TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 5801
~ 5806
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.517
5
5801
Re
cei
v
ed
No
vem
ber 2
0
, 2013; Re
vi
sed
March 25, 20
14; Accepted
April 10, 201
4
Resear
ch on Electrical Energy Consumption Efficiency
Based on GM-DEA
Mei Liu
Dep
a
rtment of Econom
ic and
Mana
geme
n
t, No
rth Ch
ina El
ectric Po
w
e
r U
n
iversit
y
,
H
e
be
i
Ba
od
in
g, C
h
i
n
a
,
0
7
1
000
email: li
ume
i
_
w
@
1
6
3
.com
A
b
st
r
a
ct
In today'
s
envi
r
on
me
nt w
h
ich
e
m
ph
asis on ener
gy
effici
en
cy,
predi
cti
ng t
he tre
nd
of el
ectric
a
l
ener
gy cons
u
m
pti
on effici
en
cy, and rese
a
r
chin
g the
effi
cient op
erati
o
n mode
l of p
o
w
e
r industry
has
practica
l si
gnifi
cance. By
esta
blish
i
n
g
GM-D
EA metho
d
sy
stem, w
e
us
e
GM mo
del
to
pred
ict four i
n
p
u
ts
and
outp
u
t in
d
i
cators i
n
2
0
1
1
an
d
201
2 i
n
Beij
in
g first, and t
hen
use
DEA to g
i
ve
p
r
edicti
ng y
ears
a
reaso
nab
le
an
alysis for
the
e
fficiency
of en
e
r
gy cons
u
m
pt
i
on. T
h
e
resu
lt
show
s that effi
ciency
of e
l
ectr
ical
ener
gy cons
u
m
pti
on i
n
Bei
j
i
ng is gr
adu
all
y
incr
eas
in
g, GM-DEA mo
d
e
l can
ana
ly
ze the trend
of the
efficiency effec
t
ively in a
d
van
c
e, and it pro
v
ides a
sci
enti
f
ic basis for the r
api
d deve
l
o
p
ment of pow
e
r
ind
u
stry.
Ke
y
w
ords
: ele
c
trical en
ergy, consu
m
ption
efficien
cy, Grey mo
de
l, data en
velo
p
m
ent a
nal
ysis
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
Electri
c
al e
n
e
rgy i
s
an
in
disp
en
sable
strat
egi
c
re
source fo
r ev
ery country,
it is al
so
essential in our daily life. It
plays an important role in su
staining so
cio-ec
ono
mic develo
p
m
ent
and imp
r
ovin
g the living standard. In rece
nt y
ears,
steady an
d rapid
develo
p
m
ent of Chin
a's
eco
nomy is
greatly in
cre
a
se
d the d
e
m
and fo
r el
ectri
c
al e
n
e
r
gy, the tren
d that econ
omic
depe
ndent
s o
n
electri
c
al e
nergy is al
so
contin
ue to st
rength
en.
Und
e
r the e
n
v
ironme
n
t of the rapid
dev
elopme
n
t of Chin
a's p
o
we
r indu
stry, there a
r
e
still exist phe
nomen
on tha
t
energy effici
ency waste
s
seri
ou
sly and
energy con
s
umption is l
o
w.
As commo
dities
su
ch
as elect
r
icity is sen
s
itive a
nd ha
s
a lo
ng con
s
tru
c
ti
on pe
rio
d
, o
n
ly
establi
s
h th
e
early p
r
edi
cti
on an
d an
alysis
ca
n
we truly achi
eve the requi
reme
nt of "eco
no
mic
developm
ent, power first"
. Establish
the ea
rl
y pre
d
iction
and
analysi
s
can
also l
a
y the
foundatio
n for plannin
g
the electri
c
al e
n
e
r
gy con
s
u
m
pt
ion sol
u
tion
s.
No
wad
a
ys,
many
schola
r
s have
an
al
yzed
and
in
vestigated
China'
s
ele
c
tri
c
e
n
e
r
gy
con
s
um
ption
from
differe
nt pe
rspectiv
e
s [1
-5]
ba
sed o
n
diffe
re
nt re
se
arch
method
s [6
-1
2].
