Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 4
,
A
p
r
il
201
5, p
p
.
54
1
~
55
1
I
S
SN
: 208
8-8
6
9
4
5
41
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Vibration Analysis of Industr
ial Drive for Broken Bearing
Detection Using Probabilisti
c Wavelet Neural Network
K. J
aya
kumar*
, S.
T
h
a
n
gav
el**
* Departm
e
nt
of
Ele
c
tri
cal
and
E
l
ectron
i
cs
Eng
i
neering, Periy
a
r M
a
niammai Univ
ersity
** Departmen
t
o
f
Electr
i
cal
and
Electronics
Eng
i
neering
,
K.S
.
R.
College of
Tech
nolog
y
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 30, 2014
Rev
i
sed
D
ec 29
, 20
14
Accepte
d
Ja
n 15, 2015
A reliable monitoring of industrial drives
play
s a vital role to prevent from
the per
f
ormance degrad
ation
of
machin
er
y
.
Tod
a
y
’
s f
a
ult detection s
y
stem
m
echanis
m
us
es
wavele
t trans
f
o
r
m
for pr
oper detection of fau
lts, however it
required more
attention
on detecting high
er fau
l
t
rates wi
th lowe
r exe
c
utio
n
tim
e. Ex
isten
ce
of faults on
indu
strial dr
ives lead
s to higher
current flow rate
and the broken
bearing d
e
tected
s
y
stem
determined the number
of unhealth
y
bearings but need to develop
a faster
s
y
stem with
constant fr
equen
c
y
domain
.
Vibration data
acquisition was u
s
ed in
our proposed work to detect broken
bearing
faults in
induction mach
ine. To
g
e
ner
a
te an
effectiv
e f
a
u
lt detection
of industrial
drives, Biortho
gonal Posterio
r Vibration Signal-Data
Probabilisti
c Wavelet Neural Net
w
or
k (BPPVS-WNN) sy
stem
was proposed
in this paper.
T
h
is sy
st
em
was
focuse
d to redu
cing the cur
r
ent flow and to
identif
y
fau
lts
with lesser
exe
c
ution
tim
e wit
h
harm
onic va
l
u
es obtain
e
d
through fifth
der
i
vativ
e. Initially
, the
c
onstructio
n
of Biorthogon
al vibr
atio
n
signal-data based wavelet tr
ansf
orm
in BPP
V
S
-
W
NN
s
y
s
t
em
local
izes
the
time and frequency
domain
.
Th
e Bior
thogonal wavelet approximates the
broken bearing
using double scaling and factor, iden
tifies the transien
t
disturbance due to fault on induction mo
tor through approximate coefficien
ts
and de
tai
l
ed
coe
ffici
ent.
P
o
s
t
erio
r P
r
obabilistic
Neural Network detects
th
e
final l
e
vel of f
a
ults using the de
tail
ed co
effic
i
en
t till f
i
fth der
i
va
tive and
the
results obtain
e
d
through it at a faster ra
te at
constant frequ
ency
signal on the
industrial dr
ive. Experiment thr
ough th
e Simulink tool detects
the health
y
and unhealth
y
m
o
tor on measuring parametr
ic f
a
ctors such as f
a
u
lt detection
rate based
on
time, curr
ent fl
ow
rate and execu
tion
time.
Keyword:
Bio
r
tho
gon
al
Wav
e
let
tran
sform
B
r
o
k
en
bea
r
i
n
g
Fre
que
ncy
do
m
a
i
n
I
ndu
ctio
n m
o
to
r
Po
steri
o
r prob
ab
ilistic n
e
ural
net
w
or
k
Vibratio
n d
a
ta
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
K
.
Jayaku
m
a
r
,
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
cs E
n
gi
nee
r
i
n
g,
Periyar Man
i
amma
i Un
iversi
ty,
Periy
a
r Naga
r,
Vallam
,
Tha
n
javu
r - 61
3
4
0
3
,
Tam
ilnadu,
I
n
dia.
Em
a
il: rk
jk
u
m
ar70
@g
m
a
il.c
o
m
1.
INTRODUCTION
B
eari
ng
fa
ul
t
det
ect
i
on i
s
o
n
e o
f
t
h
e m
o
st
si
gni
fi
can
t
prob
lem
s
measu
r
ed
in
t
h
e ind
u
s
t
r
ial d
r
i
v
e.
Early d
e
tectio
n
o
f
fau
lt in
th
e b
eari
n
g
in
in
du
ctio
n
m
o
to
rs
h
e
lp
s to
red
u
ce
n
o
t
on
ly th
e wo
rk
fl
o
w
in
th
e
in
du
stry bu
t also
d
e
grad
ation
o
f
m
achines
can be reduc
e
d to a certa
in extent. Ma
ny researche
r
s have
co
n
c
en
trated
on
th
e early fau
l
t d
e
tectio
n in
i
n
du
strial
d
r
i
v
e, bu
t certain li
mitatio
n
s
were
no
t addressed
.
B
a
si
c Vi
br
at
i
o
n Si
gnal
Pr
oce
ssi
ng
(B
VSP
)
[1]
a
d
d
r
esse
d t
h
e
pr
obl
em
s rel
a
t
e
d t
o
det
ect
i
o
n
o
f
f
a
ul
t
s
in the bea
r
ing
at an early stage ap
pl
y
i
ng a
m
pli
t
ude m
odu
l
a
t
i
on an
d Hi
l
b
ert
t
r
ans
f
o
r
m
.
One
of t
h
e al
t
e
rnat
i
v
e
m
e
t
hods
was
d
e
si
gne
d i
n
[
2
]
cal
l
e
d as t
h
e
C
u
r
r
ent
Fre
q
uen
c
y
Spect
ral
Su
bt
ract
i
o
n t
h
at
r
e
gul
a
r
l
y
m
oni
tor
e
d
t
h
e i
n
d
u
ct
i
o
n m
achi
n
e bea
r
i
ngs
usi
n
g F
o
ur
i
e
r and
Di
scret
e
W
a
vel
e
t
Tra
n
sf
orm
.
Th
ou
g
h
earl
y
det
ect
i
on
wa
s
pos
si
bl
e, a
u
t
o
m
a
t
i
c
det
ect
i
o
n o
f
fa
ul
t
i
n
be
ari
n
g was
n
o
t
add
r
esse
d.
A
m
e
t
hod
usi
n
g
vi
b
r
at
i
on si
g
n
a
l
anal
y
s
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
54
1
–
55
1
54
2
was st
r
u
ct
u
r
ed
i
n
[3]
usi
ng
t
i
m
e
do
m
a
i
n
techni
que
s. H
o
weve
r, m
easur
es were
not
i
n
cl
u
d
ed
fo
r p
e
ri
o
d
i
c
v
i
bratio
n
s
. One o
f
th
e m
a
j
o
r
m
ach
in
e failu
res is d
u
e
to
th
e o
c
cu
rren
ce
o
f
fau
lts in
b
e
aring
wh
ich
h
a
s to
b
e
identified at a
n
ea
rly stage i
n
a
pla
nne
d m
a
nne
r
rathe
r
than at t
h
e c
o
st
of m
achinery.
A
varia
b
le m
a
chine
sp
eed
was ap
plied
[4
] to
id
en
tify th
e fau
lt. However,
t
h
e v
i
b
r
ation
d
a
ta was no
t m
eas
u
r
ed
with
respect to
ti
m
e
. An
on
line fau
lt d
e
tection
m
ech
an
ism
was d
e
sign
ed
i
n
[5
] u
s
ing
Fou
r
ier t
r
an
sfo
r
m at v
a
ried
tim
e
in
terv
al
and also the i
m
pact of im
balances in powe
r was al
so
m
e
asu
r
ed
. Bu
t the
m
ech
an
ism
was d
e
si
g
n
e
d
with
th
e
pu
r
v
i
e
w t
h
at
n
e
ural
net
w
o
r
k capt
u
res
the nonlinea
r system dynamic. As a
resu
lt, a meth
od
th
at cou
l
d
d
e
tect
t
h
e fa
ul
t
at
t
h
e st
art
u
p
pe
ri
od
wa
s
desi
g
n
e
d i
n
[
6
]
cal
l
e
d as
Ti
m
e
St
eppi
ng
Fi
ni
t
e
E
l
em
ent
m
e
t
hod
b
y
co
nsid
er
i
n
g th
e sp
atial d
i
str
i
bu
tio
n of
stator
w
i
nd
ing
s
.
In
t
h
e recent years,
m
a
intenan
ce
of m
achi
n
ery and induction m
o
tors
has t
o
be perform
ed at a
pre
d
i
c
t
i
v
e rat
e
wi
t
h
t
h
e i
n
cre
a
se i
n
t
h
e cost
and m
a
i
n
t
e
nance o
f
m
achi
n
es. A m
e
t
hod cal
l
e
d Hi
l
b
ert
Hua
n
g
Transfo
r
m
(HHT)
[7
] with
th
e aid
of Discrete
W
a
velet Tran
sfo
r
m
(DWT) resu
lting
in
b
e
tter su
i
t
ab
ility
.
