TELKOM
NIKA
, Vol.12, No
.4, Dece
mbe
r
2014, pp. 84
7~8
5
4
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i4.305
847
Re
cei
v
ed Au
gust 28, 20
14
; Revi
sed O
c
t
ober 1
8
, 201
4; Acce
pted
No
vem
ber 3,
2014
Diagnostic Study Based on Wavelet Packet Entropy
and Wear Loss of SVM
Yunjie Xu*
1
, Shudong
Xiu
2
Schoo
l of ji
ya
n
g
, Z
hejia
ng Agr
i
cultur
al &
F
o
re
str
y
Univ
ersit
y
,
3118
00, Z
huj
i, Chin
a
Ph./F
ax:+
86 05
758
77
600
68
*Corres
p
o
ndi
n
g
author, em
ail
:
xyj9
000
@16
3
.
com
1
,99386
95
5@q
q
.com
2
A
b
st
r
a
ct
Agai
nst the pr
obl
e
m
s, the ratio of sign
al to
nois
e
of bear
in
g w
ear is low
,
the feature ext
r
action is
difficult, there
are few
fault sampl
e
s and it i
s
difficult
to establis
h the reli
abl
e fault reco
gniti
on
mod
e
l, the
dia
gnostic
met
hod
is p
u
t for
w
ard base
d
o
n
w
a
ve
let
pac
ket features
a
nd b
ear
ing w
e
ar loss
of
Sup
port
Vector Machine
(SVM). F
i
rstly, choose c
o
mentropy w
i
th st
r
ong fa
ult toler
ance
as char
a
c
teristic para
m
eter,
then throu
gh
w
a
velet packet
deco
m
p
o
sitio
n
, extract feat
ure entro
py of w
a
velet pack
e
t in fault sen
s
itivity
ban
d as in
put
vector and fi
nally, a
p
p
l
y the W
r
apper
me
thod of le
ast squar
e SVM to choos
e o
p
ti
ma
l
character su
b
s
et. T
he appl
i
c
ation i
n
actu
al be
arin
g
faul
t diagn
osis i
n
dicates the
effectiven
ess of the
prop
osed
meth
od in the
article
.
Ke
y
w
ords
: be
arin
g w
ear loss
, w
a
velet packet feature entro
py, SVM, optimi
z
at
io
n
1. Introduc
tion
The bea
ring
wea
r
fault diagno
si
s is to make u
s
e
of signal p
r
o
c
e
ssi
ng and
analysi
s
te
ch
nics to
analy
z
e th
e
sign
al
that c
ontain
s
info
rmatio
n
on
we
arin
g, to find
out t
he
cha
r
a
c
teri
stic paramete
r
s related to
we
a
r
ing
and
u
s
e
these
pa
ram
e
ters to di
stin
guish the
we
ar
state and rea
l
-time techn
o
l
ogy stat
e of beari
ng. He
re it involves
two aspect
s
: first, to cond
uct
feature
extra
c
tion i
n
u
s
e
o
f
sign
al p
r
o
c
e
ssi
ng te
ch
nol
ogy; se
co
nd,
to co
ndu
ct fa
ult diag
no
sis
in
use of mod
e
reco
gnition te
chn
o
logy [1].
Becau
s
e
of it
s
stron
g
n
onli
nearity
sep
a
rating
cap
a
cit
y
, the algo
rithm of SVM
h
a
s
bee
n
widely u
s
ed i
n
fault diagn
osi
s
field. Ho
wever,
the S
V
M classifie
r
need
s to e
s
timate normali
ze
d
para
m
eter, th
e ke
rnel fu
nction sh
ould
meet the
co
n
d
ition of Me
rcer. M
ean
whi
l
e, as the
sol
v
ed
spa
r
sity is n
o
t
required in
the model of
the SVM
classifier, it results in many su
pport ve
ctors,
makin
g
th
e computation
complexity
of cla
ssifie
r
got
incre
a
sed.
There m
a
tters a
r
e
e
s
pe
ci
ally
importa
nt for the on-lin
e wearin
g dete
c
tion t
hat highly
requi
re
s inst
antaneity [2]-[4].
