TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6198 ~ 6204
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.558
3
6198
Re
cei
v
ed
Jan
uary 5, 2014;
Re
vised Ma
rch 26, 2014; A
c
cepted Ap
ril 10, 2014
Gear Fault Diagnosis and Classification Based on
Fisher Discriminant Analysis
Haiping Li
1
, Jianmin Zha
o
1
, Xinghui Z
h
ang*
1
, Hongz
h
i Teng
1,2
, Ruifeng Yang
1
1
Mechan
ical E
ngi
neer
in
g Col
l
ege, Shi
jiaz
h
u
ang, Ch
in
a
2
Lanzh
ou Eq
ui
pment Mai
n
ten
ance C
enter, L
anzh
ou, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: d
y
namic
bnt
@gmai
l
.com
A
b
st
r
a
ct
Gears ar
e th
e
most ess
entia
l p
a
rts in
rotati
ng
machi
nery.
So
ge
ar fau
l
t mod
e
s d
i
a
g
n
o
sis
an
d
levels
cl
assific
a
tion
are
very
i
m
p
o
rtant
in
en
gin
eeri
n
g
pract
i
ce. T
h
is
pa
per
pres
ent
a n
o
v
e
l
method
i
n
g
e
a
r
fault recog
n
iti
o
n and i
d
e
n
tific
a
tion us
in
g F
i
sher
discri
m
in
ant ana
lysis (
F
DA) due to F
D
A can redu
ct
di
me
nsio
n w
h
e
n
a
nalys
e si
gn
al. T
h
e
rea
l
d
a
ta co
llecte
d
fr
om a
ge
arbox
test rig
is us
e
d
to v
a
li
date t
h
e
meth
od
this
pa
per pr
op
osed.
And th
e effecti
v
eness
of
the
meth
od
olo
g
y w
a
s de
monstrat
ed by
the r
e
su
l
t
s
obtai
ne
d fro
m
the a
n
a
l
ysis.
T
h
ree k
i
nds
of fault
mo
des
and
lev
e
ls w
e
re i
d
e
n
tified.
And
ener
gy w
a
s
selecte
d
as feature par
a
m
et
er. T
he
fault modes (n
or
mal,
breakto
oth an
d
crack) w
e
re diag
nose
d
at first,
then th
e fau
l
t l
e
vels
of bre
a
kt
ooth
and
crack
are c
l
assi
fi
ed.
T
he acc
u
rate r
a
te of th
e
meth
od is
ap
prox
imate
89%.
Ke
y
w
ords
:
ge
ar, fault diag
no
sis, dimens
ion
reducti
on, F
i
sh
er discri
m
i
n
a
n
t ana
lysis
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Gears a
r
e im
portant
comp
onent
s of rot
a
ting ma
ch
in
ery. Typical f
aults of ge
ars incl
ude
pitting, chippi
ng, and more
serio
u
sly, crack [1].
Failures of gears u
s
ually ca
use signifi
cant loss.
Therefore, it i
s
ba
dly need
to redu
ct the
num
be
rs of g
ear b
r
e
a
kd
own and m
a
inte
nan
ce
co
sts.
To
this end, man
y
techniqu
es
have been u
s
ed in early fa
ult diagno
sis
and cl
assifica
tion to monitor
the condition
of the
s
e
sy
stem
s. Su e
t
c. [2]
pro
p
o
s
ed
an
improved meth
od
of ge
ar fa
u
l
t
identificatio
n
based o
n
Hilbert-Hu
a
ng tran
sf
orm (HHT) to overcome
the proble
m
of
recon
s
tru
c
tin
g
a feature matrix of sin
gular va
l
ue d
e
com
p
o
s
ition
.
In the pape
r, HHT tech
n
i
que
wa
s utilized
to acq
u
ire i
n
stantan
eou
s
freque
ncy a
n
d
amplitud
e
matrices f
r
o
m
faulted ge
ar
sign
als. Th
e
adaptive variable
st
ep
-le
ngth natu
r
al
gradi
ent bl
i
nd so
urce
separation (B
SS)
algorith
m
wa
s u
s
e
d
in [3
] to analyse
the vibratio
n si
gnal to
i
m
pleme
n
t fa
ult diagn
osi
s
on
helicopter
ge
arbox. Lei
an
d Zuo [4] p
r
o
posed a n
e
w
algorith
m
in
cla
ssifying th
e different lev
e
ls
of gea
r
cra
c
ks ba
se
d
on
wei
ghted
K
nearest
nei
g
hbor.