Banke
r
R.D [
6
] (19
8
6
)
co
mpared th
ree
situatio
ns
which
are the
fixed othe
r n
o
n
-en
e
rgy inp
u
ts,
redu
ce e
nerg
y
factor alon
e and red
u
ce
all input
factors o
ne time
with the input-ori
ented DEA
model, the
result
sho
w
e
d
that the fo
rmer
ca
n save mo
re e
nergy. Qun-wei
Wan
g
[7] (20
08)
looked the el
ectri
c
ity con
s
umption, labo
r and
capi
tal
stock a
s
inpu
t indicators ,a
nd loo
k
ed G
D
P
as the
output
indicator, stu
d
ied t
he
effici
ency of el
ectricity con
s
um
p
t
ion in differe
nt part of
Chi
na,
and a
nalyze
d
the impa
ct
factors relat
ed to el
e
c
tri
c
ity con
s
um
p
t
ion efficien
cy using of
DEA
method.
Cui
he-rui [13]
(2
014) u
s
ed
G
M
(1,1
) m
o
d
e
l of the
gre
y
theory to p
r
edi
ct the
ru
ral
energy
con
s
umption as well as
the prop
ortio
n
of
total en
ergy
co
nsumptio
n ratio
of
Hebei
Province. Yi Zhang [1
4] (2
013) u
s
e
d
DEA model to
cal
c
ulate, an
alysis
rea
s
on
s for po
or be
nefit
of deci
s
ion
-
m
a
kin
g
unit, find out improve
m
ent dire
ctio
n and qu
antity for changi
n
g
.
Most
schola
r
s h
a
s
mu
ch
deep
stu
d
y in comp
ri
sin
g
the en
ergy
efficien
cy in
different
regio
n
s
,there
a
r
e also
m
u
ch stu
d
y on
the issue
s
o
f
factors which influence e
l
ectri
c
al en
ergy
con
s
um
ption
significantly, but
there is less
schola
r
to con
d
u
c
t a systemati
c
study on t
h
e
efficien
cy of electri
c
al
ene
rgy consump
t
ion
in Beijin
g usi
ng G
M
-DEA model.
Therefore, th
e
study of efficiency of po
we
r ene
rgy co
nsumption
in B
e
ijing ha
s an
importa
nt value for a
c
hievi
ng
energy savin
g
in the regio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 580
1 –
5806
5802
2. Building Model and S
e
lecting Indi
cator
s
Gray m
odel i
s
a
model
wh
ich lo
oks
eve
r
y ra
ndom
variable
s
as th
e
study ta
rget,
looks
a
rand
om p
r
o
c
ess as
a gray pro
c
e
ss
relat
e
to a
ce
rtain
rang
e variati
on and time.
the gray
syst
em
is ch
ara
c
te
rized by part of the in
formatio
n system is
known, part
of the information is un
kno
w
n,
and it has m
any advantag
es, su
ch a
s
the sam
p
le d
a
ta is less re
quire
d, no ne
ed to cal
c
ula
t
e
statistical feature
s
, etc. In t
he gray sy
ste
m
studie
s
, G
M
(1, 1) mod
e
l has b
een reco
gni
zed an
d
followe
d clo
s
ely by resea
r
che
r
s b
o
th at home and a
b
roa
d
from o
peratio
nal an
gle to theoret
ical
angle. Mod
e
li
ng step
s of G
M
(1, 1) are a
s
follows:
Cal
c
ulate th
e
accum
u
lated
gene
ratin
g
seque
nc
e of o
r
iginal
seque
nce. A
c
cumul
a
te the
origin
al seq
u
ence
(0)
(
0)
(0
)
(
0)
(
(
1
)
,
(
2
)
...
(
)
)
x
xx
x
n
on
ce
and
gen
erate
the
seq
uen
ce, that is
(1
)
(
1
)
(1
)
(
1
)
(
(
1
)
,
(
2
)
...
(
)
)
x
xx
x
n
.
Parameter Estimation
. In
accordan
ce
with the la
w
of expone
ntia
l gro
w
th, we
can
se
e
the followin
g
first-ord
e
r lin
e
a
r differe
ntial equatio
ns:
(1
)
(1
)
dx
ax
u
dt
(1)
(
(1
)
x
is the function of time
t
, it is the gray equation,
part of the data is un
kn
own
)
Kee
a
A
u
is pe
nding.