SVM base
d
on stati
s
tical
learni
ng the
o
ry is
u
s
e
d
i
n
many ap
pl
ication
s
of m
a
chi
ne
learni
ng b
e
cause of its
g
ood g
ene
rali
zation
ca
pabi
lit
ies. SVM classifies
better tha
n
Artificia
l
Neu
r
al Network (ANN) b
e
ca
use
of
the
pri
n
ci
ple
of risk mini
mization. In
ANN, tra
d
itional
Empirical
Risk Minimi
zatio
n
(ERM) i
s
u
s
ed
on traini
ng data
set to minimi
ze t
he e
rro
r. But
in
SVM, Structu
r
al
Ri
sk Mini
mization
(S
RM) i
s
used
to
minimi
ze an
uppe
r boun
d on
the
expe
ct
ed
risk [2]-[4].
These p
a
ra
meters of S
V
M mainly i
n
clu
de the
penalty con
s
tant C, an
d
the
para
m
eters i
n
ke
rnel fun
c
t
i
on, and they
affect t
he performan
ce of
SVM. Theref
ore, in this
study,
The
high
fre
quen
cy d
e
m
odulatio
n a
n
a
lysis was u
s
ed
to
ab
stra
ct the
charac
teristic of
sig
nals,
The si
gnal
s
were de
com
p
ose
d
into eig
h
t freque
ncy
band
s an
d th
e informatio
n
in the high b
and
wa
s u
s
ed
a
s
a characte
rist
ic ve
ctor, a
n
i
n
telli
gent di
a
gno
stic m
e
th
od ba
se
d o
n
Geneti
c
-Su
p
p
o
rt
Vector Ma
chi
ne (GSVM)
approa
ch is
pre
s
ente
d
fo
r fault diagno
sis of roll
er
beari
n
g
s
in the
woo
d
-wool p
r
odu
ction devi
c
e [7].
Therefore, th
e articl
e put
s forwa
r
d th
e
online i
n
sp
ection method
based o
n
the
wavelet
packet entro
py and beari
ng wea
r
of SVM [5]. The
ar
ticle
cho
o
ses the co
me
ntropy with st
rong
fault tolerance to d
e
scribe
overall fe
atures
of
si
gnal
a
s
the
featu
r
e
para
m
eters,
condu
cts wave
let
packet de
co
mpositio
n in use of multire
s
olutio
n f
eature of wavelet
transfo
rm, extract the feature
entropy of wavelet packet
in the fault b
and as in
put vector, esta
bl
ish discrimina
t
ion function
by
usin
g the available fault sa
mples a
nd m
a
ke wea
r
loss and fault cl
assifier of SVM [6]. After the
test on th
e cl
assifier i
n
u
s
e of ne
w
sa
mples, it
in
di
cate
s that th
e metho
d
ha
s well
solved
the
feature extra
c
tion of wear vibr
ation si
g
nal and th
e nonlin
earity
of fault in the state of small
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 847
– 854
848
sampl
e
as
well as the ide
n
tification of high-dime
n
s
i
onal mod
e
, can well di
stin
guish the sev
e
rity
of fault and greatly decrea
s
e the time to det
ect fault while ke
ep of h
i
gh dete
c
tion
rate.
2. Featur
e e
n
tropy
of
w
a
v
e
let packe
t of v
i
bration signal
The inner and outer weari
ng as
well as
spa
lling of
rolling bearing
are the
reasons t
o
cau
s
e the im
pact of 207 rolling bea
ring
, which ha
s
b
een proved a
fter dissectio
n
. The vibration of
beari
ng is m
a
inly from wearin
g, so th
e vibration
si
gnal is to be
extracted a
s
the characte
ristic
quantity of the analy
s
is
of wea
r
lo
ss. F
o
r the vib
r
ati
on si
gnal
u(t), the followin
g
re
cu
rsi
on(1
)
to
c
o
nduc
t wavelet pack
e
t dec
o
mpos
ition [7].
k
n
n
k
n
n
k
t
u
k
g
t
u
k
t
u
k
h
t
u
)
2
(
)
(
2
)
(
)
2
(
)
(
2
)
(
1
2
2
(1)
h is the high
-pass filter gro
up,
g is the lo
w-p
a
ss filter
grou
p.
