AU2021102131A4

AU2021102131A4 - Fault diagnosis method of rolling bearing based on generalized composite multi-scale weighted permutation entropy and supervised isometric mapping

Info

Publication number: AU2021102131A4
Application number: AU2021102131A
Authority: AU
Inventors: Yongwu Cai; Jiaxin DING; Gaosong Li; Zhenya WANG; Ligang YAO
Original assignee: Fuzhou University
Current assignee: Fuzhou University
Priority date: 2021-04-22
Filing date: 2021-04-22
Publication date: 2021-06-10
Anticipated expiration: 2029-04-22

Abstract

The invention relates to a fault diagnosis method for rolling bearing based on generalized composite multi-scale weighted permutation entropy and supervised isometric mapping, which comprises the following steps: The rolling bearing signals under different fault states are collected; The generalized composite multi-scale weighted permutation entropy algorithm (GCMWPE) is used to extract fault features, and the high-dimensional fault feature set of rolling bearings is constructed comprehensively from multiple scales; A novel manifold learning algorithm, named supervised isometric mapping (S-Isomap), is used to reduce the dimensionality of high-dimensional fault features and obtain a low-dimensional fault feature set; The low-dimensional fault feature set is used to train PSO-SVM, and the trained particle swarm optimization support vector machine PSO-SVM is used for diagnosing bearing faults. The method solves the problem of difficulty in extracting fault features of rolling bearings, and can effectively and accurately diagnose various fault types of the rolling bearing. 1/5 FIGURES Vib rationacceleration signal Trainingsample Testsample Constructing high-dimensional fault feature set usingGCMWPE Dimension reduction using S-Isornap manifold leading algorithm Low W itt Collection of Training Samples Test sample low W itt collection Train PSO-SVM classifier Trained PSO-SVM classifier model Diagnostic fault type Figure I

Description

1/5

FIGURES

Vib rationacceleration signal

Trainingsample Testsample

Constructing high-dimensional fault feature set usingGCMWPE

Dimension reduction using S-Isornap manifold leading algorithm

Low W itt Collection of Training Samples Test sample low W itt collection

Train PSO-SVM classifier Trained PSO-SVM classifier model

Diagnostic fault type

Figure I

Fault diagnosis method of rolling bearing based on generalized composite multi

scale weighted permutation entropy and supervised isometric mapping

TECHNICAL FIELD

The invention relates to the technical field of rolling bearing fault analysis, in

particular to a fault diagnosis method of rolling bearing based on generalized composite

multi-scale weighted permutation entropy and supervised isometric mapping.

BACKGROUND

Rolling bearings are widely used and easily damaged parts of rotating machinery, so

it is of great theoretical and practical significance to diagnose their faults.

The vibration signals of rolling bearings are usually non-stationary and nonlinear.

Therefore, many methods to measure the complexity of nonlinear time series of mechanical

dynamic systems have been proposed one after another and applied to the field of fault

diagnosis. Among them, multi-scale weighted permutation entropy (MWPE) combines the

advantages of multi-scale entropy and weighted permutation entropy, and can measure the

complexity of time series from multiple scales, so it is widely used in many fields.

However, when MWPE is applied to feature extraction of rolling bearings, there are still

three shortcomings: (1) The entropy estimation deviation of MWPE will increase with the

increase of coarse-grained scale factor; (2) The coarse-grained process of MWPE ignores

the useful information on other coarse-grained sequences, which affects the accuracy of

entropy. (3) When constructing the coarse-grained serious of MWPE, the dynamic

mutation behavior of the original signal will be neutralized to a certain extent using mean

processing, which will affect the feature extraction results. Feature extraction is the key for fault diagnosis of rolling bearings. However, the extracted fault features often have redundant information, which is not conducive to subsequent processing.

SUMMARY

In view of this, the purpose of the present invention is to propose a fault diagnosis

method of rolling bearing based on generalized composite multi-scale weighted

permutation entropy and supervised isometric mapping, which solves the problem of

difficulty in extracting fault features of rolling bearings and can effectively and accurately

diagnose various faults of rolling bearings.

