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

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 S_m∈R^1024×m, wherein m indicates the number of entire time-domain signal training sample set, S_n∈R^1024×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∈R^d×m；There is exemplar feature set Close X^* _n∈R^d×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 X_m∈R^d×m；There is exemplar characteristic set X after normalization_n∈R^d×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 S^ulbWith divergence S in Local Clustering^ulwRegularization term, and have exemplar X in the Fisher discriminant analysis of part_nInstitute is right The local class scatter S answered^lbDivergence S in drawn game category^lwIt optimizes together, determines final projection vector T_ss-KLFDA∈ R^m×r, wherein dimensionality reduction dimension is r < < d；

(6) projection vector T obtained in step (5) is utilized_ss-KLFDASolve X_mProjection vector in r dimension reduced order subspace Set Z_m∈R^r×mAnd X_nProjection vector set Z_n∈R^r×n；

(7) projection vector set Z after the dimensionality reduction acquired in step (6) is utilized_n∈R^r×nTraining extreme learning machine model M_elm；

(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∈R^d×1, the projection vector T that is obtained using step (5)_ss-KLFDASolve X_new? R ties up the projection vector set Z in reduced order subspace_new∈R^r×1It is then input to trained model M_elmThe 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 simultaneously_i, σ_i, 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 X_mClustering is carried out, Specific step is as follows: data-oriented collection X_m={ x₁, x₂..., x_i..., x_m}∈R^d×m, wherein x_i∈R^dRepresent i-th of sample to Amount, for each sample point x_iIts local density values ρ is quantitatively calculated first_iWith Distance Density higher sample point away from From δ_i, embody are as follows:

d_ijFor x_iAnd x_jEuclidean distance, d_cFor 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 obtained_iWith the distance δ of the higher sample point of Distance Density_iAfterwards, with part Density p_iFor horizontal axis, distance δ_iDraw 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 X_mInclude n_cA cluster,For the corresponding data point of each cluster centre Number, i.e. m_jA sample is the cluster centre of j-th of cluster,For the cluster labels set of all data points, i.e., c_iIndicate data set X_mIn i-th of data point x_iBelong to c_iA cluster, its initialization definitions are as follows:

d_cPoint 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 h_i=1 is expressed as boundary point, otherwise h_i=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 Clustering^ulbS is expressed as with matrix form^ulb=X_mL^ulbX_m ^T, wherein L^ulb=D^ulb-W^ulb∈ R^m×m, D^ulb∈R^m×mIt is a diagonal matrix, its i-th of diagonal entry isLikewise, office Portion clusters interior divergence S^ulwS can also be expressed as with matrix form^ulw=X_mL^ulwX_m ^T, wherein L^ulw=D^ulw-W^ulw∈R^m×m, D^ulw ∈R^m×mIt is a diagonal matrix, its i-th of diagonal entry is

Here W^ulb, W^ulwIt is the matrix of m × m, and

WhereinRepresentative belongs to cluster c_iSample size,σ_i=| | x_i-x_i ^(k)| |, x_i ^(k)It is x_iKth=7 neighbours, | | | | indicate Euclidean distance；

Construct local class scatter matrix S^lbScatter Matrix S in drawn game category^lw, S^lbIt can also be expressed as with matrix form S^lb=X_nL^lbX_n ^T.Wherein, L^lb=D^lb-W^lb∈R^n×n, D^lb∈R^n×nIt is a diagonal matrix, its i-th of diagonal entry isLikewise, S^lwS can also be expressed as with matrix form^lw=X_nL^lwX_n ^T.Wherein, L^lw=D^lw-W^lw∈ R^n×n, D^lw∈R^n×nIt is a diagonal matrix, its i-th of diagonal entry isHere W^lb, W^lwIt is n The matrix of × n, and

It indicates in class y_iThere is the quantity of exemplar in ∈ { 1,2 ..., c }, c classification number is 4 here,

By L^lbAnd L^lwIt is extended to m m matrix by zero-padding, is embodied as follows:

Thenβ=0.5,

Construction feature equation KL^sslbKa=λ KL^sslwKa, above formula can regard generalized eigenvalue λ as₁≥λ₂>=..., >=λ_m Generalized eigenvector corresponding with itsGeneralized-grads Theory.K represents nuclear matrix, wherein K_ij=κ (x_i, x_j), κ (x_i, x_j) it is gaussian kernel function: κ (x_i, x_j)=exp (- | | x_i-x_j||²/σ²), σ represents core width, here σ= 0.5；Therefore, final projection vector T_ss-KLFDA∈R^m×rIt is expressed asφ(X_m) represent X_mIn 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=T^T _ss-KLFDAφ (x)=(a₁, a₂..., a_r)^Tφ(X_m)^Tφ(x)