In the
analy
s
i
s
of
multireso
l
ution, the
e
s
sen
c
e
of
wav
e
let pa
cket
d
e
com
p
o
s
ition
is to let
sign
al u get
throug
h hig
h
and lo
w-p
a
ss jun
c
tion filter g
r
oup, al
ways ma
ke th
e origi
nal si
g
nal
decompo
se
d
into 2 chan
n
e
ls of hi
gh a
nd lo
w freq
u
ency, then
d
e
com
p
o
s
e th
e part
of high
and
low freq
uen
cy respe
c
tively in the same
way till the demand is m
e
t.
The wavelet packet
d
e
co
mpositio
n se
quen
ce s(
j
, k) ( k
get 0
～
2j - 1
)
i
s
obta
i
ned afte
r
the J level
wavelet p
a
cket of si
gna
l has
been
decompo
se
d. Here the
wavelet pa
cke
t
decompo
sitio
n
of
signal
can b
e
rega
rd
ed a
s
th
e pa
rtition of
sign
al. Defin
e
the
mea
s
u
r
e of
th
e
partition.
N
i
k
j
F
k
j
F
i
S
i
S
i
k
j
1
)
,
(
)
,
(
)
(
/
)
(
)
)(
,
(
(2)
S F( j , k) (i) is the ith value of Fourie
r transfo
rm se
qu
ence of S ( j
, k) ( k get 0
～
2j - 1); N
is the origi
nal
signal le
ngth
[
8].
Acco
rdi
ng to
the b
a
si
c th
eory of
co
m
entr
opy, d
e
fine the
feature entropy of
wavel
e
t
packet a
s
H j. k the kth feature ent
ropy o
f
wavelet packet in the jth level of signal.
)
1
2
~
0
(
)
)(
,
(
lg
)
)(
,
(
1
,
j
N
i
k
j
k
i
k
j
i
k
j
H
(3)
3. Featur
e Extra
c
tion
Usi
ng Shannon
Entrop
y
Entropy is
a
measure of
uncertainty t
hat is
u
s
e
d
i
n
variou
s fau
l
t conditio
n
s
after the
sign
al processing
of the o
r
iginal
sig
nal
by using
WPT. To red
u
c
e d
a
ta set in si
ze, wavelet
entropy i
s
ap
plied to
wave
let co
efficient
s. The
wavel
e
t entro
py is
the su
m of
square of
deta
iled
wavelet tran
sform
co
efficients. Th
e e
n
tropy of
wa
velet coeffici
ents i
s
varyi
ng ove
r
diffe
rent
scale
s
dep
en
dent on the In
put sign
als. T
h
is wave
let e
n
tropy of coef
ficients
can b
e
defined a
s
.
2
7
0
,
log
n
k
j
n
n
W
E
(4)
Whe
r
e
k
j
W
n
,
is the coefficient
s of the subsp
a
ce after
wa
velet packet decompo
sitio
n
and
7
,
2
,
1
,
0
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Diag
no
stic Study Ba
sed o
n
Wavelet Packet En
trop
y a
nd We
ar Lo
ss of SVM (Yunjie Xu)
849
Let
)
7
...,
1
,
0
(
3
j
E
j
is seq
u
e
n
ce of the en
ergy of wavel
e
t packet de
compo
s
ition of
The
third layer, th
ere a
r
e:
2
1
,
3
n
k
k
j
j
W
E
(5)
Orde
r by sca
l
e, feature ve
ctor i
s
co
mp
os
e
d
of each
layers hi
gh-f
r
equ
en
cy Sequen
ce
wavelet of en
ergy as a
sub
-
vecto
r
, that,
]
,
,
,
,
,
,
,
[
37
36
35
34
33
32
31
30
E
E
E
E
E
E
E
E
T
Normali
z
ed, Let
2
/
1
2
7
0
3
j
j
E
E
then
]
/
,
/
,
/
,
/
,
/
,
/
,
/
,
/
[
37
36
35
34
33
32
31
30
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
T
(6)
T
is the normali
zed ei
genve
c
tor.
