AU2020104428A4

AU2020104428A4 - A rolling bearing fault diagnosis method based on GRCMSE and manifold learning

Info

Publication number: AU2020104428A4
Application number: AU2020104428A
Authority: AU
Inventors: Yongwu Cai; Zhenya WANG; Ligang YAO
Original assignee: Fuzhou University
Current assignee: Fuzhou University
Priority date: 2019-12-31
Filing date: 2020-11-05
Publication date: 2021-07-22
Anticipated expiration: 2028-11-05
Also published as: ZA202102516B; WO2021135630A1; CN111103139A

Abstract

of Descriptions The invention relates to a rolling bearing fault diagnosis method based on GRCMSE and manifold learning, including the following steps: using the acceleration sensors to collect the vibration acceleration signals of the rolling bearings. Using GRCMSE algorithm to extract features of vibration acceleration signals. Using the DDMA manifold learning method to reduce the dimensionality of the rolling bearing fault feature information, and divide the reduced dimensionality of the rolling bearing fault feature information into into low-dimensional feature set of training sample and low-dimensional feature set of test sample in proportion. Train the PSO-SVM classifier according to the low-dimensional features of the training sample to obtain the trained PSO-SVM classifier. Input the low-dimensional feature set of the test sample into the trained PSO-SVM classifier, and diagnose the fault types. The invention overcomes the shortcomings of coarse-graining in multi-scale sample entropy, solves the problem of information redundancy in high-dimensional fault features, and can effectively diagnose different state types of rolling bearings. Drawings of Descriptions Vibration Acceleration Signal Training Samples Test Sample Use GRCMSE to Construct a High-dimensional Fault Feature Set Use DDMA Manifold Learning Algorithm for Dimensionality Reduction [ Low-dimensional Feature Low-dimensional Feature Set of the Training Sample Set of the Test Sample Train the PSO-SVM Classifier Trained PSO-SVM Classifier Model Diagnosing Fault Type Figure 1 Nor Z 0 0.0 0.2 0.4 0.6 0.8 Time/s -. Tq '17" 1 I '79 IRF . 0 0.0 0.2 04 0.6 0.8 Time/s -8 -2 O RF - 011111111i' ili111111 0.0 0.2 0.4 0.6 0.8 Times .8,2 0.0 0.2 0.4 0.6 0.8 Times Figure 2

Description

Drawings of Descriptions

Vibration Acceleration Signal

Training Samples Test Sample

Use GRCMSE to Construct a High-dimensional Fault Feature Set

Use DDMA Manifold Learning Algorithm for Dimensionality Reduction

[ Low-dimensional Feature Low-dimensional Feature Set of the Training Sample Set of the Test Sample

Train the PSO-SVM Classifier Trained PSO-SVM Classifier Model

Diagnosing Fault Type

Figure 1

Nor Z 0

0.0 0.2 0.4 0.6 0.8 Time/s

-. Tq '17" 1I '79 IRF . 0

0.0 0.2 04 0.6 0.8 Time/s -2 O RF -8 - 011111111i' ili111111

0.0 0.2 0.4 0.6 0.8 Times

.8,2

0.0 0.2 0.4 0.6 0.8 Times

Figure 2

Descriptions

A Rolling Bearing Fault Diagnosis Method Based on GRCMSE and Manifold Learning

This application claims the priority of a Chinese patent application filed with the

Chinese Patent Office on December 31, 2019. The application number is 201911407048.3

and the invention title is " a rolling bearing fault diagnosis method based on GRCMSE and

manifold learning." The reference is incorporated in this application.

Technical Field

The invention relates to the technical field of mechanical fault diagnosis and signal

processing, in particular to a rolling bearing fault diagnosis method based on GRCMSE

(Generalized Refined Composite Multiscale Sample Entropy) and manifold learning.