Ho
we
ver
,
t
h
e
pat
t
e
rns
we
re not
cl
eare
r
an
d t
h
e
num
ber
of
rot
a
t
i
o
ns w
a
s not
t
a
ke
n i
n
t
o
c
onsi
d
erat
i
o
n
.
T
o
o
b
t
ain
th
e
fau
l
ts at v
a
rio
u
s
sp
eed
with
wh
ich
th
e m
o
to
rs g
e
ts ro
tated, Gau
ssian-En
v
e
l
o
p
e
d
Oscillatio
n
-
typ
e
Wavel
e
t
[8]
w
a
s use
d
.
Thi
s
m
e
t
hod
p
r
o
v
e
d
t
o
be ef
fi
ci
ent
t
h
at
i
n
a
way
i
d
ent
i
f
i
e
d t
h
e
fa
ul
t
s
at
va
ri
o
u
s
rot
a
t
i
n
g
spee
d.
A
statistical analysis usi
n
g m
ean,
entropy a
n
d
varian
ce
was ap
p
lied in [9
] t
o
d
e
tect th
e fau
lts in
in
du
ctio
n m
o
to
rs at
v
a
ried
ro
t
a
tio
n
a
l sp
eed.
In
or
der t
o
i
d
e
n
t
i
f
y
and
det
e
c
t
t
h
e faul
t
s
occ
u
r
r
ed i
n
i
n
d
u
ct
i
on m
o
t
o
rs,
on
e of t
h
e m
o
st
si
gni
fi
ca
nt
m
easures t
h
at
can be t
a
ken
i
s
t
h
e
m
oni
t
o
ri
ng
of
m
achines i
n
an a
u
tom
a
tic
m
a
nner
.
C
o
m
m
on
Vect
o
r
Ap
pr
oac
h
(C
V
A
) [
1
0]
was u
s
ed t
o
det
ect
t
h
e faul
t
s
i
n
i
n
duct
i
o
n m
o
t
o
r
s
usi
n
g wavel
e
t
energy
com
pone
nt
.
Bu
t, m
easu
r
es were
n
o
t
tak
e
n to
v
i
b
r
ation
si
g
n
a
ls in
d
a
tabase. On
e o
f
the so
lu
tion
s
was to
d
i
sin
t
egrate th
e
vi
b
r
at
i
o
n
si
g
n
a
l
usi
n
g
Di
scret
e
W
a
vel
e
t
Tra
n
sf
orm
(D
WT
) [1
1
]
. As a
resu
lt, th
e fau
lt si
ze was id
en
tified
and
al
so pr
o
v
i
d
e
d
a
m
eans for e
a
rl
y
det
ect
i
on of fa
ul
t
s
. I
n
t
h
i
s
pa
per, a
n
effect
i
v
e b
eari
ng fa
ul
t
det
ect
i
on i
n
in
du
ctio
n
m
o
to
rs u
s
ing
,
Bi
o
r
t
h
ogo
n
a
l Po
sterio
r Vibra
tio
n Sig
n
a
l-Data Prob
ab
ilistic
W
a
velet Neural Network
(BPPVS-WNN) is
pres
ente
d. T
h
e system BPPVS-WN
N
first id
en
tifies th
e transien
t d
i
st
u
r
b
a
n
c
es b
y
lo
calizin
g
tim
e
and
frequ
en
cy
. Fro
m
it th
e
detailed
co
efficien
t is ex
tracted
u
n
til th
e fi
fth
d
e
ri
v
a
tiv
e
form
is
ach
iev
e
d
.
Nest
, Po
sterio
r
Prob
ab
ilistic Vib
r
atio
n
Sign
al-D
ata Neu
r
al
Network
is ap
p
lied
fo
r
faster
d
e
tectio
n
of
fi
nal
l
e
vel
o
f
fa
ul
t
s
usi
n
g fi
ft
h deri
vat
i
v
e f
o
rm
.
The rest
of
t
h
e pape
r has bee
n
o
r
ga
ni
zed
as f
o
l
l
o
w
s
.
Sect
i
o
n
2
gi
ves
a
bri
e
f m
odel
f
o
r
fa
ul
t
det
ect
i
o
n
o
f
b
eari
n
g in
i
n
du
ction
m
o
to
rs. Section
3
inclu
d
e
s t
h
e rev
i
ew work
s
related
to
i
n
du
ction
m
o
to
rs i
n
indu
strial
d
r
i
v
e an
d
several fau
lt d
e
tectio
n
m
ech
an
ism
s
with
th
eir b
r
iefing
and
li
mitatio
n
s
. Sectio
n
3
presents th
e
propose
d
syst
e
m
with neat archit
ecture di
agram
and algorithm
i
c descri
bed incl
ude
d
with an ela
b
orated
descri
pt
i
on
of t
h
e sam
e
. Sect
ion
4 p
r
ese
n
t
t
h
e expe
ri
m
e
nt
al anal
y
s
i
s
and
m
e
t
r
i
c
s consi
d
ered f
o
r t
h
e de
si
gn
of
t
h
e m
odel
w
h
ereas Sect
i
o
n
5 i
n
cl
udes
si
m
u
l
a
t
i
on
res
u
l
t
s
.
Sect
i
on
6 c
o
ncl
u
des t
h
e
w
o
r
k
wi
t
h
c
oncl
udi
ng
rem
a
rks.
2.
RELATED WORKS
Th
e im
p
r
ov
emen
t of
reliab
ility facto
r
of mech
an
ism
syste
m
b
y
d
i
agnosin
g
t
h
e
fau
lts o
f
ro
llin
g
el
em
ent
i
s
hi
g
h
l
y
si
gni
fi
cant
as break
d
o
w
n
s on bea
r
i
n
g are t
h
e
m
o
st
fr
eque
nt
p
r
o
b
l
e
m
s
rel
a
t
e
d t
o
rot
a
t
i
ng
m
achi
n
ery
.
A
hy
b
r
i
d
m
odel
i
n
cl
u
d
i
n
g Em
pi
ri
cal
M
odel
D
ecom
posi
t
i
on
and
Hi
l
b
ert
H
u
an
g T
r
ans
f
or
m
was
in
clu
d
e
d
i
n
[12] to
d
i
agno
se t
h
e fau
lts in
b
e
aring
b
y
app
l
yin
g
v
a
ried
l
o
ad
co
nd
itio
ns.
Howev
e
r, t
h
e life
o
f
t
h
e
com
pone
nt wa
s not c
onsi
d
ere
d
. An intellige
n
t m
e
thod
us
ing Artificial Neural Net
w
ork (ANN)
was structure
d
in
[13
]
th
at efficien
tly re
m
o
v
e
d
th
e n
o
n
b
e
aring
fau
lt co
mp
on
en
ts d
e
sp
ite th
e in
clu
s
io
n o
f
no
ise. Howev
e
r,
th
e irreg
u
l
arities in
lo
ad
were n
o
t
co
nsid
ered
. M
o
to
r C
u
rren
t Si
g
n
a
t
u
re
An
alysis (MC
S
A)
[1
4
]
d
e
tected
th
e
fau
lts in
b
eari
n
g
s
u
s
ing
2D
wav
e
let scalo
g
ram
.
Co
n
d
itio
n
m
o
n
ito
rin
g
is
on
e of th
e m
o
st efficien
t m
ech
an
ism
s
with
wh
ich
t
h
e rate
o
f
fau
lts
can
b
e
red
u
c
ed to
a sign
ificant rate.
An
in
teg
r
ated
form
o
f
HAAR
wav
e
l
e
t and
FFT [
15]
was
appl
i
e
d t
o
m
e
asure t
h
e f
r
e
que
nci
e
s of fa
u
lts wh
ich
resu
lted in
co
st effectiv
en
ess. However, the
reliab
ility o
f
the
m
o
d
e
l rem
a
i
n
s un
ad
dressed. Bearing
fa
u
lt d
e
tectio
n
was
effectiv
ely ev
alu
a
ted
in
[16
]
u
s
ing
SVM an
d KNN th
at i
d
en
tified
an
d classified
th
e fau
lts at
an ea
rlier stage
.
Based on t
h
e
fre
que
ncy
of the
fault
bei
n
g
gene
rat
e
d, a
va
ri
at
i
o
n
a
l
go
ri
t
h
m
was d
e
si
gne
d i
n
[
1
7]
fo
r brok
en
b
e
aring
s
in
ro
tor bars fau
lt d
e
tectio
n
.
Noise a
n
d spa
r
sene
ss of
vibration si
gnals are posi
ng
g
r
eater th
reat
while d
e
tectin
g
fau
lt in
the
beari
ngs i
n
i
n
duct
i
o
n m
o
t
o
r
s
. In [
1
8], efficient
m
eans for re
ducing no
ise an
d
early
fau
lt d
e
tectio
n
was
prese
n
t
e
d
usi
n
g pi
ece
wi
se r
ecom
b
i
n
at
i
on
and i
nve
rse
w
a
vel
e
t
t
r
ans
f
o
r
m
.
