TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3994 ~ 40
0
1
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4332
3994
Re
cei
v
ed O
c
t
ober 1
7
, 201
3; Revi
se
d Decem
b
e
r
23, 2013; Accept
ed Ja
nua
ry 1
2
, 2014
An Effe
ctive Method to Improve Electronic Equipment
Condition Monitoring Based on KPCA-EDA and MMSH-
SVDD
Yang Sen, Meng Ch
en, Lv
Meng
Dep
a
rtment of Missile En
gi
ne
erin
g, Ordnanc
e Engi
ne
erin
g Coll
eg
e
Shiji
azh
u
a
ng, Heb
e
i, Chi
na, 050
00
3
A
b
st
r
a
ct
In ord
e
r to
i
m
prove
the
val
i
d
ity of
electr
o
n
ic
equ
ip
ment
con
d
itio
n
mo
nitori
ng, ov
erc
o
me th
e
shortag
e
of n
o
rmal KPCA (
K
erne
l Princ
i
p
a
l Co
mp
o
nent
Analysis)
an
d SVDD (Su
p
port Vector D
a
t
a
Descripti
on)
monitor
i
ng
mo
de
l, a
met
hod
o
n
el
ectronic
eq
u
i
p
m
e
n
t con
d
iti
on
monitor
i
n
g
base
d
o
n
KP
C
A
-
EDA (KPCA- Estim
a
tion of Distribution Algorit
hm
) and MMSH-SVDD (Maxim
a
l Margin
S
e
parating
Hypers
pher
e S
V
DD Mod
e
) is
put forw
ard. F
i
rstly, the fe
a
t
ure of ori
g
in
al
mo
nitori
ng
da
ta is extracted
by
KPCA-EDA algorithm
,
and a
group
of features with eno
ugh
state identifying infor
m
ation are obtained; then
the MMSH-SV
DD
mod
e
l is t
r
ain
ed by th
e
nor
mal st
ate
a
nd a
little b
i
t of fault state features, a
nd t
h
e
unkn
o
w
n
state feature is ap
p
lied to
the trai
ned
mo
del; F
i
nally, a filter
ci
rcuit is taken
as an exa
m
ple
in
simulati
ons, th
e result sh
ow
s that this method is
th
e
effective meth
od i
m
pr
ove th
e perfor
m
a
n
ce
of
electro
n
ic eq
ui
pment con
d
iti
o
n mo
nitor
i
ng.
Ke
y
w
ords
: PC
A-EDA, MMSH-SVDD, electro
n
ic eq
uip
m
ent, cond
ition
mo
nit
o
rin
g
, meth
od
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
There a
r
e
many
kind
s of el
ectron
ic e
qui
p
m
en
t in el
ectro
n
ic fiel
d, a
nd thei
r
cha
r
a
c
teri
stics a
r
e
differe
nt, most of
the exis
ting
literatures
re
sea
r
che
s
o
n
the ele
c
tro
n
ic
equipm
ent fa
ult diag
no
sis
sho
w
little
co
nce
n
trate
on
circuit
con
d
ition mo
nitori
ng
. But actu
ally in
the pro
c
e
ss
of circuit ope
ration, we n
eed to
monitor the circuit
state online
and pay more
attention to t
he h
ealth
de
grad
ation
of the
circuit,
so
as to ju
dge
the a
c
tual
he
alth state
of t
he
c
i
rc
uit [1, 2].
Starting fro
m
the p
o
int o
f
electroni
c
equipm
ent
condition
mon
i
toring, a
m
onitorin
g
method
ba
se
d on
KPCA-E
D
A a
nd M
M
SH-SVDD is p
u
t forward in
the p
ape
r. Fi
rst, it ado
pts EDA
(Estimation
of Dist
ributio
n Algorith
m
) to
ch
oose
the KPCA
prin
cipal
compon
ent fe
ature
informatio
n, so a
s
to reta
in more i
dent
ifying informa
t
ion unde
r th
e pre
m
ise
of adequ
ate st
ate
feature i
n
formation; an
d t
hen
on th
e b
a
si
s
of t
r
aditi
onal SV
DD, t
he MMS
H-S
V
DD
monito
ri
ng
model
i
s
pro
posed acco
rding
to
the sample dat
a
a
fter the featu
r
e extractio
n
. The
mod
e
l
can
make
s a t
r
ad
e-off b
e
twe
e
n
the
minim
u
m volume
d
e
s
cription
a
n
d
the m
a
ximu
m cl
ass i
n
terval,
increa
se the
gene
rali
zati
on ability of the model; t
he filter ci
rcu
i
t is taken
a
s
the exampl
e in
simulatio
n
s, the analy
s
is result
s sh
ow t
hat the metho
d
is effective.