Background Technology

Rolling bearing is a key component of rotating machinery, and its complex working

environment makes rolling bearing prone to failure due to fatigue after long-term operation,

which in turn leads to a series of accidents. Therefore, fault diagnosis has realistic

theoretical and practical significance.

The key to fault diagnosis of rolling bearings is feature extraction. In recent years,

with the development of non-linear theory, feature extraction methods based on entropy

have been favored by scholars, such as approximate entropy, sample entropy, permutation

entropy, fuzzy entropy, multi-scale entropy and multi-scale sample entropy (MSE), etc.

Among them, multi-scale sample entropy integrates multi-scale entropy to fully

characterize fault feature information from other scales, and sample entropy has the

advantage of being suitable for measuring the complexity of short data sequences and

making up for the shortcomings of approximate entropy matching. Therefore, it is well

applied in many fields. However, the application of MSE to the feature extraction process

of rolling bearings still has the following two defects: ( Through the coarse-graining

process of the homogenized data, the dynamic mutation behavior of the original signal is "neutralized" to a certain extent, so that the estimated entropy value is biased; @ The

Descriptions

stability of the MSE entropy value will increase with the increase of the coarse-grained

scale factor.

In addition, in order to fully characterize the fault information of rolling bearings, the

constructed fault features are usually high-dimensional, nonlinear and redundant, which

increase the burden of classifier recognition and affect the recognition effect.

Invention Summary

Based on this, the purpose of the present invention is to provide a rolling bearing fault

diagnosis method based on GRCMSE and manifold learning, which overcomes the

deficiency of coarse-grained in multi-scale sample entropy and solves the problem of

information redundancy in high-dimensional fault features.

In order to achieve the above objective, the present invention provides a rolling

bearing fault diagnosis method based on GRCMSE and manifold learning, including the

following steps:

Step Sl: Use the acceleration sensors to collect the vibration acceleration signals of

the rolling bearings;

Step S2: Use GRCMSE algorithm to extract features of vibration acceleration signals

to obtain fault feature information of rolling bearings;

Step S3: Use the DDMA manifold learning method to reduce the dimensionality of the

rolling bearing fault feature information, and divide the reduced dimensionality of the

rolling bearing fault feature information into low-dimensional feature set of training sample

and low-dimensional feature set of test sample in proportion;

Step S4: Train the PSO-SVM classifier according to the low-dimensional features of

the training sample to obtain the trained PSO-SVM classifier;

Step S5: Input the low-dimensional feature set of the test sample into the trained

PSO-SVM classifier, and diagnose the fault type.

Optionally, the vibration acceleration signals include a normal state, an outer ring

failure state, an inner ring failure state, and a rolling element failure state using the drive

shaft radial sensors.

Descriptions

Optionally, the GRCMSE algorithm is specifically: (1) For time series {x(i), i 1,2,...,N} , use the following formula to calculate the generalized composite coarse-grained series y(s) =y YGG {h G,Ji hj , y YG,h 'j, ... y }: ( js+h-1 YG, hj W =- Y (X x-X S i=(j-1)s+h

1 j 1 h S,2 s, x - Xi+h S Sh=0

(2) For the scale factor s, calculate the number of m-dimensional and

m+1-dimensional space vectors of each generalized coarse-grained sequence yG(S under m±1h the scale factors, which are defined as n h G+1 G,h,s'h,

(3) In the range 1 hs , calculate the average value of nG,h,s and n+,sas

nG and nm,h,s respectively, and then the GRCMSE entropy value of time series x(i) under the scale factor s can be obtained:

EGRCMSE (X Sm rG,h,s (2) m nG,h,s 1 1 In the formula, n ,h,s GZhlGhs -,h,s , ~G,h,s n± = h1s ZfG,h,s •

S h=1 S h=1

Optionally, the DDMA manifold learning method is specifically:

Assuming that (X,P,p) is the measurement space, data setXe RD, P represents the

- -algebraic subset, and P represents the distributed on X. The specific process of

DDMA is as follows:

(1) Construct a discriminant Gaussian kernel:

k,(x,y)= exp (x,y) Vxy EX (3)

pe(x, y), 1 (x) = 1 (y) = L, VLe 0 p (x, y) =.I- (4) 1PL(minp), ),,pBL

In the formula, p(x,y) represents the kernel width, (x) and 1(y) represent the

label information of sample points x and y respectively, 0) represents the discriminant

constant, p, is the kernel width of the same type of label sample, PB is the kernel

width of the heterogeneous label sample, and Q is the label information of the entire data

set;

Descriptions

PW(L)(x,y= mMin x-y ,x X (5) NA }E 6X

pB, xe X (6)

A=min{NA, NI(, N}I(Y) (7)

In the formula, NA represents the preset neighborhood size, and NL represents the

number of sample points under the same label L;

(2) Any data point x can be regarded as a vertex on the weighted graph G, and then a

Markov chain is constructed on the data graph to find the relevant structure in the complex

geometry. The degree of x in the weight graph G: deg(x)= k,(x,y) (8) Then the transition probability expression from x to y is as follows: k,(x, y) q(x, y)= d(x) (9) deg(x)

(3) Use the transition probability matrix Q to describe the Markov chain, among them,

Q includes all q(xy); then the transition distance between x and y is defined as: d

(4) Dy"2(X,Y) = 1 (P, W(x-,(y))2 (10) n=1

(5) (11)

In the formula, 7 and 9 respectively represent the left and right eigenvectors of the

matrix Q, / represents the eigenvalue, and d represents the data dimension after

dimensionality reduction; the eigenvalue satisfies 1= A > >, - -1_ 0;

The results of diffusion mapping are as follows: X'= [(x),(12(x),--,dd (12) Optionally, the step S4 is specifically:

Step S41: Perform row normalization processing on the low-dimensional features of

the training sample;

Step S42: According to the SVM model, the radial basis function is selected as the

kernel function, and the particle swarm optimization algorithm is used to use the average

correct recognition rate of the normalized training samples after three-fold crossover as the

fitness value to determine the optimal SVM model Optimal penalty factor and kernel

Descriptions

function parameters.

According to the specific embodiments provided by the present invention, the present

invention discloses the following technical effects:

1. The present invention overcomes the shortcomings of coarse-grained in multi-scale

sample entropy, and solves the problem of information redundancy in high-dimensional

fault features.

2. The present invention can effectively diagnose different types of rolling bearings.

Brief Description of Drawings

In order to explain the embodiments of the present invention or the technical

solutions in the prior art more clearly, the following will briefly introduce the drawings that

need to be used in the embodiments. Obviously, the drawings in the following description

are only some of the present invention. For the embodiments, for those of ordinary

technicians in this field, other drawings may be obtained based on these drawings without

creative labor.

Figure 1 is a flowchart of the diagnosis method of the present invention;

Figure 2 is a time-domain waveform diagram of rolling bearings under different states

in an embodiment of the present invention;

Figure 3 is a flowchart of GRCMSE in an embodiment of the present invention;

Figure 4 shows four-state high-dimensional feature mean values in an embodiment of

the present invention: (a) MSE and RCMSE mean value curves; (b) GMSE and GRCMSE

mean value curves;

Figure 5 shows the entropy deviation of four methods in an embodiment of the present

invention: (a) MSE entropy standard deviation; (b) RCMSE entropy standard deviation; (c)

GMSE entropy standard deviation; (d) GRCMSE entropy standard deviation;

Figure 6 shows a PSO-SVM recognition result of high-dimensional features in an

embodiment of the present invention;

Figure7 shows the result of dimensionality reduction of GRCMSE by DDMA in an

embodiment of the present invention;

Descriptions

Figure 8 shows a PSO-SVM recognition result of low-dimensional features in an

embodiment of the present invention.

