Rolling Bearing Fault Diagnosis Fusion Model Based on Gene Expression Programming?

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Journal of Information & Computational Science 7:12 (2010) 2437{2442
Available at http://www.joics.com
Rolling Bearing Fault Diagnosis Fusion Model Based on
Gene Expression Programming
?
Jiangtao Huang
a;¤
,Minghui Wang
b
,Kaikuo Xu
c
a
Institute of Image and Graphics,Sichuan University,Chengdu 610064,China
b
School of Computer Science,Sichuan University,Chengdu 610064,China
c
College of Computer Science and Technology,Chengdu University of Information Technology
Chengdu 610225,China
Abstract
Traditionally,a single sensor is always used to provide several machine components operating condition
for fault diagnosis.Fault diagnosis based on this approach is di±cult to obtain satisfactory results,
especially in the severe operating environment.This paper proposes a new feature-level fusion model
based on gene expression programming.And the new fusion model fuses machine component operating
features from more than one sensor in parallel.Firstly,calculate time-domain feature parameters of
each sensor signal.Secondly,construct multi-sensor feature-level fusion model by using gene expression
programming.Finally,identify the integration information and make decisions for machine components
fault diagnosis.Experiments show that the new approach can achieve better performance than single
sensor approach,and it is able to further improve the accuracy of fault diagnosis.
Keywords:Information Fusion;Gene Expression Programming;Fault Diagnosis
1 Introduction
Rotating machinery is very common in industrial systems,and it plays an important role in
industrial development and economic development.Although the reliability and robustness of
mechanical systems have been improving,the occasional failure events of components often lead
to unexpected downtime while resulting in huge losses.Rolling element bearing is often at the
heart of machinery systems and su®ers from fault frequently.So,it is an urgent problem to
exactly diagnose the incipient faults in these bearings.
Fault diagnosis is still an ongoing research subject over a decade attracting a huge number
of researchers from di®erent areas.And there are various methods in use for fault diagnosis,
such as vibration analysis,frequency analysis,statistical methods and intelligent systems.During
operating process,the machine set can generate all kinds of signals,and involve in many correlated
?
Project supported by the National Nature Science Foundation of China (No.61071162).
¤
Corresponding author.
Email address:jiangtao
huang@163.com (Jiangtao Huang).
1548{7741/Copyright ©2010 Binary Information Press
December 2010
2438 J.Huang et al./Journal of Information & Computational Science 7:12 (2010) 2437{2442
features [1].Those approaches based on the vibration analysis are advantageous because of their
visual feature,easy measurability,high accuracy and reliability [2].A wide variety of techniques
have been introduced for fault diagnosis using raw vibration signals,such as wavelet and wavelet
packet methods,blind source separation,arti¯cial neural networks,support vector machines
and fuzzy technique.These techniques mainly deal with single-source data.Many researches
have shown that an individual decision system with a single data source can only acquire a
limited classi¯cation capability which may not be enough for a particular application [3].So,it is
necessary to carry out the research of multiple data sources information fusion for fault diagnosis.
Information fusion for fault diagnosis mainly includes feature fusion and decision fusion.In
recent years,decision-level fusion approaches have been of major concern.In contrast,the feature-
level fusion has probably not received the amount of attention it deserves [4].This paper presents
a novel feature-level fusion method for fault diagnosis by using gene expression programming
(GEP),and the newfusion method uses parallel strategy.The remainder of this paper is organized
as follows.Section 2 gives a brief overview of GEP.Feature-level fusion model for fault diagnosis
using GEP is studied in Section 3.Section 4 discussed the performance of the new fusion model.
Conclusions are given in Section 5.
2 Overview of Gene Expression Programming
GEP was invented by Ferreira [5],and it is the natural development of genetic algorithms and
genetic programming.GEP uses linear chromosome which is composed of genes containing ter-
minal and non-terminal symbols.Chromosomes can be modi¯ed by mutation,transposition,root
transposition,gene transposition,gene recombination,one-point and two-point recombination.
