TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 10, Octobe
r 20
14, pp. 7361
~ 736
8
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.528
9
7361
Re
cei
v
ed
De
cem
ber 5, 20
13; Re
vised
June 30, 20
14;
Accept
ed Jul
y
20, 201
4
Combine Multi-predictor of Gas Concentration
Prediction Based on Wavelet
Transforms
Wu Xiang*
1
,
2
，
Qian Jian
-Sheng
1
1
School of Infor
m
ation a
nd El
e
c
trical Eng
i
ne
e
r
ing, Ch
ina U
n
i
v
ersit
y
Mi
nin
g
&
T
e
chnol
og
y,
Xuz
h
o
u
, Jian
g
s
u 221
11
6, Chi
n
a
2
School of Med
i
cal Informatics
, Xuzh
ou Me
di
cal Col
l
e
ge, Xu
zhou, Jia
ngs
u 221
11
6, Chin
a
Email: dmsh
xz
mc@163.c
o
m
A
b
st
r
a
ct
A meth
od of co
mb
in
e multi-pr
edictor is pr
op
os
ed b
a
se
d on
w
a
velet transform to i
m
pr
ove
the
pred
iction
prec
ision
of co
al
mine
gas c
onc
e
n
tration
ti
me s
e
ries. F
i
rstly, the pr
op
osed
mo
de
l e
m
p
l
oy
Mallat a
l
g
o
rith
m to d
e
co
mp
o
s
e an
d reco
nstruct the
gas co
ncentrati
on ti
me series to is
ol
ate the low
-
freque
ncy
and
hi
gh-freq
ue
nc
y infor
m
ation.
T
hen, AR
MA
mo
de
l
is
b
u
ilt for
the pre
d
icti
on of
h
i
gh-
freque
ncy info
rmati
on a
nd rectifies dev
iati
ons of t
he predicte
d
valu
es
by Markov bi
as correctio
n
meth
od
w
h
il
e t
he SVM
mo
del
is
use
d
to
fit the
pre
d
ictio
n
o
f
the l
o
w
-
frequ
ency
infor
m
ati
on. At
last,
these
pred
icte
d val
ues
are
su
peri
m
p
o
se
d to
obtai
n the
pr
ed
icted v
a
lu
es of
the ori
g
i
nal
seq
uenc
e. T
h
i
s
m
e
tho
d
ma
ke
s a
n
e
ffe
cti
v
e
sep
a
r
a
t
io
n
o
f
th
e
fe
a
t
u
r
e
in
fo
rm
ati
o
n
o
f
ga
s co
nce
n
t
ra
ti
on
tim
e
se
ri
e
s
and
takes full adv
antag
e of the
featur
es of different pre
d
i
c
tion mod
e
ls
to achiev
e co
mp
le
me
ntary
adva
n
tag
e
s. T
he c
o
mpar
iso
n
exp
e
ri
me
nt w
i
th the
sin
g
l
e
-pred
i
ctor
mo
d
e
ls (BP, SVM)
an
d si
ngl
e-
pred
ictor
mo
de
ls bas
ed
on w
a
vel
e
t dec
o
m
p
o
sitio
n
(W
-BP, W
-
SVM)show
that the
prop
o
s
ed
meth
od
improves the o
v
erall pr
edicti
o
n pr
ecisi
on. T
he results show
that
meth
od ha
s high prec
isio
n and stron
g
practica
bil
i
ty.
Ke
y
w
ords
:
wavelet transforms, m
u
lti-predictor, co
mb
in
e pr
edicti
on, dev
iat
i
on corr
ection
Co
p
y
rig
h
t
©
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
Coal
mine
ga
s
con
c
e
n
trati
on ex
cee
ded
discha
rge
sta
ndard i
s
one
of the m
o
st i
m
porta
nt
factors
of co
a
l
mine se
curit
y
in
produ
ctio
n. The
accu
rate predi
ct
ion
and
re
al-tim
e monito
ring
and
control of coa
l
mine ga
s co
nce
n
tration a
r
e import
ant m
easure
s
to prevent gas ex
plosi
on and g
a
s
outburst [1]. Since
safety monitori
ng sy
stem ha
s
be
en install
ed i
n
most coal
mine, there i
s
a
large
numb
e
r of coal min
e
safety data. Therefore,
it is sig
n
ifica
n
t to take adva
n
tage of the
s
e
histori
c
al to
make a
n
accurate an
d effective trend
s
predi
ction the
of mine gas
con
c
e
n
tration
.
