Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
9
, No
.
3
,
J
un
e
201
9,
pp. 150
6~15
13
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v9
i
3
.
pp
1506
-
15
13
1506
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Relevan
ce
ve
ctor ma
chin
e based faul
t classi
ficatio
n in
wind
energy c
onversion s
ystem
Rekha
S. N.
1
,
P.
Aruna
Je
yant
h
y
2
, D
.
De
vara
j
3
1
Sa
ptha
giri Col
l
ege
of
Eng
ine
e
ri
ng
,
Indi
a
2,3
Kala
sal
inga
m
Aca
dem
y
o
f
R
ese
arc
h
and
Edu
cation
(KA
RE)
,
In
dia
Art
ic
le
In
f
o
A
BST
R
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
y
15
, 201
8
Re
vised
Dec
9
,
201
8
Accepte
d
Ja
n 2
, 201
9
Thi
s
Paper
is
a
n
at
t
empt
to
d
eve
lop
the
m
ulticlass
cl
assificat
ion
in
th
e
Benc
hm
ark
fau
l
t
m
odel
appl
i
ed
o
n
wind
ene
rg
y
c
onver
sion
s
y
st
e
m
using
the
r
el
ev
ance
ve
ct
or
m
ac
hine
(RVM
).
The
RVM
coul
d
app
l
y
a
st
ruc
tural
risk
m
ini
m
iz
at
ion
b
y
int
rodu
ci
ng
a
prope
r
ke
rne
l
for
tra
ini
ng
and
te
sting
.
The
Gauss
ia
n
Kerne
l
is
used
fo
r
thi
s
purpose
.
T
he
c
la
ss
ifi
c
at
ion
of
sensor
,
proc
ess
and
ac
tu
at
ors
fau
l
ts
are
observe
d
and
cl
assifi
e
d
i
n
th
e
implementa
t
ion.
Tra
in
ing
differ
ent
fau
lt
cond
it
i
on
and
te
st
ing
i
s
ca
rrie
d
ou
t
using t
he
RVM
i
m
ple
m
ent
at
ion
c
arr
ie
d
out
using
Matl
ab
on
th
e
W
ind
Ene
r
g
y
Conversion
S
y
st
em
(W
ECS).
Th
e
training
ti
m
e
b
ec
om
es
importa
nt
while
the
tra
ini
ng
is
ca
rr
i
ed
out
in
a
b
ig
ger
W
ECS,
and
the
har
dwar
e
f
ea
sibil
ity
is
prime
while
th
e
te
sting
is
c
arr
i
e
d
out
on
an
online
fau
l
t
detec
t
io
n
sce
nar
io
.
Matl
ab
b
ase
d
im
ple
m
ent
a
ti
on
is
ca
rri
ed
out
on
th
e
benc
hm
ark
m
odel
for
the
fau
lt
d
etec
t
ion
i
n
the
W
ECS.
T
he
result
s
are
co
m
par
ed
wit
h
th
e
pre
vious
l
y
implemente
d
fa
ult
det
e
ct
ion
t
echnique
and
found
to
be
per
form
ing
bet
te
r
in
te
rm
s of
tr
ai
ning
ti
m
e and
h
ard
w
are
f
ea
sib
il
i
t
y
.
Ke
yw
or
d
s
:
Fault detect
io
n
Gau
s
sia
n ke
rn
e
l
Re
le
van
ce
vect
or m
achine
Syst
e
m
W
i
nd e
nergy c
onve
rsion
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Re
kh
a
S. N
.
,
Sapth
a
giri C
ollege
of Engine
e
rin
g
,
Ba
ng
al
or
e,
In
di
a
.
Em
a
il
:
sn
_r
e
kha@re
diff
m
ai
l.com
1.
INTROD
U
CTION
The
fa
ult
detec
ti
on
in
the W
E
CS
is
an
i
m
po
r
t
ant
aspect
in
the
w
orkin
g
of the
wind
po
we
r
ge
ner
at
io
n
syst
e
m
,
as
the
fau
lt
s
occ
urri
ng
i
n
the
syst
e
m
wo
ul
d
inc
rease
the
m
ain
te
na
nce
co
st.
Dev
el
op
m
ent
of
the
ov
e
rall
fa
ult
de
te
ct
ion
inclu
di
ng
the
t
urbine, gen
e
rato
r,
c
on
ver
te
r
, p
it
ch
a
nd
the drive
trai
n
beco
m
es
i
m
po
rta
nt
consi
der
i
ng
th
e
cost
i
nvolv
e
d
in
the
m
ai
ntenan
ce
of
the
W
ECS.
T
he
be
nc
hm
ark
m
od
el
wind
tu
r
bin
e
f
or
fa
ult
identific
at
ion,
wh
ic
h
incl
ud
es
the
sen
sor,
process
a
nd
act
ua
tor
fa
ult
co
nd
it
ion
,
is
de
velo
ped
[
1].
A
4.8
M
W
WECS
m
od
el
i
s
de
velo
pe
d
in
or
de
r
to
obse
r
ve
the
fa
ults
in
the
syst
em
.
SV
M
ba
sed
fa
ul
t
detect
ion
is
c
arr
ie
d
ou
t
in
W
i
nd
t
urbi
nes
an
d
c
om
par
ed
with
th
e
ANN
for
the
accuracy,
t
rainin
g
an
d
t
un
i
ng
ti
m
es
[2
]
.