Thi
s
e
nable
d
the
f
ault cha
r
a
c
te
ristic
freque
ncy
of gea
rs can
be dete
c
ted
effectively.
In addition,
so
me othe
r te
chniqu
es
are
all
utilized in thi
s
aspect,
such
as Hi
dden Markov
Model (HMM
) [5, 6], support
vector machi
n
e
(SVM) [7, 8],
wavelet
pa
cket tra
n
sfo
r
m
a
tion (W
PT
) [9] and
artifical neu
ral
net
work
(ANN) [10]
and so on.
Sometimes t
he pro
b
lem
can n
o
t be solved by u
s
ing o
n
ly on
e techni
que
as the
equipm
ents
b
e
comi
ng mo
re and mo
re
complicated.
He
reby, the combinatio
n of
two or three
o
f
methods m
a
y be
utilized. A
fault detection method
that com
b
ines
Hilbert
transform and
wavel
e
t
packet t
r
an
sf
orm
wa
s
pro
posed [1
1] to
extra
c
t mod
u
lating
sig
nal
and
hel
p to
detect th
e e
a
r
ly
gear fa
ult. Wu et
c [12] develope
d
an intellige
n
t diagno
si
s for fault gea
r identi
fi
cation
and
cla
ssi
fi
cation based
o
n
vib
r
ation sig
nal usin
g
di
sc
ret
e
wavelet tra
n
sform a
nd
adaptive n
e
u
r
o-
fuzzy infe
ren
c
e sy
stem (A
NFIS) for solvi
ng the pro
b
le
m of abnorm
a
l transi
ent si
gnal
s.
As de
scrib
e
d
above, the
a
c
curate
rate
of early
fault
diagn
osi
s
a
n
d
cla
s
sificatio
n
is ve
ry
importa
nt wh
en im
pleme
n
t
con
d
ition
m
onitorin
g
on
system
s. It
must
be
more a
c
curacy t
hat
con
s
id
er the
compl
e
te si
g
nal than a
pa
rt if adopt
a ap
prop
riate m
e
thod. However, som
e
of the
s
e
method
s
m
e
n
t
ioned above take a se
ctio
n
of
vibrat
e
si
gnal i
n
to a
c
count (i.e.
WP
T and
EMD)
and
some
of the
m
rej
e
ct
a lot
inform
ation t
hat th
e
s
e m
e
thods thin
k u
s
ele
s
s,for in
stance, SVM.
No
matter sele
ct a part o
r
reje
ct som
e
information, so
me
useful d
a
ta that co
ul
d reveal re
al condi
tion
of a equipm
e
n
t may be left out [9, 13]. If sepa
rate
the
freque
ncy sp
ectru
m
into m
any se
ction
s
to
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Gear F
ault Di
agno
si
s and
Cla
ssifi
cation
Based on Fi
sher Di
scrim
i
n
ant Analysis
(Haipi
ng Li)
6199
consider, it will be more accura
cy the number of
the sections
larger. But this will
produce
anothe
r p
r
obl
em, the procedure of calc
ulation
will be
hard to i
m
pl
emented.
In order
to s
o
lve
the
dillema, this
pape
r pro
p
o
s
ed a gea
r fault diagno
sis
and cla
s
sifica
tion method
based on Fi
sher
discrimi
nant analysi
s
(F
DA) [14]. The objective
is to prese
n
t a novel method which
can
diagn
ose ge
a
r
faults an
d
cl
assify fault le
vels ex
a
c
tly b
y
taking th
e t
o
tal si
gnal i
n
to con
s
ide
r
ati
o
n
at
first
th
an d
i
mensi
on re
d
u
ction. The
p
e
rform
a
n
c
e
o
f
this m
e
thod
ha
s b
een
va
lidated
by re
al
data.
The
rem
a
inin
g sectio
ns o
f
this
pap
er
are
organi
ze
d a
s
foll
ows.
In Se
ction
2, the
methodol
ogy
of the
met
hod thi
s
pa
per
propo
se
d is intro
d
u
c
ed. Sectio
n
3 de
scrib
e
s
the
experim
ent, the pro
c
e
dure
of fault diagnosi
s
and
cl
a
ssifi
cation. M
ean
while, the
result
s analy
s
is
is implem
ent
ed in this sect
ion. Finally, the co
ncl
u
si
on
s are d
r
a
w
n i
n
se
ction 4.