In re
cent
ye
ars,
several
method
s a
r
e
rep
o
rte
d
in
the literatu
r
e
for
ga
s
con
c
entration
predi
ction. P
apers [2
-4] show th
at
the
gas
co
ncentration sequ
en
ce i
s
chaoti
c
time se
rie
s
. In [2],
a
predi
ction model wa
s constructe
d
by
an addin
g
-w
eight o
ne-ran
k
lo
cal
-
region
method
in t
h
e
recon
s
tru
c
tio
n
pha
se spa
c
e. In [3], a predictio
n mod
e
l wa
s built u
s
ing time
seri
es an
d ada
ptive
fuzzy
rea
s
o
n
i
ng ne
ural sy
stem. In [4], it pr
op
osed a
max Lyapu
n
o
v index mo
del. In LS-S
VM
ca
se, the
sp
arsene
ss a
n
d
ro
bu
stne
ss may lo
se, a
nd the
estim
a
tion of the
sup
port val
u
es i
s
optimal only i
n
the case o
f a Gau
ssi
an
distrib
u
tion of
the error va
ri
able
s
. In [5], it propo
se
d the
weig
hted LS
-SVM to overcome the
s
e d
r
aw b
a
cks.
In[6], the c
h
aotic
phase space rec
o
ns
truc
tive
method was
use
d
to re
co
nstru
c
t the sample spa
c
e
of gas co
ncentration in
multivariate time
seri
es an
d th
e Ga
ussia
n
p
r
ocess
re
gre
ssi
on m
odel
wa
s u
s
e
d
to
predi
ct the
g
a
s
co
ncentrat
i
on
arou
nd the
work face. These method
s provid
e a good g
u
idan
ce for g
a
s
data pre
d
icti
on.
Ho
wever,
th
e ga
s concentration
tim
e
seri
es
a non-station
a
ry
time
seri
e
s
with a strong
rand
omn
e
ss whi
c
h co
ntain
s
m
u
lti-dime
n
s
ion
a
l
in
fo
rm
ation a
nd
sin
g
le p
r
edi
ction
method
can
not
fit for information on ea
ch d
i
mensi
on.
The wavelet decompo
sitio
n
and recon
s
tru
c
tion
can
deco
m
po
se
the multi-co
mpone
nt
sign
al inform
ation into a low-f
r
eq
uen
cy
approx
imate
signal a
nd a
set of high-f
r
equ
en
cy detail
sign
als. Th
e l
o
w-f
r
eq
uen
cy
sign
al re
act t
he inh
e
re
nt variation t
r
en
d
of the inform
ation while the
high-f
r
eq
uen
cy signal rea
c
t the stoch
a
stic distu
r
ba
nc
e influen
ce o
f
it. In
view of the differe
nt
rule
s
of the
s
e t
w
o
type
s of
si
gnal
s differe
nt m
odel
s a
nd
p
a
ram
e
ters
can b
e
utili
ze
d to
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 736
1
– 7368
7362
indep
ende
ntly predict th
ese
signal
s
[7]. Based on this idea,
this pape
r prop
osed a
gas
con
c
e
n
tration
pre
d
ictio
n
combine
multi
-
predi
ctor
ba
sed
on
wav
e
let tran
sfo
r
m. It make
s a
combi
ned
predictio
n for the g
a
s con
c
entration
tim
e
serie
s
whil
e differe
nt p
r
edictio
n mo
d
e
l is
utilized
for these
different
si
gnal
s d
e
comp
osed by
the
wavel
e
t d
e
com
p
o
s
ition
and
recon
s
tru
c
tio
n
. Base
d o
n
the re
se
arch
and
appli
c
at
ion in th
e II8
26
Coal
Fa
ce of Luli
ng
coal
mine of Huai
bei Minin
g
Group
Comp
an
y in Anhui Pr
ovince, it sh
o
w
s th
at this
method
can t
a
ke
advantag
e of different predi
ctor an
d effe
ctively predict the ga
s co
nce
n
tration.