GEP genes are composed of a head and a tail.The head contains function (non-terminal) and
terminal symbols,while the tail contains only terminal symbols.For each problem,the head
length (denoted h) is chosen by users,and then the head length is used to evaluate the tail length
(denoted t) by:t = (n ¡1) £h + 1,where n is the number of arguments of the function with
most arguments.
The °ow of GEP is as follows:
Step 1
To set control parameters,select function classes,initialize population.
Step 2
To parse chromosome,evaluate population.
Step 3
To take use some operation such as selection,mutation,inserts sequence,recombine,
mutation of randomconstant and inserts sequence of randomconstant to create newpopulation.
Step 4
To implement best preservation strategy.
Step 5
If obtain most precision of computing,evolution would be ¯nished,else turn to Step 2.
3 Feature-level Fusion Model for Fault Diagnosis
In this section,a new feature-level fusion model for fault diagnosis will be proposed.And the
new approach is based on multiple sensors which collect vibration signals.
J.Huang et al./Journal of Information & Computational Science 7:12 (2010) 2437{2442 2439
Assume that there are I sensors used in machine condition monitoring.For each sensor,the
original data set is divided into some signals of the same data points.Each of these signals
is processed to extract eleven feature parameters (p
1
¡ p
11
) which are time-domain statistical
characteristics.These feature parameters are presented in Eqs.(1-11),where x(t) is a signal
series and N is its number of data points.When faults occur in rotating machinery,the time-
domain signal may change.That is to say,its feature parameters may be di®erent from those
under normal condition.Then,use these feature parameters to compose single sensor's feature
vector.For example,P
i
= [p
i
1
;p
i
2
;p
i
3
;p
i
4
;p
i
5
;p
i
6
;p
i
7
;p
i
8
;p
i
9
;p
i
10
;p
i
11
] is the feature vector of the i-th
sensor in machine condition monitoring,where i 2 f1;¢ ¢ ¢;Ig.
p
1
=
1
N
X
N
n=1
x(n):(1)
p
2
= (
P
N
n=1
(x(n) ¡p
1
)
2
N ¡1
)
1
2
:(2)
p
3
= (
1
N
X
N
n=1
x(n)
2
)
1
2
:(3)
p
4
= (
1
N
X
N
n=1
p
jx(n)j)
2
:(4)
p
5
= maxjx(t)j:(5)
p
6
=
P
N
n=1
(x(n) ¡p
1
)
3
(N ¡1)p
3
2
:(6)
p
7
=
P
N
n=1
(x(n) ¡p
1
)
4
(N ¡1)p
4
2
:(7)
p
8
=
p
5
p
3
:(8)
p
9
=
p
5
p
4
:(9)
p
10
=
p
3
1
N
P
N
n=1
jx(n)j
:(10)
p
11
=
p
5
1
N
P
N
n=1
jx(n)j
:(11)
Fault diagnosis can be seen as a pattern recognition problem.Assume that there are M con-
ditions in fault diagnosis,and let S
i
m
represent the set of all training samples belonging to m-th
condition (1 · m · M) from the i-th sensor source.Then,feature-level fusion model is used
to fuse features from di®erent sensors and look for a feature recognition function'which maps
the feature space to another space where samples in the same class are similarity and samples
dissimilarity otherwise.Here,feature recognition function'is constructed by using GEP,and
functions +;¡;£;=;sqrt;exp are selected as input functions of GEP.When training the feature
recognition function,all source features are used to train.The ¯tness function is de¯ned as follow:
Fitness =
P
M¡1
m=1
P
M
m
0
=m+1

m
¡¾
m
0
)
2
P
M
m=1
P
I
i=1
P
k2S
i
m
('(P
i
k
) ¡¾
m
)
2
:(12)
2440 J.Huang et al./Journal of Information & Computational Science 7:12 (2010) 2437{2442
where ¾
m
is the mean of all m-th condition samples function mapping values,its formula is:
¾
m
=
1
I
I
X
i=1
1
jS
i
m
j
X
k2S
i
m
'(P
i
k
):(13)
After ¯nd the feature recognition function,we propose a multiple sources feature fusion model.