Th
e
li
near
SV
M pe
rfor
m
ed
bette
r
in co
m
par
is
on
with th
e A
N
N.
Th
e cl
assifi
cat
ion
u
si
ng
RVM
perform
ed
bette
r
than
the
SV
M
wh
il
e
th
e
trai
ning
ti
m
e
is
sai
d
to
be
hi
gh
e
r
[
3].
W
i
nd
ge
ne
rato
r
be
arin
g
fa
ult
are
sense
d
by
t
he
so
un
d
and
vibrat
io
n
in
the
t
ow
e
r
usi
ng
em
pirical
m
od
e
deco
m
po
sit
ion
m
et
ho
d
[4
]
.
A
ni
ne
tu
rb
i
ne
base
d
wi
nd
far
m
chall
enge
t
o
de
te
ct
the
wind
t
urbine
fa
ults
in
the
in
div
i
du
al
tur
bin
e
are
ca
rr
ie
d
out
[5
]
.
A
sta
te
est
im
ation
s
et
m
e
m
ber
sh
ip
a
ppr
oach
base
d
i
m
ple
m
entat
io
n
is
fou
nd
in
f
ault
detect
io
n
of
be
nc
hm
ark
m
od
el
with
no
ise
[6
]
.
A
m
ulti
-
ob
j
ect
ive
op
ti
m
iz
ati
on
fr
am
ewo
r
k
fo
r
la
r
g
e
sca
le
wind
tu
rb
i
ne
syst
e
m
is
dev
el
op
e
d
us
ing
th
e
H
¥
/
H
-
ob
se
rv
e
r
to
de
te
ct
the
sensor
and
act
uat
or
fau
lt
[7
]
.
Es
pe
ci
al
ly
fau
lt
detect
ion
is
a
cl
a
ssific
at
ion
betwee
n
tw
o
c
la
sses;
norm
al
sta
te
or
fa
ult
and
for
the
cl
assifi
cat
ion
,
s
uppo
rt
ve
ct
or
m
achine
(SV
M)
is
a
us
ef
ul m
achine
learni
ng m
et
h
od [7],
[8
]
, [
9] and appli
cat
ions t
o fault
detect
ion
s
are re
ported
[10].
This
pa
pe
r
ta
ke
s
up
t
he
im
pl
e
m
entat
ion
fro
m
the
ben
c
hma
rk
m
od
el
an
d
i
m
ple
m
ent
the
RVM
on
the
ben
c
hm
ark
m
o
del
for
the
wi
nd
f
ault
ide
nti
ficat
ion
pro
ble
m
.
The
ov
e
rall
fau
lt
s
li
ke
the
sensor,
pr
oces
s
and
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Rel
evan
ce
vect
or
ma
c
hi
ne base
d
f
au
lt
clas
sif
ic
ation
i
n
wi
nd
….
(
Rek
ha
S. N
.
)
1507
act
uator
fa
ults
are
inclu
de
d
in
orde
r
to
cl
assi
fy
the
fa
ults
ac
cordin
g
the
m
easur
em
ent
fro
m
diff
eren
t
se
ns
or
s
from
the
W
EC
S.
Furthe
r
the
pap
e
r
is
sect
ion
ed
as
fo
ll
ows,
Sect
ion
-
II
would
ta
lk
ab
out
the
dif
fer
e
nt
sect
ions
of
t
he
W
EC
S
wh
e
re
the
fau
lt
is
detect
ed.
Se
ct
ion
-
III
ta
lks
about
the
R
V
M
i
m
ple
m
enta
ti
on
on
the
wi
nd
fa
ult
detect
ion.Sect
ion
-
I
V
i
nf
e
rs
t
he
r
es
ults an
d di
scussion
f
ollo
wed b
y t
he
c
oncl
us
io
n
a
nd the
r
efe
re
nces.
1
.
1.
Win
d
en
er
gy conver
sion
s
ystem m
odel
The
be
nc
hm
ark
m
od
el
dev
el
op
e
d
in
[
1]
is
us
e
d
in
the
pre
sent
i
m
ple
m
entat
ion
.
It
com
pr
ise
s
of
the
wind
m
od
el
,
blade
a
nd
pitch
m
od
el
,
dr
i
ve
tr
ai
n
m
od
el
,
ge
ne
rator
/c
onve
rter
m
od
el
,
co
ntr
oller
an
d
pa
ra
m
et
ers.
In
t
he
wind
m
od
el
t
he
di
f
fe
r
ent
seq
ue
nce
of
wi
nd
is
sto
re
d
as
a
vect
or
v
w
,
wh
ic
h
would
be
us
e
d
f
or
the
i
nput
to
the
wi
nd
t
urbi
ne.
T
he
Bl
ade
an
d
Pit
ch
m
od
el
com
pr
ise
s
of
t
he
aer
odynam
ic
and
the
pitch
m
od
e
l
of
th
e
tur
bin
e as
d
e
fi
ned in
(
1)
.
2
)
(
))
(
).
(
(
)
(
2
3
t
v
t
t
C
R
t
w
q
r
(1)
The
ae
r
od
y
na
m
ic
torque
is
def
i
ned
in
eq
ua
ti
on
(1)
w
here
r
is
t
he
Air
de
ns
it
y
(
kg
/m
3
)
,
R
is
the
r
ot
or
rad
i
us
,
C
q
r
oto
r
to
rque c
oeffici
en
t,
l
ti
p
s
peed rati
o,
b
blade
p
it
c
h
a
ng
le
.