The
re
st of th
is p
ape
r i
s
o
r
gani
zed
a
s
fo
llows. Sectio
n II analy
s
e
s
corre
s
p
ondin
g
ba
si
c
theorie
s an
d method
s. Th
e wavelet de
comp
ositio
n and re
co
nstruction alg
o
rit
h
m is de
scrib
ed in
se
ction II-A
a
nd the
Ma
rko
v
co
rre
ction
method fo
r th
e ARMA
mod
e
l is de
sig
n
e
d
in
se
ction
II-B.
The p
r
op
ose
d
ga
s con
c
en
tration p
r
edi
ct
ion comb
in
e multi-predi
cto
r
ba
se
d
on wavelet
tran
sfo
r
m
is presented in Section III. T
he proposed prediction model is te
sted by the g
a
s concentration
data and th
e
result is
com
pare
d
with th
at of ot
her m
odel
s in Secti
on IV. Section V includ
es
the
con
c
lu
sio
n
s o
f
this paper.
2. Analy
s
is o
f
Basic T
h
eo
ries and Me
thods
2.1. Wav
e
let Decomp
ositi
on and Re
co
nstru
c
tion
The e
s
sen
c
e
of the wave
let deco
m
po
sition an
d re
con
s
tru
c
tion i
s
to divide a
set of
primitive se
q
uen
ce contai
ning comp
reh
ensive info
rm
ation into sev
e
ral g
r
ou
ps of
sequ
en
ce
s with
different
ch
aracteri
stics by
a g
r
oup
of
ba
nd p
a
ss
filte
r
s [8]. In thi
s
p
aper,
The
Ma
llat algo
rithm
is
adopt a
s
the
wavelet d
e
co
mpositio
n an
d re
con
s
tructi
on metho
d
, let
12
{,
,
}
N
Yy
y
y
be the
origin
al se
qu
ence, whe
r
e
N is the sequ
ence lengt
h, the algo
rithm
can b
e
de
scri
bed a
s
follow.
1
1
()
,0
,
1
,
()
jj
jj
aH
a
j
J
dG
a
(1)
()
H
and
()
G
rep
r
e
s
ent
the low-pa
ss filter and h
i
gh-p
a
ss filter.
1
j
a
and
1
j
d
are th
e
comp
one
nts
of the o
r
igin
a
l
sig
nal in
ad
jace
nt freq
ue
ncy b
and
un
der th
e
re
sol
u
tion of
(1
)
2
j
while
1
j
a
re
pre
s
ent the lo
w-f
r
eque
ncy a
p
p
r
oximate
com
pone
nt and
1
j
d
rep
r
e
s
ent the
high-
freque
ncy d
e
tail com
pon
ent. Let
J
b
e
the de
co
mpositio
n le
vel. We can
get
J
detai
l
comp
one
nts
12
,,
J
dd
d
and an approximate
compo
nent
J
a
. For the length of the
decompo
se
d
seq
uen
ce i
s
the half of tha
t
of t
he origin
al one, bin
a
ry interpolatio
n method
wa
s
adapte
d
in the recon
s
tru
c
ti
on se
que
nce recon
s
tru
c
tin
g
[9].
*
*1
*
()
,0
,
1
,
()
j
jj
j
jj
AH
a
j
J
DG
G
d
(
2
)
*
H
and
*
G
are th
e d
ual op
erators of
H
and
G
. Det
a
il seque
nce
s
12
,,
J
DD
D
and
approximate seq
uen
ce
J
A
are the recon
s
tru
c
tion
seq
uen
ce
s of
12
,,
J
dd
d
and
J
a
. They
have the
sam
e
len
g
th
with
origin
al
seq
u
ence. And
th
e o
r
iginal
seq
uen
ce
ca
n b
e
re
pre
s
e
n
ted
as
the sum of re
con
s
tru
c
tion
seq
uen
ce
s.