2. Metho
dolog
y
The m
e
thod
this
pap
er
prop
osed i
s
based
on Fi
she
r
discrimi
nant
a
nalysi
s
(F
DA).
“Dim
en
sion disa
ster”
is a
chall
eng
e whi
c
h
oft
en
confront whe
n
solve p
r
ob
lems of patt
e
rn
recognitio
n
, some m
e
thod
s are
ap
plicative wh
en
in
hi
gh dim
e
n
s
ion
sp
ace b
u
t th
ey do
not wo
rk
in below dim
e
nsio
n spa
c
e.
Ho
wever, ma
ny methods a
r
e more accu
rate in high di
mensi
on spa
c
e
than belo
w
.
This mo
ment
dimen
s
ion
redu
ction
can
achieve ve
ry good re
sul
t
s and it is t
h
e
obje
c
tive that utlize FDA in
this pape
r.
If project the
dots in
dim
ensi
o
n
s
spa
c
e to a line, t
he spa
c
e
ca
n be redu
ce
to one
dimen
s
ion. B
u
t so
me
sa
m
p
les that a
r
e
simple
to
be
sep
a
rate
d in
high
dimen
s
i
on
spa
c
e
will
be
mixed after redu
ce the di
mensi
on, a
s
Figure 1 (a
)
sho
w
s. In this situatio
n, maybe proj
ect
the
sampl
e
s to
a
line which rot
a
ted around the ori
g
in
will obtain
a better
result,
as depicted i
n
Figure
1(b
)
. So sele
ct the line is very im
portant, it is
the res
u
lt vec
t
or
W*
F
D
A need.
Figure 1. The
Sketch Ma
p of FDA Princi
ple
Ho
w to cal
c
ul
ate the re
sult
vector
W*
an
d cla
s
sify the sampl
e
s, the
spe
c
ific p
r
o
c
edure
s
are as
follows:
(1)
Comp
ute the mean valu
e vector
m
i
of every sampl
e
:
1
12
i
i
X
mX
i
,
N
(1)
Whe
r
e
N
i
i
s
the amou
nt of the sampl
e
ω
i
.
(2)
Cal
c
ul
ate
the discrete
level vector
S
i
,
S
w
of eve
r
y sam
p
le a
n
d
amon
g all
sampl
e
s,
r
e
spec
tively.
12
i
T
ii
i
X
SX
m
X
m
i
,
(2)
12
w
SS
S
(3)
(3)
Comp
ute the discrete le
vel vector
S
b
whi
c
h bet
wee
n
two sa
mple
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 619
8 –
6204
6200
12
1
2
T
b
Sm
m
m
m
(4)
(4) Cal
c
ulate the
vector
W*
.
The ideal
re
sult after proje
c
tion is the
di
stan
ce
s amo
ng all sa
mple
s in one
dime
nsio
n
Y
spa
c
e
are a
s
far a
s
p
o
ssi
b
le. Na
mely, the mea
n
val
ue differen
c
e
°°
12
mm
of
t
w
o
sa
m
p
les i
s
as la
rg
e a
s
possibl
e. Me
anwhile, a
b
e
low
discrete
level of on
e
sam
p
le i
s
v
e
ry well. So, the
Fishe
r
fun
c
tio
n
can b
e
defi
ned a
s
:
T
b
F
T
w
WS
W
JW
WS
W
(5)
To make the value of
J
F
(
W
)
maximum,
W*
should b
e
:
1
12
w
W*
S
m
m
(6)
(5) All the sa
mples p
r
oj
ect
to
W*
.
T
yW
*
X
(7)
(6) Compute
the threshold
value i
n
p
r
oj
ective
spa
c
e.
