CN109100142A - A kind of semi-supervised method for diagnosing faults of bearing based on graph theory - Google Patents

Abstract

The present invention provides a kind of semi-supervised method for diagnosing faults of the bearing based on graph theory, and the original vibration acceleration signal of the bearing obtained by sensor is converted into complex network first with visual nomography by this method；The structural parameters of complex network, the mean value and standard deviation and network complex exponent of degree of extraction distribution are calculated again；It finally utilizes the semi-supervised learning based on figure to handle unlabeled exemplars, realizes bearing failure diagnosis.The present invention is based on a small amount of exemplar and unlabeled exemplars, moreover the present invention realizes the bearing failure diagnosis under exchanging work sample class imbalance in situation, and fault identification accuracy rate is high, has significant use value.

Description

A kind of semi-supervised method for diagnosing faults of bearing based on graph theory

Technical field

The present invention relates to a kind of semi-supervised method for diagnosing faults of the bearing based on graph theory, belong to component of machine fault diagnosis Technical field.

Background technique

Rolling bearing is the most used one of component of machine.According to statistics, in all mechanical breakdowns, more than 40% Failure caused by bearing.In industry spot, the collection of exemplar is a difficult job, especially rare failure Sample, but there is a large amount of unlabeled exemplars.It the case where for this only a small amount of label data and class imbalance, passes The fault diagnosis algorithm of system often shows very poor.In addition, bearing generally operates under uncertain variable working condition, this also can be to failure Diagnosis interferes.Therefore, it is of great significance to by improving fault diagnosis accuracy rate using no label data.

Visual nomography is a kind of method that time series data is converted to complex network, and this method is by each of sample Point constructs complex network as the node in figure, using the visual principle of physics.Network architecture parameters are extracted as bearing fault Feature, Visual Graph feature have natural insensitivity to variable working condition.

Semi-supervised learning is a kind of sorting algorithm that fault diagnosis accuracy rate can be improved using no label data, this method A small amount of exemplar data are only needed, optimal smoothing is met by solution and assumes that the optimal solution of target equation passes a small amount of label Being multicast to institute, whether there is or not the state identifications on label data, realizing unlabeled exemplars.

Summary of the invention

The invention proposes a kind of semi-supervised method for diagnosing faults of the bearing based on graph theory, and signal is passed through Visual Graph first Algorithm is converted into complex network, extracts the structure feature of complex network as bearing fault characteristics, as semi-supervised classifier Input, then utilizes the semi-supervised learning algorithm based on figure to travel to label on no label data and realizes fault diagnosis.

The invention proposes a kind of semi-supervised method for diagnosing faults of the bearing based on graph theory, specifically includes the following steps:

(1) the original vibration acceleration signal of the bearing obtained by sensor is converted into first with visual nomography Complex network；

(2) structural parameters of complex network, the mean value and standard deviation and network complex exponent of degree of extraction distribution are calculated.

(3) it finally utilizes the semi-supervised learning based on figure to handle unlabeled exemplars, realizes bearing failure diagnosis.

Preferably, step (1) uses visual nomography specifically:

For a sample with N number of data point, being first by the following method converted to vibration acceleration signal can View:

Any two points (the t of signal_a,x_a), (t_b,x_b), two nodes in Visual Graph are corresponded to, if any between this two o'clock It is a little (t_c,x_c), the condition that two nodes are connected meets

Obtain describing the connection adjacency matrix W of each node_D, matrix W_DFor the symmetrical matrix of N*N dimension, w_ij=1 generation Table node i is connected with node j；

For any point, it is connected thereto the degree that number a little is known as the pointThen degree is distributed as D_V= [d₁,…,d_n]。

Preferably, the structural characteristic parameter circular of step (2) complex network is as follows:

(1) degree distribution mean value:

(2) distribution standard deviation is spent:

(3) figure complex exponent GIC is defined as follows:

C=4c (1-c)

Wherein,

λ_maxIndicate the maximum eigenvalue of Visual Graph adjacency matrix.