The method is realized by adopting the following scheme: the fault diagnosis method

of rolling bearing based on generalized composite multi-scale weighted permutation

entropy and supervised isometric mapping comprises the following steps:

Collecting rolling bearing signals under different fault states;

The generalized composite multi-scale weighted permutation entropy algorithm

(GCMWPE) is used to extract fault features, and the high-dimensional fault feature set of

rolling bearings is constructed comprehensively from multiple scales;

A novel manifold learning algorithm, named supervised isometric mapping (S

Isomap), is used to reduce the dimensionality of high-dimensional fault features and obtain

a low-dimensional fault feature set;

The low-dimensional fault feature set is used to train PSO-SVM, and the trained PSO

SVM is used for diagnosing bearing faults.

Further, collecting different fault state signals of the rolling bearing specifically

comprises collecting radial vibration acceleration signals of the rolling bearing under normal state, outer ring fault state, inner ring fault state, and ball fault state by using the acceleration sensors.

Furthermore, the generalized composite multi-scale weighted permutation entropy

algorithm (GCMWPE) is used to extract fault features and comprehensively construct a

high-dimensional fault feature set of rolling bearings from multiple scales, specifically, the

generalized composite multi-scale weighted permutation entropy algorithm (GCMWPE) is

used to extract entropy features of each group of vibration signals and construct the original

high-dimensional feature set.

Further, the entropy feature extraction of each group of vibration signals by using

generalized composite multi-scale weighted permutation entropy algorithm (GCMWPE),

and the construction of the original high-dimensional feature set specifically comprises the

following steps:

Step S11: For the time series of different fault state signals X = {x1, X2,..., XN}, the

generalized composite coarse-grained sequence is calculated by the

following formula:

- ~ A 1L.i

i=(- A 1 sf

1 k__t s, 2< xs Xi-i.A

In the formula, represents the k-th generalized composite coarse-grained

sequence under scale s, s is the scale factor, r is the time delay, and N is the time series

length;

S12: for each scale factor s, calculate the WPE value of each generalized coarse

grained sequence;

S13: homogenize a plurality of WPE values at the same scale to obtain the GCMWPE

value of the corresponding fault signal at the s scale, and the corresponding expression is

as follows:

GCMWPE (X. r, n,s)- 1WPE(y ,m,r) S k=1

Further, setting GCMWPE parameters as follows: setting the time series length N as

the number of sampling points, scale factor s = 20, time delay r = 1, and embedding

dimension m = 6.

In addition, the low-dimensional fault feature set is used to train PSO-SVM, and the

trained PSO-SVM is used for diagnosing faults specifically including the following steps:

S21: randomly dividing each fault sample in the low-dimensional fault feature set into

a training sample set and a testing sample set according to the ratio of 1:4. And normalizing

the training sample set and the testing sample set respectively;

S22: defining the kernel function in the SVM model as a radial basis function, and

optimizing and selecting parameters by using the particle swarm optimization algorithm

(PSO);

S23: using the training sample set to train the PSO-SVM model, and then using the

trained PSO-SVM model to diagnose and identify the testing sample set.

Additionally, in step S2, the average correct recognition rate of training samples after

3-fold crossover is defined as fitness value, and the particle swarm size is set to 10, the

iteration termination is set to 100, the local search ability is set to 2, and the global search

ability is set to 2, so as to obtain the optimal penalty factor and kernel function parameters

of PSO-SVM model.

Compared with the prior art, the invention has the following beneficial effects:

1. Aiming at the shortcomings of coarse-grained of the MWPE, this paper proposes a

new GCMWPE algorithm and uses this algorithm to comprehensively extract the fault

feature information of rolling bearings.

2. The invention introduces the S-Isomap algorithm to carry out secondary feature

extraction on the high-dimensional fault feature set, to obtain a low-dimensional fault

feature set which is easy to distinguish faults, and improves the fault diagnosis

performance.

3. In this invention, the PSO-SVM classifier is introduced to diagnose the

GCMWPE+S-Isomap feature set, and the fault type of rolling bearing is effectively

identified.

BRIEF DESCRIPTION OF THE FIGURES

Fig. 1 is a schematic flowchart of a method according to an embodiment of the present

invention.

Fig. 2 is a time-domain waveforms diagram of rolling bearings at different states

according to an embodiment of the present invention.

Fig. 3 is a flowchart of the GCMWPE algorithm according to an embodiment of the

present invention.

Fig. 4 is the feature extraction result of GCMWPE according to an embodiment of the

present invention.