=(a₁, a₂..., a_r)^TK (:, x)

Enable T^a _ss-KLFDA=(a₁, a₂..., a_r), then above formula can be further expressed asHere K (:, x)=[κ (x₁, x), κ (x₂, x) ..., κ (x_m, 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 P_Input∈R^L×r, hidden neuron biasing B_input∈R^L×1, extend B_inputFor B ∈ R^L×(n), calculate hidden layer output matrix H ∈R^L×(n):

Construct data category matrix of consequence T ∈ R^(n)×c, t_ij=1, work as x_ijWhen ∈ j class, other are -1, acquire output weight Matrix β ∈ R^L×c, β=H⁺T, H⁺For the Moore-Penrose generalized inverse matrix of H, extreme learning machine mould after training is finally obtained Type: M_elm={ P_input, B_input, 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) storage_i, σ_i, i=1,2 ... d carry out z-score standardization, utilize step Suddenly the T that (5) obtain_ss-KLFDACalculate X_newProjection vector Z in r dimension reduced order subspace_new∈R^r×1, the determination of end-state by M_elmModel is determining,

T_test=H_test ^T×β

Take max (H_test) 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 x_i∈R^dI-th of sample vector is represented, corresponding class label is y_i∈ { 1,2 ..., c }, c are classification number.It enables X_n={ x₁, x₂..., x_i..., x_n}∈R^d×nRepresentative has exemplar data matrix, X_m={ x₁, x₂..., x_i..., x_m}∈R^d×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 X_m= {X_n, X_u, X_uIt is the set of unmarked sample.Assuming that z_i∈R^r(1≤r≤d) is by matrix T ∈ R^d×rConvert obtained low-dimensional The projective representation of subspace: z_i=T^Tx_i。

Local Fisher Discrimination Analysis Algorithm (LFDA) can be stated with following optimization problem:

Here, S^lb, S^lw∈R^d×dRespectively indicate Scatter Matrix in local class scatter matrix drawn game category, definition difference Are as follows:

Here W^lb, W^lwIt is the matrix of n × n, and

It indicates in class y_iThere are the quantity of exemplar, A in ∈ { 1,2 ..., c }_ijIt is heuristic based on local scaleization x_iAnd x_jBetween similarity measurement, A_ijIt is defined as

Parameter σ_iIndicate x_iLocalization scale parameter, be defined as σ_i=| | x_i-x_i ^(k)||

Wherein, x_i ^(k)It is x_iKth 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…≥λ_d

Wherein λ_i, i=1,2 ..., d are corresponding generalized eigenvectorsGeneralized eigenvalue, most Eventually, T_LFDAIt 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.S^lbIt can use down The pairs of form in face is expressed:

Equally, S^lbS can also be expressed as with matrix form^lb=X_nL^lbX_n ^T

Wherein, L^lb=D^lb-W^lb∈R^n×n, D^lb∈R^n×nIt is a diagonal matrix, its i-th of diagonal entry is

Likewise, S^lwS can also be expressed as with matrix form^lw=X_nL^lwX_n ^T

Wherein, L^lw=D^lw-W^lw∈R^n×n, D^lw∈R^n×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 X_m={ x₁, x2 ..., x_i..., x_m}∈R^d×m, wherein x_i∈R^dI-th of sample vector is represented, for Each sample point x_iIts local density values ρ is quantitatively calculated first_iWith the distance δ of the higher sample point of Distance Density_i, it Be defined as follows:

Here parameter d_cIt need to be specified in advance for truncation distance, d_ijRepresent x_iAnd x_jEuclidean 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 δ_iIt can be than the δ of other sample points_jIt is worth much bigger.Therefore, those δ_iThe very big sample point of value is probably cluster centre.