2. Featur
e Extra
c
tion
Ba
sed on KP
CA-E
DA
The feature
extraction al
gorithm ba
se
d on KPCA is a nonlin
ea
r prom
otion to PCA
(Prin
c
ipal
Co
mpone
nt Ana
l
ysis) [3], wit
h
high a
b
ility of nonline
a
r
feature extra
c
tion, and it
has
been wi
dely use
d
in pattern re
cog
n
itio
n field. But it still has sh
o
r
tcomi
n
g
s
in the pro
c
e
ss
of
feature extra
c
tion,
du
ring
the
analy
s
is pro
c
e
ss;
KP
CA takes
all
of the sampl
e
s a
s
a
whol
e and
see
k
di
re
ctio
n with maxim
u
m divergen
ce. Ho
wever, i
n
many
case
s the di
re
ctio
n with maxim
u
m
diverge
n
ce i
s
not
con
s
i
s
te
nt with th
e i
d
entificatio
n
of
the m
o
st fav
o
rabl
e di
re
cti
on [4]. Th
erefore,
it is ne
ce
ssa
r
y to sel
e
ct t
he pri
n
ci
pal
comp
one
nt o
b
tained
after KPCA, with
the pu
rpo
s
e
o
f
improvin
g the
sample
re
co
gnition rate [5
, 6].
In this
pap
er,
the featu
r
e
e
x
traction
process of
the monitoring data, it firs
tly uses
KPCA
algorith
m
to
extract the
fe
ature
of o
r
igi
nal
sampl
e
s,
the la
rge
r
n
e
igenvalu
e
s (
nN
,
N
is
the
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Effective Method to Impro
v
e Ele
c
tro
n
ic Equipm
en
t Condition M
onitorin
g
… (Y
ang Sen
)
3995
total numb
e
r of sample
s) and
corre
s
p
ondin
g
eig
e
n
v
ectors a
r
e
obtaine
d thro
ugh
solvin
g t
h
e
nucl
ear
matri
x
cha
r
a
c
teri
stic eq
uation; T
hen a
c
co
rdin
g to some
cri
t
eria, it ado
pts EDA to
sel
e
ct
the eig
enve
c
tors, t
he p
r
in
cipal
comp
one
nt com
b
inatio
n with
optim
al ide
n
tifiable
inform
ation i
s
obtaine
d; Finally, the proje
c
ting monito
ri
ng data to
this prin
cip
a
l co
mpone
nt and
the final feature
data are g
o
t. The algo
rithm
sch
ematic i
s
as sho
w
n in
Figure 1.
Figure 1. Fea
t
ure Extractio
n
Process Ba
sed
on KPCA-EDA
Figure 2. Co
mpari
s
o
n
of EDA and GA
2.1. Principle of EDA Alg
o
rithm
EDA algo
rith
m is
pro
p
o
s
ed a
s
a
ne
w type of i
n
telligent o
p
timization
me
thod by
M
uhle
nbe
in
in 1996. Th
ere a
r
e no
cro
s
sove
r an
d mutation o
peratio
ns in
the distrib
u
te
d
estimation al
gorithm a
nd the tradition
al geneti
c
algo
ri
thm [7-10].
The ba
si
c id
ea of EDA al
gorithm i
s
th
at, in
the first step, a po
rt
ion of individ
uals
are
prefe
rre
d fro
m
the curren
t population
and ge
nerate
s
statisti
cal i
n
formatio
n a
c
cordi
ng to these
prefe
rre
d ind
i
viduals, its prob
ability distribut
io
n is
estimated; T
hen the nex
t generatio
n
of
individual
s ta
king
is produ
ced
a
c
cordi
n
g to the
adva
n
tage
of this
prob
ability di
stributio
n. E
D
A
algorith
m
and
genetic al
gorithm are com
pare
d
as
sho
w
n in Figu
re
2.