Preferably, the specific method is as follows for step (3) realization bearing failure diagnosis:

(1) building of figure

Firstly, calculating the similarity between all samples by kernel function, point x is calculated_iAnd x_jBetween adjacency matrix K: K∈R^n×n, K_ij=k (x_i,x_j),

By will abut against Matrix Multiplication with two values matrix B ∈ B^n×nWith distance matrix H ∈ R^n×nComplete rarefaction:

After rarefaction adjacency matrix, the weight matrix W recalculated between two o'clock, point are calculated by Gaussian kernel weighting algorithm x_iAnd x_jBetween weight calculation formula it is as follows:

Wherein, d (x_i,x_j) represent x_iWith x_jBetween Euclidean distance, δ indicate data point standard deviation；

(2) label is propagated

Using smooth item and tag match item as final optimization pass target:

s.t.y_ij∈{0,1},

y_ij=1, for label (x_i)=j, j=1 ..., c.

Wherein, weight matrix Λ=diag ([λ based on degree₁,…,λ_n]), Y={ y_ij}∈Β^n×cFor the label square of data Battle array, Λ Y are standardization tag variable；

Wherein, d be certain sample degree, p be the prior distribution of categorical data and

A=P^TLP+μ(P^T- I) (P-I)=P^TLP+μ(P-I)²

Wherein, P is propogator matrix, and L is normalized Laplacian Matrix；

Above formula is solved by greedy gradient Max-Cut algorithm, finally obtains the label of unlabeled exemplars, realizes that failure is examined It is disconnected.

Preferably, the greedy gradient Max-Cut algorithm flow are as follows:

(1) it inputs: figure G_A={ X, A } exemplar X_lWith label Y；

(2) it initializes:

Pass through exemplar X_lConstruct initial cut set { S_j}:

S_j={ x_i|y_ij=1 }, j=1,2 ..., c；

Unlabeled exemplars collection:

X_u=X X_l；

(3) following steps recycle, until meeting condition

Extremely for z=0 | X_u| do following calculating:

Calculate connectivity:

Unlabeled exemplars are added into optimal label, and put it into label cut set { S_j}；

By x_iIt is put into exemplar X_l:X_l←X_l+x_i；

Sample X is deleted from unlabeled exemplars_u:X_u←X_u-x_i；

(4) it exports

S_j, j=1,2 ..., c.

Wherein sample xi and the connectivity of exemplar subset S are defined as follows:

S_j={ x_i|yi_j=1 }, i=1,2 ..., n；J=1,2 ..., c.

Advantages of the present invention with have the active effect that

(1) visual nomography be it is a kind of by when ordinal series be converted into the algorithm of complex network, this method believes bear vibration It number is mapped in figure, the change of scale (revolving speed of corresponding shaft bearing and negative both horizontally and vertically of the structure feature of figure to signal Carry) there is natural insensitivity.

(2) the semi-supervised bearing fault based on figure that can balance class label influence for improving standardization tag variable is utilized Diagnosis algorithm handles class imbalance without label data.It is influenced to solve data category imbalance bring, utilizes bivariate Objective function, wherein standardization tag variable be used to the other influence of balanced class.

(3) compared to other method for diagnosing faults, semi-supervised fault diagnosis algorithm only needs a small amount of exemplar can Obtain high fault diagnosis accuracy rate.

(4) the method for the present invention belongs to data-driven method, and without establishing model, the detection and identification of failure can be realized, Professional requirement is reduced, engineer application is increased；

Detailed description of the invention

Fig. 1 is the overall step flow chart of method for diagnosing faults of the present invention.

Fig. 2 is visual nomography schematic diagram.

Fig. 3 is certain fault sample vibration signal figure.

Fig. 4 is corresponding fault sample degree distribution.

Fig. 5 is the classification accuracy curve graph under the different classes of ratio of minor failure.

Fig. 6 is the classification accuracy curve graph under the different classes of ratio of conventional fault.