After the discretizatio
n we
get
n
YB
A
. Usi
ng th
e MATLAB software,
we
can o
b
tain th
e approximat
e solutio
n
:
1
()
TT
A
BB
B
Y
n
ˆ
ˆ
a
u
，
(2)
Among the fo
rmula
(1
)
(
1
)
(1
)
(
1
)
(1
)
(
1
)
1
[(
1
)
(
2
)
]
1
2
1
[(
2
)
(
3
)
]
1
2
..
.
1
[(
1
)
(
)
]
1
2
xx
xx
B
xn
xn
,
(0
)
(0
)
(0
)
(2)
(3
)
..
.
()
n
x
x
Y
x
n
Take th
e app
roximation
ˆ
a
，
ˆ
u
into the origin
al differential
equatio
n:
(1)
(1
)
ˆ
ˆ
dx
ax
u
dt
(3)
Get the pre
d
icted
v
a
lue
of
(1)
x
.
Appro
x
imate soluti
on of the
o
r
iginal
differe
ntial
equatio
n is:
ˆ
(1
)
(
1
)
ˆ
ˆ
()
[
(
1
)
]
ˆ
ˆ
at
uu
xt
x
e
aa
, t=
1
，
2
，
…
，
n
(4)
Written the
a
pproxim
ate solution of differential
equ
a
t
ions in the
o
r
iginal
discrete form,
we can get th
e predi
cted v
a
lue
s
that is:
ˆ
(1
)
(
0
)
(
1
)
ˆ
ˆ
ˆ
(1
)
[
(
1
)
]
ˆˆ
ak
uu
xk
x
e
aa
, k
=
0
，
2
，
…
，
n;
(5)
Get the pred
icted v
a
lue o
f
(0
)
x
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Electri
c
al Ene
r
gy
Con
s
um
p
t
ion Efficiency Base
d on G
M
-DEA (M
ei Liu)
5803
ˆ
(0
)
(
0
)
(
)
ˆ
ˆ
(1
)
[
(
1
)
]
(
1
)
ˆ
ak
a
u
xk
x
e
e
a
k
=
0
，，
，
2
…
n
(6)
Model che
c
k
i
ng
. Posteriori error test an
d small
error
probability test. The hi
stori
c
al data
var
i
anc
e
is
2(
0
)
(
0
)
2
1
1
1
((
)
)
n
i
Sx
k
x
n
. The hi
sto
r
ical average i
s
(0
)
(
0
)
1
1
()
n
k
x
xk
n
. The
resi
dual va
ria
n
ce i
s
22
2
1
1
((
)
)
n
i
Sk
n
. The mean resi
dua
l is
1
1
()
n
k
k
n
.
Ev
aluate the
Efficiency
of Electric
En
erg
y
Consumption Usin
g DEA Mo
de
l.
DEA's
basi
c
idea i
s
to make the a
ppro
p
ri
ate evaluation
for e
a
ch de
ci
sion
-makin
g unit throu
gh e
s
tabl
ish
a mathematical prog
rammi
ng model.
Fo
r the evaluation system ha
s
n
DMU, su
pp
ose the
r
e are
0
x
kind
s of
inp
u
t
,
0
y
kin
d
s
of ou
tput,
is the efficien
cy value
s
of DM
Uj0,
j
x
is a
collection of
input el
ement
,
j
y
is a
coll
ect
i
on of
output
elem
ent,
j
is a
ratio,
s
a
nd
s
a
r
e th
e s
l
a
c
k
variable
s
, the
y
form the BCC-DEA model
under V
R
S togethe
r.
The BCC-DE
A model is a
s
follows: min
0
1
0
1
1
.
1
,
,
0
,
1
,
2
,
......,
n
jj
i
n
jj
j
n
j
j
j
xs
x
xs
y
St
s
s
j
n
(7)
The optimal
solutio
n
in Equation
(7), if
1
, the deci
s
io
n-ma
kin
g
unit
is efficien
cy, if
1
, the decisi
o
n
-
ma
king u
n
it is non
-DEA ef
ficien
cy.