W
i
t
h
t
h
i
s
,
t
h
e det
ect
i
o
n
of t
h
e
syste
m
was prove
d t
o
e
fficie
n
t and
was
also easy t
o
im
p
l
e
m
en
t. Ho
wever, t
h
e en
erg
y
requ
ired
to elimin
ate
th
e no
ise increased
with
the
in
crease i
n
th
e un
h
ealth
y
b
e
aring
s
. To
so
l
v
e th
is issu
e, an
in
teg
r
ated
meth
od
co
m
b
in
in
g
Hilb
ert Hu
an
g
Tran
sform
(HHT) and
Singu
lar Valu
e
Deco
m
p
o
s
ition
(SVD) was in
t
r
odu
ced
in
[1
9]
res
u
l
t
i
ng
i
n
hi
g
h
e
r
p
r
eci
si
on
. A
ne
w
m
e
t
hod cal
l
e
d
as t
h
e C
o
m
p
l
e
m
e
nt
ary
Ense
m
b
l
e
Em
pi
ri
cal
M
ode
Decom
position (CEEMD) [20] was design
e
d
to accurately identify the
faul
ts
in beari
n
gs in induction m
o
tors
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Vib
r
a
tion
Ana
l
ysis o
f
Indu
stria
l
Drive fo
r
Bro
ken
Bea
r
ing
Detectio
n
Usi
n
g
Prob
ab
ilistic… (K. Ja
ya
kuma
r)
54
3
B
a
sed o
n
t
h
e a
f
o
r
em
ent
i
oned
m
e
t
hods a
n
d t
echni
que
s di
sc
usse
d, i
n
t
h
i
s
wo
rk
an e
ffi
ci
ent
sy
st
em
t
o
reduc
e
th
e curren
t
flo
w
and
i
d
en
ti
fy fau
lts in
l
e
sser tim
e
i
s
desi
g
n
e
d
.
In
t
h
e
fo
rt
hc
om
i
ng sect
i
o
ns,
de
t
a
i
l
e
d
d
e
scri
p
tio
n
abo
u
t
Bio
r
t
h
ogon
al Po
steri
o
r
V
i
bratio
n
Si
g
n
al D
a
ta Prob
ab
ilistic W
a
v
e
l
e
t N
e
u
r
al N
e
t
w
ork
is
p
r
esen
ted in
d
e
tail.
3.
BIORTHOGONAL POST
ERIO
R VIBRATION
SIGN
AL-DAT
A PROBABILISTIC WAVELET
NEU
RAL
NE
TWOR
K
Maj
o
r indu
stri
al d
r
i
v
e is in
t
e
rested
i
n
co
nstru
c
ting
th
e in
du
ction
m
o
to
r wit
h
ou
t an
y tran
sient
d
i
stu
r
b
a
n
ce wh
ile sp
eed
i
n
g
u
p
t
h
e m
o
to
r sp
eed. Th
e m
a
i
n
go
al in
th
is
work
is to
constru
c
t a Bio
r
t
h
o
gon
al
wavel
e
t
t
r
ans
f
orm
usi
ng t
h
e
vi
b
r
at
i
on si
g
n
a
l
-dat
a of t
h
e ind
u
s
t
r
ial d
r
iv
e. Th
e wav
e
let tran
sform rep
r
esen
t th
e
vi
b
r
at
i
o
n
si
g
n
a
l
-dat
a si
m
u
l
t
a
neou
sl
y
at
t
i
m
e
‘t
’
wi
t
h
a f
r
e
que
ncy
‘f
’. B
i
ort
h
o
g
onal
a
n
a
l
y
s
i
s
of t
h
e
wa
vel
e
t
s
decom
poses the vibration signal-data
in
to
frequ
e
n
c
y an
d
also
th
e ti
m
e
f
actor on which the fre
quenc
y
gets
fl
uct
u
at
e
d
. B
P
PVS
-
WN
N sy
st
em
freque
nc
y
range i
s
m
a
int
a
i
n
ed
wi
t
h
ou
t
any
t
r
ansi
ent
di
st
ur
bance a
nd al
s
o
ach
iev
e
s
h
i
gh
er fau
lt d
e
tection
on
th
e in
du
ct
io
n
m
o
to
r with
m
i
n
i
mal ex
ecu
tio
n
tim
e
wit
h
d
e
tailed
co
efficien
t
o
b
t
ain
e
d
till fifth
d
e
riv
a
tiv
e fo
rm
. Th
e Bi
o
r
t
h
ogo
n
a
l
wav
e
let tran
sform
in
BPPVS-WNN syste
m
is illu
strated
in
Figur
e
1
.
Fi
gu
re
1.
Pr
oce
d
u
r
al
st
ep
o
f
bi
ort
h
o
g
onal
wa
vel
e
t
t
r
ans
f
orm
Th
e Bi
o
r
thog
on
al wav
e
let tran
sfo
r
m
with
v
i
b
r
ation
sign
al-d
ata is
u
s
ed
t
o
easily lo
calize th
e tim
e an
d
fre
que
ncy
d
o
m
a
i
n
. T
h
e t
i
m
e
and
fre
q
u
ency
d
o
m
a
i
n
vari
at
i
on p
o
i
n
t
hel
p
t
o
easi
l
y
det
ect
t
h
e br
o
k
en
bea
r
i
ng i
n
t
h
e i
n
d
u
ct
i
on
m
o
t
o
r. The det
ect
i
on of
br
o
k
e
n beari
ng i
s
b
a
sed o
n
t
h
e t
r
ansi
ent
di
st
u
r
b
a
nce o
n
t
h
e fre
que
ncy
value. T
h
e FD approxim
a
t
e and detailed c
o
efficients
ar
e co
m
p
u
t
ed
u
s
ing Bio
r
thog
on
al
W
a
v
e
let Tr
an
sf
or
m
.
Th
e ov
erall d
i
ag
ramm
at
ic fo
rm
o
f
p
r
o
p
o
s
ed
BPPVS-WN
N system is il
lu
strated
in
Fig
u
re 2. Th
e
ov
erall
stru
cture
o
f
the Bio
r
tho
gon
al Po
sterior Vi
b
r
ation
Si
g
n
a
l
-
Data Prob
ab
ilistic W
a
v
e
let Neural Network
is
p
r
esen
ted. Th
e v
i
br
atio
n
si
g
n
al-
d
ata of
inductio
n
m
o
to
r
is tak
e
n
as t
h
e inp
u
t
p
a
r
a
m
e
ter
u
s
ing
th
e
Simu
lin
k
M
A
TLAB
c
o
d
e
. The
vi
b
r
at
i
o
n dat
a
a
r
e anal
y
zed t
h
r
o
ug
h t
h
e B
i
ort
h
o
g
o
n
a
l
W
a
vel
e
t
Tra
n
sf
orm
.
The
w
a
vel
e
t
t
r
ans
f
o
r
m
carri
es out
t
h
e
do
u
b
l
e
scal
i
ng fac
t
or w
h
i
c
h l
o
c
a
l
i
zed t
h
e t
i
m
e
and
fre
qu
ency
dom
ai
n. The
no
n-
transient disturbance on
the freque
nc
y range (i.e.,
50
Hz), th
en
th
e
h
ealt
h
y in
du
ction
m
o
to
r is u
s
ed
o
n
t
h
e
in
du
strial driv
e with
m
a
x
i
m
a
l sp
eed
rate.
B
i
ort
h
og
o
n
al
Wavel
e
t
va
ri
es
based o
n
t
h
e
fre
que
ncy
d
o
m
ai
n, and t
h
e
n
t
h
e fa
ul
t
occur
r
ed
on t
h
e
i
n
d
u
ct
i
on m
o
t
o
r i
s
m
easured.
The fa
ul
t
i
n
t
h
e i
nduct
i
o
n m
o
t
o
r i
s
m
easure
d
base
d o
n
t
h
e br
o
k
en bea
r
i
n
g
usi
n
g
th
e Po
sterior
Prob
ab
ilistic Vibratio
n
Signal-Data
Neural Netwo
r
k
.
The b
r
ok
en b
e
ari
n
g d
e
tection
t
h
rou
g
h
n
e
ural n
e
t
w
ork in
BPPVS-WNN
Syste
m
resu
lts in
two
coefficient val
u
e
s
called the approxim
a
t
e coefficient
an
d d
e
tailed
co
efficien
t. Th
e d
e
tailed
co
effi
cien
t v
a
lue is
ap
p
lied un
til fi
fth
d
e
ri
v
a
tiv
e i
s
ob
tain
ed
.
Posterio
r
Prob
ab
ilistic
Wav
e
let Neu
r
al n
e
twork
com
b
in
e th
e th
eo
ry of th
e fifth
d
e
ri
v
a
tiv
e wav
e
lets and
n
e
ural
net
w
or
ks
i
n
t
o
one
t
o
fee
d
-
f
o
r
war
d
ne
ural
ne
t
w
o
r
k
t
o
i
d
en
ti
fy th
e
fau
lts i
n
th
e ind
u
c
ti
o
n
m
o
to
r at a fast
er rate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
54
1
–
55
1
54
4
F
i
g
u
r
e
2.
