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h
e
f
au
l
t
lo
ca
tio
n
m
ak
e
s
it
ea
s
ier
to
d
etec
t
an
d
r
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m
o
v
e
o
f
t
h
e
f
a
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lt.
He
n
ce
,
f
au
lts
ar
e
r
eq
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ir
ed
to
b
e
d
etec
t
ed
f
ast,
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d
lo
ca
ted
ac
cu
r
atel
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to
r
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r
e
n
o
r
m
al
p
o
w
er
f
lo
w
at
t
h
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ea
r
lies
t.
T
h
e
p
r
o
p
o
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ed
w
o
r
k
i
s
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te
n
d
ed
to
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ev
elo
p
a
s
i
m
p
le
P
C
A
b
ased
p
o
w
er
s
y
s
te
m
p
r
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tectio
n
alg
o
r
ith
m
s
u
itab
le
f
o
r
th
e
class
if
ica
tio
n
an
d
lo
ca
lizatio
n
o
f
d
if
f
er
en
t
t
y
p
es
o
f
p
o
w
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y
s
te
m
f
au
l
ts
in
a
th
r
ee
p
h
ase
r
ad
ial
lo
n
g
tr
a
n
s
m
i
s
s
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n
s
y
s
te
m
,
u
s
in
g
p
atter
n
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n
d
ices
a
n
d
f
a
u
lt
s
ig
n
at
u
r
es
d
ev
elo
p
ed
b
y
ap
p
licatio
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o
f
P
C
A
,
lead
in
g
to
th
e
d
ev
elo
p
m
e
n
t
o
f
p
r
in
cip
al
co
m
p
o
n
en
t
d
is
ta
n
ce
i
n
d
ex
(
P
C
DI
)
[
2
2
]
.
Si
m
ilar
it
y
a
n
al
y
s
i
s
o
f
th
e
P
C
DI
b
ased
f
a
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lt
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g
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r
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en
ti
f
ies
t
h
e
m
ax
i
m
u
m
p
r
o
x
i
m
it
y
o
f
t
h
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test
d
ata
w
i
th
an
y
o
f
t
h
e
f
au
l
t
p
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to
ty
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s
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n
g
m
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n
i
m
u
m
s
q
u
ar
e
er
r
o
r
(
MSE
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c
r
iter
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th
u
s
class
i
f
y
in
g
t
h
e
u
n
k
n
o
w
n
f
a
u
lt
.
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lt
lo
ca
lizatio
n
h
as
b
ee
n
ca
r
r
ied
o
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t
u
s
in
g
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tat
is
tical
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al
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lik
e
m
u
ltip
le
li
n
ea
r
r
eg
r
ess
io
n
(
M
L
R
)
[
2
3
]
o
v
er
th
e
th
r
ee
p
h
ase
P
C
DI
.
T
h
is
h
elp
s
i
n
d
ev
elo
p
i
n
g
a
g
e
n
er
al
r
eg
r
es
s
io
n
m
o
d
el
w
h
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h
is
f
u
r
th
er
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s
ed
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tes
t
u
n
k
n
o
w
n
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ata
f
o
r
f
au
lt
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ca
lizatio
n
.
A
tr
an
s
m
is
s
io
n
lin
e
p
r
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to
ty
p
e
h
as
b
ee
n
m
o
d
eled
in
E
MT
P
-
A
T
P
s
i
m
u
lat
io
n
[
2
4
]
,
f
o
llo
w
ed
b
y
a
n
al
y
s
i
s
o
f
q
u
ar
ter
c
y
cl
e
p
r
e
-
f
au
l
t
an
d
h
al
f
c
y
cle
p
o
s
t
-
f
a
u
lt
r
ec
ei
v
in
g
e
n
d
cu
r
r
en
t
w
a
v
e
f
o
r
m
s
in
th
e
M
A
T
L
A
B
en
v
ir
o
n
m
e
n
t,
u
s
i
n
g
ten
d
if
f
er
en
t
f
au
lt
p
r
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to
t
y
p
es
co
n
d
u
cted
at
v
ar
y
i
n
g
f
a
u
lt
lo
ca
tio
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s
alo
n
g
th
e
li
n
e
s
p
an
a
n
d
h
ea
lt
h
y
co
n
d
itio
n
,
u
s
in
g
P
C
A
b
ased
p
r
o
p
o
s
ed
p
r
o
tectio
n
s
ch
e
m
e
2.
SYST
E
M
DE
SI
G
N
A
s
i
n
g
l
e
e
n
d
f
e
d
4
0
0
k
V
,
1
5
0
k
m
l
o
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,
s
i
n
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c
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c
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,
t
h
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p
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p
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m
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s
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t
p
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r
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m
m
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(
E
M
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P
)
j
o
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i
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c
a
b
l
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n
s
t
a
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t
s
(
L
C
C
)
b
l
o
c
k
s
,
e
a
c
h
o
f
1
0
k
m
i
n
c
a
s
c
a
d
e
a
n
d
i
s
s
h
o
w
n
i
n
F
i
g
u
r
e
1
.
T
e
n
d
i
f
f
e
r
e
n
t
t
y
p
e
s
o
f
f
a
u
l
t
s
v
i
z
.
,
S
L
G
-
A
,
S
L
G
-
B
,
S
L
G
-
C
,
D
L
-
A
B
,
D
L
-
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C
,
D
L
-
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A
,
D
L
G
-
A
B
,
D
L
G
-
B
C
,
D
L
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-
CA
,
a
n
d
L
L
L
h
a
v
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n
c
o
n
d
u
c
t
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d
a
t
f
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d
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a
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,
1
0
k
m
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p
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,
t
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g
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t
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f
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5
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k
m
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d
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a
r
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a
k
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s
0
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0
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Ω
/
k
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(
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2
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7
.