Fig. 5 is a dimensionality reduction result of the GCMWPE feature set by S-Isomap

according to an embodiment of the present invention.

Fig. 6 is the recognition result of PSO-SVM on the feature set after dimensionality

reduction according to the embodiment of the present invention.

DESCRIPTION OF THE INVENTION

The invention will be further explained regarding the drawings and examples.

It should be noted that the following detailed description is exemplary and is intended

to provide further explanation for the application. Unless otherwise specified, all technical

and scientific terms used herein have the same meanings as commonly understood by those

of ordinary skill in the technical field to which this application belongs.

It should be noted that the terms used here are only for describing specific

embodiments, and are not intended to limit exemplary embodiments according to this

application. As used herein, unless the context clearly indicates otherwise, the singular

form is also intended to include the plural form. In addition, it should be understood that

when the term "comprising" and/or "containing" is used in this specification, it indicates

the presence of features, steps, operations, devices, components and/or combinations

thereof.

As shown in Fig. 1, this embodiment provides a rolling bearing fault diagnosis method

based on generalized composite multi-scale weighted permutation entropy and supervised

isometric mapping, and takes the rolling bearing signal data collected by the power

transmission system fault diagnosis test bench developed by Spectra Quest as an example

to verify the method. The input shaft speed is 20 Hz, the load current is 0 A, the sampling

frequency is 3000 HZ, and the sampling points are set to 4096. It comprises the following

steps:

Collecting different fault state signals of rolling bearings;

The generalized composite multi-scale weighted permutation entropy algorithm

rolling bearings is constructed comprehensively from multiple scales;

The supervised isometric mapping manifold learning algorithm (S-Isomap) is used to

reduce the dimensionality of high-dimensional fault features and obtain its low

dimensional fault feature set;

The low-dimensional fault feature set is used to train the particle swarm optimization

support vector machine (PSO-SVM), and the trained PSO-SVM is used for diagnosing

bearing faults.

In this embodiment, collecting different fault state signals of the rolling bearings

specifically comprises collecting radial vibration acceleration signals of the rolling

bearings under normal state, outer ring fault state, inner ring fault state, and ball fault state

by using acceleration sensors. In this embodiment, acceleration sensors are used to

respectively collect 100 sets of vibration acceleration signals in four states of normal

(NOR), outer ring fault (ORF), inner ring fault (IRF) and ball fault (BF), and a total of 400

sets of sample signals in the four states. The corresponding time-domain waveforms are

shown in Fig. 2.

In this embodiment, the generalized composite multi-scale weighted permutation

entropy algorithm (GCMWPE) is used to extract fault features and comprehensively

construct a high-dimensional fault feature set of rolling bearings from multiple scales,

specifically, the generalized composite multi-scale weighted permutation entropy

algorithm (GCMWPE) is used to extract entropy features of each group of vibration signals

and construct an original high-intensity collection. the algorithm flowchart of GCMWPE is shown in Fig. 3, and the mean entropy curves for different states of rolling bearings are shown in Fig. 4.

The principle of GCMWPE is as follows:

Weighted permutation entropy (WPE) overcomes the disadvantage that permutation

entropy (PE) only considers the sequence structure characteristics of sequences and ignores

the amplitude characteristics. The specific process is as follows:

(1) Reconstruct the phase space of time series X ={x1, X2,..., XN) to obtain a series of

subsequences

In the formula, r is the time delay, and m is the embedding dimension.

(2) The weight of each subsequence wi is calculated.

VV PZ - AC,

/It,

(3) The feature information of any subsequence ' is expressed by the weight

value wi and the arrangement pattern 7ri. There are q permutation modes in this time series

X, and the weighted probability value of the q-th permutation mode tq is as follows:

(4) The weighted permutation entropy WPE of time series Xis calculated.

Multi-scale weighted permutation entropy (MWPE) overcomes the shortcomings of

WPE with single-scale analysis, and can comprehensively characterize the complexity of

time series from multiple scales. The specific process is as follows:

(1) Coarsening the time series X to obtain a coarse-grained sequence y(S) = {y(s)()}.

y"(f) x, ,C j N/s) i=<~)

(2) Calculate the WPE value of coarse-grained sequence y() under different scale

factors:

WPE(X, m, )WPE (y(s), ; In which WPE(-) is the weighted

permutation entropy algorithm.

