels set of all data points, i.e., ciIndicate data set XmIn i-th of data point xiBelong to ciA cluster.Its initialization definitions are as follows:
For data set XmIn all local densities compare xthiIn the big data point of a data point with xiNearest number Strong point number, is defined as follows:
ForSample point, cluster labels is defined as:
The determining strategy of cluster labels for ease of description, provides cluster labels schematic diagram here.(serial number as shown in Figure 1 For qi, arranged according to density size descending), it is assumed that sample point 1 and sample point 2 are determining cluster centre, respectively represent cluster 1 With cluster 2.The cluster labels of sample point 3 should be clustered according to belonging to the point for being higher than it away from nearest density and are consistent.No Hardly possible discovery is exactly to put 1, therefore 3 cluster labels of sample point are exactly 1 apart from the point that nearest density is higher than it with sample point 3.Together Reason, the cluster labels of sample point 4 should be consistent with the point 3 that is higher than it away from nearest density, as cluster 1.And so on, sample The cluster labels of this point 5 are 2, and the cluster labels of sample point 6 are also 2.
After the cluster labels of all sample points determine, for erased noise point, algorithm is each cluster definition first One borderline region is assigned to the cluster but is less than d at a distance from the point in other clusterscPoint set.It then is every A cluster finds the highest point of density in its borderline region, and the noise of the cluster is screened using the density of the point as threshold values Point only retains the point that density in cluster is greater than or equal to the threshold values.It enablesRepresent cluster core and cluster Halo mark, the former corresponds to normal point, and the latter corresponds to boundary point, if hi=1 is expressed as boundary point, otherwise hi=0 indicates to be positive Chang Dian.It enablesFor sample xiAffiliated cluster ciCorresponding density threshold, then
For ease of description, schematic diagram is equally provided here.As illustrated in fig. 2, it is assumed that belong to cluster 1 in sample point 7 with The cluster of point 5 of other clusters 2 is less than dc, then determine that the sample point 8 of cluster 1 is noise spot as threshold value using the density for putting 7.
It should be noted that parameter d in algorithmcInfluence of the determination to cluster result it is very big, if dcIt is excessive to be easy to cause The local density values of sample point are all approximately equal to be divided into same cluster, generate and owe cluster phenomenon.If dcIt is too small, often It is a to cluster the sample point meeting for including seldom, it is more likely that the case where same cluster is divided into several parts occur, generated Cluster phenomenon.Herein according to experience, d is setcTo make the average distance number of each data point be the 1%- of data point sum 2%.
Embodiment 3:
Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, the pseudo label semi-supervised kernel Local Fisher discriminant analysis Method for Bearing Fault Diagnosis comprises the following specific steps that:
Using based on density peaks clustering algorithm to all sample set XmClustering is carried out, the cluster of sample point is obtained Tally set platformAnd whether be boundary point logo collectionWhat needs to be explained here is that the number n of clusterc Do not need identical as classification number, this can better adapt to multi-modal data distribution situation.According to above- mentioned information construction office The poly- class scatter S in portionulbWith divergence S in Local ClusteringulwRegularization term embodies as follows:
Here Wulb, WulwIt is the matrix of m × m, and
It indicates in cluster ci∈ { 1,2 ..., ncIn sample quantity.
First by LlbAnd LlwIt is extended to m m matrix by zero-padding, is embodied as follows:
Furthermore by SulbAlso S is expressed as with matrix formulb=XmLulbXm T
Wherein, Lulb=Dulb-Wulb∈Rm×n, Dulb∈Rm×mIt is a diagonal matrix, its i-th of diagonal entry is
Likewise, SulwS can also be expressed as with matrix formulw=XmLulwXm T
Wherein, Lulw=Dulw-Wulw∈Rm×m, Dulw∈Rm×mIt is a diagonal matrix, its i-th of diagonal entry is
Then
Therefore, the corresponding generalized eigenvalue problem of semi-supervised part Fisher Discrimination Analysis Algorithm can further indicate that as Under:Introduce the further construction feature equation K of nuclear theoryLsslbKa=λ KLsslwKa, above formula can regard generalized eigenvalue λ as1≥λ2>=..., >=λmGeneralized eigenvector corresponding with itsGeneralized-grads Theory.K represents nuclear matrix, wherein Kij=κ (xi, xj), κ (xi, xj) it is Gaussian kernel letter Number: κ (xi, xj)=exp (- | | xi-xj||22), σ represents core width, here σ=0.5;Therefore, final projection vector Tss-KLFDA∈Rm×rIt is expressed asφ (Xm) represent XmIn the projection vector of nuclear space.