2.2. Featur
e Extrac
tion Algorithm Bas
e
d on KPCA-EDA
The main
ste
p
s of the feature extra
c
tion
algorithm b
a
s
ed o
n
KPCA-EDA are as f
o
llows:
Step 1 is to
prod
uce initi
a
l pop
ulation
(0
)
l
Dl
. Use KP
CA
algorith
m
to
analyze the
prin
cipal
co
m
pone
nt of mo
nitori
ng
data i
n
feature spa
c
e, an
d
N
eigen
values and correspon
ding
eigenve
c
tors
r
are obtai
ne
d, whe
r
e
1,
2
,
rN
(
N
is the total number of mo
n
i
toring data
sampl
e
s). Th
en the eigen
values a
r
e sorted in de
scen
ding o
r
de
r, and the eigenve
c
tors a
r
e
cho
s
e
n
whi
c
h
are corre
s
po
nding to the l
a
rge
r
()
nn
N
eigenv
alue
s as th
e can
d
idate p
r
i
n
cip
a
l
c
o
mponent. If we set
1
(,
,
)
n
KP
a
a
and
1
(,
,
)
n
KP
diag
, and ta
ke
s
(1
,
2
,
)
r
rn
a
s
the
rand
om varia
b
le, and the
initial populat
ion
0
D
of M individuals
will b
e
gene
rated.
The bina
ry
encodin
g
wa
y is obtained
in encodi
ng
the
n
eigenve
c
tors
r
, every
cod
e
bit represe
n
ts that
wheth
e
r the
corre
s
p
ondin
g
eigenve
c
to
r has b
een
se
lecte
d
or no
t, 1 denotes
it is sele
cted,
0
denote
s
it i
s
unsele
c
ted. T
he le
ngth
of coding
is n, a
n
d
the
pro
babil
i
ty of the vari
able i
s
1 o
r
0
is
the same d
u
ri
ng the initial popul
ation proce
s
s.
Step 2 i
s
the
Cal
c
ul
ation
of the fitne
ss, and
choo
si
ng the
ex
cell
ent individ
ual
Se
l
D
. The
desi
gn of fitness function i
s
the key of KPCA-ED
A a
l
gorithm, the excelle
nt individual is ch
o
s
en
in the statisti
cal an
alysi
s
i
n
gene
ratin
g
new
sam
p
le
s. In KPCA-EDA algo
rith
m, we ne
ed
to
con
s
id
er both
the identifica
t
ion ability and adeq
uate
informatio
n co
ntent, so the fitness fun
c
ti
on
is de
sign
ed a
s
follows:
()
()
ii
i
f
itn
e
s
s
J
KP
F
K
P
(1)
princip
a
l
co
m
po
n
e
n
t
KPC
A
Sa
mple
1
Sa
mple
2
.
.
.
Sa
mple
N
.
.
.
ED
A
.
.
.
()
nn
N
n
KP
k
KP
2
KP
1
KP
2
KP
1
KP
()
kk
n
dimension
s
dimension
s
princip
a
l
co
m
po
n
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3994 – 40
01
3996
W
h
er
e
()
i
J
KP
repre
s
ent th
e id
e
n
tification
abi
lity of the
ch
ose
n
ei
genv
ectors,
()
i
J
KP
represent the information
contain ability.
Thro
ugh equ
ations we kn
ow
that
afte
r feat
ure extra
c
tion throug
h
KPCA, every sample
j
i
x
is cha
nge
d a
c
cordi
ng to
()
(
)
()
(
)
j
rT
j
r
T
j
T
j
ii
i
i
xw
x
K
P
,
the ce
nt
re of
cla
ss j s
a
mpl
e
s
j
m
will
be satisfi
ed with
()
(
)
(
)
rT
F
r
T
T
j
jj
j
mw
m
K
P
, and t
he
centre of t
he
whol
e
sa
mples
m
is
turned into
()
()
(
)
rT
F
r
T
T
mw
m
K
P
.