(1) For the time series X = {xi, X2,..., XN) of different fault state signals, the

1AP = WsyI generalized composite coarse-grained sequence " Gj is calculated by the

following formula;

I~ A

In the formula, YU represents the k-th generalized composite coarse-grained

sequence under scale s.

(2) For each scale factors, calculate theWPE value of each generalized coarse-grained

sequence .

(3) The GCMWPE value of the corresponding fault signal at the s scale can be

obtained by homogenizing multiple WPE values at the same scale, and the corresponding

expression is as follows:

GCMWPE(Xr,m,s)= Y WPE(yj, 1f1

In this embodiment, GCMWPE parameters are set as follows: set the time series

length as N= 4096, the scale factor s = 20, the time delay r = 1, and the embedding

dimension m= 6. According to Fig. 4: (1) As far as the initial scale is concerned, the entropy

value of the normal state is the largest among the four states of rolling bearings obtained

by GCMWPE. For actual working conditions, when the rolling bearing is in the normal

state, the vibration signal fluctuates randomly, the signal irregularity is high, and the self

similarity is low, so the entropy value is large. However, when the bearing has a local fault,

the vibration signal fluctuation has certain regularity, and the signal regularity and self

similarity are high, so the entropy value is small. Therefore, the GCMWPE algorithm is

suitable for judging whether the rolling bearing fault occurs. (2) The entropy mean curve

extracted by the proposed GCMWPE method is smooth, and it can effectively distinguish

four types of samples, which verifies the effectiveness of using this algorithm to

comprehensively extract fault features of rolling bearings.

Better, because the fault feature set extracted by the GCMWPE algorithm is

characterized by high-dimensionality, nonlinearity, and redundancy, directly using PSO

SVM classifier for fault recognition will increase the recognition time and even affect the

recognition effect. Therefore, in this embodiment, the supervised isometric mapping (S

Isomap) algorithm is used to reduce the dimension, and the low-dimensional sets which

are easy to distinguish the fault types are extracted. The dimensionality reduction result is

shown in Figure 5. The parameters of the S-Isomap algorithm are set as follows: the

intrinsic dimensionality is set to 3, the nearest neighbor parameter is set to 70, and the

parameter Pis the average of Euclidean distances of all sample points; Parameter a is set

to 0.4. In the dimensionality reduction result of GCMWPE feature set by S-Isomap, the four types of samples can be effectively distinguished completely, and the aggregation of the four types of samples is good, which shows that the feature extraction method of combining GCMWPE with S-Isomap proposed in this embodiment can effectively extract low-dimensional and sensitive feature sets which are easy to distinguish the fault feature information of rolling bearings.

Among them, the principle of the S-Isomap manifold learning algorithm is as follows:

For the input sample set U=[ui, U2,..., uN]T, the specific procedure of S-Isomap are as

follows.

(1) Define a neighborhood graph G containing all samples and construct a supervised

distance matrix Ds = {ds(ui, j)}. If a sample point ujis a K-nearest neighbor of uj, then u

is edge-connected to uj with edge length ds(u, u); otherwise, no edge connection.

(2) The shortest path is calculated by the Dijkstra method, and the shortest path

between any two points on graph G is defined as the geodesic distance between two points.

(3) Using multidimensional scale analysis (MDS) algorithm, the geodesic distance

matrix is mapped in a low-dimensional space, and the low-dimensional embedding result

Y is obtained.

In this embodiment, the training of particle swarm optimization support vector

machine (PSO-SVM) by using the low-dimensional fault feature set and the fault diagnosis

by using the trained PSO-SVM specifically includes the following steps:

S21: randomly dividing each fault in the low-dimensional fault feature set into a

training sample set and a testing sample set according to the ratio of 1:4. And normalizing

the testing sample set and the training set respectively;

S22: the kernel function in the SVM model is defined as the radial basis function, and

parameters are optimized and selected by PSO algorithm;

S23: use the training set to train the (PSO-SVM) model, and then use the trained (PSO

SVM) model to diagnose and identify the testing samples.

In this embodiment, in step S2, the average correct recognition rate of training samples

after the 3-fold crossover is defined as fitness value, and the particle swarm size is set to

, the iteration termination is set to 100, the local search ability is set to 2, and the global

search ability is set to 2, so as to obtain the optimal penalty factor and kernel function

parameters of PSO-SVM model.