The local density values ρ of all sample points is obtained_iWith the distance δ of the higher sample point of Distance Density_iAfterwards, with part Density p_iFor horizontal axis, distance δ_iX-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 X_mInclude n_cA cluster,For the corresponding data point of each cluster centre Number, i.e. m_jData point is the cluster centre of j-th of cluster.For the cluster labels set of all data points, i.e., c_iIndicate data set X_mIn i-th of data point x_iBelong to c_iA cluster.Its initialization definitions are as follows:

For data set X_mIn all local densities compare xth_iIn the big data point of a data point with x_iNearest 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 q_i, 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 clusters_cPoint 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 h_i=1 is expressed as boundary point, otherwise h_i=0 indicates to be positive Chang Dian.It enablesFor sample x_iAffiliated cluster c_iCorresponding 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 d_c, 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 algorithm_cInfluence of the determination to cluster result it is very big, if d_cIt 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 d_cIt 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 set_cTo 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 X_mClustering 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 cluster_c 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 portion^ulbWith divergence S in Local Clustering^ulwRegularization term embodies as follows:

Here W^ulb, W^ulwIt is the matrix of m × m, and

It indicates in cluster c_i∈ { 1,2 ..., n_cIn sample quantity.

First by L^lbAnd L^lwIt is extended to m m matrix by zero-padding, is embodied as follows:

Furthermore by S^ulbAlso S is expressed as with matrix form^ulb=X_mL^ulbX_m ^T

Wherein, L^ulb=D^ulb-W^ulb∈R^m×n, D^ulb∈R^m×mIt is a diagonal matrix, its i-th of diagonal entry is

Likewise, S^ulwS can also be expressed as with matrix form^ulw=X_mL^ulwX_m ^T

Wherein, L^ulw=D^ulw-W^ulw∈R^m×m, D^ulw∈R^m×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 theory^LsslbKa=λ KL^sslwKa, above formula can regard generalized eigenvalue λ as₁≥λ₂>=..., >=λ_mGeneralized eigenvector corresponding with itsGeneralized-grads Theory.K represents nuclear matrix, wherein K_ij=κ (x_i, x_j), κ (x_i, x_j) it is Gaussian kernel letter Number: κ (x_i, x_j)=exp (- | | x_i-x_j||²/σ²), σ represents core width, here σ=0.5；Therefore, final projection vector T_ss-KLFDA∈R^m×rIt is expressed asφ (X_m) represent X_mIn the projection vector of nuclear space.

For new samples x, the feature representation of reduced order subspace is as follows:

X → z=T^T _ss-KLFDAφ (x)=(a₁, a₂..., a_r)^Tφ(X_m)^Tφ(x)

=(a₁, a₂..., a_r)^TK (:, x)

Enable T^a _ss-KLFDA=(a₁, a₂..., a_r), then above formula can be further expressed as

Here K (:, x)=[κ (x₁, x), κ (x₂, x) ..., κ (x_m, 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 (z_j, t_j), z_j=[z_j1, z_j2... z_jr]^T∈R^r, t_j=[t_j1, t_j2... t_jc]^T∈R^c.According to y_i∈ { 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, P_Input ⁱ=[P_i1, P_{I, 2}..., P_{I, r}] it is input weight, β_icFor i-th of hidden layer list The output weight of corresponding c-th of the output unit of member, b_iIt is the biasing of i-th of Hidden unit.P_Input ⁱ·z_jIndicate P_Input ⁱAnd z_jIt 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 β_i, P_Input ⁱAnd b_i, 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 P_Input ⁱ With the biasing b of hidden layer_iIt 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. being based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, it is characterised in that: this method includes Following steps:

(1) axis is collected using the vibration acceleration sensor being mounted on the spring bearing upper end casing of induction conductivity output shaft Hold the vibration signal under different work shapes, if altogether there are four types of work shape: normal condition, inner ring malfunction, outer ring malfunction and Rolling element malfunction, then carrying out length to the signal under various operating conditions respectively is that 1024 segment processings obtain entire time domain letter Number set S_m∈R^1024×m, wherein m indicates the number of entire time-domain signal training sample set, S_n∈R^1024×nTo there is label time domain Sample of signal 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 that letter can be vibrated under the various operating conditions of effecting reaction Number characteristic set, if sharing d feature, then entire training sample characteristic set X^* _m∈R^d×m；There is exemplar characteristic set X^* _n ∈R^d×n；

(3) the feature training sample set obtained to step (2) is standardized, and makes the numberical range of each characteristic index Determine that in mean value be 0, in the standardized normal distribution section that variance is 1；Entire training sample characteristic set X after then normalizing_m∈R^{d ×m}；There is exemplar characteristic set X after normalization_n∈R^d×n；

(4) the entire training sample characteristic set X after the normalization obtained to step (3)_mIt is acquired using density peaks clustering algorithm Cluster labels setAnd whether be boundary point logo collection