5
c
m
b
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t
w
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a
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j
a
c
e
n
t
h
o
r
i
z
o
n
t
a
l
l
i
n
e
s
.
Fig
u
r
e
1
.
Si
m
u
latio
n
m
o
d
el
o
f
th
e
r
ad
ial,
s
in
g
le
en
d
f
ed
,
lo
n
g
tr
an
s
m
i
s
s
io
n
li
n
e
3.
DATA P
R
E
P
ARA
T
I
O
N
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
tr
ain
ed
w
it
h
o
n
l
y
o
n
e
s
et
o
f
tr
ain
i
n
g
f
au
l
t
d
ata
o
f
ten
d
if
f
e
r
en
t
t
y
p
es
o
f
f
au
l
ts
co
n
d
u
cted
at
al
m
o
s
t
th
e
m
id
p
o
in
t
o
f
th
e
li
n
e,
i.e
.
,
at
7
0
k
m
f
r
o
m
s
e
n
d
in
g
en
d
o
f
th
e
1
5
0
k
m
lo
n
g
tr
an
s
m
is
s
io
n
li
n
e
an
d
h
ea
l
th
y
co
n
d
itio
n
d
ata.
Qu
ar
ter
cy
cle
p
r
e
-
f
a
u
lt
an
d
h
alf
c
y
c
le
p
o
s
t
-
f
au
lt
r
ec
eiv
i
n
g
en
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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P
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r
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eg
r
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(
A
lo
k
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kh
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)
115
lin
e
f
au
lt
c
u
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t
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s
co
llected
at
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a
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ata
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it
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r
o
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3
co
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ated
as:
X
i
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[
I
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1
;
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w
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Fu
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[
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[
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d
[
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tain
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d
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DI
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m
atr
i
x
o
f
th
e
o
r
d
er
1
×3
.
T
w
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v
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s
u
c
h
p
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o
to
t
y
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ar
e
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a
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p
le
te
P
C
DI
m
atr
i
x
o
f
th
e
d
i
m
e
n
s
io
n
1
2
×3
,
d
en
o
ted
b
y
P
,
ea
ch
r
o
w
o
f
w
h
ich
co
r
r
esp
o
n
d
to
th
e
t
w
el
v
e
f
a
u
lt
ca
s
e
s
an
d
test
co
n
d
it
io
n
an
d
ea
ch
co
lu
m
n
r
ep
r
ese
n
ts
t
h
r
ee
in
d
i
v
id
u
al
p
h
a
s
es.
As
m
en
tio
n
ed
b
ef
o
r
e,
P
C
A
r
ec
o
n
s
t
r
u
cts
a
d
ata
s
et
i
n
th
e
asce
n
d
i
n
g
o
r
d
er
o
f
i
m
p
o
r
tan
ce
a
n
d
f
o
r
t
h
e
s
a
k
e
o
f
ea
s
e
o
f
a
n
al
y
s
is
,
o
n
l
y
t
w
o
m
o
s
t
i
m
p
o
r
ta
n
t
d
ir
ec
tio
n
s
(
P
C
s
)
an
d
th
e
co
r
r
esp
o
n
d
in
g
s
co
r
e
d
ata
a
r
e
co
n
s
id
er
ed
f
o
r
th
e
p
r
esen
t
p
u
r
p
o
s
e,
h
en
ce
u
s
ed
to
co
n
s
tr
u
ct
P
C
DI
m
atr
i
x
.
T
h
ese
P
C
DI
v
alu
es
ar
e
ap
p
r
o
x
i
m
ate
esti
m
atio
n
o
f
th
e
d
ev
iatio
n
o
f
ea
ch
f
au
l
t
cu
r
r
en
t
f
r
o
m
h
ea
lt
h
y
co
n
d
itio
n
.
T
h
e
d
ir
ec
tio
n
s
o
f
v
ar
iatio
n
is
g
iv
e
n
b
y
th
e
eig
e
n
v
ec
to
r
s
o
b
tain
ed
f
r
o
m
th
e
c
o
v
ar
ian
ce
m
atr
i
x
o
f
th
e
tr
an
s
f
o
r
m
ed
d
ata
p
o
in
ts
o
r
s
co
r
es
an
d
th
e
m
a
g
n
itu
d
e
s
o
f
d
ev
iatio
n
f
r
o
m
t
h
e
o
r
ig
i
n
(
o
r
ig
i
n
is
as
s
ig
n
ed
to
th
e
n
o
f
au
l
t c
o
n
d
itio
n
)
ar
e
g
i
v
en
b
y
th
e
co
r
r
esp
o
n
d
in
g
ei
g
en
v
alu
e
s
.
4.
P
CA
AL
G
O
RI
T
H
M
4
.
1
.
G
ener
a
lized
P
C
A
a
lg
o
rit
h
m
I
n
p
u
t: N
x
d
d
ata
m
a
tr
ix
X
(
ea
ch
r
o
w
co
n
ta
in
a
d
d
i
m
e
n
s
io
n
a
l d
ata
p
o
in
t )
C
o
m
p
u
t
m
ea
n
:
N
i
i
x
N
1
)
(
1
Su
b
tr
ac
t
m
ea
n
f
r
o
m
r
o
w
s
o
f
X
:
X
X
~
C
o
m
p
u
te
co
v
ar
ian
ce
m
atr
i
x
:
X
X
N
T
~
~
1
C
alcu
late
eig
e
n
v
alu
e
s
an
d
ei
g
en
v
ec
to
r
s
o
f
P
ick
f
e
w
ei
g
en
v
ec
to
r
s
(
d
’
<d
)
co
r
r
esp
o
n
d
in
g
to
th
e
lar
g
est
eig
en
v
al
u
es
an
d
p
u
t
th
e
m
i
n
th
e
co
lu
m
n
o
f
A
i
n
d
escen
d
i
n
g
o
r
d
er
o
f
e
i
g
en
v
al
u
e
s
i.e
.