Detailed Description of the Presently Preferred Embodiments

The technical solutions in the embodiments of the present invention will be clearly

and completely described below in conjunction with the accompanying drawings in the

embodiments of the present invention. Obviously, the described embodiments are only a

part of the embodiments of the present invention, rather than all the embodiments. Based

on the embodiments of the present invention, all other embodiments obtained by those of

ordinary technicians in this field without creative work shall fall within the protection

scope of the present invention.

The purpose of the present invention is to provide a rolling bearing fault diagnosis

method based on GRCMSE and manifold learning, which overcomes the deficiency of

coarse-grained in multi-scale sample entropy and solves the problem of information

redundancy in high-dimensional fault features.

In order to make the above objectives, features and advantages of the present

invention more obvious and understandable, the present invention will be further described

in detail below with reference to the accompanying drawings and specific embodiments.

Figure 1 is a flowchart of the diagnosis method of the present invention. As shown in

Figure 1, the present invention provides a rolling bearing fault diagnosis method based on

GRCMSE and manifold learning, which includes the following steps:

Step SI: Use the acceleration sensors to collect the vibration acceleration signals of

the rolling bearing.

In this embodiment, the vibration acceleration signals of the rolling bearings under

normal operation (Nor), inner ring failure (IRF), outer ring failure (ORF), and rolling

element failure (BF) are analyzed. Under the condition of a sampling frequency of 5120 Hz,

100 sets of vibration acceleration signals in the four states of self-aligning ball bearings are

collected respectively. Each set of signal samples contains 4096 sampling points, and a

total of 400 sets of samples for the four types. Among them, 20 groups are randomly

Descriptions

selected as training samples for each type, and the remaining 80 groups are used as test

samples. There are a total of 80 groups of training samples and 320 groups of test samples

for 4 types. The time-domain waveform diagrams of the four states of rolling bearings are

shown in Figure 2. It can be seen from Figure 2 that it is difficult to distinguish the fault

types based on the time-domain waveforms of the bearing vibration signals.

to obtain fault feature information of rolling bearings;

rolling bearing fault feature information into into low-dimensional feature set of training

sample and low-dimensional feature set of test sample in proportion;

the training sample to obtain the trained PSO-SVM classifier;

PSO-SVM classifier, and diagnose the fault type.

In this embodiment, the GRCMSE algorithm is specifically:

(1) For time series {x(i), i 1,2,...,N} , use the following formula to calculate the generalized composite coarse-grained series y(s)Yh =y {Y,h y,JiYV,22 -- *YG,h ,

(s) 1 I=js-1-h _ i2 Y ,h, j

N 1 1 j ,1 h s,2 s,x =- Xih S S h0

x(i) represents the time series of the vibration acceleration signal, and N represents

the number of sample points included in the time series.

(2) For the scale factor s, calculate the number of m-dimensional and

m+1-dimensional space vectors of each generalized coarse-grained sequence yGh which

are defined as nm,h,s +G,h,s

(3) In the range 1 h s, calculate the average values of nhs and nmG as

nG,h,s and G,h,s respectively. Then, the GRCMSE entropy value of time series x(i) under the scale factor s can be obtained:

Descriptions

EGRCMSE (X,Sm,r) In,s G m (2) nGh,s

Intheformula, nZh,s G,h,s and s,, -y<2 s . Among them, set the

GRCMSE algorithm parameters as N=4096, m=2, r--0.15SD (SD represents standard deviation), and smax=25. In this embodiment, the flowchart of the GRCMSE algorithm is shown in Figure 3. This algorithm is compared with three algorithms such as multi-scale sample entropy (MSE), refined composite multi-scale sample entropy (RCMSE), and generalized multi-scale sample entropy (GMSE). Figure 4 shows the mean entropy values of the above four algorithms for the four types of rolling bearings, and Figure 5 shows the standard deviation of the entropy values of the above four algorithms for the four types of rolling bearings. Among them, the algorithm parameters are set as follows: N=4096, m=2, r=0.15SD (SD stands for standard deviation), and smax=25. According to Figure 4 and Figure 5, it can be seen that: (1) MSE and RCMSE algorithms have relatively close entropy mean curves for the four types of rolling bearings, as shown in Figure 4(a). However, compared with MSE, the entropy values extracted by RCMSE under the same scale have smaller standard deviation values, as shown in Figure 5(a) and Figure 5(b). In the same way, the GMSE and GRCMSE algorithms are closer to the mean curves of the four types of rolling bearing entropy, as shown in Figure 4(b). However, compared with GMSE, the entropy values extracted by GRCMSE under the same scale have smaller standard deviation values, as shown in Figure 5(c) and Figure 5(d). It verifies that the entropy value extracted by the refined compound idea is more accurate. (2) Compared with the MSE and RCMSE algorithms, the four types of rolling bearing entropy curves extracted by the GMSE and GRCMSE algorithms are smoother, and at most scales, the four types are distinguished more clearly. It shows that the use of generalized coarse-grained idea can extract feature information that is easy to distinguish fault types. In this embodiment, all the features of GRCMSE are directly input into the PSO-SVM classifier for training and testing, and the recognition result is shown in Figure 6. As shown in Figure 6, the fault features extracted by the GRCMSE algorithm inevitably have information redundancy. Therefore, there are still some sample fault categories that are misjudged, and the high-dimensional fault feature set needs to be reduced by a dimensionality reduction algorithm. In this embodiment, when the DDMA manifold learning method is used to perform dimensionality reduction on the high-dimensional feature set, the dimensionality reduction result of the GRCMSE feature set is shown in Figure 7. Among them, the DDMA parameters are set as follows: according to the correlation dimensionality method, the best intrinsic dimension is determined to be 3, the

Descriptions

nearest neighbor parameter is 20, the discrimination constant is 2, and the transition time is 1. According to Figure 7, in the dimensionality reduction result of the GRCMSE feature set by DDMA, the four types of samples can be completely separated, there is no sample aliasing, and the four types of samples have good aggregation. In this embodiment, the DDMA manifold learning method is specifically:

Assuming that (X,P,p) is the measurement space, data set Xe RDPrepresents the 0 -algebraic subset, P represents the distribution on X, the specific process of DDMA is as follows: (1) Construct a discriminant Gaussian kernel:

k,(x,y)= exp - y Vx,ye X (3) 2p (x, y)j

rwpw((xy), (x)=(y)= L,VLe 1 (4)

wI min{pw(x) pw,, pB(x, ,(x) 1(y)

In the formula, p(x,y) represents the kernel width, 1(x) and 1(y) represent the

label information of sample points x and y respectively, 0 represents the discriminant

constant, Pw is the kernel width of the same type of label sample, pB is the kernel

width of the heterogeneous label sample, and 2 is the label information of the entire data

set; X represents the original high-dimensional feature set, L represents the label category

of the sample, Pw(x)represents the kernel width of the same sample with the x category

label, Pw(y) represents the kernel width of the same sample with the y category label, and

PB(x,y) represents the kernel width of the heterogeneous label sample;

PWL)(I ) Pw(L~'Y 1 Eminx-yI2 NA ~ 1X I(x)=I(y)=L~ (55

p B(x, y)= min|x-yx(x)() X (6)

A = min{NA,NL-(x),NL(Y)} (7)

number of sample points under the same label L;

geometry. The degree of x in the weight graph G: deg(x)= Zk(x,y) (8) x,yE X

Descriptions

Then the transition probability expression from x to y is as follows:

q(x, y) k,(x,y) deg(x)

Q includes all q(x, y); then the transition distance between x and y is defined as: d ,2 __ 2( (10) n-1

rQ =n (11) j(Pn = ,n(P

matrix Q, I represents the eigenvalue, and d represents the data dimension after

dimensionality reduction; the eigenvalue satisfies 1= >, > -- > _, > 0;

The results of diffusion mapping are as follows:

X'd= R(x),I2d2 (12) In this embodiment, the step S4 is specifically:

the training sample;

correct recognition rate of the normalized training sample after three-fold crossover as the

fitness value to determine the optimal penalty factor and kernel function parameters in

SVM model. Among them, the particle swarm size is set to 20, the termination iteration is

set to 100, the local search capability is set to 2, and the global search capability is set to 2. The specific steps of particle swarm optimization algorithm for parameter optimization are as follows: (1) Normalize the input data set and divide it into training samples and test samples. (2) Initialize the parameters of the particle swarm algorithm.The particle swarm size is set to 20, the termination iteration is set to 100, the local search capability is set to 2, and the global search capability is set to 2. Since it is necessary to optimize the SVM penalty factor c and the kernel function parameter g. Therefore, the position of the particle is defined as (c, g). Among them, the upper and lower limits of each particle are set to (100, 100) and (0.01, 0.01), respectively. (3) Calculate the fitness value of each particle, and take the average correct

Descriptions

recognition rate of the training samples after the normalization process after three-fold crossover as the fitness value. That is to say, the parameter optimization problem of SVM is to find the problem of maximizing the fitness function. (4) Calculate the local optimal and global optimal of each particle under the current iteration. (5) Use the following formula to update the position of the particle:

FVid(t±1) = vVid(t)±C 2 l[Pid(t)- xld(t)]±C2A2Pgd(t)- Xld(t)] Among them, i Xid (t +1) = Xi(t)±+Vid(t +l) represents the i-th individual, d represents the individual dimension, t represents the current iteration, w represents the weight coefficient, c1=c2=2 represents the acceleration factor, 1 and 22 are random numbers between 0 and 1, xid represents the position of the particle in the current search space, Pidrepresents the best position in the history of a single particle, and pgd represents the best position in the history of the particle swarm. Vid E [-Vmax Vmax

is the propagation velocity of particles, vmax represents the maximum particle velocity, and is defined as follows: vm= k- Popmax, among them, k belongs to [0.1, 1], it is defined as 0.6 in this embodiment, andpopmax represents the upper limit of the parameter.

(6) Repeat steps (3)-(5) until the maximum number of iterations is reached, stop the

optimization process, and output SVM optimization parameters.

(7) Use the optimized penalty factor and kernel function parameters to establish an

SVM prediction model, and input the test samples into the prediction model for fault

identification.

The various embodiments in this specification are described in a progressive manner.

Each embodiment focuses on the differences from other embodiments, and the same or

similar parts between the various embodiments can be referred to each other.

Specific examples are used in this article to illustrate the principle and implementation

of the present invention. The description of the above examples is only used to help

understand the method and core idea of the present invention. At the same time, for those

of ordinary skill in the field, according to the idea of the present invention, there will be

changes in the specific implementation and the scope of application. In summary, the

content of this specification should not be construed as limiting the present invention.

Specific examples are used in this article to illustrate the principle and implementation of

the present invention. The description of the above examples is only used to help

Descriptions

understand the method and core idea of the present invention. At the same time, for those of ordinary technical personnel in this field, according to the idea of the present invention, there will be changes in the specific implementation and the scope of application. In summary, the content of this specification should not be construed as limiting the present invention.

Claims

1. A rolling bearing fault diagnosis method based on GRCMSE and manifold learning, which is characterized in that it includes the following steps: Step Sl: Use the acceleration sensors to collect the vibration acceleration signals of

the rolling bearing; Step S2: Use GRCMSE algorithm to extract features of vibration acceleration signals to obtain fault feature information of rolling bearings; Step S3: Use the DDMA manifold learning method to reduce the dimensionality of the

rolling bearing fault feature information, and divide the reduced dimensionality of the rolling bearing fault feature information into into low-dimensional feature set of training sample and low-dimensional feature set of test sample in proportion;

Step S4: Train the PSO-SVM classifier according to the low-dimensional features of the training sample to obtain the trained PSO-SVM classifier; Step S5: Input the low-dimensional feature set of the test sample into the trained PSO-SVM classifier, and diagnose the fault types.