This model fuses these feature vectors from di®erent sensors to get a integrated feature vector
P
f
.In this model,we construct a feature evaluation matrix which is composed by all correctly
classi¯ed original features'averages.When fusing di®erent sources'features,each source feature
vector will be compared with feature evaluation matrix.And the smallest di®erence between each
feature parameter and its corresponding elements in feature evaluation matrix will be selected
as evaluation result value of this feature parameter.Then,a temporary evaluation result value
matrix of all di®erent source current features can be built.All minimum evaluation result values
among the same feature component will be selected,and their corresponding feature parameters
are extracted to compose integrated feature vector P
f
.Finally,using integrated feature vector P
f
and feature recognition function',we can determine current operating condition of diagnostic
component by selecting the condition type m which has the minimum of'(P
f
) ¡¾
m
,(1 · m·
M).
4 Experiment Results and Analysis
In order to evaluate the proposed feature-level fusion model,we apply it to fault diagnosis of
rolling element bearings from the Case Western Reserve University [6].And we conducted three
experiments over there data sets as Table 1 shows whose data are collected under various operating
loads from motor driven end and fan end accelerometers.
Table 1:Description of three data sets
Data The number of The number of Defect size Operating Class
set training sample testing sample (training/testing inches) condition label
A 80 80 0/0 Normal 1
80 80 0.007/0.007 Outer race 2
80 80 0.007/0.007 Inner race 3
80 80 0.007/0.007 Ball 4
B 80 80 0/0 Normal 1
80 80 0.007/0.021 Outer race 2
80 80 0.007/0.021 Inner race 3
80 80 0.007/0.021 Ball 4
C 80 80 0/0 Normal 1
80 80 0.021/0.007 Outer race 2
80 80 0.021/0.007 Inner race 3
80 80 0.021/0.007 Ball 4
Each data set covers four di®erent operating conditions and four di®erent loads (0,1,2 and 3
hp).And each class of all data sets has 160 data samples which are divided into two equal halves,
J.Huang et al./Journal of Information & Computational Science 7:12 (2010) 2437{2442 2441
one for training and the other for testing.The task of data set A is to identify di®erent type
of faults,while the experiment over data set B is carried out to further investigate the diagnosis
performance of developing faults when the fusion model is trained by incipient faulty samples.
And the experiment over data set C is to test the diagnosis performance of incipient faults when
the fusion model is trained by the serious faulty samples.
Table 2 gives the results of these three experiments.From Table 2,we can see that the feature-
fusion model can get stable,good diagnosis performance.And in the experiment on data set C,
the testing performance is higher than the training performance.That is to say,when multiple
sensor feature-fusion model is trained by the serious faulty samples,it can easily identify incipient
faults in system.
In order to observe the performance change when feature-fusion model uses multiple source
information instead of single source information,the feature-fusion model proposed in this paper
is used to test single sensor source fault diagnosis performance.And Table 3 gives the performance
comparison result between more than one sensor (here using two sensors) and single sensor.From
Table 3,we can see multi-sensor testing performance is greatly higher than the single sensor
application using feature level fusion model.
Table 2:Fault diagnosis performance using feature-fusion model
Data set Training recognition accuracy Testing recognition accuracy
A 83.75% 81.25%
B 83.75% 72.50%
C 76.25% 81.88%
Table 3:Performance comparison between multi-sensor and single sensor
Data set A B C
Multi-sensor testing performance increasing 0.56 0.48 0.57
5 Conclusions
This paper has proposed a new multiple sources feature-level fusion model using GEP.And the
fusion model is used to fault diagnosis.At present,the research of fault diagnosis based on feature-
level fusion is still less,far from decision-level fusion attention.This is mainly because feature-
level fusion is more di±cult,but feature-level fusion application for fault diagnosis can more
e®ectively extract fault feature information to improve diagnosis performance.The new feature-
level fusion model is evaluated by the real fault diagnosis system of rotating machinery.From
the experimental results,we can see that the new feature-level fusion model for fault diagnosis
can get good performance,and its performance of multi-sensor fusion is great higher than single
sensor application.
2442 J.Huang et al./Journal of Information & Computational Science 7:12 (2010) 2437{2442
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For further detail,please visit website,http://www.eecs.cwru.edu/laborator/bearing,2006