]
,
.
.
.
.
.
,
[
'
'
2
1
d
V
V
V
A
,
w
h
er
e
V
1
,
V
2
ar
e
th
e
1
st
, 2
nd
P
C
s
an
d
s
o
o
n
.
C
o
m
p
u
te
th
e
n
e
w
d
ata
m
atr
i
x
(
P
C
s
co
r
es)
in
r
ed
u
ce
d
d
im
e
n
s
io
n
:
X
A
X
T
~
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
2
5
2
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
u
g
u
s
t 2
0
2
0
:
1
1
3
–
1
2
6
116
4.
2
.
P
CA
a
lg
o
rit
h
m
a
pp
lie
d f
o
r
t
he
pro
po
s
ed
w
o
rk
Step
1
:
A
s
s
i
g
n
i
n
p
u
t
d
ata:
th
e
in
p
u
t
d
ata
is
ta
k
e
n
as
t
h
e
p
h
a
s
e
id
en
ti
f
ied
m
a
tr
ices
:
[
Xa]
,
[
Xb
]
,
an
d
[
Xc]
eac
h
p
h
ase
d
ata
in
co
m
p
u
ted
in
d
i
v
i
d
u
all
y
,
s
a
y
,
d
en
o
ted
b
y
j
k
w
h
e
r
e
k
tak
es t
h
e
i
n
d
ices a
,
b
,
an
d
c.
Step
2
:
C
o
m
p
u
t
m
ea
n
o
f
X
k
f
o
r
ea
ch
o
f
th
e
co
lu
m
n
s
in
d
i
v
i
d
u
all
y
a
s
:
(
µ
k)
n
]
)
(
1
[
1
)
(
N
i
i
n
j
N
,
w
h
er
e
i
in
d
e
x
es
r
o
w
s
a
n
d
tak
es t
h
e
v
a
lu
e
s
1
to
1
5
0
0
an
d
n
in
d
ex
es c
o
lu
m
n
s
a
n
d
tak
es t
h
e
v
alu
e
s
1
to
1
2
.
Step
3
:
Su
b
tr
ac
t
m
ea
n
o
f
e
ac
h
co
r
r
esp
o
n
d
in
g
co
l
u
m
n
f
r
o
m
ea
c
h
o
f
th
e
r
o
w
s
o
f
J
k
f
o
r
ea
ch
co
lu
m
n
in
d
ep
en
d
en
t
l
y
to
f
o
r
m
th
e
m
o
d
if
ied
j
o
in
t
m
atr
i
x
as:
J
k
MOD
n
=
J
k
n
-
(
µ
k
)
n
.
Hen
ce
th
e
d
im
e
n
s
io
n
r
etain
s
th
e
s
a
m
e
as 1
5
0
0
×1
2
.
Step
4
:
C
o
m
p
u
te
co
v
ar
ia
n
ce
m
atr
i
x
:
N
1
(
J
k
MOD
n
)
T
(
J
k
MOD
n
)
Step
5
:
C
alcu
late
ei
g
e
n
v
al
u
e
s
an
d
eig
e
n
v
ec
to
r
s
o
f
Step
6
:
P
ick
f
e
w
ei
g
e
n
v
ec
to
r
s
(
d
’
<d
)
co
r
r
esp
o
n
d
in
g
to
th
e
lar
g
est
ei
g
en
v
al
u
es
a
n
d
p
u
t
th
e
m
i
n
t
h
e
co
lu
m
n
o
f
A
in
d
escen
d
i
n
g
o
r
d
er
o
f
eig
en
v
al
u
es
i.e
.
]
,
.
.
.
.
.
,
[
'
'
2
1
d
V
V
V
A
,
w
h
er
e
V
1
,
V
2
ar
e
th
e
1
st
,
2
nd
P
C
s
an
d
s
o
o
n
.
Fo
r
th
e
p
r
o
p
o
s
ed
w
o
r
k
,
w
e
h
a
v
e
ta
k
en
o
n
l
y
t
h
e
t
w
o
lar
g
e
s
t e
ig
e
n
v
ec
to
r
,
h
en
ce
,
V
1
an
d
V
2
.
Step
7
:
C
o
m
p
u
te
t
h
e
n
e
w
d
at
a
m
atr
ix
(
P
C
s
co
r
es)
in
r
ed
u
ce
d
d
im
e
n
s
io
n
:
J
k
MOD
n
(new)
=
A
T
J
k
MOD
n
.
Hen
ce
,
th
e
d
i
m
e
n
s
io
n
o
f
t
h
e
s
co
r
e
m
atr
ix
J
k
MOD
n
(new
)
s
h
o
u
ld
b
ec
o
m
e
th
e
s
a
m
e
a
s
1
2
×1
5
0
0
.
T
h
e
p
r
o
p
o
s
ed
w
o
r
k
u
s
es o
n
l
y
t
h
e
t
w
o
m
o
s
t
s
ig
n
if
ican
t
d
ir
ec
tio
n
s
.
