TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4258 ~ 4
2
6
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.141
9
4258
Re
cei
v
ed Se
ptem
ber 12, 2013; Revi
se
d De
ce
m
ber
11, 2013; Accepted Janu
ary 14, 201
4
Improved Compressed
Sensing Matrixes for Insulator
Leakag
e Current Data Compressing
Zhai Xueming*
1
, You Xia
obo
2
, De
w
e
n
Wang
3
Dep
a
rtment of Contro
l and C
o
mputer Eng
i
n
e
e
rin
g
,North Ch
ina El
ectric Po
w
e
r Univ
ersit
y
,
No. 689 H
u
a
d
i
an Ro
ad, Bao
d
i
ng Cit
y, He
bei
Provinc
e
, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zxm31
6
5
@
1
26.com
1
, ui
yu2
2
@1
26.com
2
, w
d
e
w
e
n
@gma
il.com
3
A
b
st
r
a
ct
Insulator
fau
l
t
may
le
ad
to th
e acc
i
de
nt of
p
o
w
e
r netw
o
rk
，
thus the
o
n
-li
n
e
mo
nitori
ng
of
ins
u
lator
is very sign
ifi
c
ant. Low
rates w
i
reless n
e
tw
ork is used for data trans
missi
on of
leaka
ge curr
ent.
Deter
m
in
atio
n of
the me
as
ur
ement
matrix
i
s
the si
gnific
a
nt step for re
a
l
i
z
i
n
g the
co
mpresse
d se
nsi
n
g
theory. T
h
is a
r
ticle co
mes
u
p
w
i
th new
sparse
matrices
w
h
ich can b
e
used as c
o
mpresse
d sens
i
n
g
matric
es to ma
ke data co
mpr
e
ssio
n
an
d rec
onstructio
n
of l
eaka
ge curr
ent
w
i
th the comp
ressed se
nsi
n
g
.
T
h
is theory ca
n achi
eve prett
y
good res
u
lts. And then this
article p
e
rforms
that the reconstitution effect
is
al
most th
e sa
me
usi
ng t
he
me
asur
e
m
ent
matrix
of T
o
e
p
lit
z
matrix, circulant matrix
or
sparse
matrix,
a
s
usin
g a classic
a
l meas
ure
m
e
n
t matrix.
Ke
y
w
ords
:
lea
k
age curr
ent, d
a
ta co
mpress
io
n, compresse
d
sensin
g, me
as
ure
m
e
n
t matrix
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
High p
r
e
c
isi
o
n detectio
n
of insulato
r leak
age
curre
n
t is con
ductive to improve the
reliability of t
r
ansmi
ssion li
nes.
Wi
reless sensor net
work i
s
a si
gni
f
i
cant technol
ogy
that
widel
y
applie
d in t
he le
akage
curre
n
t moni
toring
of tra
n
smi
ssi
on li
n
e
, whil
e the
com
m
uni
cat
i
on
band
width i
s
limited, which make the d
a
ta comp
re
ssin
g of leaka
ge
curre
n
t beco
m
e essential.
The mai
n
tra
d
itional m
e
th
od of d
a
ta
compressin
g for le
akage
current in
clud
es fractal
interpol
ation
and pie
c
e
w
ise quantizatio
n comp
re
ssi
n
g
. Based on
the fractal th
eory, docum
en
t
[3] applie
d fractal i
n
terp
ol
ation met
hod
to con
s
tru
c
t
the o
r
igi
nal
leakage
current si
gnal.
T
h
e
locality of thi
s
method
ma
kes it
quite
difficult to
refle
c
t
the ove
r
all
chara
c
te
risti
c
s of the l
e
a
k
a
ge
curre
n
t si
gnal
. Do
cum
ent [
4
] puts forwa
r
d
and
re
alizes th
e pi
ece
w
ise q
uanti
z
a
t
ion comp
re
ssing
algorith
m
, pu
tting to use t
he HSF
cod
e
with char
a
c
t
e
ri
st
ic of
n
u
meri
cal
seq
uen
ce t
o
re
a
lize
highly a
c
tive variable l
engt
h co
mpressio
n. But this
m
e
thod le
ad
s to the in
stabili
ty of the leakage
current frequency and makes it
impossi
ble to determine the pr
obability of
accuracy of the
curre
n
t value, runnin
g
co
un
ter to the origi
nal intention
of codin
g
.