For new samples x, the feature representation of reduced order subspace is as follows:
X → z=TT ss-KLFDAφ (x)=(a1, a2..., ar)Tφ(Xm)Tφ(x)
=(a1, a2..., ar)TK (:, x)
Enable Ta ss-KLFDA=(a1, a2..., ar), then above formula can be further expressed as
Here K (:, x)=[κ (x1, x), κ (x2, x) ..., κ (xm, x)]T
Embodiment 4:
Based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, the extreme learning machine includes Following specific steps:
For a neural networks with single hidden layer, it is assumed that there are n to have label training sample, wherein (zj, tj), zj=[zj1, zj2... zjr]T∈Rr, tj=[tj1, tj2... tjc]T∈Rc.According to yi∈ { 1,2 ..., c } settingOther are 0.This Invention output layer number c=4 has the output of some output layer of the neural networks with single hidden layer of L hidden node can for one To indicate are as follows:
Wherein, g (x) is activation primitive, PInput i=[Pi1, PI, 2..., PI, r] it is input weight, βicFor i-th of hidden layer list The output weight of corresponding c-th of the output unit of member, biIt is the biasing of i-th of Hidden unit.PInput i·zjIndicate PInput iAnd zjIt is interior Product.The target of neural networks with single hidden layer study is the error minimum so that output, can be expressed as There is βi, PInput iAnd bi, so that:
H β=T can be expressed as with matrix.Wherein, H is the output of hidden node, and β is output weight, and T is desired output.
In order to training neural networks with single hidden layer, it is intended that obtainWithSo that
Wherein, i=1 ..., L, this is equivalent to minimize loss function:
Traditional algorithm based on gradient descent method can be used to solve the above problem, but the study based on gradient is calculated Method needs adjust all parameters during iteration, and the training time is longer.And in ELM algorithm, once input weight PInput i With the biasing b of hidden layeriIt is determined at random, the output matrix H of hidden layer is just now uniquely determined.Training neural networks with single hidden layer can turn It turns to and solves a linear system H β=T.And exporting weight beta can be determined:Wherein, H+It is matrix H Moore-Penrose generalized inverse.And the provable solution acquiredNorm be the smallest and unique.
Embodiment 5:
In order to verify the diagnosis performance based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, this Text has carried out following experiments.Experimental data derives from rotating machinery simulation test experiment platform, and structure is as shown in Figure 3.Wherein Chief component are as follows: driving motor, transmission gear, transmission bearing, fictitious load and piezoelectric acceleration vibrating sensor and Acquisition terminal etc..Test middle (center) bearing model N205EM (outer diameter 52mm, internal diameter 25mm, rolling element diameter 7.5mm, number 12 It is a).Bearing revolving speed is 1450r/min, sample frequency 12kHZ.Experiment simulates four kinds of operating statuses of rolling bearing: 1 is normal State;2 inner ring failures;3 outer ring failures;4 rolling element failures.The sample point number of each vibration signal segment is L=1024, often Vibration signal segment under a operating condition is as shown in Figure 4.Experimental situation: Windows7 operating system, at CPU:Intel i7,3.4G Manage device, simulation software Matlab2010b.In addition, 1000 normal samples, inner ring fault sample, outer ring are respectively adopted herein Fault sample and rolling element fault sample are for statistical analysis, and DB4 small echo is used to carry out Decomposition order to vibration signal segment as 5 Wavelet transformation and extract 5 details coefficients and 1 approximation component energy spectrum and energy spectrum entropy[33]Total 6 × 2=12 dimension event Hinder feature and 5 layers of empirical mode decomposition[34]And extract the energy spectrum and energy spectrum entropy of 5 Intrinsic mode functions and 1 remainder Fault signature amounts to 6 × 2=12 dimensional feature, and 32 dimension fault signatures are amounted to after Fusion Features.