12
.
J
J
YD
D
D
A
(3)
2.2. Markov
Corre
ction
Metho
d
(M
CM)
The hig
h
-freq
uen
cy detail seq
uen
ce
s can
be seen a
s
a
strong ra
ndomn
e
ss stationary
time se
rie
s
a
nd ARMA
(A
uto-Reg
r
e
ssi
ve and M
o
ving Avera
g
e
)
model
ca
n b
e
appli
ed to
the
predi
ction
of
these
seq
u
ences.
Ho
we
ver, thes
e hi
gh-frequ
en
cy detail
se
qu
ences contai
n a
greate
r
am
ou
nt of ran
dom
ingre
d
ient
s, a
nd t
he hi
ghe
r level the wa
velet decomp
o
sition
rea
c
h
e
s,
the st
ron
ger
the rand
omn
e
ss of
the
s
e
detai
l
seque
nce
s
whil
e becom
e. Although the ARMA
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Com
b
ine Mul
t
i-pre
d
icto
r of Gas
Con
c
e
n
tration Pre
d
icti
on Base
d on
Wa
velet…
(Wu Xiang
)
7363
model exhi
bits a go
od p
e
rf
orma
nce for
nearly
statio
n
a
ry time se
ri
es, it can
not
do better fo
r
the
time seri
es wi
th strong ran
domne
ss tha
n
statisti
cal model. The spe
c
ific pe
rform
a
nce i
s
that most
predi
cted p
o
i
n
ts have
g
o
o
d
pre
d
ictio
n
pre
c
isi
on,
but
part of the p
o
ints a
ppe
ars large
pre
d
ict
i
on
deviation for
the mutation
characteri
stics. Theref
ore, considering
the singl
e point reliability, a
deviation co
rrection meth
o
d
base
d
on the Markov
constraints mo
del is pro
p
o
s
ed to corre
c
t the
result of the ARMR model. The method can
be described as follows. According to utility
evaluation of
the pre
d
icte
d
output of the
ARMA m
ode
l, it decide
s
wheth
e
r to
correct the
re
sult.
The prediction value will be kept if evaluation re
sult is consi
s
tent with the M
a
rkov predi
cti
o
n
interval, otherwise it
will be corrected. Let
i
S
be
the
stat
e value
of the
data
pre
d
icte
d by Ma
rkov
model a
nd
[,
]
ii
Lo
w
U
p
be the
co
rre
spondi
ng
cla
s
sificatio
n
bo
u
ndary. Th
e
state value of
the
predi
ction val
u
e
i
Y
of the ARMR mod
e
l is
'
i
S
and the co
rrecte
d value
is
ˆ
i
Y
. The co
rrecting
method can b
e
descri
bed a
s
follow.
'
'
'
ˆ
ii
i
ii
i
i
ii
i
Up
S
S
YY
S
S
Low
S
S
(4)
If the state value
'
i
S
is highe
r than the state value
i
S
, the prediction value will be
corre
c
ted
to the maximu
m
value of the
i
n
terval b
oun
d
a
ry. And if th
e state val
ue
'
i
S
is lower than
the state valu
e
i
S
, it will be corrected to the minimum v
a
l
ue of the int
e
rval
boundary. Otherwi
se,
it will not be corrected.
The pu
rpo
s
e
is to che
ck th
e predi
ction value of the detail sequ
en
ce and re
con
s
truction
and timely
co
rre
ct the
rel
a
tive larg
e
devi
a
tion.
With th
e thre
e
state
s
segm
entati
on meth
od
a
n
d
the state wi
n
dow p
a
ramet
e
r
s
W
and the po
ssi
bility transi
t
ion matrix wi
ndo
w pa
ram
e
ter
c
W
, the
corre
c
tion
ste
p
s for the p
r
e
d
icted valu
e of a detail se
quen
ce of the
gas con
c
entration time se
ries
12
{,
,
,
}
N
yy
y
can b
e
de
scri
bed a
s
follow.