Since the p
u
tting forwa
r
d of comp
ressed
sen
s
i
ng theory, data pro
c
e
s
sing a
nd
comp
re
ssing
come
into a new
sta
ge with
ne
w te
ch
nology
and
n
e
w m
entality. Do
cum
ent [
5
]
raises a m
e
thod of data
comp
re
ssi
n
g
of
insulato
r leakage
cu
rre
nt based
on co
mpressed
sen
s
in
g theo
ry, whi
c
h i
n
cre
a
se the
comp
re
ssion
ratio to
a
certai
n exten
t, attaining t
he
comp
re
ssion
effect for more than 10 times. A
nd the reco
nstructio
n
effect is also
ideal.
The definitio
n
of the mea
s
u
r
eme
n
t matrix
is
the impo
rt
ant step of a
c
hieving comp
resse
d
sen
s
in
g theo
ry. The tra
d
itional me
asurement ma
t
r
ix su
ch a
s
the
Gau
ss
matri
x
and Berno
u
lli
matrix can achieve high-acc
uracy
reconstruction, but
it’s still diffi
cul
t
to realize wi
th the high
cost
of storag
e. By analyzing of
the princi
ple
of comp
re
sse
d
sen
s
in
g the
o
ry, this pape
r con
s
truct
s
the
Top Li
z matri
x
, cyclic mat
r
ix and sparse matrix
to a
pply to com
p
resse
d
sen
s
i
ng of the d
a
ta
comp
re
ssion
of lea
k
a
ge
curre
n
t, co
m
pare
s
th
e m
easure
m
ent
result
and
th
e efficie
n
cy
with
results from traditional measurem
ent m
a
trix to
illustrate the advantages of these mat
r
ices.
In
con
s
id
eratio
n
of the characteri
stics of
the leaka
g
e
current t
hat
being pe
rio
d
ic an
d un
stable,
sub
s
e
c
tion
compressio
n is ad
opted in
the experi
m
e
n
t. Usin
g co
mpre
ssed
se
nsin
g to lea
k
age
curre
n
t data
of both pul
se
area
re
cogni
zed a
nd
st
abl
e zon
e
, the reco
nstructio
n
effect turns
out
to be ideal.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Im
proved
Co
m
p
ressed Se
nsin
g Matri
x
e
s
for In
sulator Leakage
Current Data
… (Zhai Xuem
ing)
4259
2. The Char
a
c
teris
t
ics of
Leaka
ge Cu
r
r
ent
Pollutants in
the air dep
osit on the insu
lato
r su
rfa
c
e
for days an
d
months, an
d
finally
format the po
llution layer. The pollutio
n
layer re
du
ce
s the electri
c
strength of insulators greatl
y
,
leadin
g
to th
e accid
ent b
e
ca
use of th
e co
ntam
in
ation
flashove
r
durin
g
the n
o
rmal ope
rati
on.
Curre
n
t lea
k
age
cu
rre
nt i
s
defin
ed
as the flow
through th
e in
sulator
su
rface pollutio
n
la
yer
measured un
der op
erating
voltage wh
e
n
filth is wet. Whe
n
the op
erating voltag
e is co
nsta
nt, the
leakage
current increa
se
s with the le
vel of po
llution. Thus le
a
k
ag
e cu
rrent
can be u
s
e
d
to
cha
r
a
c
teri
ze t
he imp
a
ct of
insul
a
tor
cont
amination,
a
n
d expe
rien
ce
sho
w
s that it
is
scie
n
tific t
o
use le
akage
curre
n
t value
s
as
cha
r
a
c
te
ristic valu
e to
reflect the run
n
ing statu
s
of
insulato
rs [1]
.