In order to verify the dimensionality reduction performance of semi-supervised kernel part Fisher Discrimination Analysis Algorithm, normal sample is taken in experiment, it is interior It encloses fault sample, outer ring fault sample and each 50 samples of rolling element fault sample and constitutes overall data set progress dimensionality reduction, In each classification have exemplar number be 20, non-exemplar number be 30.And it is unsupervised with PCA and LPP two Dimension-reduction algorithm and FDA dimension-reduction algorithm are compared.In view of the dimension of traditional FDA dimension reduction space is limited to classification number, experiment Dimensionality reduction dimension is set r=3 by middle unification.Two before after the projection vector dimensionality reduction that all samples obtain after various algorithm optimizations Dimensional feature is respectively displayed in Fig. 5,6,7 and Fig. 8.The drop that semi-supervised kernel part Fisher distinguished number proposed by the present invention obtains Dimension data has apparent distinction, and not only same class has exemplar to flock together, but also different classes of no label sample This also achieves and efficiently separates.
Pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing is based in order to quantitatively more proposed by the present invention The performance of fault diagnosis, we take normal sample, and inner ring fault sample, outer ring fault sample and rolling element fault sample are each 1000 samples constitute overall data set and are tested.500 sample groups wherein chosen in each classification sample set are combined into Training sample set, remaining 500 sample groups are combined into test sample set.By this paper algorithm with other 7 dimension-reduction algorithms into Row comparative analysis, parameter setting method are same as above.Compare for convenience, in experiment choose nearest neighbor classifier as base classifier simultaneously Performance Evaluating Indexes are used as using correct classification rate (Correct classification rate CCR), are in experimentation Elimination Random Effect, we randomly choose 200 as having exemplar, remaining 300 conduct to the sample of each classification Unlabeled exemplars, count their average correct classification rate for each algorithm independent operating 30 times, and experimental result is as shown in Figure 9.From The experimental result of Fig. 9, which can be seen that algorithm proposed by the present invention, can fully consider that the Local Clustering structure between unlabeled exemplars is believed Breath, and LFDA algorithm dimensionality reduction is instructed by two standardization items of divergence in poly- class scatter and cluster, so that the feature after dimensionality reduction Differentiation performance is stronger, is more advantageous to the classifier classification in later period, therefore obtained classification performance is optimal.
Embodiment 6:
It is proposed by the present invention based on pseudo label semi-supervised kernel part Fei Sheer under different characteristic combined situation in order to compare 12 dimensions statistics temporal signatures, 12 dimension Wavelet Energy Spectrums are respectively adopted in experiment for the classification performance of discriminant analysis bearing failure diagnosis With Energy-Entropy feature, the totally 6 groups of progress events of 12 dimension empirical mode decomposition energy spectrums and Energy-Entropy feature and their combination of two Hinder diagnostic test.As above-mentioned experiment, normal sample, inner ring fault sample, outer ring fault sample and rolling element failure are chosen Each 500 samples composing training data acquisition system of sample, remaining 500 samples composition test sample collection are closed.It is same to use recently Adjacent classifier is correct classification rate (CCR) as base classifier, evaluation index, and other parameter settings are same as above.Dimensionality reduction dimension is r= 3, to eliminate Random Effect, each algorithm independent operating 30 times, experiment, which randomly selects 200 training samples and is used as, every time label Sample, remaining to be used as unlabeled exemplars, final statistical result is as shown in fig. 10-15.From experimental result it can be seen that this hair Bright proposition based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis under different characteristic combined situation Classification performance is superior to other dimension-reduction algorithms, this also indicates that the dimensionality reduction feature of algorithm proposed by the present invention can not only be farthest It maintains and distinguishes information between the class of exemplar, while it is consistent also to have taken into account the Local Clustering structure of unlabeled exemplars to each other Property, so that the coefficient vector after projection all has good separating capacity under different characteristic combination.
Pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis is based in order to more proposed by the present invention Nicety of grading comparative situation under different dimensionality reduction dimensions is based on difference herein by changing from dimensionality reduction dimension r comes from 2 to 11 The nicety of grading of the bearing fault recognition methods of dimension-reduction algorithm, wherein data set still chooses 1000 normal samples, inner ring failure Sample, outer ring fault sample and rolling element fault sample, wherein 500 sample composing training data acquisition systems in each classification, remain Remaining 500 samples composition test sample collection is closed, and feature is the feature combination in three domains.This experiment is equally classified using arest neighbors Device is correct classification rate (CCR) as base classifier, evaluation index, and other parameter settings are same as above.Due to FDA algorithm dimensionality reduction dimension Classification number need to be less than, therefore this experiment only has chosen PCA, LPP, SKMFA, KSFDA algorithm and this paper algorithm carries out performance pair Than analysis.To eliminate Random Effect, each algorithm independent operating 30 times, experiment randomly selects 200 training sample conducts every time There is exemplar, it is remaining to be used as unlabeled exemplars, take average classification accuracy rate as evaluation performance indicator, other parameter settings Ibid, experimental result is as shown in figure 16.The experimental results showed that proposed by the present invention be based on pseudo label semi-supervised kernel part Fei Sheer Classification performance of the discriminant analysis bearing failure diagnosis under different dimensionality reduction dimensions is all substantially better than the axis based on other dimension-reduction algorithms Hold the classification performance of method for diagnosing faults.The experimental result again demonstrates the spy after dimension-reduction algorithm dimensionality reduction proposed by the present invention Sign has good separating capacity.
Finally, in order to verify the bearing fault identity after combining herein based on SS-KLFDA algorithm with different classifications device Can, we use Various Classifiers on Regional algorithm and compare experiment, including support vector machines (one-all), SVM (one-one), RBF nerve net (RBFNN), multi-layer perception (MLP) nerve net (MLP), extreme learning machine ELM.SVM algorithm parameter is adopted With Gaussian kernel, penalty factor and core width are through 5 cross validations using trellis search method from C={ 2-2, 2-1, 1,21, 22, 23, 26, 28, 210And σ={ 0.1,0.5,0.7,1,1.2,1.5,2,2.5,3 } determine, the RBF nuclear parameter of RBF algorithm from σ= { 0.1,0.5,0.7,1,1.2,1.5,2,2.5,3 } it is determined using 5 cross-validation methods, the Hidden unit of RBF, MLP and ELM Number is 30, and dimensionality reduction dimension is r=3, and other parameter settings are same as above, each algorithm independent operating 30 times and to calculate classification accuracy rate flat Mean value, experimental result are as shown in figure 17.It can be found that algorithm of the invention is calculated with various classifiers by the experimental result of the figure Performance of fault diagnosis after method combination is superior to other dimension-reduction algorithms, which further demonstrates that through proposed by the present invention SS-KFDA algorithm can effectively utilize unlabeled exemplars and keep the supervision algorithm study of Local Clustering Structural Guidelines to make to obtain Separating capacity between dimensionality reduction feature and class with higher substantially increases the diagnostic accuracy of the classifier of same a combination thereof.

Claims (8)