If
t
he
wi
n
d
tur
bin
e
has
t
hr
ee
blades
a
nd
th
us
w
ou
l
d
hav
e
t
hr
ee
blade
pitc
h
a
ng
le
s.
Th
us
the
to
rqu
e
equ
at
io
n w
ou
l
d be as
d
e
fine
d i
n (2),
w
hich
i
s the sum
o
f
t
orq
ues
i
n
al
l t
he
thr
ee
b
la
des.
.
6
)
(
))
(
).
(
(
)
(
3
1
2
3
i
w
i
q
w
t
v
t
t
C
R
t
(2)
The
re
as
on
th
at
b
value
va
ries
f
or
each
blad
e
intr
oduces
li
tt
le
var
ia
ti
on
in
t
he
to
r
qu
e
de
velo
ped
by
e
ac
h
blade,
th
ough
the
overall
be
hav
i
or
of
t
he
m
od
el
is
sim
il
ar
to
that
of
the
m
od
el
w
it
h
sim
il
ar
b
value.
The
hy
dr
a
ulic
pitch
syst
em
i
s
a
cl
os
ed
lo
op
m
od
el
def
in
ed
by
a
seco
nd
orde
r
tran
sfe
r
functi
on
w
hi
ch
is
a
pisto
n
se
rvo
sy
stem
.
2
2
2
2
)
(
)
(
n
n
n
c
s
s
s
s
(3)
Eq
uation
(3)
de
fines
the
sec
ond
orde
r
tran
sf
er
f
un
ct
io
n
of
hydrauli
c
pitc
h
syst
em
wh
ere
V
is
the
dam
ping
factor,
nat
ur
al
fr
e
qu
e
ncy
de
fi
ned
by
w
n
.
The
tr
ansf
e
r
f
unct
ion
is
def
ine
d
f
or
al
l
three
-
pitc
h
syst
e
m
in
si
m
ilar
way.
T
he
dam
ping
fact
or
is
t
he
sam
e
fo
r
al
l
the
three
-
pitc
h
syst
em
if
there
are
no
dist
urba
nces.
Hyd
rau
li
c
powe
r
dro
p
an
d
the
increase
in
ai
r
pr
ess
ure
is
are
the
par
a
m
et
ers
that
var
y
wh
en
the
re
is
a
fau
lt
occu
r
r
ence
in
the
pitch
syst
em
.
The
par
am
et
ers
for
po
wer
d
r
op
is
def
ine
d
as
2
n
and
2
and
tha
t
of
the
ai
r
pres
su
re
is
3
n
and
3
.
The
cl
ose
d
lo
op
pitch
a
ct
uator
bein
g
the
li
near
syst
e
m
with
change
in
sens
or
gain
aff
ect
in
g
it
wo
ul
d
need
m
ean
of
two
sens
or
va
lues
to
be
fe
d
to
the
act
uator
.
T
hu
s
the
pitch
ref
e
re
nc
e
would
be
c
hange
d
accor
ding t
o
th
e cha
ng
e
s se
nsor
v
al
ue
s
wh
ic
h
is i
nd
ic
at
ed
a
s foll
ow
s
.
,
,
[
]
=
,
[
]
−
∆
,
1
[
]
+
∆
,
2
[
]
2
(4)
Wh
e
re
∈
{
1
,
2
,
3
}
and
,
,
[
]
is
the
re
fer
e
nce
pitch
that
gets
gen
e
rated
a
fter
the
distu
r
ban
c
e.
T
he
m
od
el
of
tra
nsfer
rin
g
th
e
torque
from
ro
t
or
to
t
he
ge
ner
at
or
is
de
fi
ned
as
t
he
dri
ve
trai
n
m
od
el
.
A
gea
r
box
in
th
e
m
idd
le
to
conver
t
the
lowe
r
sp
eed
to
the
hig
he
r
sp
ee
d
is
rep
resen
te
d
as
a
tw
o
m
ass
m
od
el
def
ine
d
in
(
5) an
d (
6)
.
(
)
=
(
)
−
∆
̇
(
)
−
(
+
)
(
)
+
(
)
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
3
,
June
2019
:
1506
-
1513
1508
̇
(
)
=
Δ
(
)
+
r
(
)
−
(
2
+
)
(
)
−
(
)
(6)
̇
Δ
(
)
=
(
)
−
1
(
)
Wh
e
re
the
m
ome
nt
of
inerti
a
of
lo
w
s
pee
d
sh
aft
is
,
is
the
torsion
sti
ffnes
s
of
the
dri
ve
trai
n,
is
the
torsion
dam
ping
c
oeffici
ent o
f
the drive
t
rain,
is
the v
isc
ous
f
rict
ion
o
f
t
he
high
s
pee
d
s
ha
ft.
is
the g
e
a
r
rati
o,
is
the
m
ome
nt
of
ine
rtia
of
t
he
high
spe
ed
s
ha
ft.
is
the
ef
fici
ency
of
the
dr
i
ve
t
rain.
Δ
(
)
is
t
he
torsion
a
ng
le
of
t
he
dri
ve
tr
ai
n.