The characte
ristics of lea
k
age current can be
summe
d up a
s
peri
o
dic an
d un
sta
b
le. The
leakage current pollution
flashove
r
pro
c
e
ss i
s
di
vided into 3 se
ction
s
, safety zone (<2
0
m
A
),
forecast
zo
ne
(<50mA
)
a
n
d
dan
ger zone
(>5
0
mA).
Lea
kag
e
cur
r
e
n
t
of
saf
e
t
y
zon
e
is
v
e
ry
smal
l,
and i
s
u
s
e
d
to re
pre
s
e
n
t the cha
r
a
c
teri
stics of le
aka
ge current th
at is d
r
y an
d
with lo
w d
egree
surfa
c
e
conta
m
ination, m
o
st of
whi
c
h
a
r
e th
e
si
ne
waves. L
e
a
k
ag
e current
of f
o
re
ca
st
zon
e
is
alway
s
in sta
ge of instabil
i
ty,
the amplitude of
the current pul
se increa
se
s an
d pulse g
r
o
u
p
appe
ars eve
r
y now
and
then. Lea
ka
g
e
cu
rrent of
dang
er
zon
e
is la
rge, p
u
lse
amplitu
de
increa
se
s
ra
pidly an
d the
high
amplitu
de p
u
lse
d
e
n
sit
y
al
so i
n
cre
a
s
ed
sig
n
i
f
icant
ly
.
For
t
h
e
freque
ncy
do
main, the
safety zon
e
of
le
aka
ge
cu
rren
t is m
a
inly fu
ndame
n
tal a
n
d
the
r
e i
s
mu
ch
high orde
r ha
rmoni
c comp
onent in the p
u
lse a
r
ea that
reflect
s
the d
r
asti
c chang
e
s
.
3. The Comp
resse
d Sens
ing Theor
y
Comp
re
ssed
sen
s
ing th
eory mainly
includ
es th
ree a
s
pe
cts,
they are the sp
arse
rep
r
e
s
entatio
n of si
gnal
s,
cod
e
for
me
asu
r
em
ent a
nd recon
s
tru
c
tion al
go
rith
m. If most of
the
element
s a
r
e
ze
ro i
n
the
sign
al, then
the
sign
al is
calle
d
spa
r
se
. Accordi
ng t
o
the th
eory
of
harm
oni
c an
alysis, a di
screte time si
g
nal
f
with length of
n
can
be expresse
d as a lin
ear
combi
nation
of the stan
da
rd o
r
thog
onal
basi
s
, whic
h
is called th
e
spa
r
se tra
n
sf
orm. Th
e form is
as
follows
:
1
N
ii
i
f
x
(
1
)
Or,
f
x
(
2
)
Whe
r
e
12
,,
N
,
i
is a
colum
n
v
e
ct
or.
The
col
u
mn v
e
ct
o
r
x
of
1
N
is the
weig
hted coe
fficient
se
que
nce of
f
. If high co
efficient
of
x
is q
u
ite a
few, then th
e
sign
al
f
is
calle
d comp
ressible. Su
bstrate of tra
n
sformation
ma
trix for sparse tran
sform
can be
sele
cted
ac
cor
d
ing
t
o
t
he
sign
al
cha
r
act
e
ri
st
ic
s,
s
u
ch
a
s
su
bstrate of th
e fa
st Fou
r
ie
r tran
sform,
sub
s
trat
e
of discrete cosin
e
tran
sfo
r
m, sub
s
trate
of di
screte wavelet tran
sform, sub
s
tra
t
e of Curvele
t
,
sub
s
trate of
Gabo
r and
re
dund
ant dicti
onary.