As the
p
r
o
c
e
s
s of
co
nditio
n
mo
nitorin
g
is b
a
sed
on
cla
ssifi
cation
ideolo
g
y in
e
s
sen
c
e,
the criteri
on
based
on di
stance
in
cla
s
sificatio
n
defi
n
ition i
s
intro
duced. In th
e
pap
er,
we t
a
ke
()
i
J
KP
as th
e
within
-cla
ss a
nd th
e cl
ass di
stan
ce
cr
ite
r
ion, t
he former is
repre
s
e
n
ted
b
y
within–
cla
ss sc
at
t
e
r
mat
r
ix
w
S
, and the latter is repre
s
e
n
ted b
y
between
-cl
a
ss scatter
matrix
b
S
. The
expre
ssi
on of
the criteri
on
based on
within-cla
ss a
n
d
betwee
n
-cla
ss di
stan
ce i
s
as follows [1
2]:
()
(
)
/
(
)
ib
w
J
KP
tr
S
t
r
S
(2)
Among them,
1
1
()
(
)
c
T
bj
j
j
j
SN
m
m
m
m
N
(3)
11
1
()
(
)
j
N
c
j
jT
wi
j
i
j
ji
Sx
m
x
m
N
(4)
Whe
n
the
value of
1
()
J
KP
an
d
2
()
J
KP
are
almost the
same, the i
n
dividual
corre
s
p
ondin
g
to the
large
r
eig
envalu
e
sho
u
ld
be
ch
ose
n
, which i
n
clu
d
e
s
the
l
a
rge
r
amou
nts of
informatio
n. So the functio
n
()
i
FK
P
is desi
gne
d as follo
ws:
()
()
e
,
0
,
0
1
ab
i
FK
P
a
b
(5)
Whe
r
e
11
()
/
(
)
mn
ik
j
kj
, m indicate
s the
n
u
mbe
r
of ch
ose
n
eig
env
ectors, n i
s
t
h
e
length of cod
e
size, whi
c
h
is the num
b
e
r of c
andid
a
t
e eigenve
c
to
rs; b rep
r
e
s
e
n
ts the threshold
of
; a repre
s
e
n
ts the adju
s
tment coeffici
ent,
which i
s
use
d
to adjust the weight of
()
i
F
KP
in the
whol
e fitness function.
After de
sign
pro
c
e
s
s of th
e fitness fun
c
tion, the
num
ber
()
Se
Se
M
of individu
als
are
sele
cted, u
s
u
a
lly the fittest
one
s.
Step 3 is to b
u
ild the prob
a
b
ility model
()
l
p
x
according to the
excellent indi
vidual. Since
the eige
nvect
o
rs bet
wee
n
each ot
he
rs
are
statisti
cal
l
y unco
r
relate
d, the UM
DA
algo
rithm wit
h
indep
ende
nt variable i
s
chosen as the
EDA probab
ility model. Every margin
a
l
distributio
n is
deci
ded by th
e freque
ncy o
f
1 in every bit l. T
he proba
bility distributi
on is a
s
follo
ws [13]:
1
11
(|
)
()
(
|
)
(
)
Se
Se
ji
i
l
nn
j
Se
ll
l
i
ii
Xx
D
px
p
x
D
p
x
Se
(6)
Whe
r
e,
1
1,
(|
)
0,
Se
ii
Se
ji
i
l
j
X
x
Xx
D
ot
he
r
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Effective Method to Impro
v
e Ele
c
tro
n
ic Equipm
en
t Condition M
onitorin
g
… (Y
ang Sen
)
3997
Step 4 i
s
the
random
samp
ling. After M
t
i
mes sampling from
probability vector
()
l
px
, the
new g
ene
rati
on pop
ulation
1
l
D
is obtain
ed.
Then the fitn
ess value of
each ne
w ind
i
vidual ca
n
be cal
c
ul
ated
.
Step 5 i
s
the
terminatio
n
condition j
udg
ment. If a termination
co
n
d
ition i
s
satisf
ied, it will
go to next step; Else
1
ll
, and turn ba
ck to st
ep 2.
Step 6 is to output re
sults.
The pop
ulatio
n
1
l
D
is the soluti
on.
The algo
rithm
flow is sh
own in Figure 3.
Figure 3. The
Flow of Algorit
hm
Figure 4. MMSH-SVDD M
odel
3. Condition
Monitoring
Bas
e
d on M
M
SH-SVDD
The bet
wee
n
-cl
a
ss ma
rgin and
within-cla
ss
co
hesi
on are
two impo
rta
n
t factors
impactin
g
on
the perfo
rm
ance of cla
ssifiers [14
]. No
rmal SVDD
model o
n
ly take the l
a
rg
e
s
t of
within-cla
ss i
n
to con
s
ide
r
a
t
ion, and
do
e
s
n
o
t ta
ke th
e bet
wee
n
-cl
a
ss ma
rgi
n
i
n
to a
c
count [
15,
16]. In this se
ction, we
con
s
ide
r
both fa
ctor
s a
bove a
nd put forward a new SV
DD mod
e
l ba
sed
on maximal
margi
n
se
parating hypersp
her
e, which is sho
w
n in Fig
u
re 4.