(5) the cluster labels set obtained using step (4)And logo collectionDivergence between construction Local Clustering S^ulbWith divergence S in Local Clustering^ulwRegularization term, and have exemplar X in the Fisher discriminant analysis of part_nCorresponding Local class scatter S^lbDivergence S in drawn game category^lwIt optimizes together, determines final projection vector T_ss-KLFDA∈R^m×r, Wherein dimensionality reduction dimension is r < < d；

(6) projection vector T obtained in step (5) is utilized_ss-KLFDASolve X_mProjection vector set in r dimension reduced order subspace Z_m∈R^r×mAnd X_nProjection vector set Z_n∈R^r×n；

(7) projection vector set Z after the dimensionality reduction acquired in step (6) is utilized_n∈R^r×nTraining extreme learning machine model M_elm；

(8) axis is collected by the vibration acceleration sensor being mounted on the spring bearing upper end casing of induction conductivity output shaft The vibration signal held 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∈R^d×1, the projection vector T that is obtained using step (5)_ss-KLFDASolve X_new? R ties up the projection vector set Z in reduced order subspace_new∈R^r×1It is then input to trained model M_elmThe middle current bearing of determination Final working condition.

2. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It is characterized in that, is to extract 12 statistical natures of vibration signal time-domain snapshots to method used by the feature extraction in step (2), Including average value, root mean square, variance, standard deviation, rectified mean value, peak-to-peak value, kurtosis value, peak factor, waveform because Son, the kurtosis factor, the pulse factor, the nargin factor carry out 5 layers of wavelet decomposition simultaneously to vibration signal time-domain snapshots using DB4 small echo The energy spectrum and energy spectrum entropy totally 12 dimension fault signature of 5 details coefficients and 1 approximation component are extracted, and when to vibration signal Domain segment carries out 5 layers of empirical mode decomposition and extracts the energy spectrum and energy spectrum entropy totally 12 of 5 Intrinsic mode functions and 1 remainder Fault signature is tieed up, d=32 dimensional feature is amounted to after combination.

3. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It is characterized in that, method used by being standardized in step (3) to each index value is z-score method, specific to walk It is rapid as follows: to setTo any indexIt is standardized institute The method of use is as follows:

μ is recorded simultaneously_i, σ_i, the standardization of i=1 ..., d in case of new samples.

4. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It is characterized in that, to acquisition cluster labels set in step (3)And whether be boundary point logo collectionInstitute The method of use is utilized based on density peaks clustering algorithm to all sample set X_mClustering is carried out, specific steps are such as Under: data-oriented collection X_m={ x₁, x₂..., x_i..., x_m}∈R^d×m, wherein x_i∈R^dI-th of sample vector is represented, for each A sample point x_iIts local density values ρ is quantitatively calculated first_iWith the distance δ of the higher sample point of Distance Density_i, specific table It reaches are as follows:

d_ijFor x_iAnd x_jEuclidean distance, d_cFor distance is truncated, it is arranged so that the average distance number of each data point is data The 2% of point sum, further setsIt indicatesThe lower sequence of descending arrangement, i.e. satisfaction:Then

The local density values ρ of all sample points is obtained_iWith the distance δ of the higher sample point of Distance Density_iAfterwards, with local density ρ_iFor horizontal axis, distance δ_iX-Y scheme is drawn for the longitudinal axis, is called decision diagram, chooses those with higher local density and opposite Compared with rise from point as cluster centre, it is determined that after cluster centre, remaining each point is attributed to away from nearest Density is higher than cluster belonging to its point, if X_mInclude n_cA cluster,For the volume of the corresponding data point of each cluster centre Number, i.e. m_jA sample is the cluster centre of j-th of cluster,For the cluster labels set of all data points, i.e. c_iTable Show data set X_mIn i-th of data point x_iBelong to c_iA cluster, its initialization definitions are as follows:It enablesFor data set X_mIn all local densities compare xth_iNumber In the big data point in strong point with x_iNearest data point number, is specifically defined are as follows: ForSample point, cluster labels is defined as:When the cluster labels of all sample points determine it Afterwards, for erased noise point, algorithm is that each cluster defines a borderline region first, that is, is assigned to the cluster but gathers with other The distance of point in class is less than d_cPoint set, then for it is each cluster find the highest point of density in its borderline region, and Using the density of the point as threshold valuesThe noise spot of the cluster is screened, i.e., only retains density in cluster and is greater than or equal to the valve The point of value enablesNormal point and boundary point identification are represented, if h_i=1 is expressed as boundary point, otherwise h_i=0 indicates to be positive Chang Dian,

5. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It is characterized in that, T in step (5)_ss-KLFDACalculation method is as described below:

Divergence S between construction Local Clustering^ulbS is expressed as with matrix form^ulb=X_mL^ulbX_m ^T, wherein L^ulb=D^ulb-W^ulb∈R^m×m, D^ulb∈R^m×mIt is a diagonal matrix, its i-th of diagonal entry isLikewise, part is poly- Divergence S in class^ulwS can also be expressed as with matrix form^ulw=X_mL^ulwX_m ^T, wherein L^ulw=D^ulw-W^ulw∈R^m×m, D^ulw∈R^{m ×m}It is a diagonal matrix, its i-th of diagonal entry is

Here W^ulb, W^ulwIt is the matrix of m × m, and

WhereinRepresentative belongs to cluster c_iSample size,σ_i=| | x_i-x_i ^(k)| |, x_i ^(k) It is x_iKth=7 neighbours, | | | | indicate Euclidean distance；

Construct local class scatter matrix S^lbScatter Matrix S in drawn game category^lw, S^lbS can also be expressed as with matrix form^lb= X_nL^lbX_n ^T.Wherein, L^lb=D^lb-W^lb∈R^n×n, D^lb∈R^n×nIt is a diagonal matrix, its i-th of diagonal entry isLikewise, S^lwS can also be expressed as with matrix form^lw=X_nL^lwX_n ^T.Wherein, L^lw=D^lw-W^lw∈ R^n×n, D^lw∈R^n×nIt is a diagonal matrix, its i-th of diagonal entry isHere W^lb, W^lwIt is The matrix of n × n, and

n_yiIt indicates in class y_iThere is the quantity of exemplar in ∈ { 1,2 ..., c }, c classification number is 4 here,

By L^lbAnd L^lwIt is extended to m m matrix by zero-padding, is embodied as follows:

Thenβ=0.5,

Construction feature equation KL^sslbKa=λ KL^sslwKa, above formula can regard generalized eigenvalue λ as₁≥λ₂>=..., >=λ_mWith its correspondence Generalized eigenvectorGeneralized-grads Theory.K represents nuclear matrix, wherein K_ij=κ (x_i, x_j), κ (x_i, x_j) it is gaussian kernel function: κ (x_i, x_j)=exp (- | | x_i-x_j||²/σ²), σ represents core width, here σ=0.5；Therefore, final throwing Shadow vector T_ss-KLFDA∈R^m×rIt is expressed as φ(X_m) represent X_mIn the projection vector of nuclear space.

6. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It 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, dimensionality reduction The feature representation of subspace is as follows:

X → z=T^T _ss-KLFDAφ (x)=(a₁, a₂..., a_r)^Tφ(X_m)^Tφ(x)

=(a₁, a₂..., a_r)^TK (:, x)

Enable T^a _ss-KLFDA=(a₁, a₂..., a_r), then above formula can further be expressed as x → z=T^aT _ss-KLFDAK (:, x), here K (:, x)=[κ (x₁, x), κ (x₂, x) ..., κ (x_m, x)]^T。

7. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It is characterized in that, M in step (7)_elmModel is trained by following method: determining hidden layer number L, the number of output layer first As classification number c is set as 4, as 4 kinds of operating conditions, random initializtion input weight and bias matrix here, is set as input power Weight P_Input∈R^L×r, hidden neuron biasing B_input∈R^L×1, extend B_inputFor B ∈ R^L×(n), calculate hidden layer output matrix H ∈ R^{L ×(n)}:

Construct data category matrix of consequence T ∈ R^(n)×c, t_ij=1 works as x_ijWhen ∈ j class, other are -1, acquire output weight matrix β ∈R^L×c, β=H⁺T, H⁺For the Moore-Penrose generalized inverse matrix of H, extreme learning machine model after training: M is finally obtained_elm ={ P_Input, B_input, β }.

8. according to claim 1 be based on pseudo label semi-supervised kernel part Fei Sheer discriminant analysis bearing failure diagnosis, It is characterized in that, the feature vector, X of new samples in step (8)_newDetermination using the feature extracting method in step (2), mark That standardization processing method utilizes is the μ of step (3) storage_i, σ_i, i=1,2 ... d carry out z-score standardization, utilize step (5) Obtained T_ss-KLFDACalculate X_newProjection vector Z in r dimension reduced order subspace_new∈R_r×1, the determination of end-state is by M_elmMould Type is determining,

T_test=H_test ^T×β

Take max (H_test) corresponding to subscript be current bearing equipment working condition output.