4. Support v
ector ma
chine
The mai
n
ai
m of an SVM cla
ssifie
r
is
o
b
taining a fu
n
c
tion f(x)
whi
c
h i
s
use to d
e
termin
e
the deci
s
io
n hyper pla
ne. Margi
n
is the
distan
ce
fro
m
the hyper
plane to the
clo
s
e
s
t point for
both cla
s
se
s of data points [9].
Given a trai
ning data
se
t
n
i
i
i
y
x
)}
,
{(
, where
n
i
R
x
de
notes the i
n
put vector,
R
y
i
denote
s
the corre
s
p
ondin
g
output value and
n
denot
es the num
b
e
r of training
data set. Th
e
reg
r
e
ssi
on fu
nction i
s
defin
ed as:
b
x
w
x
f
)
(
)
(
(7)
whe
r
e
w
denote
s
the wei
ght vector a
n
d
b
den
otes the bia
s
term.
The c
o
effic
i
ents
w
and
b
can th
us be g
a
ine
d
by minimizin
g
the regula
r
i
z
ed risk fun
c
tion.
n
i
w
y
L
n
C
C
R
1
2
2
1
)
(
1
)
(
(8)
0
)
(
)
(
y
x
f
y
L
y
x
f
y
x
f
)
(
)
(
whe
r
e C
de
notes a
cost
function me
asu
r
ing
th
e empiri
cal risk.
2
2
w
denote
s
th
e
Euclide
an no
rm. The
-insensitive loss function is
em
ployed to stabilize estimation.
The L
agrang
e multiplie
rs
i
a
an
d
*
i
a
are introdu
ced,
whi
c
h
satisfy the eq
u
a
lities
i
a
0
*
i
a
,
0
i
a
,
0
i
a
. This co
nstrained o
p
timization p
r
obl
e
m
is solved
usin
g the followin
g
Lag
ra
nge
form:
Maximize
n
i
n
i
i
i
i
i
i
a
a
a
a
y
11
*
*
)
(
)
(
)
,
(
)
)(
(
2
1
*
*
,
j
i
i
i
j
j
n
j
i
x
x
k
a
a
a
a
(9)
Subject to
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 847
– 854
850
0
)
(
1
*
n
i
i
i
a
a
]
,
0
[
,
*
C
a
a
i
i
whe
r
e
)
(
)
(
)
,
(
j
i
j
i
x
x
x
x
K
is po
si
tive definite kernel fu
nctio
n
.
The kern
el f
unctio
n
can
have different
forms, and at
present, Gau
ssi
an fun
c
tion
is the most widely use
d
.
Hen
c
e, the re
gre
ssi
on fun
c
tion is:
b
x
x
k
a
a
x
f
i
n
i
i
i
)
,
(
)
(
)
(
1
*
(10
)
5. SVM
w
e
ar
loss diagnos
is based on
w
a
v
e
le
t pac
ket feature e
n
tropy
5.1. Diagnos
tic model bu
ilding of SVM of bearing
w
e
a
r
Bearin
g we
ar extend can
be divided in
to non-
wea
r
, slight-we
a
r a
nd seve
re
-we
a
r. The
article
co
nst
r
ucts th
e multi
p
le cla
s
sifier
by us
ing
one
-to-one
metho
d
. Its basi
c
id
ea is: e
s
tabli
s
h N
(N- 1)/2 SVM for the
c
l
as
sific
a
tion
problems of
N yu
an, trai
n a
S
V
M between
2 catego
rie
s
to
sep
a
rate e
a
ch other. The
article i
s
abo
ut the ident
ifying the pro
b
le
m of 3 catego
ries,
so it nee
d to
con
s
t
r
u
c
t
3 S
V
M
clas
sif
i
er
s.
The a
c
curate
diagn
osi
s
of
rolling
beatin
g wa
s
studie
d
. The hi
gh freque
ncy d
e
m
odulatio
n
analysi
s
wa
s used to
ab
stract th
e
cha
r
acteri
st
ic
of signal
s
[10].