Hen
ce
,
t
h
e
w
o
r
k
i
n
g
J
k
MOD
n
(new)
d
i
m
e
n
s
io
n
r
ed
u
ce
s
to
a
1
2
×
2
w
h
ic
h
ac
ts
a
s
th
e
P
C
s
co
r
e
m
atr
i
x
f
o
r
th
e
p
r
o
p
o
s
ed
w
o
r
k
.
Step
8
:
Fo
r
m
i
n
g
P
C
DI
m
at
r
ix
:
P
C
A
di
s
tan
ce
i
s
f
o
r
m
e
d
b
y
f
i
n
d
i
n
g
o
u
t
th
e
v
ec
to
r
d
is
tan
ce
o
f
ea
ch
o
f
th
e
tr
ain
i
n
g
an
d
th
e
test
s
c
o
r
e
(
2
D)
f
r
o
m
th
e
n
o
-
f
a
u
lt
s
c
o
r
e
(
2
D)
w
h
ich
is
th
e
o
r
ig
i
n
,
th
u
s
f
o
r
m
i
n
g
P
C
DI
m
atr
i
x
f
o
r
ea
ch
p
h
ase
a
n
d
p
r
o
d
u
cin
g
1
2
×1
P
C
DI
v
ec
t
o
r
f
o
r
ea
ch
p
h
a
s
e
a
n
d
t
h
e
to
tal
P
C
DI
1
2
×3
m
atr
i
x
co
n
s
id
er
in
g
a
ll
t
h
e
t
h
r
ee
p
h
ases
,
s
a
y
,
d
en
o
ted
b
y
S
1
2×
3
.
T
h
e
to
p
elev
en
r
o
w
s
o
f
S
co
r
r
esp
o
n
d
to
th
e
ele
v
e
n
d
i
f
f
er
e
n
t
tr
ai
n
i
n
g
co
n
d
itio
n
s
a
n
d
ea
ch
co
lu
m
n
r
ep
r
esen
t
s
t
h
e
t
h
r
ee
i
n
d
i
v
id
u
al
p
h
ase
s
an
d
th
e
t
w
el
f
t
h
r
o
w
i
n
d
icate
s
t
h
at
o
f
t
h
e
test
co
n
d
it
io
n
,
g
i
v
e
n
b
y
,
S
=[
P
C
DI
-
A
i
P
C
DI
-
B
i
P
C
DI
-
C
i
]
12
×
3
w
h
er
e
i
=1
to
1
2
in
th
e
s
eq
u
en
ce
as
NO
-
FL
T
(
h
ea
lth
y
)
,
SLG
-
A
,
S
L
G
-
B
,
SL
G
-
C
,
D
L
-
AB
,
DL
-
B
C
,
DL
-
C
A
,
DL
G
-
A
B
,
D
L
G
-
B
C
,
D
L
G
-
C
A
,
L
L
L
,
an
d
T
E
ST
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
d
is
c
u
s
s
ed
s
o
f
ar
an
d
th
e
f
o
r
m
atio
n
o
f
P
C
DI
f
o
llo
w
s
t
h
e
f
lo
w
c
h
ar
t
as g
i
v
en
i
n
F
i
g
u
r
e
2
.
Fig
u
r
e
2
.
Flo
w
c
h
ar
t ill
u
s
tr
ati
n
g
th
e
f
o
r
m
atio
n
o
f
P
C
DI
m
a
tr
ix
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
P
o
w
er sys
te
m
fa
u
lt id
en
tifi
ca
tio
n
a
n
d
lo
ca
liz
a
tio
n
u
s
in
g
mu
lt
ip
le
lin
ea
r
r
eg
r
ess
io
n
o
f…
(
A
lo
k
Mu
kh
erjee
)
117
Fu
r
t
h
er
,
th
e
to
tal
P
C
DI
m
atr
i
x
S
is
s
eg
m
e
n
ted
in
to
t
w
o
m
a
tr
ices,
v
iz.
tr
ain
i
n
g
P
C
DI
m
atr
i
x
(
d
en
o
ted
b
y
P
)
an
d
test
P
C
DI
m
atr
i
x
o
r
v
ec
to
r
(
d
en
o
ted
b
y
Q)
,
h
e
n
c
e
r
ed
u
cin
g
t
h
e
1
2
×3
m
atr
i
x
i
n
to
t
w
o
m
atr
ices
as
g
iv
e
n
h
er
e:
P
i
=[
P
C
DI
-
A
i
P
C
DI
-
B
i
P
C
DI
-
C
i
]
11
×
3
Q
i
=[
P
C
DI
-
A
TE
S
T
P
C
DI
-
B
TE
S
T
P
C
DI
-
C
TE
ST
]
1×
3
S
=
[
P
; Q
]
12×
3
Fu
r
t
h
er
,
s
i
m
i
lar
it
y
a
n
al
y
s
i
s
h
as
b
ee
n
ca
r
r
ied
o
u
t
in
o
r
d
er
to
c
o
m
p
ar
e
th
e
e
x
p
er
im
en
tal
d
ata
(
Q
v
ec
to
r
)
w
it
h
t
h
e
tr
ai
n
in
g
f
a
u
lt
s
ig
n
at
u
r
es
(
P
m
atr
i
x
)
f
o
r
ea
ch
in
d
i
v
id
u
a
l
p
h
ase
s
an
d
f
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Evaluation Warning : The document was created with Spire.PDF for Python.
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118
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ates th
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Fig
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it
h
m
to
p
r
o
d
u
ce
P
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m
atr
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as
s
h
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w
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i
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th
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in
itia
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co
lu
m
n
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o
f
T
ab
le1
w
h
ich
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s
a
co
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b
i
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ed
v
ie
w
o
f
t
h
e
[
P
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]
,
[
R
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,
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d
[
R
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.