Wh
ere the
mean
value
of every
sampl
e
in on
e dimen
s
ion
Y
space and t
he discrete le
vel vector
2
i
s
%
,
w
s
%
are:
°
1
12
i
i
y
i
my
i
,
N
(8)
°
2
2
12
i
i
i
y
sy
m
i
,
%
(9)
22
12
w
ss
s
%%
%
(10
)
The sele
ction
of thresh
old
value
y
0
ha
s
some
differen
t
methods, on
e kind of the
usu
a
lly
use
d
is:
±
±
12
12
0
12
22
ln
P
/
P
mm
y
NN
(11
)
Another i
s
also this paper utilized:
°°
12
12
0
12
Nm
N
m
y
NN
(12
)
(7) To the test s
a
mple
X
, the projec
tive dot
y
to
W*
ca
n be com
pute
d
as follo
ws:
T
yW
*
X
(13
)
(8)
Cla
s
sify on the b
a
si
s of deci
s
io
n
regul
ation
(i.e. if
y>
y
0
, than the te
st sample
X
belon
g to the cla
s
s1. Otherwise, it belon
gs to cla
s
s2).
01
02
yy
X
yy
X
(14
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Gear F
ault Di
agno
si
s and
Cla
ssifi
cation
Based on Fi
sher Di
scrim
i
n
ant Analysis
(Haipi
ng Li)
6201
Two
cla
s
se
s
FDA
sho
u
ld b
e
implem
ente
d
at first whe
n
identify a te
st sample, it
will giv
e
out the nea
re
st cla
ss
whi
c
h the test sa
mple
belo
ng t
o
. Then the n
eare
s
t cl
ass
and an
other
new
cla
ss could constitute
a
co
nferen
ce sam
p
les
an
d co
n
duct the two
cla
s
ses F
D
A, A new neare
s
t
cla
ss
can b
e
obtained,
contin
ue carry out t
he proce
dure abo
ve until all the cla
s
se
s are
considered.
At last, the
class
whi
c
h the test
sa
mpl
e
bel
ong to
will be
classi
fied. Thi
s
i
s
the
pro
c
ed
ure this pap
er u
s
ed.
3.
Experiment
Specifica
tio
n
s and Resu
lts Analy
s
is
3.1. Experiment Speci
fic
a
tions
In engine
eri
n
g pra
c
tice, ge
ar b
r
ea
ktooth
and cr
a
c
k are the mo
st se
riou
s fault mo
des [1].
They a
r
e
often the
rea
s
o
n
s
that l
ead
to
bre
a
kdo
w
n
o
f
a ma
chin
e.
Figure 2
(
a
)
i
s
a real
photo
o
f
gear
bre
a
kto
o
th in practi
ce.Other
kind
s of fault
mode
s are al
so
co
mmon, such as the g
e
a
r
wear,
gluing o
r
fatig
ued. But due
to gear
bre
a
ktooth and
cra
ck
are
more
seri
ou
s than t
hem, so i
n
thi
s
approa
ch, the
two fault
mo
des are mai
n
l
y
analyze
d
. T
he dia
g
ram o
f
them can
be
se
en in
Figu
re
2(b
)
.
Figure 2. Fau
l
t Modes: (a
)
real ph
oto of fault
gears in
engin
eeri
ng p
r
acti
ce, (b
) th
e diagram of
the fault modes in this exp
e
rime
nt: brea
ktooth an
d crack
Figure 3. The
Fault Gears
uesd in this Study
Figure 4. The
Structure of
Gearbox the Experiment u
s
ed
The expe
rim
ent data thi
s
stu
d
y use
d
is
o
b
taine
d
from the
RCM l
abo
rat
o
ry of
Mech
ani
cal Enginee
ring
Colle
ge.
Th
e
Electro-Di
scharg
e
M
a
chi
n
ing (EDM
) method
i
s
used
to
introdu
ce fa
ul
ts to the test
gears. And t
w
o faul
t
s
mo
des (b
rea
k
to
oth
and crack) we
re
d
e
sig
ned
with differe
nt levels, the d
i
ameters of b
r
ea
ktooth a
n
d
crack a
r
e 2
mm, 5mm, 1
0
mm an
d 2m
m,
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046
TELKOM
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Vol. 12, No. 8, August 2014: 619
8 –
6204
6202
5mm, 8mm,
respe
c
tively. Figure 3
sho
w
s the
fault
gears ue
sd
i
n
this
study. The
sampli
ng
freque
ncy of this experim
e
n
tal system i
s
20
kH
z and
sampli
ng time is 6s. Each
fault mode has
60 sa
mple
s, the 1-3
sam
p
les a
r
e
sele
cted as the
re
feren
c
e
sets
and the 4
-
13
, 24-33, 4
4
-5
3
sampl
e
s a
r
e
cho
o
sen a
s
the test sa
mpl
e
s. T
he lo
ad
gene
rated by
brake is 10
N•m and the input
rotary spe
ed of
motor
is 8
00rp
m
.