T
he signal
s were de
comp
o
s
ed
into eight fre
quen
cy ba
nd
s an
d the inf
o
rmatio
n in
t
he hig
h
ba
nd
wa
s u
s
ed
a
s
a
cha
r
a
c
teristic
vector. GSV
M
we
re
used
to re
alize th
e map
bet
we
en the fe
ature and
dia
gno
sis. Ba
se
d o
n
the
cha
r
a
c
teri
stics of differe
nt fault types o
f
rolle
r b
e
a
r
in
gs, thre
e SVM’s a
r
e deve
l
oped to id
en
tify
the four state
s
, inclu
d
ing n
o
rmal, ball fa
ult, outer ring
fault, inner ring fault, which is
sho
w
n i
n
Fig.2. With al
l training
sa
mples
of the
four st
ate
s
,
GSVM1 is trained to
se
p
a
rate n
o
rm
al
state
from fault states. With sample
s of fault st
ates, G
SVM2 and GSVM3 is trained to se
p
a
rate
discha
rge fro
m
thermal he
ating [11]-[13]
.
5.2 Extrac
tio
n
of fea
t
ur
e entro
p
y
of
w
a
v
e
let packe
t
The obviou
s
impulse sig
n
a
l can be
se
en from ori
g
i
nal sam
p
led
sign
al of Figure 2. But
the amount of
information o
b
tained i
s
limited, so it
can
not make fu
rther dia
gno
si
s. Therefore, use
the dau
be
chi
e
s5
wavel
e
t
packet to
co
ndu
ct thre
e-l
e
vel de
com
p
osition
of the
origi
nal
sam
p
led
sign
al, to make the
origi
nal sig
nal di
vided onto 8
band
s. As
sho
w
n in fig
u
re 3,
choo
se
recon
s
itution
of
(3,0
) de
co
mpositio
n ba
nd (As
sho
w
n
in
figure
4
)
and (3,1
) ba
nd (As
sho
w
n
in
figure 5)that contai
n
defect
sign
al frequency
of 207
rolling bear
ing. By using
wavelet packet
decompo
sitio
n
, power
sp
e
c
trum
analy
s
i
s
of
reco
n
s
itution technol
ogy, the defe
c
t sig
nal
of the
rolling b
eari
n
g inner race
, which i
s
subme
r
s
ed by
noise
signa
l, has been
detecte
d. After
analysi
s
, the
inner an
d o
u
ter
ring
weari
ng a
nd
s
palli
ng of
bea
ring
are
the
re
ason to
ca
use t
h
e
impact of 207
rolling be
arin
g, which ha
s been p
r
oved
after disse
c
tion.
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TELKOM
NIKA
ISSN:
1693-6
930
Diag
no
stic Study Ba
sed o
n
Wavelet Packet En
trop
y a
nd We
ar Lo
ss of SVM (Yunjie Xu)
851
Figure 1.
T
he
frame
w
ork
of
optimizin
g the SVM’s para
m
eters with g
enetic al
gorit
hm
Figure 2.
F
aul
t
dia
gno
sis
for gearb
o
x
bas
e
d
on ge
netic- S
V
M classifier
5.3 Optimiza
tion diagnos
is
SVM algo
rith
m, whi
c
h
is
again
s
t the
p
r
edi
ction
on
small
sample
s, ha
s big
a
d
vantage
itself. Becau
s
e the obtai
ne
d sam
p
le
s a
r
e few a
c
co
rdi
ng to the a
c
t
ual test, In ta
ble 1, the first
10
grou
p of d
a
ta
of the 20
group
s of data
obtaine
d in
t
he expe
rime
n
t
are u
s
e
d
a
s
training
sam
p
le
and the la
st 10 grou
ps a
r
e
use
d
as the t
e
st
sa
mple to
examine and
predi
ct the re
sults.