T
he
fa
ult
in
the
dri
ve
tr
ai
n
is
due
to
va
riat
ion
in
t
he
dr
i
ve
trai
n
e
ff
i
ci
ency
wh
ic
h would
be de
no
te
d by
2
instea
d o
f
.
The
el
ect
rical
m
od
el
wh
ic
h
c
om
pr
ise
s
of
th
e
ge
ner
at
or
a
nd
the
c
onve
rter
wh
ic
h
works
in
f
re
qu
e
ncy
wh
ic
h
is
m
uch
highe
r
than
the
ben
c
hm
a
rk
m
od
el
is
def
i
ned
by
the
f
irst
order
trans
fer
f
unct
ion
a
s
def
i
ned in
(7).
(
)
,
(
)
=
+
(7)
Wh
e
re
is t
he g
ener
at
or
a
nd c
onve
rter
par
am
et
er.
T
he
ge
nerat
or
powe
r
is
de
fine
d by
(
8)
(
)
=
(
)
(
)
(8)
w
he
re
is
the
ef
fici
ency
of
the
gen
e
rato
r.
T
he
con
t
ro
l
sc
hem
e
ch
os
en
f
or
t
hi
s
i
m
ple
m
entation
sim
ple
as
the
fo
c
us
is
on
the
fa
ult
detect
io
n
of
WECS.
I
n
order
to
sim
pli
fy
the
be
nc
hma
rk
m
od
el
the
dr
i
ve
trai
n
da
m
per
is
avo
i
ded. T
her
e
are
tw
o
m
od
es
in whi
c
h
this i
m
ple
m
entat
ion
wou
l
d work,
one is the
po
wer o
pti
m
iz
at
ion
m
od
e
and
the
ref
e
rence
powe
r
m
ode.
The
po
wer
op
ti
m
iz
ation
m
od
e
is
wh
e
n
the
sp
ee
d
of
th
e
wind
is
gr
eat
er
tha
n
the nom
inal speed
. T
he
c
on
t
r
oller starts w
he
n
the
re is less p
owe
r
ge
ner
at
e
d
f
ro
m
t
he
wind en
e
r
gy due to
wi
nd
sp
ee
d
le
ss t
han the
no
m
inal sp
ee
d.
It is
denot
ed
as
[
]
≥
[
]
⋁
[
]
≥
w
he
re
is t
he nom
inal gen
e
rato
r
s
peed an
d
t
he
m
od
e cha
ng
e
s
f
r
om
this m
od
e 2
t
o
the
m
ode 1
i
f
[
]
≤
−
Δ
w
he
re
Δ
is
the
offset
that
is
s
ubtract
ed
from
t
he
nom
inal
sp
ee
d
to
a
void
the
change
from
m
od
e
1
to
m
ode
2
and
vice
ve
rsa
freq
ue
ntly
.
T
he
c
onditi
ons
of
fa
ult
an
d
th
e
m
od
e
va
riat
ion
al
on
g
with
the
m
od
el
pa
ra
m
et
ers
are
us
ed
as it i
s
f
r
om
[
1].
2.
RELE
VAN
C
E VECT
OR MAC
HI
NE B
AS
ED
I
MPL
EMENT
ATION
OF F
A
UL
T DETE
C
TI
ON
The
diff
e
re
nt
f
ault
co
nd
it
io
ns
are
trai
ne
d
on the
Re
le
va
nce V
ect
or
Ma
chi
ne
(RVM)
an
d
a
m
ult
i
cl
ass
RVM
str
uctu
re
is
de
vel
op
e
d
i
n
orde
r
to
te
st
the
diff
e
ren
t
fa
ult
co
ndit
ion
of
th
e
wi
nd
f
aul
t
that
is
c
onsid
ered
in
[
1].
T
he
m
ulti
ple
RVM
str
uctu
res
a
re
de
ve
lop
e
d
as
disc
us
se
d
in
[
11]
.
The
dif
fer
e
nt
f
ault
co
ndit
ion
s
are
a
s
giv
e
n
in
the
Ta
ble 1 is i
ntr
oduc
ed fo
r
trai
ning the
RVM a
nd test
in
g
it
.
Table
1.Diff
e
r
ent Fa
ult Co
ndit
ion
s T
raine
d U
sin
g
R
VM
Fau
lt No.
Fau
lt T
y
p
e
Fau
lt Site
Sy
m
b
o
ls
1a
Fix
ed
Value
Sen
so
r
Fau
lts Blad
e
Po
sitio
n
s
∆
1
,
1
,
∆
1
2
∆
2
,
1
,
∆
2
,
2
∆
3
,
1
,
∆
3
,
2
1b
Gain
Factor
2a
Fix
ed
Value
Sen
so
r
Fau
lt Ro
to
r
Sp
eed
∆
,
1
,
∆
,
2
2b
Gain
Factor
3a
Fix
ed
Value
Sen
so
r
Fau
lt Gene
rator Speed
∆
,
1
,
∆
,
2
3b
Gain
Factor
4a
Of
f
set
Actu
ato
r
Fau
lt con
v
erter
s
y
ste
m
∆
5a
Ab
rup
t Ch
an
g
ed
Dy
n
a
m
ics
Actu
ato
r
Fau
lt
Pitch
Sy
ste
m
s
∆
1
,
∆
2
,
∆
3
5b
Slo
w Ch
an
g
ed
Dyn
a
m
ics
6
Ch
an
g
ed
Dy
n
a
m
ic
s
Sy
ste
m
Fault
Driv
e T
r
ain
∆
,
∆
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
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S
N: 20
88
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8708
Rel
evan
ce
vect
or
ma
c
hi
ne base
d
f
au
lt
clas
sif
ic
ation
i
n
wi
nd
….