Indicator Sel
ecting.
Assu
me that Beijing's
econo
mic a
c
tivity require
s inp
u
ts o
f
capita
l
stock, labo
r, energy co
nsumption a
nd
output of GDP. Sele
cting
the data of 2
005-201
0, an
d
usin
g of GM
(1, 1
)
mod
e
l and
DEA
model to
e
v
aluate
the efficien
cy
of electri
c
al en
ergy
con
s
um
ption.
Data of lab
o
r, ene
rgy consum
ption
and the G
D
P are all fro
m
the "Beijin
g
Statistical Ye
arbo
ok 20
11.
" The
cal
c
ul
a
t
e method
of
the capital
st
ock d
r
a
w
s Zh
ang
Ju
n [4] a
nd
others re
se
arch re
sult
s directly, and
extend
s the cal
c
ulation to 201
2.
3. Empirical
Analy
s
is
Cal
c
ulate th
e
pre
d
icte
d value of th
e i
nput-o
utput i
ndex; test th
e Rel
a
tive error and
poste
rio
r
erro
r with GM (1, 1) mod
e
l. The results a
r
e
sho
w
n in Ta
b
l
e 1 to Table 3.
Table 1. The
Origin
al Data
of Input and Output Indica
tors
ye
a
r
capital sto
c
k
(hundred million)
Labor
(ten thousand
)
Po
w
e
r energ
y
cons
um
pti
o
n
(hundred million)
GDP
(hundred million)
2005
6802.6
878
570.54
7387.8
2006
7316.2
919.7
611.57
8404.4
2007
7829.8
942.7
667.01
9557.8
2008
8343.6
980.9
689.72
10872.2
2009
8857.2
998.3
739.15
12365.6
2010
9380.4
1031.6
809.9
14064.5
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 580
1 –
5806
5804
Table 2. The
Gray Fo
re
ca
st Result
s of Input and Outp
ut Indicators
ye
a
r
capital sto
ck
(h
undred
million)
Labor
(Ten th
ousand)
Po
w
e
r e
n
e
r
gy
co
n
s
um
pt
i
on
(hundred million)
GDP
(hundred million)
Actual
value
Predictive
value
Actual
value
Predictive
value
Actual value
Predictive value
Actual
value
Predictive
value
2005
6802.6
6906.4
878
893.5
570.54
572.3
7387.8
7387.8
2006
7316.2
7346.1
919.7
919.5
611.57
612.1
8404.4
8404.4
2007
7829.8
7813.2
942.7
946.3
667.01
654.5
9557.8
9557.8
2008
8343.6
8311.1
980.9
973.8
689.72
700
10872.2
10872.2
2009
8857.2
8839.7
998.3
1002.1
739.15
748.5
12365.6
12365.6
2010
9380.4
9402.5
1031.6
1031.2
809.9
800.5
14064.5
14064.5
2011
10001.3
1061.2
856
15997.8
2012
10637.9
1092
915.4
18196.7
Table 3. The
Accu
ra
cy of t
he Input and
Output Indica
tors
year
capital sto
c
k
(hundred million)
Labor
(Ten th
ousand)
Po
w
e
r energ
y
cons
um
pti
o
n
(hundred million)
GDP
(hundred million)
Actual
value
Predicti
ve
value
Residu
als
Relat
ive
error
%
Actual
value
Predicti
ve
value
Resi
duals
Relat
ive
error
%
Actual
value
Predicti
ve
value
Resi
duals
Relat
ive
error
%
Actual
value
Predictiv
e value
Residu
als
Relat
ive
error
%
2005
6802.6
6906.4
103.8
1.5
878.0
893.
5
15.5
1
.8
570.5
572.3
1.8
0.3 6969.5
7387.8
418.3
6.0
2006
7316.2
7346.1
29.9
0.4
919.7
919.
5
-0.2
0.0
611.6
612.1
0.
5 0.1
8117.8
8404.4
286.6
3.5
2007
7829.8
7813.2
-16.6
0.2
942.7
946.3
3.6
0.4
667.
0
654.5
-12.5
-
1.9
9846.