Figure 3. Ra
w vibration
si
gnal of 207 b
earin
gs
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Vol. 12, No. 4, Dece
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er 201
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852
Figure 4. The
first three
-
ba
nd wavel
e
t packet de
com
positio
n
Figure 5. The
second three
-
ban
d wavel
e
t packet deco
m
positio
n
Table 1. The
data of experiment
Number
Characteristic vib
r
ation signal
Load
/N
Speed/
(r.mi
n
-1
)
Running time
(10min)
Temper
ature
Of Oi
l
/
Wear
Loss Q
Mean
μ
Peak P
Kurtosis K
1 -17.613
1001
4.100
35.1
500.1
5
25.1
21.2
2 -18.215
998
3.988
79.8
500.1
10
24.5
35.2
3 -19.064
1285
3.984
135.9
500.1
20
26.9
52.6
4 -18.920
1396
4.102
165.1
500.1
35
30.4
83.9
5 -20.862
1402
4.126
173.2
500.1
45
31.1
90.1
6 -21.042
1408
4.065
30.5
1000.4
10
30.5
95.6
7 -21.348
1211
4.108
60.1
1000.4
80
33.1
98.9
8 -20.912
861
4.213
121.4
1000.4
90
35.1
108.5
9 -21.004
970
4.234
156.9
1000.4
105
34.8
116.9
10 -20.897
1065
3.996
179.8
1000.4
115
34.9
129.8
Table 2 ta
ke
s the last 10 d
a
ta as the d
a
t
a to
predi
ct and testify an
d verify the predi
cted
results
of the propo
sed
the SVM alg
o
rithm of
o
p
timal sche
duli
ng mo
del.
Apply the SVM
algorith
m
of radial b
a
si
s
ke
rnel
paramet
er o
p
ti
mize
d
by optimal
scheduli
ng mo
d
e
l metho
d
in t
he
article to p
r
e
d
ict we
ar lo
ss. It is clear t
hat the
articl
e provide
a very favoura
b
l
e
new m
e
tho
d
to
s
o
lve
th
e
we
ar
p
r
ed
ic
tion
iss
u
es
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Diag
no
stic Study Ba
sed o
n
Wavelet Packet En
trop
y a
nd We
ar Lo
ss of SVM (Yunjie Xu)
853
Table 2. The
later 10 sa
m
p
le’s results o
f
4 optimized
algorith
m
6. Conclusio
n
Thro
ugh the
prop
osed the
applicatio
n of extrac
tion method of en
ergy feature
of wavelet
packet ban
d and pattern
reco
gnition
m
e
thod of
SVM
in
the
dia
g
nosi
s
of antifriction
bea
ring
we
ar
loss, extractio
n
of vibration sign
al by usin
g wavele
t pa
cket entropy
as the ch
ara
c
teristic q
uanti
t
y o
f
the analysi
s
on the we
ar loss, the o
p
t
imization mo
del bein
g
ob
tained with
radial ba
si
s kernel
para
m
eter of
SVM algorithm optimization to be us
e
d
in predi
ctio
n of wear lo
ss, and the wearin
g
verification t
o
be co
ndu
cted in the example of
the beari
ng wear data. It indicates tha
t
the
comp
utationa
l efficien
cy of
the dia
gno
sti
c
meth
od
of
SVM wea
r
i
s
high, ba
se
d o
n
wavelet pa
cket,
and th
e SVM
ha
s ve
ry go
od
re
cog
n
ition capa
bility in the
state
of
sm
all
sam
p
le. Fro
m
the
above
,
the SVM ha
s very good
p
r
acti
cal valu
e
and a
ppli
c
at
ion prospe
ct in solvin
g problem
s of be
aring
fault diagno
si
s.
Ackn
o
w
l
e
dg
ements
This
wo
rk wa
s
sup
porte
d i
n
pa
rt by the
Nation
al Natu
ral S
c
ien
c
e
F
ound
ation of
Zhejian
g
Province of Chin
a (G
rant
No. Y12C1
6002
3), Woo
d
pro
c
e
s
sing
indust
r
y an
d techn
o
logy
innovation of
Zhejian
g
of
Chin
a(G
r
a
n
t No
. 20
10R5002
3-1
9
). A
nd Fou
ndati
on of Zheji
a
ng
Agricultural &
Fore
stry Uni
v
ersity (G
rant
No. 2012F
R101). Corre
s
p
ondin
g
autho
r:Yunjie Xu.
Referen
ces
[1]
Gong h
uan-c
h
un. F
ault id
enti
f
ication i
n
ge
ar
bo
x bas
ed o
n
Elman n
eur
al n
e
t
w
o
r
k.
Lifting t
he transp
o
rt
mac
h
i
nery
. 20
09; 5: 70-7
3
.