(
Rek
ha
S. N
.
)
1509
The
pitc
h
pos
i
ti
on
s
are
c
onsidere
d
f
or
t
he
im
ple
m
entat
ion
of
the
1a
an
d
1b
fau
lt
s
that
would
be
ta
ken
as
the
ve
ct
or
f
or
the
R
VM
trai
ning
.
The
vect
or
tha
t
ref
le
ct
s
the
sens
or
fa
ults
in
blade
posit
ions
is
as
giv
e
n
in
the
foll
ow
in
g
x
=
b
k
,
m
1
(
t
j
)
-
b
k
,
m
2
(
t
j
)
b
k
,
m
1
(
t
j
)
-
b
k
,
m
1
(
t
j
-
1
)
b
k
,
m
2
(
t
j
)
-
b
k
,
m
2
(
t
j
-
1
)
é
ë
ê
ê
ê
ê
ù
û
ú
ú
ú
ú
W
he
re
k=1,2,3
wh
ic
h
is
the
denotin
g
bla
de
nu
m
ber
a
nd
i=
1,
2
de
no
te
s
the
m
od
e
in
wh
ic
h
the
WE
CS
is
work
i
ng.
A
nd
t
j
and
t
j
-
1
are
the
tim
e
instant
at
j
and
j
-
1
res
pecti
ve
ly
.
The
abs
ol
ute
value
of
b
k
,
m
1
(
t
j
)
-
b
k
,
m
2
(
t
j
)
w
ou
l
d
var
y
be
tw
een
.
001
a
nd
2,
but
in
or
der
to
dif
fer
e
nt
ia
te
fr
om
the
fau
lt
a
nd
th
e
norm
al
scenari
o
t
he
value
is
pr
e
def
i
ned
as
5000.
The
para
m
et
e
rs
for
the
fa
ults
de
fine
d
by
2a
,
2b,
3a
and
3b
,
,
,
are
used
for t
rainin
g
.
Th
e
ve
ct
or
for
tra
i
ning is
g
ive
n by t
he follo
wing
.
x
=
b
k
,
m
1
(
t
j
)
-
b
k
,
m
2
(
t
j
)
b
k
,
m
1
(
t
j
)
-
b
k
,
m
1
(
t
j
-
1
)
b
k
,
m
2
(
t
j
)
-
b
k
,
m
2
(
t
j
-
1
)
é
ë
ê
ê
ê
ê
ù
û
ú
ú
ú
ú
The
m
easur
em
ent
is
filt
ered
in
orde
r
to
a
void
s
udde
n
va
riat
ion
by
us
i
ng
g
with
t
=
0.02
s
an
d
r
with
t
=0.
06s
.
I
n
ord
er
to
i
ncr
ease
the
a
bili
ty
to
m
easur
e
disti
nctl
y
the
Ga
us
sia
n
var
ia
nce
is
in
creased
to
15
wh
il
e
m
easur
in
g.
For
f
a
ults 4a
a
nd
6 t
he vect
or is a
s d
e
fine
d
in
the
foll
ow
i
ng
,
x
=
w
p
,
m
1
(
t
j
)
-
w
p
,
m
2
(
t
j
)
t
g
d
(
t
j
)
-
t
g
m
(
t
j
)
l
2
X
w
g
d
(
t
j
)
-
(
w
g
,
m
1
(
t
j
)
-
w
g
,
m
2
(
t
j
)
)
/
2
é
ë
ê
ê
ê
ê
ù
û
ú
ú
ú
ú
wh
e
re
w
g
d
is
the
desire
d
ge
nerat
or
s
pee
d,
t
g
d
is
the
desire
d
gen
e
rato
r
t
orq
ue
giv
e
n
by
t
he
c
ontrolle
r
(
P
r
t
g
d
wh
ere
P
r
is
the
power
wh
ic
h
is
desired
to
be
produce
d).
The
facto
r
l
2
=
1
0
-
6
X
J
w
i
n
d
6
is
us
ed
in
th
e
third com
pone
nt of
x
i
n order
to uti
li
ze the
wind s
pee
d
a
nd
for norm
al
izati
on
.
Re
le
van
ce
vect
or Mac
hin
e
for Fault
Det
ect
io
n
in
W
i
nd T
urbines:
RVM
is
us
e
d
t
o
dev
el
op
te
n
s
epar
at
e
trai
ning
m
od
el
s
f
or
di
ff
ere
nt
fa
ult
c
onditi
ons.
F
or
te
n
dif
fe
ren
t
fau
lt
s
te
n
dif
fe
ren
t
regressio
n
functi
ons
is
a
rtic
ulate
d.
T
he
regressi
on
f
unct
ion
is
us
e
d
to
m
ap
the
input
to
diff
e
re
nt r
e
gions
o
f
the
sta
te
sp
ace.
Th
e
fu
nc
ti
on
that
is us
ed fo
r
the
r
e
gr
e
ssion f
unct
ion
is give
n
as
b
el
ow,
(
)
=
∑
(
,
)
+
=
1
wh
e
re
(
.
,
.