Suppo
sing th
at the measu
r
eme
n
t matri
x
R(
)
MN
M
N
, and the measured val
ue
R
M
y
, then the reconstructe
d si
gnal can be
calcul
ated a
s
follows:
yf
(
3
)
The dim
e
n
s
io
n of
y
is m
u
ch
lowe
r than
the dime
nsi
o
n
of
f
, thus the
above e
quat
ion
has infinitely
many soluti
ons, so the sign
al
f
cann
ot be recon
s
tructed. But if
f
can be
expre
s
sed sp
arsely as
f
x
, th
en the expre
s
sion i
s
as foll
ows:
y
fx
x
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4258 – 4
263
4260
Whe
r
e
is a
matrix of
M
N
, which i
s
calle
d
the se
nsi
ng
matrix. Can
d
é
s a
nd
Tao [8] con
s
i
der that only if
sat
i
sf
ie
s r
e
st
ri
ct
ed iso
m
et
ry
,
t
he
sign
al can b
e
re
constructe
d wi
th
high p
r
o
babili
ty, and the
signal
f
ca
n be
recon
s
tru
c
ted
accu
rately b
y
solving th
e
optimal n
o
rm
of the mea
s
u
r
ed valu
e
y
. Due to
have been
sel
e
cte
d
usually, the
n
the sen
s
in
g matrix
can
be
satisfi
ed fo
r rest
rict
ed i
s
omet
ry b
y
defining
me
asu
r
em
ent m
a
trix
. The G
auss
ran
dom
matrix is u
s
u
a
lly use
d
to
meet the ab
o
v
e requi
re
m
e
nts. Pra
c
tice
has
prove
d
th
at Gau
ss
ran
dom
matrices
can
achi
eve the a
c
curate
re
con
s
tru
c
tion of th
e sign
al
f
.
The matchin
g
pursuit alg
o
rithm can a
c
hiev
e the si
gnal re
co
nstruction of co
mpre
ssed
sen
s
in
g. The
basic id
ea o
f
classic mat
c
hin
g
pursu
it
algorithm is to select the best match
i
ng
element
s wit
h
the sig
nal
usin
g the me
asu
r
em
ent
m
a
trix in the al
gorithm, go
round a
nd be
gin
again th
e iterative, and ma
ke the
maxim
u
m correlatio
n from th
e re
sults i
n
e
a
ch i
t
eration
with t
he
origin
al si
gnal
. In orde
r to solve the probl
em that
the n
u
mbe
r
of iterations
i
s
too
many du
ring t
he
matchin
g
pu
rsuit alg
o
rithm
,
the ortho
g
o
nal matc
hing
pursuit alg
o
rithm is then
prop
osed. Th
e
algorith
m
sp
e
ed the iteratio
n via orthogo
nalization,
an
d then to reali
z
e the faste
r
reco
nstructio
n
.
4. Measurem
e
nt Ma
trixes
in Compres
s
e
d Sensing
Theor
y
The commo
n
measure
m
e
n
t matrices t
hat sati
sfy the re
stri
cted
isomet
ry co
ndition
s
inclu
de Ga
uss mea
s
u
r
em
ent matrix, Berno
u
lli mea
s
urem
ent matrix and Fou
r
ie
r mea
s
u
r
em
e
n
t
matrix. In the actual
appli
c
ation, the mo
re rand
om
th
e matrix is, th
e more difficu
lt is the phy
si
cal
impleme
n
tation. In general, for matrix with r
and
om
elements, th
e impleme
n
tation will be
very
high pri
c
e [1
0]. Bajwa pro
v
ides two
kin
d
s of me
a
s
u
r
ement matri
c
es, Toeplit
z matrix and cy
clic
matrix. He al
so sugg
est
s
that rand
om T
oeplit
z a
nd cyclic matrix can be imple
m
ented in vario
u
s
appli
c
ation
s
easily, and
proves that the
s
e two
kin
d
s
of matrice
s
h
a
ve the sam
e
effect with
the
cla
ssi
cal
st
oc
hast
i
c mat
r
ix
in comp
re
s
s
e
d
sen
s
in
g an
d rec
o
n
s
t
r
u
c
t
i
on pro
c
e
s
s.
Toeplitz
matrix has the fol
l
owin
g form,
whi
c
h in a
ddi
tion to the first ro
w an
d the first
colum
n
, each
element is th
e same a
s
th
e element on
its uppe
r left corne
r
, that is
,1
,
1
ij
i
j
aa
.