1.基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于:该方法包括以下步骤:1. Bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis, characterized in that: the method comprises the following steps: (1)利用安装在感应电动机输出轴的支撑轴承上端机壳上的振动加速传感器收集该轴承在不同工状下的振动信号,设共有四种工状:正常状态、内圈故障状态、外圈故障状态和滚动体故障状态,然后分别对各种工况下的信号进行长度为1024分段处理得到整个时域信号集合Sm∈R1024×m,其中m表示整个时域信号训练样本集合的个数,Sn∈R1024×n为有标签时域信号样本集合,其中n表示有标签时域信号训练样本集合的个数n<<m;(1) Use the vibration acceleration sensor installed on the upper casing of the support bearing of the output shaft of the induction motor to collect the vibration signals of the bearing under different working states. There are four working states: normal state, inner ring fault state, outer ring Fault state and rolling element fault state, and then separately process the signals under various working conditions with a length of 1024 to obtain the entire time domain signal set S m ∈ R 1024×m , where m represents the entire time domain signal training sample set. The number, S n ∈ R 1024×n is the labeled time-domain signal sample set, where n represents the number of the labeled time-domain signal training sample set n<<m; (2)对步骤(1)获取的训练样本信息进行特征提取,得到能有效反应各种工况下振动信号特征集合,设共有d个特征,则整个训练样本特征集合X* m∈Rd×m;有标签样本特征集合X* n∈Rd×n(2) Perform feature extraction on the training sample information obtained in step (1), and obtain a feature set that can effectively reflect the vibration signal under various working conditions. If there are d features in total, then the entire training sample feature set X * m ∈ R d× m ; labeled sample feature set X * n ∈ R d×n ; (3)对步骤(2)获取的特征训练样本集合进行标准化处理,使每个特征指标的数值范围确定在均值为0,方差为1的标准正态分布区间内;则归一化后整个训练样本特征集合Xm∈Rd ×m;归一化后有标签样本特征集合Xn∈Rd×n(3) Standardize the feature training sample set obtained in step (2), so that the numerical range of each feature index is determined within the standard normal distribution interval with a mean of 0 and a variance of 1; then the entire training after normalization The sample feature set X m ∈ R d ×m ; the labeled sample feature set X n ∈ R d ×n after normalization; (4)对步骤(3)获取的归一化后的整个训练样本特征集合Xm利用密度峰值聚类算法求得聚类标签集合以及是否为边界点的标识集合 (4) Using the density peak clustering algorithm to obtain the cluster label set for the normalized entire training sample feature set X m obtained in step (3) and whether it is a set of identifications of boundary points (5)利用步骤(4)得到的聚类标签集合和标识集合构造局部聚类间散度Sulb和局部聚类内散度Sulw正则化项,并同局部Fisher判别分析中的有标签样本Xn所对应的局部类间散度Slb和局部类内散度Slw一起进行优化求解,确定最终投影向量Tss-KLFDA∈Rm×r,其中降维维度为r<<d;(5) Use the cluster label set obtained in step (4) and logo collection Construct the local inter-cluster scatter S ulb and the local intra-cluster scatter S ulw regularization term, and compare it with the local inter-class scatter S lb and the local intra-class scatter corresponding to the labeled sample X n in the local Fisher discriminant analysis The optimization solution is carried out together with the degree S lw , and the final projection vector T ss-KLFDA ∈ R m×r is determined, where the dimension reduction dimension is r<<d; (6)利用步骤(5)中得到的投影向量Tss-KLFDA求解Xm在r维降维子空间中的投影向量集合Zm∈Rr×m,以及Xn的投影向量集合Zn∈Rr×n(6) Use the projection vector T ss-KLFDA obtained in step (5) to solve the projection vector set Z m ∈ R r×m of X m in the r-dimension-reduced subspace, and the projection vector set Z n ∈ of X n R r×n ; (7)利用步骤(6)中求得的降维后投影向量集合Zn∈Rr×n训练极限学习机模型Melm(7) using the projected vector set Z n ∈ R r×n obtained in step (6) after dimensionality reduction to train the extreme learning machine model Melm ; (8)通过安装在感应电动机输出轴的支撑轴承上端机壳上的振动加速传感器收集该轴承的振动信号,经长度为1024分段处理根据步骤(2)的方法计算特征向量经过步骤(3)的方法归一化后得Xnew∈Rd×1,利用步骤(5)得到的投影向量Tss-KLFDA求解Xnew在r维降维子空间中的投影向量集合Znew∈Rr×1然后输入到训练好的模型Melm中确定当前轴承最终的工作状态。