Pr
opo
s
e
d
BP
PV
S -
W
N
N
s
y
s
t
em
3.
1.
B
i
or
th
og
on
al
Vi
br
a
t
i
o
n Si
g
n
al
-D
at
a
B
a
sed
Wa
vel
e
t tr
ans
f
orm
Let u
s
con
s
i
d
er
th
e V
i
b
r
ation Sign
al
d
a
ta ‘X
’ of
t
h
e inductio
n
m
o
to
r that p
r
ov
id
es h
i
gh
er d
e
gr
ee
o
f
free
dom
on m
easuri
ng t
h
e t
i
m
e
and fre
q
u
e
n
cy
dom
ai
n. The B
i
ort
h
o
g
o
n
a
l
wavel
e
t
con
s
t
r
uct
s
t
h
e sy
m
m
e
t
r
i
c
wavel
e
t
fu
nct
i
on
u
s
i
n
g
vi
b
r
a
t
i
on si
gnal
-
dat
a
. B
i
o
r
t
h
o
gon
al wav
e
let transform
g
e
n
e
rates th
e
do
ub
le scalin
g
factor
s in BPPVS-
WN
N Sy
st
em
differs
wit
h
‘A
’ (i.e.
,
A
p
p
r
oxim
a
te co
e
fficient) c
o
efficient and ‘D’ (i.e.,
Detailed
co
efficien
t) v
a
lu
es. Bio
r
tho
gon
al Vibratio
n Signal-d
a
ta
Wav
e
let co
nd
itio
n is
fo
rm
u
l
arized
as,
∑
(1)
Th
e Biorthogo
n
a
l
Wav
e
let Tran
sform
‘B
W
T
’ in
itia
ll
y o
b
t
ains th
e app
r
ox
im
a
t
ed
and
d
e
tailed
coefficient val
u
es. T
o
obtain the fi
ft
h d
e
ri
vat
i
v
e (F
D
)
fo
rm
, our w
o
r
k
pr
o
pose
d
sy
st
em
uses t
h
e de
t
a
i
l
e
d
coefficient
value
‘D’. This
‘D’ val
u
e is it
erated
fiv
e
times. Th
e fift
h d
e
riv
a
tiv
e fo
rm
is th
e fin
a
l
ou
tpu
t
obt
ai
ne
d t
h
ro
u
gh B
W
T. I
n
a
sim
i
l
a
r
m
a
nner
,
B
PPV
S-
WN
N sy
st
em
t
a
kes t
h
e app
r
oxi
m
a
t
e
d coef
fi
ci
en
t
val
u
e
o
n
c
e and
d
e
tailed
co
efficien
t v
a
lu
e with the fifth d
e
riv
a
ti
v
e
form
o
f
‘N’ indu
ctio
n m
o
to
rs
o
f
th
e i
ndu
strial
dri
v
e. B
i
o
r
t
h
og
onal
T
r
an
sf
or
m
usi
ng t
i
m
e and
fre
q
u
ency
wavel
e
t
s
a
nd i
d
ent
i
f
y
t
h
e
faul
t
s
. As a re
sul
t
,
t
h
e d
u
al
scalar fun
c
tio
ns are i
n
terrelat
e
d
an
d with th
i
s
th
e
fau
lts
o
f
th
e indu
ction
mo
tor are easily id
en
tified.
Th
e Bio
r
t
h
ogon
al w
a
velets usin
g
th
e
v
i
br
atio
n
sign
al-d
ata ar
e sup
p
o
r
ted
b
y
sy
mm
e
t
r
i
c
w
a
v
e
lets of
dual
scal
i
n
g f
act
or. T
h
e
det
a
i
l
e
d coef
fi
ci
ent
s
ap
pr
o
x
i
m
at
ed val
u
e
s
usi
ng
FD
of B
i
ort
h
o
g
onal
W
a
vel
e
t
Transfo
r
m
is il
lu
strated
i
n
Fi
g
u
re
3
.
Th
e
dual scalin
g
factor uses
the vibration
Si
gnal-Data on
detecting t
h
e
b
eari
n
g
brok
en
fau
lts of th
e in
du
ctio
n m
o
t
o
r.
O
n
pa
rt
o
f
t
h
e
du
al
scal
i
ng,
d
u
ri
ng
fi
r
s
t
deri
vat
e
f
o
r
m
t
h
e
co
efficien
t v
a
l
u
esA_N
g
e
n
e
rated
b
y
th
e l
o
w
p
a
ss
filter an
d th
e
o
t
h
e
r p
a
rt is th
e
v
i
bratio
n
signal-d
a
ta
D_Ng
en
erated
ap
pro
x
i
m
a
ted
v
a
lu
e
b
y
th
e
h
i
g
h
-p
ass
filter is ob
tain
ed. The d
e
tailed
co
efficien
t v
a
l
u
e fro
m
th
e
first deriv
a
te is ob
tain
ed and
t
h
is v
a
l
u
e
pr
oce
ss i
s
fe
d as
i
n
p
u
t
t
o
t
h
e i
n
d
u
st
ri
al
dri
v
e
resul
t
i
ng i
n
a
p
p
r
oxi
m
a
t
e
d
and detailed coefficient
of sec
o
nd
de
rivative.
Fi
gu
re
3.
B
i
ort
h
o
g
onal
wa
vel
e
t
s
wi
t
h
c
o
ef
fi
ci
ent
an
d a
p
pr
oxi
m
a
t
e
d val
u
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Vib
r
a
tion
Ana
l
ysis o
f
Indu
stria
l
Drive fo
r
Bro
ken
Bea
r
ing
Detectio
n
Usi
n
g
Prob
ab
ilistic… (K. Ja
ya
kuma
r)
54
5
Th
is pro
cess is co
n
tinu
e
d
un
til th
e fifth
d
e
riv
a
tiv
e fo
rm
is
o
b
t
ain
e
d
th
at help
s in
id
en
tify
i
n
g
h
i
g
h
er
num
ber
of
fa
ul
t
s
at
m
i
nim
u
m
t
i
m
e
i
n
t
e
rval
.
In a
similar
m
a
n
n
e
r, to
all th
e cases, co
efficien
ts of
ap
pro
x
i
m
a
ted
an
d d
e
tailed valu
es are id
en
t
i
fied
for ‘N’ i
n
du
ction
m
o
tor. BPPVS-WNN System
u
s
es th
e
o
r
i
g
in
al v
i
bratio
n
sign
al-d
ata to
p
r
o
cess and
d
e
tect th
e fau
lts o
f
th
e ind
u
s
t
r
ial d
r
iv
e in
du
ct
io
n
m
o
to
r. BPPVS-
WNN
System
solves
the c
o
e
f
fi
ci
ent
s
as desc
ri
be
d bel
o
w:
0
∑
(2)
Ev
id
en
tly, Co
effcien
t
s So
lv
er FD (z) corresp
ond
s
to
p
e
rform th
e fifth
d
e
riv
a
tiv
e filter an
d
id
en
tify
the breake
d
be
arings on t
h
e
in
du
ction
m
o
to
r. Th
e co
efficien
t so
l
v
er i
n
Eq
u
a
tion
(2)
h
e
lp
s to
easily id
en
tify
th
e f
r
e
qu
en
cy r
a
ng
e
o
f
t
h
e ru
nn
ing
indu
ctio
n
m
o
to
r.
T
h
is is beca
use the zero-phase
characte
r
istic on t
h
e
coefficient sol
v
er C
N
(0) m
e
e
t
s the require
m
ent of symmetric wave
lets. Sy
mmetric wav
e
let h
e
lp
s to id
en
tify
t
h
e t
i
m
e
and
f
r
e
que
ncy
dom
ai
n.
3.1.1
Algorithmic P
r
ocedure
The BP
PVS-WNN System
through
dual
s
caling fact
or is
form
ularized as:
Beg
i
n
St
ep
1:
Vi
brat
i
o
n
Si
g
n
al
-
D
at
a
t
a
ken
as i
n
p
u
t
on
Si
m
u
l
i
nk
Step
2
:
In
itiali
ze zero
facto
r
o
n
id
eal state
of indu
ctio
n m
o
to
r
St
ep 3:
B
i
ort
h
o
g
o
n
al
Wavel
e
t
t
r
ans
f
orm
obtain the
dual scali
n
g fact
or’
Step
3
.
1
:
In
itial Scalin
g
facto
r
co
m
p
u
t
es the
co
efficien
t solv
er t
o
id
en
tify
wh
eth
e
r tran
si
en
t
di
stur
bance
occ
u
rre
d
or
not
St
e
p
3.
2:
Sec
o
n
d
s
cal
i
n
g
fac
t
or at
t
a
i
n
t
h
e a
p
p
r
oxi
m
a
t
i
on v
a
l
u
es i
.
e.