Two co
ncentric sup
r
a
s
ph
eres of
differe
n
t
radi
us
a
r
e bu
ilt, th
e
ta
r
get s
a
mp
le
s a
r
e in
th
e
small
one
a
nd n
on-ta
rge
t
sampl
e
s a
r
e o
u
tsid
e t
he big
on
e. Make
sure
that the
small
sup
r
a
s
ph
ere is minimi
zed,
and the dist
ance betwee
n
target an
d non-ta
rg
et sa
mples i
s
larg
est,
while the g
e
n
e
rali
zation a
b
ility of
the model is imp
r
ov
ed.
The re
alizatio
n pro
c
e
ss of
the model is
as
follo
ws, first make the assumptio
n
that two
cla
s
ses t
r
aini
ng sample
s
are
11
(,
)
,
,
(
,
)
,
,
{
1
,
1
}
n
ll
xy
xy
x
R
y
, whe
r
e t
he nu
mbe
r
o
f
target
sampl
e
s a
r
e
m, non
-target
sa
mple
s
are
n, the
total n
u
mbe
r
i
s
()
ll
m
n
. Th
roug
h
nonlin
e
a
r
mappin
g
, the traini
ng
sa
mples a
r
e
projecte
d to th
e hig
h
dim
e
n
s
ion
feature
spa
c
e, i
n
whi
c
h
two con
c
ent
ric sup
r
a
s
phe
res
1
S
and
2
S
of
different radi
us are built,
the centre
of sph
e
re
s
i
s
a,
and th
e radiu
s
i
s
1
R
and
2
R
12
()
RR
,
1
H
an
d
2
H
are th
e b
ound
ary
surf
ace
of
1
S
and
2
S
,
d
is
the distan
ce
betwe
en
1
H
and
2
H
. The optimal
goal is to mini
mize
1
S
and ma
ximize
d
.
As shown in
Figure 4,
the betwe
en-cla
s
s
ma
rgin
21
dR
R
, maximized d i
s
equivalent
to maximized
2
R
and mi
nimized
1
R
, or maximized
2
2
R
and
mini
mized
2
1
R
. Then
the optimization
probl
em can
be de
scribe
d as:
22
12
1
2
11
mi
n
mn
ij
ij
RR
C
C
(8)
22
1
||
(
)
||
ii
xa
R
1
im
(9)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3994 – 40
01
3998
22
2
||
(
)
||
jj
xa
R
1
j
n
(10)
Whe
r
e
is the trade-off pa
rameter of rad
i
us, whi
c
h is
use
d
to comp
romi
se
2
1
R
and
2
2
R
;
,
ij
are the sla
c
k variabl
e;
12
,
CC
are the pe
na
lty coefficient
;
1
R
is the ra
diu
s
of the sma
ll
sup
r
a
s
ph
ere and
2
R
is the big one.
In orde
r to sol
v
e the optimization p
r
obl
e
m
in (8)~(10),
we co
nst
r
uct
the Lagra
ngi
an:
22
2
12
1
2
1
11
1
22
2
2
1
11
[
(
()
()
2(
)
)
]
[
(
(
)
(
)
2
(
)
)
]
mn
m
ij
i
i
i
i
ij
i
n
ij
j
j
j
j
j
mn
ii
j
j
ij
L
RR
C
C
a
R
x
x
ax
a
a
R
x
x
a
x
a
(11)
We set the partial de
rivatives to zero, and u
s
e ke
rn
el function
(,
)
ij
kx
x
to repla
c
e th
e
inner p
r
o
d
u
c
t
()
(
)
ij
x
x
, the quadratic dual pro
b
lem
of the optimization p
r
obl
e
m
is as follo
ws:
11
1
1
11
1
1
1
mi
n
(
,
)
(
,
)
[
(
,
)
1
(,
)
2
(,
)
]
mn
m
m
ii
i
j
j
j
i
k
i
k
ij
i
k
nn
m
n
ip
i
p
i
j
i
j
jp
i
j
ak
x
x
a
k
x
x
a
a
k
x
x
aa
k
x
x
a
a
k
x
x
(
1
2
)
12
11
.