11
12
12
NN
NN
NM
NM
M
aa
a
aa
a
A
aa
a
(
5
)
If meeting additional p
r
o
pertie
s
,
iN
i
ia
a
, then the matrix is also a cy
clic matrix.
Cyc
l
ic
matrix has
the following form.
11
12
12
NN
N
MM
M
aa
a
aa
a
C
aa
a
(
6
)
Bajwa [13] p
r
oves that fo
r the Toeplit
z ma
trix, whe
n
the measu
r
ed fre
que
ncy satisfy
2
lo
g
(
/
)
M
CK
N
K
, then the T
oeplitz m
a
trix
can
ba
sically
satisfie
s th
e re
stri
cted i
s
omet
ry
condition in very high probability.
In orde
r to further
red
u
ce the numb
e
r
of inde
pe
ndent rand
o
m
variable
s
in the
measurement
matrix, Yan
g
put fo
rward
the con
c
ept
of sp
arse
ba
nded
an
d
sp
arse
colu
mn
s in
the study [10
], to further generate a sp
arse ba
nded matrix
and
sparse colum
n
s
matrix,
red
u
ce
the step
s of matrix multiplication a
nd to impr
ove the e
fficiency of co
mpre
ssion a
n
d
recovery.
The form of sparse ba
nde
d
rando
m matrix is as follows:
11
12
1
21
2
2
2
,1
1
0
0
l
l
M
jM
l
M
M
j
aa
a
aa
a
aa
a
a
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Im
proved
Co
m
p
ressed Se
nsin
g Matri
x
e
s
for In
sulator Leakage
Current Data
… (Zhai Xuem
ing)
4261
Kinds of sp
a
r
se b
and
ed
matrix have certai
n ra
ndo
mness. Co
m
pare
d
to the cla
ssi
cal
stocha
stic ma
trix, Toeplitz matrix and cy
clic ma
trix, the indepe
nde
n
t
random ele
m
ents of spa
r
se
mat
r
ix
re
du
c
e
s.
A
c
co
rdin
g t
o
Yang
[1
0], comp
are
d
to the Ga
uss rand
om ma
trix of whi
c
h
the
multiplicatio
n
ope
ration
re
quire
s
M
N
step
s, the multipli
cation
op
erat
ion of
Toe
p
litz m
a
trix
only requi
re
s
2
O(
l
o
g
)
N
steps.
Yang Hairo
n
g
[10] also i
n
trodu
ce
s th
e con
c
e
p
t of spa
r
se col
u
mn matrix a
nd sp
arse
cy
cli
c
mat
r
ix
.
On t
h
e b
a
si
s of
ke
epin
g
t
he o
p
e
r
atio
n ste
p
s the
same
o
r
de
r
with the
To
e
p
litz
matrix, the method furthe
r redu
ce
s the numbe
r of in
depe
ndent ra
ndom ele
m
e
n
t and impro
v
es
operation efficien
cy. The form of sp
arse
column
ran
d
o
m matrix is
as follo
ws:
11
1
/1
,
1
21
22
2
/2
,
2
12
/,
1,
2
,
0
0
00
0
00
p
pN
M
p
pN
M
pp
pN
M
p
p
p
Mp
aa
a
aa
a
a
aa
a
a
a
(
8
)
5. Experimental Re
sults
Select a
se
ction
of lea
k
ag
e
curre
n
t dat
a with
f
l
ash
o
ver pro
c
e
ss, and
then use
comp
re
ssed
sen
s
in
g algo
rithm to comp
ress and
re
co
nstru
c
t the le
aka
ge current
data. In view of
the cha
r
a
c
teri
stics of peri
o
dicity
and no
n-statio
na
ry of the leakag
e curre
n
t data, each step of the
experim
ent take
s the
way of pul
se’
s
a
u
tomatic
re
cognition fi
rst,
sep
a
rate the
pulse
zon
e
and
non-pul
se
zo
ne of lea
k
ag
e
current, form
several se
cti
ons, an
d the
n
make co
mp
resse
d
sen
s
i
n
g
for
d
a
ta
of ea
ch se
ction, compa
r
e
th
e regen
erate
d
d
a
ta g
r
oup
wit
h
the
ori
g
inal
sign
al a
nd fin
a
lly
get the re
covery effect wit
h
pretty high accuracy.