,
Ap
pr
oxi
m
a
t
e
d coef
f
i
ci
ent
and
Detailed
co
efficien
t throug
h lo
w and
h
i
gh
p
a
ss
filter,
d
e
tects fau
lts
on
m
i
n
i
m
a
l
tim
e using F
D
Step
4
:
Low an
d Hi
g
h
p
a
ss asso
ciatio
n filter are symmetri
cal wav
e
lets
Step
5
:
Id
en
tifies
h
i
g
h
e
r fau
lt co
un
t o
n
m
i
n
i
mal
ex
ecu
tion
ti
m
e
Step
6
:
Bio
r
t
h
og
on
al
wav
e
lets u
s
ed
i
n
fau
lt detectio
n
o
f
i
n
du
ctio
n m
o
to
r
End
Th
e
v
i
bratio
n
sig
n
a
l-d
a
ta used to
m
easu
r
e th
e ti
m
e
an
d
frequen
c
y do
m
a
in
fo
r
d
e
tectin
g the fau
lt rate.
Th
e Bio
r
t
h
ogon
al w
a
v
e
let v
i
b
r
ation
sign
al-d
ata tr
an
sf
or
m is in
ter
r
e
lated
w
ith
d
u
a
l scalin
g
f
act
o
r
to
ach
i
ev
e
hi
g
h
er s
p
ee
d r
a
t
e
of m
o
t
o
r,
by
det
ect
i
n
g f
a
ul
t
s
at
an
earlier stage. T
h
e
lesser rate
of
current
flow leads t
o
min
i
m
a
l fau
lt o
n
th
e i
n
du
stri
al d
r
i
v
e indu
ctio
n m
o
to
r.
3
.
2
.
Neura
l
Netwo
r
k Applied
Ba
sed o
n
Posterio
r
Probabilities
Po
steri
o
r Pro
b
ab
ilistic W
a
v
e
let Neu
r
al n
e
t
w
ork
co
m
b
in
e th
e th
eory o
f
th
e wav
e
lets
an
d
n
e
u
r
al
net
w
or
ks i
n
t
o
one t
o
fee
d
-
f
o
r
war
d
ne
u
r
al
ne
t
w
o
r
k t
o
i
d
en
ti
fy th
e fau
lts in
th
e in
du
ction
m
o
to
r at a faster rate.
Po
steri
o
r
p
r
obab
ility o
n
wav
e
let n
e
ural network
is th
e
co
nd
itio
n
a
l
p
r
o
b
a
b
ility o
f
fau
lts o
c
cu
rred
in
th
e
in
du
ctio
n m
o
to
r with relevan
t
ev
id
en
ce
o
b
t
ain
e
d with
th
e
h
e
lp of th
e
p
e
rv
i
o
u
s
op
eration
.
Po
sterior
Prob
ab
ilistic
Wav
e
let Neu
r
al n
e
twork
con
s
ists o
f
an
inp
u
t
layer, fau
l
t d
e
tectin
g
process layer an
d o
u
t
p
u
t
layer. Th
e acti
v
atio
n
fu
n
c
tion
of n
e
uron
in
Po
steri
o
r
Pro
b
ab
ilistic W
a
v
e
let Neural n
e
two
r
k
uses th
e
detailed
coefficient val
u
es of the Bi
ortho
gon
al wavelet to
d
e
tect t
h
e fau
lt at faster rate. Th
e activ
atio
n
fu
n
c
ti
o
n
u
s
es
th
e pro
b
a
b
ilistic d
i
stribu
tion
fu
n
c
tion
on
the
ev
id
en
ce
o
f
‘X’ v
i
b
r
ation
signal-d
a
ta
is formu
l
arized
as:
|
(3)
Th
e prior ev
iden
ce of d
e
tected
fau
lts is u
s
ed in
th
e p
o
s
teri
or p
r
ob
ab
ility
Wav
e
let Neu
r
al n
e
twork
t
o
attain
faster
fau
lt d
e
tection
rate u
s
ing
t
h
e
d
e
tailed
co
efficien
t FD v
a
l
u
e. Po
sterior
Pro
b
a
b
ilistic
W
a
v
e
let
Neural
n
e
two
r
k
thro
ugh
th
e activ
atio
n
fun
c
tio
n is
d
e
scri
b
e
d as:
|
|
(
4
)
Wavel
e
t
Ne
ur
al
net
w
o
r
k
us
es t
h
e act
i
v
at
i
on
fu
nct
i
o
n o
n
t
h
e i
n
du
st
ri
al
dri
v
e,
w
h
er
e
m
a
xim
u
m
l
i
k
el
i
hoo
d
o
f
f
a
ul
t
s
(i
.e.
,
b
r
ok
en
bear
ing) is
assessed. T
h
e
assessed
val
u
e
s
are
u
s
ed
to
detect th
e fau
lts in
th
e
wav
e
let neural n
e
two
r
k
.
Th
e feed
forward h
e
lp
s t
o
u
tilize th
e v
i
b
r
atio
n
sign
al-d
ata in
pu
t on
th
e fau
l
t
d
e
tectin
g
p
r
o
c
ess layer to
id
en
tify th
e u
nhealth
y
m
o
to
r in
th
e ou
tpu
t
layer. Th
e FD of D_N Co
efficien
t is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
54
1
–
55
1
54
6
u
s
ed
to
id
en
tify th
e d
e
ep
layer fau
lts on
the in
du
c
tion
mo
tor. Th
e BPPVS-WNN Syste
m
d
e
tects th
e fau
l
t
s
usi
n
g t
h
e s
p
eci
fi
ed c
r
i
t
e
ri
o
n
f
unct
i
o
n,
∗
Th
e
p
o
s
terio
r
p
r
ob
ab
ility u
s
es d
i
rectly th
e d
i
stin
gu
ish
e
d freq
u
e
n
c
y pro
b
a
b
ility ran
g
e to
id
en
tify
br
o
k
en
beari
n
gs at
a fast
er
rat
e
. The act
i
v
at
i
on f
u
nct
i
o
n uses t
h
e fi
f
t
h deri
vat
i
v
e f
o
rm
of t
h
e de
t
a
i
l
e
d
co
efficien
t
v
a
lu
es
u
s
ing
Bi
o
r
t
h
ogo
n
a
l
wav
e
let to
id
en
tify the un
h
ealth
y
b
e
aring
s
.
4. E
X
PE
RIM
E
NTAL E
V
A
L
UATIO
N
The ex
pe
ri
m
e
nt
al
set
up
us
ed usi
ng
hea
l
t
h
y
m
o
t
o
r and
u
nheal
t
h
y
m
o
t
o
r f
o
r t
h
e p
r
o
p
o
se
d
Bio
r
tho
gon
al Po
sterior Vi
b
r
at
io
n
Sign
al-Dat
a Prob
ab
ilistic Wav
e
let Neu
r
al Netwo
r
k
(BPPVS-WNN) sy
ste
m
i
s
depi
ct
e
d
i
n
Fi
gu
re
4. B
P
P
V
S-
WN
N
det
e
ct
s t
h
e b
r
oke
n
beari
ngs
usi
n
g
t
h
e
harm
oni
cs
o
b
t
a
i
n
ed
t
h
ro
ug
h t
h
e
ap
pro
x
i
m
a
ted
an
d d
e
tailed coefficien
t
v
a
lu
es u
s
i
n
g h
ealth
y
m
o
to
r and
u
nhealth
y
m
o
to
r.
Fi
gu
re
4.
Ex
pe
ri
m
e
nt
al
set
up
usi
n
g
heal
t
h
y
a
n
d
u
n
h
eal
t
h
y
m
o
t
o
r
In case i
f
the i
n
dustrial drive
sy
st
em
i
s
healt
h
y
t
h
en t
h
e
r
e
doe
s n
o
t
occ
u
r
any
ha
rm
oni
c val
u
es
. Th
e
m
odulation signal is created
using
the Biorthogonal P
o
ster
ior Vibration Signal
-
Data
P
r
oba
bilistic
W
a
velet
Neu
r
al
Net
w
or
k. O
n
t
h
e
ot
he
r ha
nd
, i
f
t
h
ere
occu
rs b
r
o
k
e
n
beari
n
g i
n
t
h
e
i
ndu
st
ri
al
dri
v
e t
h
en t
h
e ha
r
m
oni
c
val
u
es are o
b
t
a
i
n
ed f
o
r m
o
t
o
r r
u
nni
ng
. D
u
ri
ng t
h
e fi
rs
t
d
e
riv
a
tion
,
two
co
efficien
t v
a
lu
es called
as th
e
approxim
a
ted coefficient and detailed coe
f
ficient is obt
ai
ned
.
Th
e ap
pr
oxi
m
a
t
e
d co
efficient values
are not
considere
d
whereas the
detailed c
o
effici
en
t
v
a
lu
e is
u
s
ed
wh
ich
is
g
i
v
e
n as inp
u
t
. In
this way th
e
p
r
ocess is
co
n
tinu
e
d
till fifth
d
e
riv
a
tive fo
rm
to
ob
tain
th
e
resu
ltan
t
ou
tpu
t
.