T
h
e
[
P
C
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]
is
f
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r
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er
r
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esen
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g
r
ap
h
icall
y
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th
e
f
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o
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a
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ee
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i
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F
ig
u
r
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4
.
C
lo
s
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o
f
F
ig
u
r
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4
r
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a
t
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.
leg
en
d
9
is
clo
s
est
to
th
e
SL
G
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G
f
a
u
lt
i.e
.
,
leg
en
d
3
co
m
p
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o
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y
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er
t
y
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e
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h
m
in
i
m
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m
E
u
clid
ian
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,
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ic
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s
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r
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er
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i
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g
[
R
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as
s
h
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i
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id
d
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n
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th
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s
a
m
e
T
ab
le
1
.
[
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is
ag
ain
r
ep
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esen
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g
r
ap
h
icall
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in
F
i
g
u
r
e
5
.
C
lo
s
e
o
b
s
er
v
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n
o
f
[
P
C
DI
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an
d
[
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ev
ea
l
a
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tain
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is
ti
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is
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f
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t
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r
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f
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r
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ch
p
ar
ticu
lar
ty
p
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o
f
f
a
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i.e
.
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e
test
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lt
P
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alu
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r
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ted
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R
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m
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s
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m
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F
i
g
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r
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5
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E
u
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ig
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r
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4
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s
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h
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test
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atter
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e
SL
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B
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th
M
SE
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iter
ia.
T
h
u
s
,
f
o
r
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at
io
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R
g
r
ea
tl
y
e
m
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h
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izes
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is
is
also
test
ed
w
ith
v
ar
y
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g
f
a
u
lt l
o
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tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
P
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r
ess
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f…
(
A
lo
k
Mu
kh
erjee
)
119
T
ab
le
1
.
P
C
DI
,
r
atio
m
atr
i
x
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d
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atio
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atr
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f
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d
ata
s
et
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a
u
l
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t
y
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e
[
P
C
D
I
]
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R
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R
E]
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a
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r
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(
R
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)
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H
EA
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0
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T
EST
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NA
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Fig
u
r
e
4
.
3
D
p
lo
t o
f
th
r
ee
p
h
ase
P
C
DI
v
alu
e
s
f
o
r
tr
ain
in
g
(
te
n
d
if
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er
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t t
y
p
es o
f
f
a
u
lts
a
n
d
h
ea
lt
h
y
co
n
d
it
io
n
)
an
d
test
d
ata
Fig
u
r
e
5
.
3
D
p
lo
t o
f
th
e
th
r
ee
p
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ase
R
atio
I
n
d
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s
f
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s
e
v
en
d
if
f
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n
t t
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p
e
s
o
f
f
a
u
lt
s
(
D
L
f
au
lt e
x
c
lu
d
ed
)
an
d
test
d
ata
I
t
is
f
u
r
th
er
o
b
s
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at
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ce
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n
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f
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is
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R
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T
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ef
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s
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.
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th
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it
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s
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D
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.
Hen
ce
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f
o
r
th
e
s
a
m
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ted
ab
o
v
e,
DL
f
au
l
ts
ar
e
n
o
t
in
clu
d
ed
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:2
2
5
2
-
8792
I
n
t J
A
p
p
l P
o
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g
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9
,
No
.
2
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A
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g
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:
1
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6
120
f
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f
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F
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r
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5
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t
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ticu
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ata
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le.
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h
e
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e
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ac
t
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al
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ep
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n
Fi
g
u
r
e
6
w
h
ic
h
is
co
n
s
tr
u
c
ted
u
s
i
n
g
th
e
th
r
ee
p
h
ase
[
P
C
DI
]
an
d
[
R
]
v
alu
e
s
o
f
T
ab
le
1
w
h
er
e,
as
d
escr
ib
ed
ea
r
lier
,
SL
G
-
B
f
a
u
lt i
s
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e
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f
o
r
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a
m
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le
f
o
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d
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n
t f
a
u
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ca
tio
n
s
.
T
ab
le
2
.
R
atio
m
atr
i
x
f
o
r
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ed
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y
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h
e
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d
is
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n
ce
s
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h
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iatio
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g
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etr
ic
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is
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es
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a
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t
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Fig
u
r
e
6
.
Var
iatio
n
o
f
th
r
ee
p
h
ase
P
C
DI
an
d
r
atio
in
d
ices
w
it
h
d
if
f
er
en
t
g
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m
e
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ic
f
a
u
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is
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ce
s
I
t
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w
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o
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ed
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r
m
F
i
g
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th
at
th
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v
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iatio
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o
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R
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ar
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ic
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ase
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ed
P
C
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-
R
atio
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ased
class
if
ier
alg
o
r
ith
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
P
o
w
er sys
te
m
fa
u
lt id
en
tifi
ca
tio
n
a
n
d
lo
ca
liz
a
tio
n
u
s
in
g
mu
lt
ip
le
lin
ea
r
r
eg
r
ess
io
n
o
f…
(
A
lo
k
Mu
kh
erjee
)
121
T
ab
le
3
.
F
au
lt
class
i
f
ier
r
es
u
lt
s
w
ith
o
n
l
y
o
n
e
s
et
o
f
tr
ai
n
i
n
g
d
ata
F
a
u
l
t
t
y
p
e
P
U
R
E
AG
BG
CG
AB
BC
CA
A
B
G
BCG
C
A
G
A
B
C
P
U
R
E
13
0
0
0
0
0
0
0
0
0
0
AG
0
13
0
0
0
0
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0
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0
BG
0
0
13
0
0
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0
0
0
CG
0
0
0
13
0
0
0
0
0
0
0
AB
0
0
0
0
13
0
0
0
0
0
0
BC
0
0
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0
0
13
0
0
0
0
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0
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13
0
0
0
0
A
B
G
0
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13
O
v
e
r
a
l
l
a
c
c
u
r
a
c
y
:
1
0
0
%
6.