8
9557.8
-289.0
-
2.9
2008
8343.6
8311.1
-32.5
0.4
980.
9
973.8
-7.1
-0.7
689.7
700
10.
3
1
.5 1111
5
1087
2.2
-242.8
-
2.2
2009
8857.2
8839.7
-17.5
0.0
998.3
1002.1
3
.8
0.4
739.2
748.5
9.
4 1.3
1215
3
1236
5.6
212.6
1.7
2010
9380.4
9402.5
22.1
0.0
1031.6
1031.2
-
0.4 0.0
809.9
800.5
-9.4
-1
.2 1411
3.6
1406
4.5
-49.1
-0.3
2011
1000
1
1061.2
856
1599
7.8
2012
1063
8
1092
915.4
1819
6.7
The averag
e
accur
a
c
y
%
99.6
The averag
e
accur
a
c
y
%
99.7
The averag
e
accur
a
c
y
%
99
The averag
e
accur
a
c
y
%
97.2
Posterior err
o
r
%
0.04
Posterior err
o
r
%
0.13
Posterior err
o
r
%
0.11 Posterior
err
o
r
%
0.28
Test results o
f
Gray predi
cti
on are ab
ove
the table, relative error of
each ind
e
x a
v
erage
is le
ss tha
n
1
0
%, and
accura
cy is mo
re
than
90%
. P
o
steri
o
r erro
r
ratio i
s
le
ss t
han
0.35; val
u
e
of small p
r
ob
ability erro
r is 1. Resi
dual t
e
st and Po
st
erio
r erro
r test show th
at the model
can
get
a very good p
r
edi
ction resu
lt; it can be u
s
ed for follo
w-up stu
d
y.
DEA Evaluati
on of Efficien
cy of
Elect
r
ical Energy Co
nsum
ption
B
a
se
d on
the
histori
c
al
data of the in
put and outp
u
t element
s and g
r
ay pr
e
d
ictive value
of each
elem
ent in 2011
a
nd
2012, using
DEAP (Versi
on 2.1), we calcul
ate the
ov
erall effici
ency, technical
efficiency, scale
efficien
cy an
d sla
ck va
ria
b
le dist
ributio
n of Be
ijing electri
c
e
nerg
y
consumptio
n in 2005
-2
0
12,
results a
r
e sh
own in Ta
ble
4 and Tabl
e 5
.
Table 4. DEA
Evaluation of Electric
al Energy Consum
ption in Beijing
y
ear cr
ste
vr
ste
scale
scale
effic
i
ency
2005
0.651
1
0.651
Increase
2006
0.691
0.986
0.701
Increase
2007
0.721
0.977
0.738
Increase
2008
0.790
0.988
0.802
Increase
2009
0.842
0.987
0.853
Increase
2010
0.877
0.979
0.895
Increase
2011
0.940
0.988
0.952
Increase
2012
1.000
1.000
1
constant
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Electri
c
al Ene
r
gy
Con
s
um
p
t
ion Efficiency Base
d on G
M
-DEA (M
ei Liu)
5805
Table 5. Dist
ribution of Ele
c
tri
c
al
Energy Con
s
umptio
n Slack Va
ria
b
le (
s
)
year
2005
2006
2007
2008
2009
2010
2011
2012
s
0
-50.058
-76.68
-207.745
-170.996
-14.025
-23.611
0
From Ta
ble 4
we kn
ow tha
t
the compre
hen
sive effici
ency in 20
11
is less than 1
but very
clo
s
e to 1, it is non-DEA efficient. All the ele
c
tr
ical energy efficie
n
cy value
s
in
2012 are 1, it
rea
c
he
s th
e
optimal
state, it indicates t
hat
the in
put
and
output i
n
201
2 i
s
m
o
re
rea
s
o
nab
le.