(8) Collect the vibration signal of the bearing through the vibration acceleration sensor installed on the upper casing of the support bearing of the output shaft of the induction motor, and calculate the eigenvector according to the method of step (2) after the length of 1024 segment processing X new ∈R d×1 is obtained after normalization by the method in step (3), and the projection vector T ss-KLFDA obtained in step (5) is used to solve the projection vector set Z new of X new in the r-dimension reduction subspace ∈R r×1 is then input into the trained model Melm to determine the final working state of the current bearing. 2.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,对步骤(2)中的特征提取所采用的方法是提取振动信号时域片段12个统计特征,其中包括平均值、均方根、方差、标准差、整流平均值、峰-峰值、峭度值、峰值因子、波形因子、峭度因子、脉冲因子、裕度因子,利用DB4小波对振动信号时域片段进行5层小波分解并提取5个细节分量和1个近似分量的能量谱和能量谱熵共12维故障特征,以及对振动信号时域片段进行5层经验模式分解并提取5个基本模式分量和1个余项的能量谱和能量谱熵共12维故障特征,组合后共计d=32维特征。2. bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis according to claim 1, is characterized in that, the method adopted for feature extraction in step (2) is to extract vibration signal time domain segment 12 Statistical features including mean, rms, variance, standard deviation, rectified mean, peak-to-peak, kurtosis, crest factor, shape factor, kurtosis factor, impulse factor, margin factor, using DB4 wavelets Perform 5-layer wavelet decomposition on the time-domain segment of the vibration signal and extract the energy spectrum and energy spectrum entropy of 5 detailed components and 1 approximate component, a total of 12-dimensional fault features, and perform 5-layer empirical mode decomposition and extraction on the time-domain segment of the vibration signal The energy spectrum and energy spectrum entropy of 5 basic mode components and 1 residual term have a total of 12-dimensional fault features, and a total of d=32-dimensional features after combination. 3.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,步骤(3)中对每个指标值进行标准化处理所采用的方法是z-score法,其具体步骤如下:设对任意指标进行标准化处理所采用的方法如下:3. The bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis according to claim 1, characterized in that, in step (3), the method adopted for standardizing each index value is z-score The specific steps are as follows: for any indicator The method used for normalization is as follows: 同时记录μi,σi,i=1,…,d以备新样本的标准化处理。Simultaneously record μ i , σ i , i=1, . . . , d for standardization of new samples. 4.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,对步骤(3)中获得聚类标签集合以及是否为边界点的标识集合所采用的方法是利用基于密度峰值聚类算法对所有样本集合Xm进行聚类分析,其具体步骤如下:给定数据集Xm={x1,x2,…,xi,…,xm}∈Rd×m,其中xi∈Rd代表第i个样本向量,对于每一个样本点xi首先量化地计算它的局部密度值ρi和距离密度更高的样本点的距离δi,具体表达为:4. The bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis according to claim 1, characterized in that, in step (3), a cluster label set is obtained and whether it is a set of identifications of boundary points The method adopted is to use the density peak-based clustering algorithm to perform cluster analysis on all sample sets X m , and the specific steps are as follows: given data set X m ={x 1 , x 2 ,..., xi ,...,x m }∈R d×m , where x i ∈ R d represents the ith sample vector, for each sample point xi firstly calculate its local density value ρ i and the distance δ from the sample point with higher density i , specifically expressed as: dij为xi和xj的欧式距离,dc为截断距离,设置为使得每个数据点的平均距离个数为数据点总数的2%,进一步设表示的一个降序排列下的序列,即满足:d ij is the Euclidean distance between x i and x j , and d c is the cut-off distance, which is set so that the average number of distances for each data point is 2% of the total number of data points, and further set express A sequence in descending order of , that is: but 得到了所有样本点的局部密度值ρi和距离密度更高的样本点的距离δi后,以局部密度ρi为横轴,距离δi为纵轴绘制二维图形,称其为决策图,选取那些具有较高局部密度和相对较高距离的点作为聚类中心,确定了聚类中心以后,剩余的每个点被归属到距离其最近的密度高于其的点所属聚类,设Xm包含nc个聚类,为各个聚类中心对应的数据点的编号,即第mj个样本为第j个聚类的聚类中心,为所有数据点的聚类标签集合,即ci表示数据集Xm中第i个数据点xi归属于第ci个聚类,它的初始化定义为:为数据集Xm中所有局部密度比第xi个数据点大的数据点中与xi最近的数据点编号,具体定义为:对于的样本点,其聚类标签定义为:当所有样本点的聚类标签确定之后,为了删除噪声点,算法首先为每个聚类定义一个边界区域,即分配到该聚类但与其它聚类中的点的距离小于dc的点的集合,然后为每个聚类找到其边界区域中密度最高的点,并以该点的密度作为阀值来筛选该聚类的噪声点,即只保留聚类中密度大于或等于该阀值的点,令代表正常点和边界点标识,若hi=1则表示为边界点,否则hi=0表示为正常点, After obtaining the local density value