)
is
the
Gau
s
sia
n
kern
el
functi
on
,
,
=
1
…
,a
re
the
t
rainin
g
sam
ples
wh
ic
h
com
pr
ise
of
a
ll
the
fa
ult
condi
ti
on
an
d
non
f
ault
conditi
on
values
of
t
he
11
var
ia
ble
f
rom
al
l
the
three
blad
es
.
The
s
par
s
e
par
am
et
er
is
de
te
rm
ined
us
i
ng
the
Ba
ye
sia
n
est
im
a
ti
on
al
gorithm
.
T
he
re
gr
essi
on
is
ca
r
ried
out
us
i
ng
the
log
ist
ic
re
gr
e
ss
ion
a
s
giv
e
n by
(
=
1
|
)
=
1
1
+
e
xp
(
−
(
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
3
,
June
2019
:
1506
-
1513
1510
The
m
app
ing
functi
on
is
ge
ner
at
e
d
f
or
ea
ch
of
this
im
p
lem
entat
ion
by
app
ly
in
g
the
regressio
n
al
gorithm
exp
la
ine
d
i
n
[
12
]
.
T
he
R
VM
is
trai
ned
for
each
fa
ult
sit
ua
ti
on
an
d
t
he
trai
ne
d
m
od
el
is
ge
ner
at
e
d
aft
er
the
regressio
n p
ro
c
edure.
The
p
a
r
a
m
et
er is o
pti
m
iz
ed
by m
axim
iz
ing
the
obje
ct
ive fun
ct
io
n
(
)
=
∑
log
(
|
)
+
∑
log
(
|
∗
)
=
1
=
1
Wh
e
re
∗
is
the
m
axi
m
u
m
a
poste
rior
i
est
im
ate
of
hy
perpara
m
et
er
.
T
he
in
pu
t
x
for
al
l
th
e
fau
lt
c
onditi
on
are
de
fine
d
i
n
the
previ
ous
sect
ion
a
nd
the
RVM
tr
ai
nin
g
is
car
r
ie
d
out
by
t
he
us
e
of
the
RVM
i
m
ple
m
entat
io
n
th
us i
ntr
oduc
ed
in
the a
bo
ve
.
3.
RESU
LT
S
AND DI
SCUS
S
I
ONS
The
Ma
tl
ab
ba
sed
Im
ple
m
e
ntati
on
is
carr
ie
d
ou
t
an
d
th
e
resu
lt
s
are
as
sh
own
in
th
e
fo
ll
ow
i
ng
discuss
i
on
.
Th
e
third
fa
ult
scenari
o
as
discu
ssed
in
[
1]
is
a
pp
li
ed
for
the
im
ple
m
entat
ion
wh
ic
h
is
the
ro
t
or
sp
ee
d
sens
or
f
ault
occurri
ng
in
the
tw
o
bla
de
s
of
t
he
tur
bine
.
Wh
il
e
carrying
out
the
trai
ning
proc
ess
th
e
tim
e
ta
ken
f
or
t
he
trai
ning
proce
ss
is
cal
culat
e
d
f
or
m
aking
al
l
the
nin
e
fa
ults
trai
ne
d
a
nd
the
m
o
dels
to
be
dev
el
op
e
d f
or
each
fau
lt
.
The
m
od
el
cre
at
ed
after
the
t
rainin
g
proces
s
com
pr
ise
s
of
the
α
,the
sp
a
r
se
pa
ram
et
er,
and
the
bias
value
b
al
ong
with
the
ke
r
ne
l
structu
re.
T
he
am
ou
nt
of
m
e
m
or
y
sp
ace
nee
ded
f
or
stori
ng
it
would
be
a
par
am
et
er
for
t
he
h
ar
dware
fe
asi
bili
ty
of
the
pro
po
se
d
m
et
ho
d.
T
he
m
e
m
or
y
sp
ace
re
quir
ed
for
it
be
st
ored
is
arou
nd
160kb
of
the
m
e
m
or
y
thu
s
al
lowing
it
to
be
feasible
in
hardw
a
re
i
m
ple
m
enta
ti
on
.
By
giv
in
g
th
e
diff
e
re
nt
wind
sp
eed
,
w
hich
is
rando
m
ly
gen
erati
on.
D
ue
to
the
va
riat
ion
in
the
wind
the
tor
que
ge
ne
rated
in the Fi
gure
1.
Figure
1.
To
r
que
Wav
e
f
or
m
w
it
h ran
dom
w
ind
sup
ply Tu
r
bin
e
The
sim
ulati
on is run f
or 44
00 Sec
s.
T
he fa
ults are a
ppli
ed
at dif
fer
e
nt
places l
ike the
b
el
ow.
1.
Fault t
ype
1a,
b
1,m
1
=
-
3
o
oc
c
urrin
g b
et
wee
n 1
00
s
a
nd 20
0s.
2.
Fault t
ype
1b,
b
2,m
2
=5
o
2,
m
2
on 50
0
-
600s.
3.
Fault t
ype
1a,
b
3,m
1
=
7
o
on
900
-
10
00
s
.
4.
Fault t
ype
2a,
w
r,
m
1
=
2r
a
d.
s
-
1
on
1200
-
13
00
s
.
5.
Faults ty
pe 2
b and 3
b,
w
r,
m
2
=
0.5
w
r,
m
2
an
d
w
g,
m
1
=1
.5w
g,
m
1
on
1700
-
1800s.
6.