Fig. 7 is the classification accuracy curve graph under the different classes of ratio of catastrophe failure.

Specific embodiment

Below in conjunction with attached drawing and example, the present invention is described in further detail.

The invention proposes a kind of visual nomographys to convert the signal into complex network, by extracting the conduct of Visual Graph feature The input of semi-supervised learning algorithm, thus the method for realizing fault diagnosis.As shown in Figure 1, the specific steps are as follows:

Step 1: bearing vibration signal is converted into complex network by visual nomography.

For a sample with N number of data point, signal is converted to Visual Graph by the following method first.Such as Fig. 2 For transition diagram.

Mathematical computations mode is as follows:

Any two points (the t of signal_a,x_a), (t_b,x_b), two nodes in Visual Graph are corresponded to, what two nodes were connected Condition is as follows:

If any point is (t between this two o'clock_c,x_c), meet

This makes it possible to obtain the connection adjacency matrix W for describing each node_D, matrix is the symmetrical matrix of N*N dimension, w_ij= 1 represents node i is connected with node j.

For any point, it is connected thereto the degree that number a little is known as the pointThen degree is distributed as D_V= [d₁,…,d_n]。

Step 2: calculating the structural characteristic parameter of complex network

The essential characteristic of complex network includes degree distribution mean value and standard deviation and figure complex exponent.Calculation method is as follows:

(1) degree distribution mean value:

(2) distribution standard deviation is spent:

(3) figure complex exponent GIC is defined as follows:

C=4c (1-c)

Wherein,

λ_maxIndicate the maximum eigenvalue of Visual Graph adjacency matrix.

Step 3: realizing fault identification and diagnosis with the semi-supervised learning algorithm based on figure

Semi-supervised learning algorithm principle based on figure include the building of figure and label to propagate two parts as follows:

Mathematic sign definition: { (x₁,y₁),…,(x_l,y_l) and { x_l+1,…,x_l+uRespectively represent exemplar and without mark Signed-off sample sheet, X_l={ x₁,…,x_lAnd X_u={ x_l+1,…,x_l+uLabel is respectively represented and without label input data.L and u is indicated The quantity of exemplar and unlabeled exemplars.Y={ y_ij}∈Β^n×cFor the label matrix of data, wherein y_ij=1 representative sample x_i Label be j, j ∈ { 1,2 ..., c }, each sample has and only one label, i.e.,The target of semi-supervised learning is Identify the label { y without label data_l+1,…,y_l+u, wherein l < < n (l+u=n).

(3) building of figure

Firstly, calculating the similarity between all samples by kernel function, adjacency matrix K:K ∈ R is calculated^n×n, K_ij =k (x_i,x_j).Then, the weight between difference rarefaction adjacency matrix and resetting sample.

Coefficient: by will abut against Matrix Multiplication with a two values matrix B ∈ B^n×nWith distance matrix H ∈ R^n×nIt completes.

Two values matrix is calculated by k nearest neighbor algorithm, and mathematical expression is as follows:

Finally obtain two values matrix B:

Reset weight:

After rarefaction adjacency matrix, the weight matrix W recalculated between two o'clock is calculated by Gaussian kernel weighting algorithm.Point x_iAnd x_jBetween weight calculation formula it is as follows:

Wherein, d (x_i,x_j) represent x_iWith x_jBetween Euclidean distance.

(4) label is propagated

Semi-supervised learning based on figure is based on the basis of smooth hypothesis, and the present invention uses smooth item and tag match item As final optimization pass target.

s.t.y_ij∈{0,1},

y_ij=1, for label (x_i)=j, j=1 ..., c.

In above formula, first item is the measurement of flatness, and Section 2 is the measurement of tag match.Wherein, L is normalized drawing This matrix of pula

L=D^-1/2(D-W)D^-1/2=I-D^-1/2WD^-1/2

For the tag variable that standardizes

Wherein, weight matrix Λ=diag ([λ based on degree₁,…,λ_n])

D be certain sample degree, p be the prior distribution of categorical data andP is set herein_j=1/c.