F
AULT
D
I
S
T
ANC
E
E
ST
I
M
AT
I
O
N
T
h
e
later
an
d
an
o
th
er
v
i
tal
s
ec
tio
n
o
f
t
h
e
p
r
o
p
o
s
ed
r
esea
r
ch
is
p
r
ed
ictio
n
o
f
t
h
e
f
a
u
lt
lo
ca
tio
n
.
T
h
e
p
r
o
p
o
s
ed
f
au
lt
d
is
tan
ce
p
r
ed
icto
r
alg
o
r
ith
m
is
d
esi
g
n
ed
u
s
i
n
g
m
u
ltip
le
li
n
ea
r
r
eg
r
ess
i
o
n
(
ML
R
)
a
n
al
y
s
is
.
ML
R
ta
k
es
i
n
to
ac
co
u
n
t
t
h
e
t
r
en
d
s
an
d
c
u
r
v
at
u
r
es
o
f
m
o
r
e
th
a
n
o
n
e
d
ata
s
e
t
an
d
e
f
f
ec
ti
v
el
y
co
m
p
u
te
o
n
e
p
r
im
ar
y
d
ir
ec
tio
n
o
f
v
ar
iat
io
n
u
s
i
n
g
t
h
e
m
u
lt
ip
le
d
ata
s
et.
T
h
e
p
r
o
p
o
s
ed
w
o
r
k
u
t
ilizes
t
h
is
i
m
p
o
r
tan
t
f
ea
t
u
r
e
o
f
M
L
R
a
n
d
u
s
es
th
e
t
h
r
ee
p
h
ase
f
ea
tu
r
e
s
i
n
ter
m
s
o
f
P
C
DI
to
f
o
r
m
o
n
e
k
e
y
cu
r
v
at
u
r
e,
in
co
r
p
o
r
atin
g
th
e
f
ea
t
u
r
es
o
f
all
th
e
P
C
DI
.
Fo
r
th
is
p
u
r
p
o
s
e,
s
ix
in
ter
m
e
d
iate
n
o
n
-
eq
u
id
is
ta
n
t
lo
ca
tio
n
s
at
1
0
,
2
0
,
5
0
,
9
0
,
130
,
an
d
1
4
0
k
m
d
is
ta
n
ce
f
r
o
m
th
e
s
en
d
i
n
g
e
n
d
o
f
th
e
1
5
0
k
m
lo
n
g
li
n
e
h
a
v
e
b
ee
n
c
h
o
s
e
n
as
th
e
s
ix
tr
ai
n
i
n
g
poi
n
ts
f
o
r
th
e
p
r
o
p
o
s
ed
f
au
lt
l
o
ca
lizer
alg
o
r
ith
m
.
T
en
d
if
f
er
en
t
t
y
p
e
s
o
f
f
a
u
lt
s
h
a
v
e
b
ee
n
co
n
d
u
cted
at
t
h
ese
s
ix
tr
ai
n
i
n
g
lo
ca
tio
n
s
a
n
d
r
ec
eiv
i
n
g
e
n
d
cu
r
r
en
t
w
a
v
e
f
o
r
m
s
h
av
e
b
ee
n
r
ec
o
r
d
ed
as
th
e
tr
ain
i
n
g
d
ata,
ea
ch
o
f
w
h
ic
h
is
f
ed
to
u
n
d
er
g
o
t
h
e
p
r
o
p
o
s
ed
f
au
l
t
cla
s
s
i
f
ier
al
g
o
r
ith
m
d
is
c
u
s
s
ed
in
th
e
p
r
ev
io
u
s
s
e
ctio
n
an
d
t
h
e
t
h
r
ee
p
h
ase
P
C
DI
ar
e
f
o
u
n
d
f
o
r
ea
ch
o
f
t
h
e
s
i
x
tr
ai
n
i
n
g
p
o
in
t
s
.
T
h
is
3
D
tr
ain
in
g
d
ata
s
et
f
o
r
ea
ch
f
au
lt
p
r
o
to
t
y
p
e
is
s
av
ed
as
a
lo
o
k
u
p
tab
le
a
n
d
is
s
ca
led
to
u
n
it
y
f
o
r
g
en
er
aliza
tio
n
an
d
p
r
o
v
id
in
g
u
n
i
f
o
r
m
it
y
.
He
n
ce
,
th
e
tr
ai
n
in
g
d
ata
m
atr
ix
,
f
o
r
ea
ch
f
a
u
lt
p
atter
n
tak
e
s
t
h
e
d
im
en
s
io
n
o
f
6
×3
,
ca
lled
as
tr
ain
in
g
d
is
tan
ce
P
C
D
I
m
atr
i
x
af
ter
w
ar
d
s
a
n
d
is
g
i
v
e
n
b
y
D
i
a
s
:
D
i
=
[
P
C
DI
-
A
ij
P
C
DI
-
B
ij
P
C
DI
-
C
ij
]
6
×
3
w
h
er
e,
i=
1
to
1
0
d
ef
in
e
ea
ch
o
f
th
e
te
n
tr
ai
n
in
g
f
au
lt
p
r
o
to
ty
p
es
m
en
tio
n
ed
b
ef
o
r
e
an
d
j
=
1
to
6
d
ef
in
es
t
h
e
s
i
x
tr
ain
i
n
g
g
eo
m
e
tr
ic
d
is
ta
n
ce
s
at
1
0
,
2
0
,
5
0
,
9
0
,
1
3
0
,
an
d
1
4
0
k
m
r
esp
ec
ti
v
el
y
.