Fault t
ype
4a,
t
g
=t
g
-
100
0 N
m
on
4200
-
43
00s.
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In
t J
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om
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g
IS
S
N: 20
88
-
8708
Rel
evan
ce
vect
or
ma
c
hi
ne base
d
f
au
lt
clas
sif
ic
ation
i
n
wi
nd
….
(
Rek
ha
S. N
.
)
1511
7.
Fault t
ype
6,
h
dt
=0
.22
h
dt
8.
Fault
ty
pe
5a,
par
am
et
ers
in
pitch
act
uator
2
(w
n
,z
)
8
a
brup
tl
y
c
hange
d
from
[1
1.1
1,
0.6]
to
[
5.7
3
,
0.45]
from
3
200
a
nd
3300s.
9.
Fault
ty
pe
5b,
par
am
et
ers
in
pitch
act
uat
or
3
(
w
n
,z)
cha
ng
ed
slo
wly
(
with
a
li
ne
a
r
f
unc
ti
on
)
from
[1
1.
11,
0.6]
to
[3
.
42,
0.9]
ov
e
r
30s,
r
e
m
ai
ned
const
ant
durin
g
40s,
and
the
n
decre
ased
agai
n
ov
er
30s
from
3400
and 35
00s.
Wh
il
e
car
ryi
ng
ou
t
t
he
trai
ni
ng
pr
ocess
the
ti
m
e
ta
ken
f
or
t
r
ai
nin
g
al
l
the
f
ault
an
d
the
non
fa
ult
co
nd
it
i
on
f
or
al
l
the
nin
e
fa
ult
conditi
on
s
by
us
in
g
RV
M
is
giv
en
in
T
able
2.
Af
t
er
trai
ning
the
fau
lt
s
in
the
RVM
i
m
ple
m
entat
io
n
. T
he
f
a
ult det
ect
ion
is te
ste
d wit
h
t
he
a
bove
f
a
ults usi
ng th
e m
od
el
s d
e
velop
e
d usi
ng RV
M.
The
detect
io
n
of
fa
ult
would
sh
ow
th
e
1
in
the
detect
ion
graph
a
nd
zer
o
in
the
detect
ion
gr
ap
h
w
he
n
there
is no
f
aul
t.
Figure
s
1
a
nd
2
dis
play
s
th
e
wind
tu
rb
i
ne
tor
qu
e
a
nd
the w
in
d
s
peed
r
es
p
ect
ively
in
T
urbi
ne
.
Figure
s
3
an
d
4
dis
play
s the fault
d
et
ect
ed
in
Bl
ade 1
a
nd
B
la
de
2 120
0
-
13
00
s
an
d 170
0
-
1800s
.
T
he har
dw
a
r
e
feasibil
it
y
of
t
he
propose
d
al
gorithm
wo
ul
d
require
the
ti
m
e
ta
ken
f
or
t
he
trai
ning
po
r
ti
on
a
nd
the
m
e
m
or
y
sp
ace nee
ded
t
o
st
or
e
the
m
odel
s d
evel
op
e
d
after
the
trai
ni
ng
pr
ocess
.
T
he
Table
2
dis
pl
ay
s
the
ti
m
e
tak
en
f
or
al
l
the
nin
e fa
ul
ts
trai
ned
a
nd the
m
od
el
gene
rati
on
for
al
l
th
e
fau
lt
s
a
nd
the
sp
ace for
the
m
od
el
s
stored
in
the
m
e
m
or
y. The
table i
s
dev
el
oped
c
onsideri
ng
the i5 p
ro
ces
sor,
3.2GHz
proc
essor wit
h
the
8G
B
ram
.
Table
2.
Tim
e taken f
or
Trai
ni
ng
Each
Fa
ults Usi
ng RVM
and Me
m
or
y U
sed for
t
he
Mo
del T
hu
s
D
e
vel
op
e
d
Fau
lt No.
Fau
lt T
y
p
e
Fau
lt Site
Me
m
o
r
y
Sp
ace
f
o
r
m
o
d
el
Execu
tio
n
T
i
m
e
1a
Fix
ed
Value
Sen
so
r
Fau
lts Blad
e Pos
itio
n
s
1
6
KB
1
0
5
4
secs o
n
an av
erage f
o
r
each
m
o
d
el
1b
Gain
Factor
2a
Fix
ed
Value
Sen
so
r
Fau
lt Ro
to
r
Sp
eed
2
0
KB
2b
Gain
Factor
3a
Fix
ed
Value
Sen
so
r
Fau
lt Gene
rator Speed
1
0
KB
3b
Gain
Factor
4a
Of
f
set
Actu
ato
r
Fau
lt con
v
erter
s
y
ste
m
1
KB
5a
Ab
rup
t
Ch
an
g
ed
Dy
n
a
m
i
cs
Actu
ato
r
Fau
lt
Pitch
Sy
ste
m
s
1
6
KB
5b
Slo
w
Ch
an
g
ed
Dy
n
a
m
i
cs
6
Ch
an
g
ed
Dy
n
a
m
i
cs
Sy
ste
m
Fault
Driv
e T
r
ain
4
7
KB
Figure
2. S
pee
d
in
wi
nd tu
rb
i
ne
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
9
, N
o.
3
,
June
2019
:
1506
-
1513
1512
Figure
3. Roto
r
sp
ee
d fault
det
ect
ed
in
bla
de 1
Figure
4. Roto
r
sp
ee
d fault
det
ect
ed
in
bla
de 2
4.