Solution procedure is divided into two steps:

(1) optimization of F variable:

Fixed variable Y, derivation take zero point

Wherein, P=(L/ μ+I)^-1It is defined as propogator matrix.

(2) optimization of Y variable:

The optimal value F that previous step is solved^*Former objective function is substituted into, is obtained

Wherein, A=P^TLP+μ(P^T- I) (P-I)=P^TLP+μ(P-I)²

Final objective function can be written as follow form:

s.t.y_ij∈{0,1},

y_ij=1, for label (x_i)=j, j=1 ..., c.

Above formula is solved by greedy gradient Max-Cut algorithm:

Algorithm flow:

1, it inputs: figure G_A={ X, A } exemplar X_lWith label Y；

2, it initializes:

Pass through exemplar X_lConstruct initial cut set { S_j}:S_j={ x_i|y_ij=1 }, j=1,2 ..., c

Unlabeled exemplars collection X_u=X X_l；

3, following steps recycle, until meeting condition

Extremely for z=0 | X_u| do following calculating:

Calculate connectivity:x_i∈X_u, j=1 ..., c

It calculates

Unlabeled exemplars are added into optimal label, and put it into label cut set { S_j}；

Xi is put into exemplar X_l:X_l←X_l+x_i；

Sample X is deleted from unlabeled exemplars_u:X_u←X_u-x_i；

4, it exports: S_j, j=1,2 ..., c.

Wherein sample xi and the connectivity of exemplar subset S are defined as follows:

S_j={ x_i|yi_j=1 }, i=1,2 ..., n；J=1,2 ..., c

The label of unlabeled exemplars is finally obtained, realizes fault diagnosis.

The rolling bearing fault signal that this example takes Case Western Reserve University bearing data center to provide is verified.Respectively Using the sample signal under four kinds of normal, inner ring failure, outer ring failure and rolling element failure states to the present invention is based on graph theorys The semi-supervised method for diagnosing faults of bearing carries out detection verifying, the specific steps are as follows:

Step 1: be split with fixed points to bearing vibration signal.

Sample of signal number under four kinds of states is as shown in table 1.

Sample number (fault diameter: 0.007 inch) under 1 four kinds of states of table

For each sample, the complex network that number of nodes is N is converted thereof into, Fig. 3 and Fig. 4 are respectively the event of some bearing Hinder the time-domain diagram and its corresponding degree distribution map of sample.

Step 2: extracting Visual Graph feature

Mean value, standard deviation and the figure complexity for the distribution that xyz axis respectively represents in the Visual Graph of corresponding fault sample in table 1 Index represents the position of normal sample, inner ring failure, outer ring failure and rolling element fault sample in feature space.

Step 3: using based on figure semi-supervised learning algorithm identify the state without label data, realize fault identification with Diagnosis

Tape label every class fault sample 3 are chosen, then just if sample ratio is r for different class imbalance degree Normal number of samples is 3*r.The value range of r is 1~20.Fig. 5,6,7 show the different faults degree that respectively represents (fault point half Diameter is different) under classification accuracy, abscissa is r in figure, i.e., the failure that curve represents under different classes of sample proportion in figure is examined Disconnected accuracy rate.It is found that the semi-supervised learning algorithm (LGC and HFGF) of algorithm classics relatively has better classification accuracy.

In order to more accurately illustrate the validity of this method, each method is for each classification in the case of having counted r=16 Accuracy rate.Test result is as shown in table 2.

2 Experimental Comparison result of table

According to test result it can be seen that the semi-supervised Method for Bearing Fault Diagnosis based on figure is classical better than LGC and GFHF etc. Semi-supervised learning method.It can be seen that method of the invention can be realized fault detection and classification to bearing, failure accuracy rate is high, and Accuracy rate between normal sample and fault sample is 100%, has apparent practical application value.