.
,
1
,0
,0
mn
ij
i
j
ij
s
ta
a
a
C
a
C
(13)
Thro
ugh
solv
ing Equation
(12) a
nd (1
3), we
can g
e
t
i
a
and
j
a
. Acco
rding to relat
ed
con
d
ition, the large fra
c
tion
of the weights
i
a
and
j
a
turns to 0, only a fe
w non
-zero
weights a
r
e
calle
d the su
pport vecto
r
s (SVs).
Whe
n
1
0
i
aC
, the SVs are
on
1
H
, which i
s
the b
ound
ary surf
ace of
1
S
, by usi
ng any
SV
()
k
x
we
can g
e
t radiu
s
1
R
:
22
1
||
(
)
||
k
Rx
a
(14)
Whe
n
2
0
j
aC
, the SVs a
r
e o
n
2
H
, which i
s
th
e b
o
unda
ry surfa
c
e of
2
S
, by usin
g any
SV
'
()
k
x
we
can g
e
t radiu
s
2
R
:
2'
2
2
||
(
)
||
k
Rx
a
(15)
Acco
rdi
ng to (14
)
and (15
)
, we ca
n get the final radi
u
s
R
as
shown in (16).
12
2
RR
R
(16)
I
f
we as
sum
e
t
he t
e
st
sa
m
p
le is
z,
t
hen
if
|(
)
|
|
za
R
, z is the target
sam
p
le
; and if
|(
)
|
|
za
R
, z will be the non-ta
rg
et sa
mple.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Effective Method to Impro
v
e Ele
c
tro
n
ic Equipm
en
t Condition M
onitorin
g
… (Y
ang Sen
)
3999
4. Simulation
The biq
uad
ra
tic filter ci
rcui
t as an
exam
ple in
the
si
mulation, the
circuit i
s
a
s
sho
w
n i
n
Figure 5. T
h
e
amplitud
e of
freque
ncy
poi
nts in
amp
litu
d
e-frequ
e
n
c
y respon
se
curves i
s
ta
ken
a
s
the candid
a
te
feature
s
,
sa
mpling i
n
terv
al is i
n
[10
0
Hz, 10K
Hz]. T
he total
cha
r
acteri
stic nu
mber
is 21, and the
amplitude
-fre
quen
cy re
spo
n
se
curv
e of
norm
al output
is sho
w
n in F
i
gure 6.
Figure 5. Biquadratic Filter Circuit
Figu
re 6. Amplitude-f
r
eq
ue
ncy Re
sp
on
se
Curve of Normal Output
Thro
ugh th
e
sen
s
itivity analysis,
we fin
d
that the
ch
angin
g
of
1
R
an
d
2
C
c
a
n
in
flue
nc
e
the output voltage of the circuit. If we sup
pose that
the singl
e
soft fault is happe
n
e
d in the circuit,
inclu
d
ing no
f
ault,
1
R
,
2
C
positive
and
negative
50%, the tota
l is fi
ve
state t
y
pes. Th
e typ
e
of e
a
ch
singl
e soft fault is sho
w
n i
n
Table 1.
Table 1. Type
of Single Soft Fault
Num Fault
t
y
pe
F1
NF
F2
1
15
Rk
F3
1
5
Rk
F4
2
30
Cn
F
F5
2
10
Cn
F
In the Simul
a
tion, the
no
rmal
state
of
this
ci
rcuit
i
s
simul
a
ted by
Monte
-
Ca
rlo.
Th
e
numbe
r of th
e total origin
al sam
p
le
s is 780, and th
e dimen
s
io
n of them is 2
1
. Choo
sin
g
2/3
sampl
e
s of e
a
ch
state to
form the
traini
ng sampl
e
se
ts, the rest of
them i
s
take
n as the te
sti
ng
sampl
e
set
s
.
4.1. Featur
e Extrac
tion Based on
KPCA-EDA
KPCA-EDA a
l
gorithm i
s
ap
plied in extra
c
ting t
he feat
ure of the sa
mple set
s
. Th
e step of
feature extra
c
tion is as follo
ws:
Step 1: Choo
se RBF fun
c
ti
on as the
kernel functio
n
(,
)
ij
kx
x
of the s
a
mples [17].