The structu
r
e
of
th
e gea
rbox u
s
ed in this
exp
e
rime
nt is sh
own
as Figu
re 4.
The #2 ge
ar i
s
test gea
r.
3.2. Results Analy
s
is
The m
e
thod
this p
ape
r p
r
opo
sed
choo
se th
ree
ki
n
d
s
of fault
mode
s a
nd l
e
vels to
discu
ss. And
sele
ct en
erg
y
as feature
para
m
et
er. F
i
rst of all, no
rmal, brea
kto
o
th and
cra
ck
sho
u
ld b
e
dia
gno
sed. A
s
F
i
gure
5
sho
w
s, the
red li
ne
is the th
re
sh
old value
y
0
(
a
s sam
e
a
s
t
he
follows). F
o
r
example, y
0
i
s
-7.47*
10
16
and -3.9
0*10
16
in (a) an
d (b). O
n
the
b
a
s
is of th
e the
o
ry
in Sectio
n 2,
sel
e
ct b
r
e
a
k
tooth
and
n
o
rmal
a
s
cl
a
s
s1 a
nd
cla
s
s2, re
sp
ecti
vely. So if the
proje
c
tive val
ue
y
of on
e
sampl
e
g
r
eat
er tha
n
y
0,
th
e sa
mple
bel
ong to
cla
s
s1, otherwi
se
the
sampl
e
belo
n
g
to class2. Namely, after the firs
t com
p
arison, the bl
ack and pin
k
sampl
e
s b
e
lo
ng
to class1
(i.e. brea
ktooth
)
and the blu
e
sampl
e
s b
e
lo
ng to cla
s
s2 (i.e. normal).
Than the ne
a
r
eat
cla
ss a
nd
crack co
nstitut
e
the refe
re
nce
sets
. Si
milarly, (b),
(c)
are brea
ktooth-cra
ck
and
norm
a
l-crack.
The
con
c
lu
sion
could
b
e
give
n
out.
Blue b
e
lon
g
to no
rmal,
black
belo
n
g
to
brea
ktooth
a
nd pin
k
b
e
lon
g
to cra
ck. All
the 90
sam
p
l
e
s, the
r
e a
r
e
10 sample
s a
r
e mi
stake. So
the accurate rate of this me
thod is ap
pro
x
im
ate 89%. It is a numbe
r taht can be a
c
cepted.
0
5
10
15
20
25
30
-12
-10
-8
-6
-4
x 1
0
16
0
5
10
15
20
25
30
-6
-5
-4
-3
-2
-1
x 1
0
16
0
5
10
15
20
25
30
3
4
5
6
7
x 1
0
17
Figure 5. The
Result Figures of Gea
r
Fa
ult Modes
Dia
gno
sis
After the fault modes of the
sample
s a
r
e
kno
w
n,
the n
e
xt step is cla
ssify the fault levels.
Due
to the
proce
dures of
classi
fy bre
a
kt
ooth a
nd
cra
c
k level
s
a
r
e
the same,
so
this
pape
r ta
ke
the form
er
a
s
a
n
exam
pl
e. Similar to
the f
ault mo
d
e
s
diag
no
sed
above,
blue,
bla
c
k an
d pi
nk
stand fo
r the
diamete
r
s
of brea
ktooth
a
r
e 2mm,
5
m
m, 10mm. Fi
gure
6(a), (b) and (c) are the
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TELKOM
NIKA
ISSN:
2302-4
046
Gear F
ault Di
agno
si
s and
Cla
ssifi
cation
Based on Fi
sher Di
scrim
i
n
ant Analysis
(Haipi
ng Li)
6203
c
o
mpr
i
s
o
n
o
f
5
-
10
mm, 2-1
0
mm an
d
2
-
5
mm. Afte
r
fir
s
t
c
o
mp
a
r
is
on
, b
l
a
c
k
b
e
l
on
g
to
5mm and
the other t
w
o
belon
g to 10
mm. Whe
n
(b
) and
(c) a
r
e i
m
pleme
n
ted,
the final re
sul
t
s are
the
sa
me
as the assu
m
p
tion before a
nd the accu
ra
te rate is
als
o
89%. So the
effec
t
ivenes
s
of this
method
is validated.