ρ i of all sample points and the distance δ i from the sample point with higher density, draw a two-dimensional graph with the local density ρ i as the horizontal axis and the distance δ i as the vertical axis, which is called a decision diagram. , select those points with high local density and relatively high distance as the cluster center. After the cluster center is determined, each remaining point is assigned to the cluster whose nearest density is higher than it. X m contains n c clusters, is the number of the data point corresponding to each cluster center, that is, the m jth sample is the cluster center of the jth cluster, is the cluster label set of all data points, that is, ci indicates that the ith data point xi in the data set X m belongs to the ci th cluster, and its initialization is defined as: make is the number of the nearest data point to xi among all the data points whose local density is greater than the xi th data point in the data set X m , which is specifically defined as: for The sample points of , whose cluster labels are defined as: After the cluster labels of all sample points are determined, in order to remove the noise points, the algorithm first defines a boundary area for each cluster, that is, the points that are assigned to this cluster but whose distances from points in other clusters are less than dc collection, then find the point with the highest density in its boundary area for each cluster, and use the density of this point as the threshold to filter the noise points of the cluster, that is, to keep only the points whose density is greater than or equal to the threshold in the cluster, let Represents normal point and boundary point identification, if hi =1, it is represented as a boundary point, otherwise hi =0 is represented as a normal point, 5.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,步骤(5)中Tss-KLFDA计算方法如下所述:5. bearing fault diagnosis based on pseudo-label semi-supervised nuclear local Fisher discriminant analysis according to claim 1, is characterized in that, in step (5), T ss-KLFDA calculation method is as follows: 构造局部聚类间散度Sulb用矩阵形式表达为Sulb=XmLulbXm T,其中,Lulb=Dulb-Wulb∈Rm×m,Dulb∈Rm×m是一个对角矩阵,它的第i个对角线元素为同样的,局部聚类内散度Sulw也可以用矩阵形式表示为Sulw=XmLulwXm T,其中,Lulw=Dulw-Wulw∈Rm×m,Dulw∈Rm ×m是一个对角矩阵,它的第i个对角线元素为 Constructing the local inter-cluster divergence Sulb is expressed in matrix form as Sulb = X m L ulb X m T , where Lu ulb = Du ulb -W ulb ∈ R m×m , Du ulb ∈ R m×m is a A diagonal matrix whose ith diagonal element is Similarly, the local intra-cluster divergence S ulw can also be expressed in matrix form as S ulw =X m L ulw X m T , where L ulw =D ulw -W ulw ∈R m×m , D ulw ∈R m ×m is a diagonal matrix whose i-th diagonal element is 这里Wulb,Wulw是m×m的矩阵,且Here W ulb , W ulw is an m×m matrix, and 其中代表属于聚类ci的样本数量,σi=||xi-xi (k)||,xi (k)是xi的第k=7近邻,||·||表示欧式距离;in represents the number of samples belonging to cluster ci , σ i =||x i -x i (k) ||, x i (k) is the k=7th nearest neighbor of x i , ||·|| represents the Euclidean distance; 构造局部类间散度矩阵Slb和局部类内散度矩阵Slw,Slb也可以用矩阵形式表达为Slb=XnLlbXn T。其中,Llb=Dlb-Wlb∈Rn×n,Dlb∈Rn×n是一个对角矩阵,它的第i个对角线元素为同样的,Slw也可以用矩阵形式表示为Slw=XnLlwXn T。其中,Llw=Dlw-Wlw∈Rn×n,Dlw∈Rn×n是一个对角矩阵,它的第i个对角线元素为这里Wlb,Wlw是n×n的矩阵,且Construct the local inter-class scatter matrix S lb and the local intra-class scatter matrix S lw , S lb can also be expressed as S lb =X n L lb X n T in matrix form. Among them, L lb =D lb -W lb ∈R n×n , D lb ∈R n×n is a diagonal matrix, and its i-th diagonal element is Similarly, S lw can also be expressed in matrix form as S lw =X n L lw X n T . Among them, L lw =D lw -W lw ∈R n×n , D lw ∈R n×n is a diagonal matrix, and its i-th diagonal element is Here W lb , W lw are n×n matrices, and nyi表示在类yi∈{1,2,…,c}中有标签样本的数量,c类别个数这里为4,n yi represents the number of labeled samples in class y i ∈ {1, 2, ..., c}, the number of c categories is 4 here, 将Llb和Llw通过zero-padding扩展为m×m矩阵,具体表达如下:Extend L lb and L lw to an m×m matrix through zero-padding, and the specific expression is as follows: β=0.5,but β=0.5, 构造特征方程KLsslbKa=λKLsslwKa,上式可以看成是广义特征值λ1≥λ2≥…,≥λm和其对应的广义特征向量的广义特征问题。