Hen
ce
f
o
r
t
h
e
ten
t
y
p
e
s
o
f
f
a
u
lt
s
,
th
er
e
ar
e
ten
s
u
ch
tr
ain
i
n
g
d
is
tan
ce
P
C
D
I
m
atr
ices,
to
g
et
h
er
w
h
ic
h
f
o
r
m
s
th
e
to
tal
tr
ain
in
g
d
is
ta
n
ce
P
C
DI
m
atr
i
x
g
i
v
e
n
b
y
D
TR
AI
N
II
N
G
as:
D
TR
AI
N
II
NG
=[
D
1
D
2
D
3
….
D
10
]
6×
30
P
o
s
t
class
if
icatio
n
o
f
th
e
f
a
u
lt,
th
e
test
P
C
DI
m
atr
i
x
Q
as
f
o
u
n
d
in
th
e
ea
r
lier
s
ec
tio
n
is
s
av
ed
.
Nex
t
t
h
e
D
i
m
atr
i
x
co
r
r
esp
o
n
d
in
g
to
t
h
e
p
ar
ticu
lar
id
en
ti
f
i
ed
t
y
p
e
w
ith
in
d
e
x
i
is
tak
e
n
u
p
f
r
o
m
D
TR
AI
N
II
NG
,
f
o
llo
w
ed
b
y
in
ter
p
o
latio
n
o
f
th
e
tes
t
Q
v
ec
to
r
f
r
o
m
t
h
e
co
r
r
esp
o
n
d
in
g
D
i
u
s
i
n
g
t
h
e
Mu
ltip
le
L
in
ea
r
R
eg
r
es
s
io
n
(
M
L
R
)
m
et
h
o
d
in
o
r
d
er
t
o
p
r
e
d
ict
th
e
g
eo
m
etr
ic
d
i
s
tan
ce
o
f
t
h
e
co
r
r
esp
o
n
d
in
g
f
au
lt.
7.
CASE
S
T
UD
Y
AND
ANA
L
YSI
S
A
ca
s
e
s
t
u
d
y
i
s
s
h
o
w
n
h
er
e
w
it
h
S
L
G
-
A
f
a
u
lt.
T
h
e
v
ar
iat
io
n
o
f
r
ec
eiv
i
n
g
en
d
li
n
e
c
u
r
r
en
ts
w
it
h
v
ar
y
i
n
g
g
eo
m
etr
ic
f
au
lt
d
is
tan
ce
f
o
r
SL
G
-
A
f
a
u
lt
is
s
h
o
w
n
in
F
i
g
u
r
e
7
.
T
h
e
s
am
e
d
ata
is
p
r
o
ce
s
s
ed
th
r
o
u
g
h
th
e
P
C
A
a
lg
o
r
it
h
m
to
p
r
o
d
u
ce
[
P
C
DI
]
an
d
co
n
s
eq
u
en
ce
c
alcu
latio
n
s
.
T
ab
le4
d
escr
ib
es
th
e
ab
s
o
l
u
te
P
C
DI
v
alu
e
s
an
d
t
h
e
co
r
r
esp
o
n
d
in
g
s
ca
led
v
alu
e
s
f
o
r
S
L
G
-
A
f
au
l
t
at
s
ix
tr
ain
in
g
lo
ca
tio
n
s
.
T
h
e
D
SL
G
-
A
m
atr
i
x
is
f
o
r
m
ed
u
s
in
g
t
h
e
P
C
DI
v
al
u
es
as r
ec
o
r
d
ed
in
T
ab
le
4
u
s
in
g
v
alu
e
s
f
r
o
m
co
lu
m
n
2
,
3
,
an
d
4
.
Si
m
i
lar
l
y
,
D
s
ca
led
SL
G
-
A
m
atr
ix
is
f
o
r
m
ed
u
s
in
g
v
al
u
es
f
r
o
m
co
lu
m
n
5
,
6
,
an
d
7
w
h
ic
h
o
n
p
lo
ttin
g
ag
ain
s
t
th
e
r
esp
ec
tiv
e
f
au
l
t
g
eo
m
etr
ic
lo
ca
tio
n
s
,
r
ev
ea
l
a
cu
r
v
ili
n
ea
r
n
atu
r
e
as
s
h
o
w
n
in
F
ig
u
r
e
8
.
I
t
is
o
b
s
er
v
ed
th
at
ea
ch
o
f
t
h
e
f
a
u
lt
t
y
p
e
s
s
h
o
w
d
i
f
f
er
en
ce
i
n
cu
r
v
at
u
r
e
f
o
r
th
r
ee
in
d
i
v
id
u
al
p
h
ases
.
He
n
ce
,
th
e
p
r
o
p
o
s
ed
s
ch
e
m
e
h
as
b
ee
n
d
esi
g
n
ed
w
it
h
m
u
ltip
le
lin
ea
r
r
eg
r
es
s
io
n
(
M
L
R
)
f
o
r
ea
ch
p
r
o
to
ty
p
e
in
d
iv
id
u
all
y
,
w
h
ic
h
ta
k
e
s
in
to
ac
co
u
n
t
all
th
e
th
r
ee
p
h
ase
P
C
DI
s
to
p
r
o
d
u
ce
a
f
air
l
y
ac
cu
r
ate
esti
m
ate
o
f
th
e
f
au
lt
lo
ca
tio
n
.