2. According to Claim 1, a rolling bearing fault diagnosis method based on GRCMSE and manifold learning is characterized in that the vibration acceleration signal includes a normal state, an outer ring failure state, an inner ring failure state, and a rolling element

failure state of the drive shaft radial vibration acceleration signal.

3. According to Claim 1, a rolling bearing fault diagnosis method based on GRCMSE and manifold learning is characterized in that the GRCMSE algorithm is specifically:

(1) For time series{x(i),i =1,2,...,N}, use the following formula to calculate the (s) _O (s) (s)(s generalized composite coarse-grained series Gh GYh9j 1 G~h~ 2 *••• ,j js+h-1

YGh,j i Xi)2 S i=(j-1)s+h

N - 1 11j - h ss,2< s,xi - Xi+h S S h0 (1)

(2) For the scale factor s, calculate the number of m-dimensional and

(s) m+1-dimensional space vectors of each generalized coarse-grained sequence YG,h under

m m+1

the scale factor, which are defined as NG,h,s G,h,s.

Claims

m m G,h,s and G,h,s respectively. Then, the GRCMSE entropy value of time series x(i)

under the scale factor s can be obtained:

m+1 EGRCMSE (XI S )M G,h,s m nG,h,s (2) 1m-I rn ± 1 nG,h,s G,h,s G,h,s Gh,s In the formula, S h=1 S h1

4. According to Claim 1, a rolling bearing fault diagnosis method based on GRCMSE and manifold learning is characterized in that the DDMA manifold learning method is specifically:

Assuming that (XPP) is the measurement space, data set Xe RD, P represents the -algebraic subset, and P represents the distributed on X. The specific process of DDMA is as follows: (1) Construct a discriminant Gaussian kernel:

k,(x,y)= exp (x,y) Vxy X

COPW(L)(x,y), 1(x)=l(y)= L,VLe D co min{pW()PW(y),PB(XY)I1(x) l(Y)

In the formula, p(xy) represents the kernel width, (x and 1 (y) represent the

width of the heterogeneous label sample, and Q is the label information of the entire data set;

PW(L)(X>Y pmin||x-y 6x A(x)(y)=(5) ,xeX

PB (X Y)=- (),(

Claims

A=min{NA,N ),'NLI(Y)f (7)

In the formula, NA represents the preset neighborhood size, and NL represents the number of sample points under the same label L; (2) Any data point x can be regarded as a vertex on the weighted graph G, and then a Markov chain is constructed on the data graph to find the relevant structure in the complex geometry. The degree of x in the weight graph G: deg(x)= k,(x,y) xYX (8) Then the transition probability expression from x to y is as follows: k,,(x,y) q(x,y)= deg(x) (9) (3) Use the transition probability matrix Q to describe the Markov chain, among them, Q includes all q(x, y); then the transition distance between x and y is defined as: d D 2 (x,y)= (P,(X)-(,(y))2 n=1 (10)

In the formula, 7 and respectively represent the left and right eigenvectors of the matrix Q, / represents the eigenvalue, and d represents the data dimension after

dimensionality reduction; the eigenvalue satisfies> 2 -1 >0;

The results of diffusion mapping are as follows:

X= [.(IX, (2X,2"dqdX)]T (12)

5. According to claim 1, a rolling bearing fault diagnosis method based on GRCMSE and manifold learning is characterized in that the step S4 is specifically: Step S41: Perform row normalization processing on the low-dimensional features of the training sample; Step S42: According to the SVM model, the radial basis function is selected as the kernel function, and the particle swarm optimization algorithm is used to use the average correct recognition rate of the normalized training sample after three-fold crossover as the

C la i m s

fitness value to determine the optimal penalty factor and kernel function parameters in SVM model.