Th
e syste
m
h
ealth
in
ess an
d fau
l
ts are
checke
d
using BPPVS-WNN syste
m
and
id
en
tify th
e actu
a
l failu
re rat
e
o
f
m
o
tor at
an earlier stage. The
co
nstan
c
y on
th
e frequ
en
cy do
m
a
in
is
m
a
in
tain
ed
as 50
Hz
. If there is an
occurre
nce
of
b
r
ok
en
b
e
ar
ing, th
en
th
e cu
rren
t flow rate g
e
t in
creased
with
varyin
g
fre
que
n
c
y
range
. To
eval
uat
e
t
h
e
p
r
o
p
o
sed sy
st
e
m
,
t
h
e
Bio
r
tho
gon
al
wav
e
let tran
sform
is u
s
ed
on
m
easuri
n
g t
h
e
t
i
m
e
and f
r
e
q
u
e
ncy
d
o
m
a
i
n
.
R
eal
t
i
m
e
vi
br
at
i
on
dat
a
on
i
n
d
u
st
ri
al
dri
v
es m
easure t
h
e spee
d
‘
N
’
o
f
t
h
e
i
n
du
ct
i
o
n m
o
t
o
r.
I
n
B
PPVS
-
WN
N
sy
st
em
, sam
p
l
i
ng
fre
que
ncy
i
s
set
t
o
50 Hz
on di
ffe
rent
l
e
ngt
h o
f
vi
b
r
at
i
on dat
a
si
g
n
al
. The
m
o
t
o
r was
ru
n
n
i
n
g f
o
r di
ffe
re
nt
set
o
f
t
i
m
e (
i
.e.,
of a
b
out
1
0
m
i
nut
es) o
n
every
i
t
e
rat
i
o
n.
The
ge
nerat
e
d
res
u
l
t
tab
l
e is d
e
scri
bed
in
n
e
x
t
secti
o
n. Bio
r
t
h
ogo
nal Po
sterior
Vib
r
ation
Si
g
n
a
l
-
Data Prob
ab
ilistic W
a
v
e
let Neu
r
al
Netwo
r
k
(BPPVS-WNN) syste
m
fo
r d
e
tectin
g th
e ind
u
c
tio
n
m
o
to
r
fau
lts is co
m
p
ared ag
ain
s
t ex
isting Basic
Vi
b
r
at
i
on
Si
g
n
a
l
Proces
si
n
g
f
o
r B
e
a
r
i
n
g Fa
u
l
t
Det
ect
i
on (B
VSP
)
an
d C
u
r
r
e
nt
Fre
q
uency
Spect
ral
S
u
bt
r
act
i
o
n
(C
FSS
). Ex
per
i
m
e
nt
con
duct
e
d on
fact
ors suc
h
as faul
t
det
ect
i
on rat
e
base
d
o
n
t
i
m
e,
cu
rre
nt
fl
o
w
rat
e
,
execut
i
o
n t
i
m
e
, speed
of hea
l
t
h
y
and un
he
al
t
h
y
i
nduct
i
o
n m
o
t
o
r, fre
q
u
ency
si
g
n
al
range
of heal
t
h
y
an
d
un
heal
t
h
y
m
o
t
o
r
,
vol
t
a
ge
fact
or
o
f
h
ealth
y an
d unh
ealth
y i
n
du
ction
m
o
to
r.
Param
e
ters taken f
o
r t
h
e BPP
V
S-
WN
N sy
st
em
and
t
h
ei
r s
p
eci
fi
cat
i
on
ra
nge a
r
e de
scri
bed i
n
bel
o
w
tab
l
e:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Vib
r
a
tion
Ana
l
ysis o
f
Indu
stria
l
Drive fo
r
Bro
ken
Bea
r
ing
Detectio
n
Usi
n
g
Prob
ab
ilistic… (K. Ja
ya
kuma
r)
54
7
Tabl
e
1.
B
P
P
V
S-
WN
N
sy
st
em
param
e
t
r
i
c
t
a
bl
e
Para
m
e
ters
Specif
i
cation
Cur
r
e
nt Flow Rate
350
m
A
Voltage Rate
230 Volts
Fault Detection rate based on
T
i
m
e
600 second
s per
iter
a
tion
Speed 1550
RPM
Fr
equency
Range
50 Hz
Power
rate on E
x
ecution
0.
25 Hp
5.
RES
U
LTS
AN
ALY
S
IS
O
F
BPPV
S-
WN
N
In
th
is sectio
n, a d
e
tailed
an
alysis o
f
th
e p
r
opo
sed
Biortho
gon
al Po
steri
o
r Vi
b
r
ation
Sig
n
a
l-Data
Prob
ab
ilistic Wav
e
let
Neural Netwo
r
k
is
m
a
d
e
with
t
w
o
o
t
her ex
istin
g
work
s, B
a
sic Vibratio
n Sig
n
al
Processing for Bearing Fa
ult Detection (B
VSP
)
[1]
and
Current F
r
equency Spectral
Subtraction (C
FSS)
[2]
respect
i
v
el
y
.
F
o
r e
xpe
ri
m
e
nt
al
anal
y
s
i
s
, t
h
e val
u
es
of Ta
bl
e 1 an
d t
h
e e
x
peri
m
e
nt
al
setup i
n
Fi
g
u
re
4
i
s
use
d
to analyse t
h
e
results in a
n
ela
b
orate m
a
nner.
Tab
l
e
2
.
Tabu
l
a
tio
n
o
f
ex
ecu
t
io
n
tim
e u
s
in
g
h
ealth
y m
o
to
r
an
d unh
ealth
y
m
o
to
r with
resp
ect to
frequ
ency
Healthy Motor
Unhealthy
Motor
Fr
equency
(Hz)
E
x
ecution T
i
m
e
(m
s
)
Fr
equency
(Hz)
Ex
ecu
tio
n
Ti
m
e
(
m
s
)
BPPVS-
WNN
BVSP
CFSS
BPPVS-
WNN
BVSP
CFSS
50
0.
123
0.
135
0.
165
25
0.
205
0.
213
0.
277
100
0.
147
0.
159
0.
189
75
0.
219
0.
257
0.
300
150
0.
152
0.
164
0.
194
125
0.
234
0.
262
0.
406
200
0.
182
0.
194
0.
214
175
0.
244
0.
292
0.
326
250
0.
175
0.
187
0.
217
225
0.
257
0.
285
0.
329
300
0.
205
0.
217
0.
247
275
0.
315
0.
367
0.
359
350
0.
220
0.
232
0.
262
325
0.
330
0.
342
0.
374
The pe
rf
orm
a
nce i
ndi
ces fo
r t
h
e out
put
exe
c
ut
i
on t
i
m
e on
heal
t
h
y
m
o
t
o
r wi
t
h
respect
t
o
fre
q
u
enc
y
are sh
ow
n i
n
F
i
gu
re 5 an
d
wi
t
h
t
h
at
on
un
h
eal
t
h
y
m
o
t
o
r i
s
sho
w
n i
n
Fi
g
u
re
6. T
h
ese st
at
i
s
t
i
cal perf
or
m
a
nc
e
i
ndi
ces
of
e
x
e
c
ut
i
o
n
t
i
m
e gives a
p
r
eci
se
p
i
ct
ure
of
pe
rform
a
nce im
provem
ent for BPPVS-WNN sy
ste
m
as
com
p
ared to B
V
SP a
n
d CFSS and is lowe
r than
BVSP a
nd CF
SS s
h
owing that
BPP
V
S-WNN syst
e
m
has
im
proved
pe
rform
a
nce res
u
lts in tra
n
sient m
a
nne
r at a
stea
dy state with
re
spect to
fre
que
n
cy. T
h
e
qua
nt
itative
values
for thes
e pe
rform
a
nce
indices a
r
e ta
bulated in Ta
ble 2.
Fi
gu
re
5.
M
eas
ure
o
f
e
x
ecu
ti
on
tim
e with
resp
ect to
fre
que
ncy
usi
n
g heal
t
h
y
m
o
t
o
r
Fi
gu
re
6.
M
eas
ure
o
f
e
x
ecu
ti
on
tim
e with
resp
ect to
fre
que
ncy
usi
n
g un
heal
t
h
y
m
o
t
o
r
In
or
der t
o
ch
eck t
h
e r
o
bust
n
ess
of t
h
e
pr
op
ose
d
B
i
ort
h
og
o
n
al
Post
e
r
i
o
r
Vi
b
r
at
i
on
Si
gnal
-
Dat
a
Prob
ab
ilistic Wav
e
let
Neural Netwo
r
k
(BPPVS-WNN) syste
m
,
seri
es of frequ
en
cy is ap
p
lied to
t
h
e syste
m
.
A t
w
o st
a
g
e o
p
e
rat
i
on
wi
t
h
a du
rat
i
o
n of se
v
e
n cy
cl
es i
s
appl
i
e
d at
Freq
ue
ncy
f = 50
, 1
0
0
, …,
35
0 o
n
h
eal
t
hy
m
o
t
o
r and
f =
25
, 7
5
,
…,
32
5 o
n
un
heal
t
h
y
m
o
t
o
r.