T
h
e
m
at
h
e
m
ati
ca
l
an
al
y
s
is
o
f
th
e
M
L
R
s
c
h
e
m
e
ad
o
p
ted
h
er
e
is
ex
p
lain
ed
f
ir
s
t
f
o
llo
w
in
g
it
s
ap
p
licatio
n
in
d
esi
g
n
in
g
t
h
e
f
a
u
lt lo
ca
tio
n
p
r
ed
ictio
n
al
g
o
r
it
h
m
[
2
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
n
t J
A
p
p
l P
o
w
er
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n
g
,
Vo
l.
9
,
No
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2
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A
u
g
u
s
t 2
0
2
0
:
1
1
3
–
1
2
6
122
F
ig
u
r
e
7
.
R
e
ce
iv
in
g
en
d
l
in
e
cu
r
r
e
n
t
v
s
.
s
am
p
le
d
t
im
e
p
l
o
t
f
o
r
d
i
f
f
e
r
en
t
g
e
o
m
et
r
i
c
f
au
lt
l
o
c
a
tio
n
s
f
o
r
SL
G
-
A
f
au
lt
T
ab
le
4
.
P
C
DI
f
o
r
A
p
h
ase
to
g
r
o
u
n
d
f
au
lt a
t si
x
d
if
f
er
en
t lo
ca
tio
n
s
F
a
u
l
t
l
o
c
a
t
i
o
n
(k
m)
P
C
D
I
P
C
D
I
(
s
c
a
l
e
d
)
P
h
a
se
A
P
h
a
se
B
P
h
a
se
C
P
h
a
se
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h
a
se
B
P
h
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se
C
10
7
.
4
4
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3
0
3
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3
9
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9
9
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0
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2
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3
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1
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9
2
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7
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1
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1
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3
1
1
1
Fig
u
r
e
8
.
Geo
m
e
tr
ic
f
a
u
lt d
is
t
an
ce
v
s
.
P
C
DI
(
s
ca
led
)
p
lo
t f
o
r
th
r
ee
p
h
ase
r
ec
eiv
i
n
g
en
d
li
n
e
cu
r
r
en
ts
f
o
r
SL
G
-
A
f
a
u
lt a
t si
x
tr
ai
n
in
g
lo
c
atio
n
s
8.
AP
P
L
I
CA
T
I
O
N
O
F
M
UL
T
I
P
L
E
L
I
N
E
AR
R
E
G
RE
SS
I
O
N
(
M
L
R)
P
r
in
cip
al
co
m
p
o
n
en
t
an
al
y
s
is
(
P
C
A
)
as
e
x
p
lai
n
ed
s
o
f
ar
,
its
elf
i
s
an
i
m
p
o
r
ta
n
t
a
n
d
ef
f
ec
ti
v
e
to
o
l
i
n
o
r
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er
to
r
e
d
u
ce
a
lar
g
e
n
u
m
b
e
r
o
f
m
u
lti
v
ar
iate
d
ata
to
a
f
e
w
p
r
i
m
ar
y
d
ir
ec
tio
n
s
o
f
m
aj
o
r
v
ar
iatio
n
.
T
h
e
th
r
ee
d
if
f
er
e
n
t
p
h
ase
s
o
f
P
C
DI
h
av
e
d
if
f
er
en
ce
i
n
c
u
r
v
a
tu
r
e
w
h
ich
is
w
ell
o
b
s
er
v
ed
f
r
o
m
F
i
g
u
r
e
1
0
.
T
h
is
is
f
u
r
t
h
er
ex
ten
d
ed
f
o
r
all
te
n
d
i
f
f
er
en
t
f
a
u
lt
p
atter
n
s
.
T
h
e
t
h
r
ee
p
h
ase
P
C
DI
f
o
r
ea
ch
p
atter
n
,
is
p
r
o
ce
s
s
ed
b
y
th
e
p
r
o
p
o
s
ed
ML
R
b
ased
s
c
h
e
m
e
to
ac
h
ie
v
e
a
s
in
g
le
co
m
p
u
ted
d
ir
ec
tio
n
o
f
v
ar
iatio
n
,
ta
k
i
n
g
in
to
ac
co
u
n
t
all
th
e
th
r
ee
cu
r
v
at
u
r
es
f
r
o
m
t
h
e
th
r
ee
p
h
ases
w
h
ic
h
is
f
i
n
all
y
tak
en
as
th
e
tr
ain
in
g
d
ata
f
o
r
th
e
p
r
o
p
o
s
ed
f
au
lt
d
is
tan
ce
p
r
ed
icto
r
alg
o
r
ith
m
.
R
eg
r
es
s
io
n
a
n
al
y
s
is
i
s
an
i
m
p
o
r
tan
t
s
tati
s
tical
to
o
l
to
d
eter
m
in
e
t
h
e
r
elatio
n
s
h
ip
,
ca
lled
th
e
r
eg
r
ess
io
n
f
u
n
ctio
n
,
b
et
w
ee
n
a
d
ep
en
d
en
t
v
ar
iab
le
‘
y
’
,
an
d
a
s
in
g
le
o
r
s
e
v
er
al
in
d
ep
en
d
en
t
v
ar
iab
les
‘
x
i
’
.
R
eg
r
es
s
io
n
f
u
n
ctio
n
also
in
v
o
lv
e
s
a
s
et
o
f
u
n
k
n
o
w
n
p
ar
a
m
eter
s
‘
b
i
’
,
c
alled
th
e
r
eg
r
ess
io
n
co
ef
f
icie
n
t
s
.
A
s
i
m
p
le
lin
ea
r
r
eg
r
ess
io
n
m
o
d
el
is
d
escr
ib
ed
as
:
Evaluation Warning : The document was created with Spire.PDF for Python.