CONCL
US
I
O
N
The
Re
le
va
nce
Vecto
r
Ma
c
hin
e
base
d
im
pl
e
m
entat
ion
w
a
s
carrie
d
out
with
the
be
nc
hm
ark
m
od
el
dev
el
op
e
d
as
m
entioned
i
n
t
he
li
te
ratur
e
.
The
RVM
fun
ct
ion
wa
s
trai
ned
a
nd
te
n
di
ff
ere
nt
m
od
el
s
wer
e
dev
el
op
e
d
f
or
each
ki
nd
of
f
a
ult
and
the
res
ults
wer
e
f
ound
to
be
sat
isfac
tory.
T
he
ha
rdwar
e
f
easi
bili
ty
stud
y
ta
kes
in
t
o
c
onside
rati
on
the
exec
ution
tim
e
an
d
the
m
em
or
y
us
age
for
the
m
od
el
s
t
hu
s
de
velo
pe
d
w
hile
trai
ning.
T
he
a
m
ou
nt
of
e
xe
cution
ti
m
e
a
nd
t
he
m
e
m
or
y
us
ed
cl
ear
ly
su
pp
or
ts
the
hard
war
e
fe
asi
bili
ty
po
sit
ively
.
REFERE
NCE
S
[1]
Odgaa
rd,
P.F.
,
Stous
trup,
J.
,
and
Kinnae
rt
,
M.
“
Fault
to
le
r
ant
con
trol
of
wind
turb
ine
s
-
a
ben
chma
rk
m
odel
,
”
I
EEE
Tr
ansacti
ons on Control Sy
st
ems Tec
hnology
,
Vol
:
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y
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Santos,
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a
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Reñone
s,
A.,
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lo
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Maude
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J,
“
An
SV
M
-
Based
Sol
uti
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for
Fault
Dete
c
ti
on
in
W
i
nd
Turbi
nes
,
”
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,
15
,
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2015
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Muham
m
ad
Rafi
,
Moham
m
ad
Shahid
Shaikh
,
“
A
compari
son
o
f
SV
M
and
RVM
for
Docum
ent
Cla
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ifica
ti
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”
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CSIM
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Med
a
n
Indone
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Molla
sal
ehi
,
E,
W
ood,
D,
Sun,
Q.
“
Indic
at
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Fault
Diagnosis
o
f
W
ind
Turbi
ne
Gene
rat
or
B
ea
ri
ngs
Us
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Towe
r
Sound a
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Vibr
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ti
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In
t J
Elec
&
C
om
p
En
g
IS
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88
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8708
Rel
evan
ce
vect
or
ma
c
hi
ne base
d
f
au
lt
clas
sif
ic
ation
i
n
wi
nd
….
(
Rek
ha
S. N
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[5]
Anders
Bec
hBorce
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Jesper
Abildga
ard
La
rse
n,
JakobStoustrup,
“
Fault
D
et
ecti
on
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Loa
d
Distribut
ion
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e
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ind
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Challenge
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C
Pr
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Se
y
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Mojt
aba
Ta
ba
ta
ba
ei
pour
and
P
eter
F.
Odgaa
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and
Tho
m
as
Bak
,
“
Fault
detec
t
ion
of
a
benc
hm
ark
win
d
turbi
ne
using
interva
l
anal
y
s
is
,
”
Ame
rican
Contr
ol
Confe
ren
ce
F
airmont
Quee
n
El
izabet
h
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Mon
t
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27
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June
29,
201
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Xiukun
W
ei
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,
“
Fa
ult
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la
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sc
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ems
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”
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rnati
onal
Confe
renc
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Computer
Sc
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Aldin
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“
Broken
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l
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cla
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ca
ti
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in
duct
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m
otor
b
ase
d
on
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vec
tor
m
ac
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SVM
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“
Dam
age
detec
t
ion
of
wind
turbi
ne
bl
ade
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d
on
wave
l
et
an
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”
Im
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Signa
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Proce
ss
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(
CISP)
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e
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2015
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.
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nc
ed
sign
al
proc
essing
tec
hnique
s
for
isla
n
ding
detec
t
ion
in
a
h
y
brid
distri
bu
te
d
g
e
ne
r
at
ion
sy
stem,
"
IEEE
Tr
ansacti
ons on
Su
stainabl
e
Ene
rgy
6,
122
-
131
,
1
2
015
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[11]
Thay
an
ant
han
A
.
,
N
ava
ra
tna
m
R
.
,
Steng
er
B
.
,
Tor
r
P.H.S., Ci
pol
la R.
“
Multi
v
ariate Re
l
eva
nc
e
Ve
ctor Mac
hin
es
for
Tra
ck
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Leonardi
s
A.,
Bisc
hof
H.,
Pinz
A.
(ed
s)
Com
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te
r
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on
-
ECCV
2006,
”
Lec
ture
Note
s
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Compute
r
Sci
en
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idelber
g
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[12]
Liy
ang
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ei
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Robert
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ika
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,
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Rel
ev
an
ce
Ve
ct
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Mac
hi
ne
L
ea
rning
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Dete
c
ti
on
of
Mi
cro
calc
if
icati
ons
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Mam
m
ogra
ms
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”
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EE
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Evaluation Warning : The document was created with Spire.PDF for Python.