[2]
Yong
Z
h
ang, Xi
ao-D
an Liu, F
u
-Ding Xi
e, K
e
-Qiu Li. F
a
u
l
t classifier
of ro
tating mac
h
in
e
r
y
b
a
se
d on
w
e
ig
hted s
upp
ort vector data descri
p
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pert Systems
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i
th Applicati
o
ns
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6
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:
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9
3
2
.
[3]
Ignaci
o
Yélam
o
s, Gerard Escuder
o, Moisè
s
Grae
lls, Luis
Puigj
aner. Pe
rformance ass
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ssment of
a
nove
l
fau
l
t di
ag
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y
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u
p
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r
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mputer
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l
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55.
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6): 985
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hu Yon
g
-sh
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han
g Yo
u-
yun. T
he stud
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uter eng
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licati
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8.
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Cen
Xi
ng-
hui,
Xi
on
g
Xia
o
-
y
a
n
. F
ault dia
g
n
o
sis of ba
ll b
e
a
rin
g
bas
ed o
n
w
a
ve
let a
n
d
radia
l
bas
is
function n
eur
al
net
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rks.
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han
ical e
n
g
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ne
erin
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m
a
t
ion
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[7]
Yun-ji
e
Xu. F
a
ult Di
agn
osis f
o
r Ro
ller
be
ari
ngs Bas
ed
on
Genetic-SVM
Classifi
er.
Adv
ance
d
Mater
i
al
s
Research Vols
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99-2
0
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:
620-62
4
[8]
W
ang Guo-fe
n
g
, W
ang Z
i
-lia
n
g
. Accurate di
agn
osis
of Di
e
s
el en
gi
ne c
y
li
nder h
e
a
d
bas
ed on
w
a
ve
let
packet
an
d R
B
F
neur
al
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w
o
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Jo
urna
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n
ivers
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ce
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d
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o
lo
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e
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004;
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4-1
8
7
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[9]
Penterse
n JC.
Aspha
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x
id
a
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n
overv
i
e
w
i
n
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ud
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ne
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ng th
at
ph
ysic
ochem
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al factors domi
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uel Sci. and T
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E
NG Qing-hu
, QIU Jing, LIU Guan-
j
un. A
Method for In
cipie
n
t F
ault D
i
ag
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of Di
esel e
n
g
i
ne
c
y
l
i
nd
er he
ad
Based o
n
the
W
a
velet T
r
ansform Correl
a
tio
n
F
ilter and H
i
l
bert T
r
ansform.
International
jour
nal of pl
ant
engi
ne
erin
g a
nd man
a
g
e
m
e
n
t
. 2007; 12(
4): 192-1
98.
Number
Characteristic vib
r
ation signal
Load
/N
Speed/
(r.mi
n
-1
)
Running
time
(10min)
Tempe-
rature
Of Oi
l
/
Real
Wear
Loss Q
Predictive
Wear Loss
Q
(BP-NN)
Predicti
v
Wear
Loss Q
(GA)
Predictive
Wear
Loss Q
(AC)
Mean
μ
Peak P
Kurtosis
K
11 -21.644
1201
4.100
30.5
1500.5
120
25.1
131.1
119.1
113.5
117.2
12 -21.015
1008
4.018
50.8
1500.5
145
24.5
140.2
180.01
140.2
172.8
13 -21.100
985
3.974
100.9
1500.5
150
26.9
149.5
165.9
125.4
159.6
14 -22.120
896
4.152
140.1
1500.5
165
30.4
156.1
171.4
142.6
155.0
15 -23.162
1301
4.106
178.2
1500.5
175
31.1
158.7
189.9
168.7
187.4
16 -22.642
1318
4.085
31.0
2000.0
184
30.5
163.8
160.4
151
188.7
17 -22.438
1281
4.177
80.1
2000.0
189
33.1
164.1
191.1
144
158.9
18 -22.912
1261
4.003
111.4
2000.0
200
35.1
171.2
207.9
205.7
220.7
19 -23.004
1170
3.934
153.9
2000.0
225
34.8
190.1
223.8
201.2
205.7
20 -23.789
1160
4.096
180.9
2000.0
232
34.9
195.7
219.0
199.8
218.5
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Vol. 12, No. 4, Dece
mb
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4: 847
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854
[11]
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a
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