It
sh
o
w
s t
h
at
usi
n
g t
h
e p
r
op
ose
d
B
PPV
S-
WN
N s
y
st
em
t
h
o
u
g
h
t
h
e m
i
ni
m
u
m
out
put
exec
ut
i
o
n
t
i
m
e on
heal
t
h
y
m
o
to
r
is at f = 350
H
z
, co
m
p
ar
ativ
ely an
d on
u
n
h
ealth
y m
o
t
o
r is at f = 25 Hz, op
tim
iza
t
io
n
o
f
ex
ecu
ti
o
n
tim
e ach
iev
e
s at f = 2
0
0
Hz,
with
6.59
% and
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
54
1
–
55
1
54
8
17.58 % im
provem
ent compare
d
to BVSP and CFSS
. In
a sim
ilar
m
a
n
n
e
r u
s
i
n
g
unh
ealth
y
m
o
to
r,
opt
i
m
i
zati
on o
f
exec
ut
i
o
n t
i
m
e
i
s
achi
e
ve
d a
t
f = 12
5
Hz,
wi
t
h
1
1
.
9
6 % a
nd
7
3
.
50 % i
m
pr
o
v
em
ent
com
p
ared
to BVSP a
n
d
CFSS.
A com
p
aris
on
of the
results s
h
ow
s t
h
at BPPVS-WNN system
has
m
o
re pe
rform
a
nce
im
provem
ent
because the freque
ncy ra
nge
is
m
a
intained with
out any transie
n
t dist
urbance using doubling
scale factor as
com
p
ared t
o
si
ngle
factor, t
h
e
r
ef
ore
,
m
o
re s
u
itable fo
r t
h
e c
o
m
m
e
rcial sy
stem
s.
Tabl
e
3. T
a
b
u
l
a
t
i
on
of
fa
ul
t
d
e
t
ect
i
on rat
e
ba
sed
o
n
t
i
m
e using
heal
t
h
y
m
o
t
o
r
an
d
u
nheal
t
h
y
m
o
t
o
r
Using Healthy
Motor
Us
ing Unhealthy
Motor
T
i
m
e
Fault Detection Rate based on tim
e
(%)
T
i
m
e
Fault Detection Rate based on tim
e
(%)
BPPVS-
WNN
BVSP
CFSS
BPPVS-
WNN
BVSP
CFSS
10.
30 – 12.
0
0
58.
58
50.
55
45.
53
10.
00 – 10.
3
0
53.
56
45.
52
40.
51
12.
00 – 1.
30
61.
40
53.
27
48.
25
10.
30 – 11.
0
0
56.
38
48.
24
43.
23
1.
30 – 3.
00
64.
50
56.
37
51.
35
11.
00 – 11.
3
0
59.
48
51.
34
46.
33
3.
00 – 4.
30
71.
72
63.
67
58.
65
11.
30 – 12.
0
0
65.
70
58.
63
53.
62
4.
30 – 6.
00
62.
76
57.
47
52.
45
12.
00 – 12.
30
57.
75
52.
45
47.
42
6.
00 – 7.
30
71.
45
65.
37
60.
35
12.
30 – 1.
00
66.
44
60.
33
55.
31
7.
30 – 9.
00
74.
62
70.
46
65.
44
1.
00 – 1.
30
69.
60
65.
42
60.
43
Tab
l
e 3
su
mmarizes th
e si
mu
latio
n
resu
lts o
f
the propos
ed BPPVS-WNN system
and elaborate
com
p
arison m
a
de with t
h
e e
x
isting m
e
thods BVSP
[1]
and CFSS
[2] respectively with res
p
ect to
diffe
ri
ng
t
i
m
e
peri
od
f
r
o
m
m
o
rni
ng t
o
e
v
eni
n
g
.
Fi
gu
re 7.
M
eas
ure
o
f
faul
t
det
ect
i
on rat
e
wi
t
h
respect
to
ti
m
e
u
s
ing
health
y
m
o
to
r
Fi
gu
re 8.
M
eas
ure
o
f
faul
t
det
ect
i
on rat
e
wi
t
h
respect
to
ti
m
e
u
s
ing
un
h
ealth
y m
o
to
r
Fi
gu
re 7 a
n
d F
i
gu
re 8 s
h
o
w
t
h
e fa
ul
t
det
ect
i
on
rat
e
of t
h
e
pr
o
pose
d
B
P
P
V
S-
WN
N sy
st
em
anal
y
zed
at
di
ffere
nt
t
i
m
e
i
n
t
e
rval
s usi
n
g heal
t
h
y
an
d un
heal
t
h
y
m
o
tors
. Ex
peri
m
e
nt
s are cond
uct
e
d at
vary
i
ng l
e
vel
of
i
n
p
u
t
t
i
m
e
periods
bet
w
ee
n 1
0
.
30 a
nd
9.
00
pm
usi
ng heal
t
h
y
m
o
t
o
r an
d
bet
w
ee
n 1
0
.
0
0
and 1
.
3
0
pm
usi
n
g
un
heal
t
h
y
m
o
tors a
n
d t
h
e fa
ul
t
det
ect
i
on
r
a
t
e
are i
nvest
i
g
at
ed.
The t
e
s
t
bed
of t
h
e
p
r
o
p
o
sed
bi
o
r
t
h
og
o
n
al
wavel
e
t
s
wi
t
h
ap
pr
o
x
i
m
at
ed an
d
det
a
i
l
e
d
coef
fi
ci
ent
s
va
l
u
e i
s
de
pi
ct
ed i
n
Fi
gu
re
3.
The
m
a
xim
u
m
faul
t
det
ect
i
on
rat
e
of t
h
e p
r
op
ose
d
sy
st
em
i
s
observe
d
bet
w
ee
n t
i
m
e 10.3
0
a
m
and
9.
00
pm
on
heal
t
h
y
m
o
t
o
r a
n
d
10
.0
0 am
an
d
1.
30
pm
usi
n
g
al
l
t
h
e m
e
t
hod
s. B
u
t
com
p
ara
t
i
v
el
y
t
h
e fa
ul
t
det
ect
i
o
n
rat
e
i
s
fo
u
n
d
t
o
be
hi
g
h
er
with the proposed system th
at is
measured
as 74.62 % and it varies
according to differen
t ti
m
e
periods and
the coefficient values using fifth de
rivative form
. Howe
ve
r, the
m
a
xim
u
m
en
ergy fault de
tection rate reache
s
t
o
7
1
.
7
2 % a
n
d
65
.7
0 %
usi
n
g
heal
t
h
y
an
d
un
heal
t
h
y
m
o
t
o
r
w
h
i
c
h
decl
i
n
es t
o
6
2
.
7
6 &
an
d 5
7
.
7
5 %
wi
t
h
t
h
e
existing B
V
SP [1] a
nd C
F
SS [2] respec
tively. This is
because of the
ap
plication of
post
erior probability
Wavel
e
t
Ne
u
r
a
l
net
w
o
r
k t
h
r
o
ug
h t
h
e act
i
v
at
i
on f
u
nct
i
on
us
es th
e d
e
tailed
co
efficien
t FD
v
a
lu
e to
iden
tify th
e
fau
lt
d
e
tectio
n rate. Th
is m
a
k
e
s the system to
in
crease t
h
e fau
lt
d
e
tection
rate
u
s
i
n
g Bio
r
t
h
ogo
n
a
l
Wav
e
lets
wi
t
h
det
a
i
l
e
d
and a
p
pr
oxi
m
a
t
e
d coef
fi
ci
en
t
s
13.
7
0
% an
d 2
2
.
2
7% bet
t
er com
p
arat
i
v
el
y
t
o
t
h
e t
w
o
ot
her
ex
istin
g
m
e
th
od
s [1
], [2
] u
s
i
n
g
h
ealth
y m
o
to
r
s
an
d 14
.43 % and
23
.32 % u
s
ing
un
health
y
m
o
to
r
s
. I
t
is
therefore signi
f
icant that
t
h
e p
r
op
osed BPPVS-WNN syste
m
p
r
ov
id
es a stand
a
rd
fau
lt
d
e
tectio
n rate
m
echani
s
m
t
h
at
m
a
nages
v
o
l
t
a
ge s
u
ppl
y
a
n
d
p
o
we
r
fl
o
w
s i
s
an a
p
pr
o
p
ri
at
e
an
d
fl
exi
b
l
e
m
a
nne
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Vib
r
a
tion
Ana
l
ysis o
f
Indu
stria
l
Drive fo
r
Bro
ken
Bea
r
ing
Detectio
n
Usi
n
g
Prob
ab
ilistic… (K. Ja
ya
kuma
r)
54
9
Tabl
e
4.
Ta
bul
at
i
on
fo
r c
u
r
r
e
n
t
fl
ow
rat
e
usi
n
g
heal
t
h
y
a
n
d
un
heal
t
h
y
m
o
t
o
r
Using Healthy
Motor
Us
ing Unhealthy
Motor
Voltage
in volts
Cu
rren
t
Flo
w
Rate
(A
m
p
eres)
Cu
rren
t
Flo
w
Rate
(A
m
p
eres)
BPPVS-
WNN
BVSP
CFSS
BPPVS-
WNN
BVSP
CFSS
205
0.