First
of all, choo
se the
G
auss m
e
a
s
ur
ement mat
r
ix and th
e Be
rnoulli m
e
a
s
u
r
eme
n
t
ma
tr
ix as
th
e me
as
u
r
e
m
en
t ma
tr
ix for
comp
re
ssed
sen
s
in
g. The
n
const
r
u
c
t the To
eplitz
matrix
and
cycli
c
m
a
trix. Com
p
a
r
e th
e
re
cov
e
ry
cap
ability with
cla
s
sical me
asurem
ent matrix
a
nd
finally use th
e spa
r
se ba
nded treatm
ent and
sp
a
r
se colum
n
treatment met
hod
s to do the
recovery of G
auss mea
s
u
r
ement matrix.
The re
covery
effect is ideal
.
All the mea
s
urem
ent mat
r
ice
s
se
le
cted
in the
experi
m
ent have
M
N
elements, wh
ere
N
is th
e n
u
mb
er of
coll
ecte
d si
gnal
s, a
n
d
M
is the
me
asu
r
ing
nu
m
ber
of the
co
mpre
ssed
sen
s
in
g algo
rithm. Toeplitz matrix and
cyclic mat
r
ix are shap
ed
se
parately li
ke t
he form
ula (5
)
and the form
ula (6
), whe
r
e each eleme
n
t
,
ij
a
satisfies t
he Bernoulli
di
stribution. Sparse banded
matrix is sh
o
w
n a
s
formul
a (7), whe
r
e
non-ze
ro
el
e
m
ents o
bey the Gau
s
s distribution an
d
the
sub
s
cript
pa
r
a
met
e
r
l
sat
i
s
f
ies
[2
*
/
3
]
lN
N
M
[8]. Spars
e
column matrix is
s
h
own as
formula
(8), whe
r
e
non
ze
ro eleme
n
ts obey
the
Ga
uss di
stri
buti
on a
nd th
e
n
u
mbe
r
of
non
zero
element
s in the first colum
n
also
satisfie
s
[2
*
/
3
]
pN
N
M
[8].
The re
cove
ry
effect of orig
inal lea
k
ag
e curre
n
t data and data m
e
asu
r
ed from
different
measurement
matrice
s
a
r
e
sho
w
n in the i
m
age
s belo
w
.
Figure 1. Ra
w Data
Figure 2. Re
cons
truc
tion Effec
t
of Gauss
Measurement
Matrix
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4258 – 4
263
4262
Figure 3. Reconstruction Effect of Bernoulli
Measurement
Matrix
Figure 4. Re
constructio
n
Effect of TopeLi
z
Measurement
Matrix
Figure 5. Re
constructio
n
Effec
t
of Cyc
lic
Matrix
Figure 6. Re
constructio
n
Effect of Gauss
Measurement
Matrix
with Sparse
Banded Processing
Figure 7. Re
constructio
n
Effect of Gauss Measu
r
em
en
t Matrix with Sparse Colu
mns Proce
s
si
ng
Due to the varying de
gre
e
s of ran
d
o
m
ness
of me
asu
r
em
ent matrice
s
, thou
san
d
s of
times expe
ri
ments h
a
ve
been
ca
rrie
d
out for the
selectio
n of e
v
ery mea
s
urement matrix
. The
relativ
e
er
ro
r formula of the
matrix is
s
h
own as
follows:
A
A
A
A
A
(
9
)
Whe
r
e
A
represe
n
ts the
measured va
lue of the matrix, and
A
repre
s
e
n
ts th
e true value.