Combi
ned
with the result
s of previou
s
year’
s
data
we
can se
e that Beijing's ove
r
all efficien
cy
of
electri
c
al
ene
rgy consumpt
ion is i
n
crea
sing, it indi
cates that el
ect
r
i
c
al
con
s
um
ption efficie
n
cy
of
Beijing is g
r
a
dually increa
sing. The tabl
e also
sh
o
w
s that electri
c
a
l
energy con
s
umption in 20
11
is in
crea
sing;
this m
ean
s
that the d
e
m
and fo
r el
ect
r
ical
en
ergy i
n
20
11 i
s
u
r
gent. G
D
P will
increa
se
with
electri
c
al e
n
e
rgy con
s
um
ption gr
owth,
and G
D
P growth ratio is
greate
r
than
the
prop
ortio
n
of electri
c
al e
n
e
r
gy con
s
u
m
pt
ion.
Table 5
sho
w
s that
sla
c
k variable
s
in
2011 i
s
not 0
,
it means Be
ijing’s el
ectri
c
energy
con
s
um
ption
is hig
h
; this results in
a wa
ste of
electri
c
al
en
ergy. In 20
1
2
, the ele
c
tri
c
al
con
s
um
ption
sla
ck va
riabl
e
is 0, e
nergy
con
s
um
pt
ion
is rea
s
ona
ble
.
The sl
ack v
a
riabl
es i
n
th
e
year a
r
e
app
roa
c
hin
g
0; it
indicates th
at Beijing'
s e
fficiency
of el
ectri
c
al
ene
rgy con
s
u
m
pti
o
n
increa
se
s year by year.
4. Conclusio
n
The po
we
r
indu
stry is t
he mo
st im
port
ant b
a
si
c en
ergy in
dustry in
e
c
onomi
c
developm
ent; it operates
e
fficiency o
r
n
o
t will di
re
ct
ly affect the
su
staina
ble d
e
velopme
n
t of the
national e
c
o
nomy and th
e quality of
peopl
e's life.
In order to ensure el
ectric ene
rgy su
pply
adeq
uately a
nd effici
ently, elect
r
icity i
n
vestment
m
u
st b
e
a
r
ran
ged
ba
sed
on
so
cial
an
d
eco
nomi
c
de
velopment in
advance, we sho
u
ld
en
deavor to en
sure that there is no p
o
w
er
sho
r
tage, a
n
d
take effort
s to reali
z
e
the effi
cien
cy ope
ration
of electri
c
power ind
u
st
ry.
Therefore, th
e efficien
cy of powe
r
en
e
r
gy co
nsump
t
ion in Chi
n
a
shoul
d be i
m
prove
d
with
out
delay, it has great si
gnificance to predi
ct and eval
u
a
t
e electri
c
al e
nergy con
s
u
m
ption effecti
v
ely.
GM-DEA mo
del provid
es
a new id
ea for the
re
se
arch of po
we
r
energy con
s
umption,
esp
e
ci
ally in t
he p
r
e
s
ent,
much
hi
story
data of th
e
in
put and
outp
u
t indicators
are
missing,
usin
g
of gray fore
casting
to p
r
e
d
ict futu
re
en
ergy
in
puts
can a
c
hi
eve hi
gh fitting a
ccura
cy. Thi
s
p
aper
use
s
efficien
cy of Beijin
g
'
s el
ect
r
ical
energy
con
s
umption as an
exam
ple,
ba
sed on gray
predi
ction m
e
thod an
d the fore
ca
sting
data, us
ing
DEA techni
q
ue to evaluat
e the pre
d
ict
ed
results, we
can mana
ged
to get a lot
of usef
ul info
rmation a
nd advice, GM
-DEA provide
s
a
theoreti
c
al
su
pport
whi
c
h
make
s
ele
c
tri
c
al e
n
e
r
gy m
o
re
efficien
cy
. GM-DEA h
e
lps to
a
c
hie
v
e
optimal all
o
ca
tion of
re
sou
r
ce
s; it
al
so
provides a
relia
ble b
a
si
s fo
r
prod
uctio
n
a
n
d
di
stributio
n
of
the electri
c
e
nergy.
Ackn
o
w
l
e
dg
ements
This
wo
rk i
s
suppo
rted by t
he Fun
dame
n
tal Re
sea
r
ch Fund
s for t
he Ce
ntral
Universitie
s
(No.1
2
MS13
8).
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in
g W
a
n
g
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he
Hao,
Ye
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n
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al
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h
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rovi
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he C
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