0
5
10
15
20
25
30
0
2
4
6
8
x 1
0
17
0
5
10
15
20
25
30
-5
-4
-3
-2
-1
0
1
x 1
0
17
0
5
10
15
20
25
30
-0.5
0
0.5
1
1.5
2
2.5
x 1
0
16
Figure 6. The
Result Figures of Gea
r
Fa
ult Levels Cl
a
ssifi
cation
0
10
20
30
40
50
60
70
80
90
0
0.
5
1
1.
5
2
2.
5
x 1
0
9
Figure 7. The
Result Figures of Gea
r
Fa
ul
t Modes
Dia
gno
sis u
s
in
g Euclide
an Di
stance
To demo
n
st
rate the effect
iveness of th
e method thi
s
pap
er p
r
o
p
ose
d
, the Eu
clide
a
n
Dista
n
ce [15]
method
wa
s
utilized to
pro
c
e
ss th
e ex
p
e
rime
nt data.
The p
r
o
c
ed
u
r
e of u
s
in
g it is
the sam
e
a
s
utilizing th
e F
D
A. The n
o
rmal, bre
a
kto
o
th and
crack conditio
n
were di
agn
ose
d
at
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 619
8 –
6204
6204
first. The re
sult is as Fig
u
re 7 sh
ows. To t
he normal con
d
itio
n, the result
is pretty good.
Ho
wever, to t
he b
r
ea
ktoot
h and
cra
ck
coditio
n
, the
result are un
satisfa
c
to
ry. The a
c
curate
rate
of the Euclid
e
an Di
stan
ce
method i
s
onl
y 78%. So
it
has
no ne
ed
to cla
ssify the
fault leves d
ue
to the erro
r
of the first
stage. Furth
e
rmore, th
i
s
re
sult p
r
ove th
e sig
n
ifica
n
ce of dime
nsi
o
n
redu
ction
whi
c
h th
e Eu
clid
ean
Dist
ance
method
doe
s
not have
and
validate the
a
ppro
a
ch of thi
s
pape
r.
4. Conclu
sion
This
pap
er
p
r
esent a
nov
el metho
d
in
gea
r fault
reco
gnition
an
d cl
assificatio
n
u
s
ing
Fishe
r
discri
minant a
naly
s
is (F
DA).
Th
e re
al d
a
ta
collecte
d
fro
m
a g
earbox t
e
st
rig i
s
u
s
e
d
to
validate the method this
pape
r pro
p
o
s
ed. A
nd th
e effectivene
ss of the m
e
thodol
ogy wa
s
demon
strated
by the
re
sult
s o
b
taine
d
from the
anal
y
s
is.
First of a
ll, three
kin
d
s of fault mo
d
e
s
(no
r
mal, brea
ktooth a
nd crack)
were di
agno
se
d,
then the fault le
vels
of brea
ktooth and
cra
ck
are
cla
s
sified.
Both of th
e t
w
o
stag
es we
re
ba
sed
on
FDA. T
w
o
cla
s
ses F
D
A we
re im
pleme
n
ted
at first
whe
n
i
dentify a test
sampl
e
, the n
eare
s
t
cla
s
s
whi
c
h the
pro
c
ed
ure
give o
u
t and
anoth
e
r
new
class co
uld con
s
titute
a conferen
ce
sample
s to continue cond
uct the two cl
asse
s FDA u
n
til
all the cla
s
se
s are con
s
ide
r
ed. At last, the faul
t mod
e
s a
nd level
s
are all
cla
ssi
fied. Mean
wh
ile,
the accu
rate
rate of the m
e
thod is
app
roximate 89%
whi
c
h is
su
pe
rior to the val
ue 78% of u
s
i
n
g
the Euclide
a
n
Distan
ce met
hod.
Referen
ces
[1]
F
an XF
, Z
uo
MJ. Gearbo
x fault det
ection
usin
g Hil
bert a
nd
w
a
v
e
let p
a
cket transform
.
Mechan
ical
Systems a
nd S
i
gn
al Process
i
n
g
. 2006; 2
0
(4): 966-
982.
[2]
Su Z
Y
, Z
hang
YM, Jia MP,
Xu F
Y
, Hu JZ
. Gear faul
t ide
n
t
ification an
d
cl
assificati
on of
sing
ular
v
a
l
u
e
decom
positi
on base
d
on Hil
be
rt-Huan
g
transf
o
rm.