K 代表核矩阵,其中Kij=κ(xi,xj),κ(xi,xj)为高斯核函数:κ(xi,xj)=exp(-||xi-xj||22),σ代表核宽度,这里σ=0.5;因此,最终的投影向量Tss-KLFDA∈Rm×r表达为φ(Xm)代表Xm在核空间的投影向量。Construct the characteristic equation KL sslb Ka = λKL sslw Ka, the above formula can be regarded as generalized eigenvalues λ 1 ≥λ 2 ≥..., ≥λ m and its corresponding generalized eigenvectors The generalized characteristic problem of . K represents the kernel matrix, where K ij =κ(x i , x j ), κ(x i , x j ) is a Gaussian kernel function: κ(x i , x j )=exp(-||x i -x j || 22 ), σ represents the kernel width, where σ=0.5; therefore, the final projection vector T ss-KLFDA ∈R m×r is expressed as φ(X m ) represents the projection vector of X m in the kernel space. 6.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,步骤(6)在r维降维子空间中的投影向量的求解方法如下:对于新样本x,其降维子空间的特征表达如下所示:6. bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis according to claim 1, it is characterized in that, the solution method of the projection vector in the r-dimensional dimension reduction subspace of step (6) is as follows: for For the new sample x, the feature expression of its dimensionality reduction subspace is as follows: x→z=TT ss-KLFDAφ(x)=(a1,a2,…,ar)Tφ(Xm)Tφ(x)x→z=T T ss-KLFDA φ(x)=(a 1 , a 2 , . . . , a r ) T φ(X m ) T φ(x) =(a1,a2,…,ar)TK(:,x)=(a 1 , a 2 , ..., a r ) T K(:, x) 令Ta ss-KLFDA=(a1,a2,…,ar),那么上式可进一步表达为x→z=TaT ss-KLFDAK(:,x),这里K(:,x)=[κ(x1,x),κ(x2,x),…,κ(xm,x)]TLet T a ss-KLFDA = (a 1 , a 2 ,..., a r ), then the above formula can be further expressed as x→z=T aT ss-KLFDA K(:, x), where K(:, x) =[κ(x 1 , x), κ(x 2 , x), . . . , κ(x m , x)] T . 7.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,步骤(7)中Melm模型通过下列方法进行训练:首先确定隐层个数L,输出层的个数即为分类个数c,这里设置为4,即为4种工况,随机初始化输入权重和偏置矩阵,设为输入权重PInput∈RL×r,隐层神经元偏置Binput∈RL×1,扩展Binput为B∈RL×(n),计算隐层输出矩阵H∈RL ×(n)7. bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis according to claim 1, is characterized in that, in step (7), the Melm model is trained by the following method: first determine the number of hidden layers L , the number of output layers is the number of classifications c, which is set to 4 here, that is, 4 working conditions, randomly initialize the input weights and bias matrices, set the input weights P Input ∈ R L×r , the hidden layer neurons Bias B input ∈R L×1 , expand B input to B∈R L×(n) , calculate the hidden layer output matrix H∈R L ×(n) : 构造数据类别结果矩阵T∈R(n)×c,tij=1当xij∈j类时,其他为-1,求得输出权重矩阵β∈RL×c,β=H+T,H+为H的Moore-Penrose广义逆矩阵,最终得到训练后极限学习机模型:Melm={PInput,Binput,β}。Construct the data category result matrix T∈R (n)×c , t ij = 1 When x ij ∈ j, the others are -1, obtain the output weight matrix β∈R L×c , β=H + T, H + is the Moore-Penrose generalized inverse matrix of H, and the extreme learning machine model after training is finally obtained: Melm = {P Input , B input , β}. 8.根据权利要求1所述的基于伪标签半监督核局部费舍尔判别分析轴承故障诊断,其特征在于,步骤(8)中新样本的特征向量Xnew的确定采用的是步骤(2)中的特征提取方法,标准化处理方法利用的是步骤(3)存储的μi,σi,i=1,2,…d进行z-score标准化,利用步骤(5)得到的Tss-KLFDA计算Xnew在r维降维子空间中的投影向量Znew∈Rr×1,最终状态的确定由Melm模型确定,8. bearing fault diagnosis based on pseudo-label semi-supervised kernel local Fisher discriminant analysis according to claim 1, is characterized in that, in step (8), the determination of the feature vector X new of the new sample adopts step (2) The feature extraction method in , the standardization processing method uses μ i , σ i , i=1, 2, . The projection vector Z new ∈ R r×1 of X new in the r-dimension reduction subspace, the final state is determined by the Melm model, Ttest=Htest T×βT test =H test T ×β 取max(Htest)所对应的下标即为当前轴承设备工况的输出。Taking the subscript corresponding to max(H test ) is the output of the current bearing equipment operating condition.
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