Claims (5)

1. a kind of semi-supervised method for diagnosing faults of bearing based on graph theory, which is characterized in that specifically includes the following steps:

(1) the original vibration acceleration signal of the bearing obtained by sensor is converted into complexity first with visual nomography Network；

(2) structural parameters of complex network, the mean value and standard deviation and network complex exponent of degree of extraction distribution are calculated；

(3) it finally utilizes the semi-supervised learning based on figure to handle unlabeled exemplars, realizes bearing failure diagnosis.

2. the method as described in claim 1, which is characterized in that

Step (1) uses visual nomography specifically:

For a sample with N number of data point, vibration acceleration signal is converted to Visual Graph by the following method first:

Any two points (the t of signal_a,x_a), (t_b,x_b), two nodes in Visual Graph are corresponded to, if any point is between this two o'clock (t_c,x_c), the condition that two nodes are connected meets

Obtain describing the connection adjacency matrix W of each node_D, matrix W_DFor the symmetrical matrix of N*N dimension, w_ij=1 represents node I is connected with node j；

For any point, it is connected thereto the degree that number a little is known as the pointThen degree is distributed as D_V=[d₁,…, d_n]。

3. method according to claim 2, which is characterized in that

The structural characteristic parameter circular of step (2) complex network is as follows:

(1) degree distribution mean value:

(2) distribution standard deviation is spent:

(3) figure complex exponent GIC is defined as follows:

C=4c (1-c)

Wherein,

λ_maxIndicate the maximum eigenvalue of Visual Graph adjacency matrix.

4. method as claimed in claim 3, which is characterized in that

Step (3) realizes bearing failure diagnosis, and the specific method is as follows:

(1) building of figure

Firstly, calculating the similarity between all samples by kernel function, point x is calculated_iAnd x_jBetween adjacency matrix K:K ∈ R^n×n, K_ij=k (x_i,x_j),

By will abut against Matrix Multiplication with two values matrix B ∈ B^n×nWith distance matrix H ∈ R^n×nComplete rarefaction:

After rarefaction adjacency matrix, the weight matrix W, point x that recalculate between two o'clock are calculated by Gaussian kernel weighting algorithm_iWith x_jBetween weight calculation formula it is as follows:

Wherein, d (x_i,x_j) represent x_iWith x_jBetween Euclidean distance, δ indicate data point standard deviation；

(2) label is propagated

Using smooth item and tag match item as final optimization pass target:

s.t.y_ij∈{0,1},

y_ij=1, for label (x_i)=j, j=1 ..., c.

Wherein, weight matrix Λ=diag ([λ based on degree₁,…,λ_n]), Y={ y_ij}∈Β^n×cFor the label matrix of data, Λ Y is standardization tag variable；

Wherein, d be certain sample degree, p be the prior distribution of categorical data and

A=P^TLP+μ(P^T- I) (P-I)=P^TLP+μ(P-I)²

Wherein, P is propogator matrix, and L is normalized Laplacian Matrix；

Above formula is solved by greedy gradient Max-Cut algorithm, finally obtains the label of unlabeled exemplars, realizes fault diagnosis.

5. method as claimed in claim 4, which is characterized in that

The greediness gradient Max-Cut algorithm flow are as follows:

(1) it inputs: figure G_A={ X, A } exemplar X_lWith label Y；

(2) it initializes:

Pass through exemplar X_lConstruct initial cut set { S_j}:

S_j={ x_i|y_ij=1 }, j=1,2 ..., c；

Unlabeled exemplars collection:

X_u=X X_l；

(3) following steps recycle, until meeting condition

Extremely for z=0 | X_u| do following calculating:

Calculate connectivity:

Unlabeled exemplars are added into optimal label, and put it into label cut set { S_j}；

By x_iIt is put into exemplar X_l:X_l←X_l+x_i；

Sample X is deleted from unlabeled exemplars_u:X_u←X_u-x_i；

(4) it exports

S_j, j=1,2 ..., c；

Wherein sample xi and the connectivity of exemplar subset S are defined as follows:

S_j={ x_i|y_ij=1 }, i=1,2 ..., n；J=1,2 ..., c.