The recognition result of the test sample set samples in this embodiment is shown in

Fig. 6. As shown in Fig. 6, the fault diagnosis method proposed in this embodiment can

effectively identify each fault type, and the recognition rate reaches 100%.

The above is only a preferred embodiment of the present invention and is not meant

to limit the present invention in other forms. Any person familiar with this profession may

use the technical content disclosed above to change or modify it into an equivalent

embodiment with equivalent changes. However, any simple modifications, equivalent

changes and modifications made to the above embodiments according to the technical

essence of the present invention without departing from the technical scheme of the present

invention still belong to the protection scope of the technical scheme of the present

invention.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A fault diagnosis method of rolling bearing based on generalized composite multi-scale

weighted permutation entropy and supervised isometric mapping, characterized by

comprising the following steps:

Collecting different fault state signals of rolling bearings;

The generalized composite multi-scale weighted permutation entropy algorithm

rolling bearings is constructed comprehensively from multiple scales;

reduce the dimensionality of high-dimensional fault features and obtain its low

dimensional fault feature set;

The low-dimensional fault feature set is used to train PSO-SVM, and the trained PSO-SVM

is used for diagnosing bearing faults.

2. The fault diagnosis method of rolling bearing based on generalized composite multi

scale weighted permutation entropy and supervised isometric mapping according to claim

1, which is characterized in that collecting different fault state signals of the rolling bearing

specifically comprises collecting radial vibration acceleration signals of the rolling bearing

under normal state, outer ring fault state, inner ring fault state, and ball fault state by using

acceleration sensors.

3. The fault diagnosis method of rolling bearing based on generalized composite multi

1, which is characterized in that the generalized composite multi-scale weighted

permutation entropy algorithm (GCMWPE) is used to extract fault features and comprehensively construct a high-dimensional fault feature set of rolling bearings from multiple scales, specifically, the generalized composite multi-scale weighted permutation entropy algorithm (GCMWPE) is used to extract entropy features of each group of vibration signals and construct the original high-dimensional feature set.

4. The fault diagnosis method of rolling bearing based on generalized composite multi

3, which is characterized in that the entropy feature extraction of each group of vibration

signals by using generalized composite multi-scale weighted permutation entropy

algorithm (GCMWPE), and the construction of the original high-dimensional feature set

specifically comprises the following steps:

Step S11 : For the time series of different fault state signals X = {x1, X2,..., XN}, the

generalized composite coarse-grained sequence is calculated by the

following formula:

1 Z

In the formula, i represents the k-th generalized composite coarse-grained sequence

under scale s, s is the scale factor, r is the time delay, and Nis the time series length;

S12: for each scale factor s, calculate the WPE value of each generalized coarse-grained

sequence;

S13: homogenize a plurality of WPE values at the same scale to obtain the GCMWPE value

of the corresponding fault signal at the s scale, and the corresponding expression is as

follows:

1 GCMWPE (X, r, ns) - WPE(yg , n,

) S k=1

5. The fault diagnosis method of rolling bearing based on generalized composite multi

3 or 4, which is characterized by setting GCMWPE parameters as follows: setting time

series length N as the number of sampling points, the scale factor s = 20, the time delay r

= 1, and the embedding dimension m = 6.

6. The fault diagnosis method of rolling bearing based on generalized composite multi

1, which is characterized in that the low-dimensional fault feature set is used to train PSO

SVM, and the trained PSO-SVM is used for diagnosing bearing faults specifically

including the following steps:

S21: randomly dividing each fault sample in the low-dimensional fault feature set into a

the training sample set and the testing sample set respectively;

(PSO);

S23: using the training sample set to train the PSO-SVM model, and then use the trained

PSO-SVM model to diagnose and identify the testing sample set.

7. The fault diagnosis method of rolling bearing based on generalized composite multi

6, which is characterized in that in step S2, the average correct recognition rate of training samples after 3-folds crossover is defined as fitness value, and the particle swarm size is set to 10, the iteration termination is set to 100, the local search ability is set to 2, and the global search ability is set to 2, so as to obtain the optimal penalty factor and kernel function parameters of PSO-SVM model.

FIGURES 1/5

Figure 1