Mecha
n
ic
al Scie
nce
an
d
T
e
chno
logy
. 2
011; 2
5
(2):
267-
272.
[3]
Chen Y, Meng J
T
. Study
on BSS Algorit
hm used on Fault Diagn
osis of
Gearbox
.
TEL
K
OMNIKA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013; 1
1
(6): 2
942-
294
7.
[4]
Lei
YG, Z
uo M
J
. Gear crack
l
e
vel
id
entific
ati
on bas
ed on
w
e
ig
hted
K near
est
ne
ig
hbor
cl
assificati
o
n
algorithm.
Mec
han
ical Syste
m
s and Sig
n
a
l
Processi
ng
. 20
09
; 23(5): 153
5-1
547.
[5]
Kang
JS, Z
han
g
XH. Ap
pl
icati
on
of Hi
dde
n
Markov Mo
de
ls
in m
a
chi
n
e
fa
ult di
ag
nosis.
I
n
formation-An
Internatio
na
l Interdisp
ili
nary J
ourn
a
l
. 20
12; 1
5
(12B): 58
29-
5
838.
[6]
Hassiotis
S. Id
entificati
on
of dama
ge usin
g natura
l
freq
ue
ncies
an
d Mar
k
ov par
ameter
s.
Co
mput
ers
and Structures
.
2000; 7
4
(3): 3
65-3
73.
[7]
Baccari
ni LMR
,
Silva VVR,
Menez
es BRD
,
Caminh
as W
M
. SVM practical in
dustri
a
l a
pplic
atio
n fo
r
mechanical faults diagnostic.
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i
th Applicati
ons
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1; 38(
6): 6980-
69
84.
[8]
T
ang XL, Z
h
u
a
ng L, Ca
i J, Li
CB. Multi-fault
classi
fi
cati
on
b
a
sed
on su
ppo
rt vector machi
ne train
ed
b
y
chaos p
a
rticle
s
w
a
rm optimiz
ation.
Know
l
e
d
ge-Bas
ed Systems
. 2
010; 2
3
(
5
): 486-4
90.
[9]
Yen GG, Leong WF. Fault classi
fi
c
a
tion
on vi
bratio
n d
a
ta
w
i
th
w
a
v
e
let bas
ed fe
ature se
lectio
n
scheme.
Instru
me
ntatio
n, Systems,
an
d Auto
mati
on Soc
i
ety
. 2006; 45(
2): 141-1
51.
[10] Kumar
K.
K
n
o
w
l
e
d
g
e
E
x
tract
i
on
F
r
om T
r
ain
ed
Neur
al
Net
w
o
r
k
. T
E
LKO
M
NIKA Indo
ne
sian
Jour
na
l of
Electrical E
ngi
neer
ing
. 2
012;
1(4) :282-
29
3.
[11]
F
an XF
, Z
uo
MJ. Gearbo
x fault det
ecti
on
usin
g Hil
bert a
nd
w
a
v
e
let p
a
cket transform.
Mechan
ical
Systems a
nd S
i
gn
al Process
i
n
g
. 2006; 2
0
(4): 966-
982.
[12]
W
u
JD, Hsu CC, W
u
GZ
.
F
ault gear id
enti
fi
cation a
nd clas
si
fi
catio
n
usin
g
discrete
w
a
ve
l
e
t transform
and a
d
a
p
tive n
euro-fuzz
y i
n
fe
rence.
Expert
Systems w
i
th Appl
icatio
ns
. 2
009; 36: 6
255.
[13]
Baccari
ni LMR
,
Silva VVR,
Menez
es BRD
,
Cami
nh
as W
M
. SVM practical in
dustri
a
l a
pplic
atio
n fo
r
mechanical faults diagnostic.
Expert Systems w
i
th Applicati
ons
. 201
1; 38(
6): 6980-
69
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[14]
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L
, Qu J,
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uo MJ, Xu
HB. F
ault lev
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y gea
rbo
x
es usin
g h
y
bri
d
kern
el
feature s
e
lecti
o
n an
d ker
nel
F
i
sher d
i
scrimi
n
a
n
t ana
l
y
sis
.
Ad
vance
d
Ma
nuf
acturin
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e
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h
a
o
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hang
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eng HZ
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. Bear
in
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ault D
i
ag
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d
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n
vel
o
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e
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u
clid
ea
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i
sta
n
ce
.
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E
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ourn
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