Thro
ugh
cal
c
ulating kern
el
matrix K, the
n
we can get
K
, and the ke
rn
el para
meter
0.5
.
Table 2. Ca
n
d
idate Eigenv
alue
s
Num eigenvalues
Num
eigenvalues
1 10.692
8
0.7089
2 5.4723
9
0.4775
3 3.1001
10
0.2601
4 2.9716
11
0.1438
5 1.2631
12
0.0902
6 1.1433
13
0.0323
7 0.9898
R1
10
k
R2
10
k
R3
10
k
R4
10
k
R5
10
k
R6
10
k
C1
20
n
C2
20
n
0
+
-
OU
T
U1
O
PAM
P
+
-
OU
T
U2
O
PAM
P
+
-
OU
T
U3
O
PAM
P
0
0
Vi
Vo
0
V1
1V
ac
0V
dc
V
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
0
46
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3994 – 40
01
4000
Step 2:
Cal
c
ulate the
eig
envalue
s
and
co
rrespon
di
ng ei
genve
c
t
o
rs of
K
.we tak
e
the
eigenve
c
tors which accumulating
contributio
n
rate is 98%
as the ca
ndidate p
r
in
cipal
eigenve
c
tors
(the total nu
mber
of them
is 13
).
The
correspon
ding
can
d
idate ei
genvalu
e
s are
as
sho
w
n in Ta
b
l
e 2.
Step 3: Taki
ng the candi
date eige
nve
c
tors
a
s
the
rand
om vari
able
s
, and t
h
e initial
popul
ation is
0
D
. Thro
ugh bi
n
a
ry en
codi
ng
way to en
cod
e
it, and the length of codi
ng is 1
3
, and
the numbe
r o
f
initial popula
t
ion is 150.
Step 4: Cho
o
se th
e exce
llent eigenve
c
tors
by EDA. The fitness fun
c
tion of
EDA is
10
(
0
.98
)
()
e
,
i
FK
P
whe
r
e
10
,
0
.9
8
ab
. The
relation
shi
p
betwe
en th
e
iteratio
ns a
nd ave
r
a
ge
fitness of ea
ch gene
ration i
s
as
sho
w
n in
Figure 7.
Figure 7. Rel
a
tionship
s
be
tween Iteratio
n
and Avera
g
e
Fitness
From
Figu
re
7 we
ca
n
se
e that th
e gl
o
bally optimal
solutio
n
i
s
o
b
t
ained
after
1
9
time
s
iteration
sim
u
lation, an
d
the corre
s
po
nding fitne
ss value i
s
3.
8735. T
h
e
b
e
st in
dividual
is
1110
0110
010
10, whi
c
h i
n
dicate
s that t
he eig
enve
c
to
rs of num
b
e
r 1, 2, 3, 6
,
7, 10, 12
are
s
e
lec
t
e
d
;
the to
ta
l se
lec
t
ed
e
i
ge
n
v
ec
to
rs
ar
e 7
.
T
h
e
n
calculating
the a
c
cumula
ting contrib
u
tion
rate of
this eigenve
c
tor combi
nation,
the re
su
lt i
s
93%,
whi
c
h
is
gen
eral
conform
ed to
th
e
requi
rem
ents.
Step 5: Proje
c
t the trainin
g
sampl
e
and t
e
stin
g
sam
p
l
e
to the ch
osen eige
nvect
o
rs, a
nd
then the final feature trai
nin
g
sets a
nd fe
at
ure te
st set
s
by Equation
(10) a
r
e got.
4.2. Conditio
n
Monitoring
Based o
n
MMSH-SVDD
The feature t
r
ainin
g
set
s
are u
s
ed in trainin
g
MMSH-SVDD mo
del and no
rm
al SVDD
model,
th
e KPCA
an
d KPCA-EDA are
al
so obt
ained, and
then
te
sting
of
the co
ndi
t
ion
monitori
ng ab
ility of
the models i
s
made
throug
h usi
n
g
feature testin
g sets.
The pa
ram
e
ters
are cho
s
en
by 10 f
o
ld cro
ss va
lidation meth
od, and th
e
model
perfo
rman
ce i
s
evaluate
d
b
y
accu
ra
cy test. The test re
sults a
r
e
sho
w
n in Tabl
e 3
.