112
0.
122
0.
144
0.
232
0.
243
0.
276
210
0.
118
0.
126
0.
148
0.
235
0.
247
0.
270
215
0.
125
0.
133
0.
155
0.
242
0.
254
0.
288
220
0.
133
0.
139
0.
161
0.
248
0.
252
0.
295
225
0.
128
0.
133
0.
155
0.
240
0.
255
0.
288
230
0.
136
0.
145
0.
167
0.
252
0.
266
0.
294
235
0.
145
0.
161
0.
172
0.
263
0.
283
0.
302
Tab
l
e 4
tabu
lated
th
e curren
t
flow rate with
resp
ect
to
d
i
fferen
t
vo
ltag
e
s ap
p
lied
to
t
h
e health
y an
d
un
heal
t
h
y
m
o
t
o
rs
usi
ng t
h
e
pr
o
pose
d
m
e
t
hod a
n
d c
o
m
p
ari
s
o
n
i
s
m
a
de wi
t
h
t
w
o
ot
h
e
r m
e
t
hods
[1
]
,
[2]
respect
i
v
el
y
us
i
ng
M
A
TL
AB
fo
r
si
m
u
l
a
t
i
on pu
r
poses
.
Fi
gu
re 9.
M
eas
ure
o
f
c
u
r
r
ent
f
l
ow rat
e
wi
t
h
r
e
spect
to
vo
ltag
e
u
s
i
n
g
h
ealth
y
m
o
to
r
F
i
g
u
r
e
10
.
Me
as
u
r
e of
cu
rr
en
t
f
l
ow
r
a
te
w
ith
r
e
s
p
e
c
t
to
vo
ltag
e
u
s
i
n
g
u
n
h
ealth
y
m
o
tor
Fig
u
re
9
an
d
Fig
u
re 10
illu
strate th
e curren
t
flow ra
te with
resp
ect
t
o
d
i
fferen
t
v
o
ltages
usin
g
h
ealth
y
an
d
u
n
h
ealth
y m
o
to
r resp
ectiv
ely. Fro
m
b
o
t
h
th
e figu
res
it is ev
id
en
t th
at th
e cu
rren
t
flow rate is red
u
ced
usi
n
g b
o
t
h
hea
l
t
h
y
and
un
hea
l
t
h
y
m
o
t
o
rs i
s
com
p
arat
i
v
el
y
red
u
ce
d wi
t
h
r
e
vere
nce t
o
t
h
e t
w
o
ot
he
r ex
i
s
t
i
ng
m
e
t
hods
. Du
r
i
ng t
h
e bea
r
i
ng fa
ul
t
det
ect
i
on usi
n
g a
st
ochast
i
c
p
r
o
g
ram
,
det
a
i
l
ed coef
fi
ci
ent
and
app
r
oxi
m
a
t
e
d coef
fi
ci
ent
i
s
s
i
gni
fi
ca
nt
l
y
ge
nerat
e
d w
h
e
r
ea
s the detailed c
o
efficient is us
ed as the by-product
for d
e
tectin
g
t
h
e b
e
aring
fau
l
t d
e
tectio
n
.
In
th
is way fiv
e
deriv
a
tiv
e fo
rm
s is ap
p
lied
and th
e resu
ltan
t
ou
tpu
t
is u
s
ed
to
i
d
en
t
i
fy th
e fau
lt that h
e
lp
s in
m
i
n
i
m
i
z
i
n
g
th
e cu
rren
t fl
o
w
rate u
s
ing
th
e
p
r
o
p
o
s
ed
syste
m
. W
i
t
h
th
e
ap
p
lication
o
f
Po
steri
o
r Probab
ilistic W
a
v
e
l
e
t Neural
n
e
tw
o
r
k
t
h
at con
s
ists o
f
an inp
u
t
l
a
yer, fau
lt detectin
g
pr
ocess l
a
y
e
r and
out
put
l
a
y
e
r, t
h
e bea
r
i
n
g
faul
t
det
ec
t
i
on rat
e
effi
ci
en
cy
i
s
im
proved re
duci
ng t
h
e
curr
e
n
t
flow rate. Th
e ov
erall
p
r
ob
ab
ility d
i
strib
u
t
io
n fu
n
c
tion
on
t
h
e ev
id
en
ce of
‘X’
v
i
bratio
n sign
al-d
ata with
respect to
detailed coefficient values
obtained until the fifth deri
vative fo
rm
is reached. In this
design, the
cur
r
ent
fl
o
w
ra
t
e
i
s
m
i
nim
i
zed f
r
om
3 –
11
% an
d 1
8
–
28
% co
m
p
ared
to th
e ex
isting
meth
od
s
u
s
ing
health
y
m
o
tors and
1 – 7 % and 14
–
20 %
using
unhealthy m
o
to
rs com
p
ared to
BVSP [1]
and
CFSS [2] res
p
e
c
tively.
Th
e resu
lts sh
owed
a h
ealth
y
ag
reem
en
t u
s
ing
d
e
tailed
co
efficien
t with
resp
ect to
fifth
d
e
riv
a
tiv
e fo
rm
, wh
ich
indicates that the pe
rform
a
nce of
the BPPVS-WNN system is co
m
p
arativ
ely b
e
tter th
an
th
e ex
isting
BVSP
[
1
] an
d CFSS [2
].
6. CO
N
C
L
U
S
I
ON
Thi
s
resea
r
c
h
pr
o
v
i
d
es a
n
i
n
cl
usi
v
e st
udy
of
real
t
i
m
e
ind
u
st
ri
al
dri
v
e
vi
b
r
at
i
on
si
g
n
al
dat
a
f
o
r
b
r
ok
en
b
e
aring d
e
tectio
n u
s
i
n
g
p
r
o
b
a
b
ilistic wav
e
let
n
e
ur
al
n
e
two
r
k
for increasing
th
e fau
lt d
e
tectio
n rate an
d
t
o
ha
n
d
l
e
l
a
r
g
e
r
po
wer
dem
a
n
d
.
The
B
i
ort
h
o
g
o
n
al
vi
b
r
atio
n sign
al-d
ata b
a
sed
wav
e
let tran
sfo
r
m
is lo
cal
ized
wi
t
h
t
h
e ai
d
of
t
i
m
e
and fre
q
u
ency
dom
ai
n t
o
m
i
nim
i
ze
the current fl
ow
rate. A
pr
ototy
p
e of the
healthy and
u
n
h
ealth
y indu
ctio
n m
o
to
r
u
s
ing
starting
an
d rated
vo
ltag
e
rate
was
si
m
u
lated
and tested
.
A M
A
TLAB
en
v
i
ron
m
en
t with
Sim
u
lin
k
is u
s
ed
to
calcu
l
a
te th
e resu
lt of effectiv
e
fau
l
t d
e
tectio
n
rate. Sim
u
latio
n
resu
lts
show the
opti
m
al fault detection rate at different tim
e
zones reaches t
o
10.76 %
ob
served at 11.30 a
n
d 12.00
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
54
1
–
55
1
55
0
pm
usi
ng un
he
al
t
h
y
m
o
t
o
rs and
11
.2
2 % ob
serve
d
at
3.0
0
and
4.
30 pm
usi
ng heal
t
h
y
m
o
t
o
rs. The t
r
a
n
si
ent
response test
s
h
ows
that t
h
e
tim
e
ta
ken to identify t
h
e
fa
ult in bea
r
ing
reaches its z
e
ni
th i.e., m
a
ximum
at
fre
que
ncy
ran
g
e of
5
0
Hz and
m
i
nim
u
m
i
s
o
b
ser
v
e
d
at
fre
que
ncy
r
a
nge
o
f
3
5
0
Hz. The
ex
pe
ri
m
e
nt
al
measu
r
em
en
ts sho
w
th
at the Bio
r
thog
on
al Po
steri
o
r Vi
b
r
ation
Sign
al-Data
Pro
b
a
b
ilistic
W
a
v
e
let Neural
Net
w
or
k i
s
an
effi
ci
ent
m
e
t
hod f
o
r i
d
e
n
t
i
f
y
i
n
g
t
h
e ha
rm
oni
cs usi
n
g det
a
i
l
e
d coe
ffi
ci
ent
s
appl
i
e
d at
t
h
e r
a
t
e
of
fifth
d
e
ri
v
a
tiv
e form
. Th
is in tu
rn
id
en
tifies th
e fau
lts ob
serv
ed
at beari
n
g
i
n
indu
strial d
r
iv
e
prov
id
i
n
g
a
st
anda
rd
p
o
we
r rat
e
t
h
at
m
a
nage
s t
h
e v
o
l
t
a
ge p
r
o
f
i
l
e
an
d cu
rre
nt
fl
o
w
rat
e
am
ong s
e
veral
vol
t
a
ge
rat
e
i
n
order to
provide an e
ffecti
v
e
m
eans t
o
t
h
e i
n
dust
r
y
by
m
i
ni
m
i
zi
ng t
h
e
de
g
r
adat
i
o
n
of
m
a
chi
n
e
r
y
.
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