Re
cord every
experime
n
tal
erro
r and ta
ke the aver
ag
e, then the re
con
s
tru
c
tion
error of different
matrix duri
ng
sign
al re
cove
ring i
s
obtai
n
ed. It is
obvio
us that the
re
con
s
tru
c
tion
error of diffe
rent
matrix is in th
e ran
ge 6% t
o
9%, and th
e re
con
s
tructi
on effect
s of
Berno
u
lli mea
s
ureme
n
t matrix,
Toeplitz m
e
a
s
ureme
n
t matrix as well a
s
cycli
c
matrix are better than the traditional matrix.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Im
proved
Co
m
p
ressed Se
nsin
g Matri
x
e
s
for In
sulator Leakage
Current Data
… (Zhai Xuem
ing)
4263
Table 1. Re
constructio
n
Erro
r of
Differe
nt Measu
r
em
ent Matrices
Measurement m
a
trix
Re
construction error
(
%
)
Gauss measure
m
ent matrix
8.53
Ber
noulli measur
ement matr
i
x
6.65
Toeplitz matrix
6.90
Cy
clic matr
ix
6.68
Gauss matrix
w
i
t
h
Spar
se bande
d
processing
8.66
Gauss matrix
w
i
t
h
Sparse
columns processing
8.89
6. Conclusio
n
The expe
rim
ental re
sults
sho
w
that wh
en t
he Toe
p
litz matrix and
cycli
c
matrix are u
s
e
d
as th
e me
asu
r
eme
n
t matri
c
e
s
of
com
p
ressed
s
ensi
n
g, the mat
c
hi
ng de
gree of
the comp
re
ssion
and
re
storati
on of in
sulato
r lea
k
a
ge
current
sign
al is
pretty high i
n
the view
of si
gnal fo
rm in t
h
e
time domain,
and the error value
s
are stable in
a rathe
r
limited ran
ge in
the view of the
nume
r
ical cal
c
ulatio
n re
sul
t
s of re
cove
ry errors.
The
restori
ng effe
cts are ne
arly
the sa
me id
e
a
l
w
h
en
th
e s
p
a
r
se
me
as
u
r
e
m
e
n
t
ma
tr
ice
s
a
r
e us
e
d
in
th
e s
i
gn
al r
e
c
o
ver
y
. Co
mp
ar
e
d
to
th
e
traditional
ran
dom m
e
a
s
urement m
a
trix, the o
p
ti
mal
measurement
matrix h
a
s le
ss ind
epe
nde
nt
rand
om elem
ents, whi
c
h m
a
ke
s it easy to be implem
e
n
ted in engi
n
eerin
g.
Ackn
o
w
l
e
dg
ements
This
wo
rk i
s
supp
orte
d
by Natio
n
a
l
Na
tu
ral S
c
ience Fo
und
ation of
Chi
na (No.
6107
4078
).
Referen
ces
[1]
Gu L, Sun C. Contam
inati
on
insul
a
tio
n
of el
ectr
ical p
o
w
e
r
s
y
stem. 1st Ed
ition. Ch
on
gqi
n
g
: Cho
ngq
in
g
Univers
i
t
y
Pr
es
s. 1990.
[2]
Jian
g X, Shu
L, Sun C. Poll
ution a
nd Icin
g
Insu
latio
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w
e
r S
y
stem
. 1st Edition. Beiji
ng: Ch
ina
Electric Po
w
e
r Press. 2009.
[3]
Hui A, Lin H. C
u
rve F
i
tting of Leak
ag
e Curre
nt
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r
actal T
heor
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29.
[4]
Li M, Cai W.
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o
mpres
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e
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Q, Huan
g J, Z
hu Y. Data Compress
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akag
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hai
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arch on Insu
lator
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rr
ent De
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f
High Accurac
y
a
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a
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mpressio
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r
T
r
ansmission L
i
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hesis. Beiji
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rth Chin
a Elect
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ic Po
w
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n
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L
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dés E, R
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mberg J, T
ao
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n
a
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h
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han
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i S.
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he
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heory of
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arch o
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ureme
n
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e
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w
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aupt JD, Raz
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r
ight SJ, No
w
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o
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r
opp J, Gilbe
r
t A. Signa
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e
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eas
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a
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Evaluation Warning : The document was created with Spire.PDF for Python.