Table 3. Te
st Re
sults
Model
Feature
ext
r
action
Accur
a
cy
SVDD
KPCA
92.31%
KPCA-EDA
94.23%
MMSH-SVDD
KPCA
94.62%
KPCA-EDA
97.69%
From Ta
ble 3
,
we can se
e
that by us
ing MMSH-SV
DD mo
del an
d KPCA-EDA
feature
extraction al
g
o
rithm, the accuracy of test
ing sa
mple sets
is
the highes
t which is
about 97.6
9
%
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An Effective Method to Impro
v
e Ele
c
tro
n
ic Equipm
en
t Condition M
onitorin
g
… (Y
ang Sen
)
4001
5. Conclusio
n
In this
pap
er,
it analy
z
e
s
t
he el
ectroni
c equi
pment
condition
moni
toring
metho
d
ba
se
d
on KPCA-E
D
A and MM
SH-SVDD. Aiming at the sho
r
tag
e
of KPCA lack
of identifyin
g
informatio
n,
EDA is u
s
ed
to
choo
se
t
he p
r
in
ci
ple
comp
one
nt f
u
rthe
r, so
as to redu
ce
the
cha
r
a
c
teri
stic dimen
s
io
n, a
nd retain
more ide
n
tifying i
n
formatio
n; in
ord
e
r to
solv
e fitting p
r
obl
em
of normal SV
DD, a few no
n-target sam
p
les a
r
e im
po
rted to the model traini
ng
pro
c
e
ss, an
d the
con
d
ition m
o
nitoring
mod
e
l
based
on M
M
SH-SVDD i
s
b
u
ilt. Finally, a filter ci
rcui
t is taken
as
an
example
to v
a
lidate th
e i
m
prove
d
al
g
o
rithm
s
; the
result
sho
w
s that the
pe
rforman
c
e
of
this
method is m
o
re effective th
an normal SVDD a
nd KPCA.
Referen
ces
[1]
Sun Zhi
x
i
n
, L
i
Zili.
T
he w
o
rld e
l
ectron
ic
informatio
n
equ
ip
me
nt.
Beiji
ng: Defe
ns
e T
e
chnolo
g
y
Publ
ishi
ng. 20
01: 15-2
8
.
[2]
Ma Sasa, Che
n
Guoshu
n, F
A
NG Xin
gqi
ao.
Rese
arch on P
r
ogn
ostic and
Healt
h
Mana
ge
ment S
y
stem
of Compl
e
x Eq
uipm
ent.
Co
mp
uter Measur
en
me
nt & Control
.
2010; 18(
1): 1-4.
[3] Jolliffe
IT
.
Principal c
o
mpo
n
e
n
t analys
is.
Spring
er Series i
n
Statistics, Springer, seco
nd e
d
itio
n.20
02.
[4
]
C
a
o L
J
, Ch
ua
KS, C
h
on
g WK. A co
mpa
r
i
s
o
n
o
f
PC
A, KPC
A
an
d IC
A for d
i
me
n
s
io
na
l
i
t
y
re
du
cti
o
n i
n
supp
ort vector machi
ne.
Neur
oco
m
p
u
ting.
2
003; 55: 3
211-
336.
[5]
Johns
on RA, W
i
chern DW
.
Appl
ied
Multiv
ariate St
atistic
a
l An
alysis.
N
e
w
York: Pr
en
tice Ha
ll. 2
0
0
1
:
55-7
4
.
[6]
Xi
a Guo
en. C
u
stomer chur
n
predicti
on o
n
kern
e
l
princ
i
p
a
l
compo
n
e
n
t anal
ysis fe
ature
abstraction
.
Co
mp
uter Appl
icatio
ns.
200
8; 28(1): 14
9-1
5
1
.
[7]
W
ang
Xi
nfen
g, Qiu Ji
ng, LIU
G
uanj
un. R
e
s
earch
on F
a
ult
F
eature E
x
tra
c
tion Bas
e
d
o
n
Kern
el K-
L
T
r
ansformation.
Mechanic
a
l S
c
ienc
e an
d T
e
chno
logy.
2
006;
25(3): 288-
29
1.
[8]
Na Ch
en, Sha
opu Ya
ng, C
u
nzhi Pa
n.
App
licatio
n of F
a
u
l
t Detection
b
a
sed o
n
H
y
br
i
d
Intelli
ge
nt
Methods
. Indo
nesi
an Jo
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