Firstly, we tra
n
sform the de
tail sequ
en
ce
which ha
s a
c
W
step si
ze to
a state sequ
e
n
ce
before
the tim
e
N.
With the
boun
dari
e
s
an
d
, the items
of the detail
seque
nce are
trans
formed to
three s
t
ate
1
E
,
2
E
and
3
E
,where
1
1
s
W
Ni
i
s
y
W
and
1
1
()
s
W
Ni
i
s
y
W
.
Let
t
s
be the sta
t
e sequ
en
ce
of
t
y
，
where
t
s
=
12
{,
,
,
}
N
ss
s
．
The tran
sfo
r
mation Equati
o
n
1
2
3
0,
,
.
t
tt
t
Ey
sE
i
f
y
Ey
(
5
)
Secon
d
ly, we can
get th
e Ma
rkov tra
n
si
tion
proba
bility matrix
depe
nd
on t
he
state
seq
uen
ce.
Thirdly, we g
e
t the deviation co
rrectio
n
equatio
n and
the corre
c
ted
value
1
ˆ
ˆ
N
y
.
11
1
11
1
1
11
1
2
1
1
1
11
1
2
1
3
11
1
3
ˆˆ
,
ˆ
,
ˆ
ˆ
ˆ
ˆ
,
ˆˆ
,
ˆ
.
nN
N
NN
N
NN
N
N
N
NN
N
N
NN
N
ys
s
ss
s
E
i
f
s
s
sE
sE
y
s
ss
E
s
E
ss
s
E
(
6
)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 736
1
– 7368
7364
Whe
r
e
1
ˆ
N
y
is the predi
cted val
ue ba
sed on
the ARMA model,
1
ˆ
N
s
is the correspon
ding
state
value based
on the pred
icted value
and
1
N
s
is the state value base on the
state value
seq
uen
ce a
n
d
Markov tran
sition proba
bi
lity matrix.
3. Gas Con
c
entra
t
ion Ti
me Series Multi-predic
to
r Base
d on Wav
e
let Transform
Firstly, we u
s
e the Mallat algorith
m
to decom
po
se a
nd re
con
s
truct the gas time se
rie
s
.
Then, the di
fferent pre
d
i
c
tion mo
dels are e
s
tabli
s
he
d for the
low-frequ
en
cy app
roxim
a
te
seq
uen
ce a
n
d
high
-freq
u
e
n
cy detail
se
quen
ce
s. At
last, the final
predi
cted val
ue wa
s
cal
c
ul
ated
by the
sum
of the results
of every p
r
edi
ct
ion mo
del. Th
e blo
c
k sch
e
m
atic fo
r the
workflo
w
of t
h
e
combi
ne mult
i-predi
ctor is
sho
w
n in Fig
u
re 1.
,
m
1
D
n
D
n
A
Figure 1. Gas Con
c
entratio
n
Multi-predi
ctor
Com
b
inati
on Predi
ction
Frame
w
o
r
k Base
d on
Wavelet Tran
sform
Based o
n
the
dyadic wavel
e
t decom
po
si
tion and re
co
nstru
c
tion, th
e gas
con
c
e
n
t
ration
time s
e
ries
12
{,
,
,
}
N
Yy
y
y
ca
n be obtain
e
d
as follows:
12
,
J
J
YD
D
D
A
Whe
r
e
11
,
1
1
,
2
1
,
{,
,
,
}
N
Dd
d
d
、
22
,
1
2
,
2
2
,
{,
,
,
}
N
Dd
d
d
、
、
,1
,
2
,
{,
,
,
}
J
JJ
J
N
Dd
d
d
a
r
e there
con
s
tru
c
ted
high-f
r
eq
uen
cy seq
uen
ce
s of every l
a
yers an
d
,1
,
2
,
{,
,
,
}
J
JJ
J
N
Aa
a
a
is the
recon
s
tru
c
ted
low-frequ
en
cy seque
nce o
f
the
J
layer.
The high
-fre
q
uen
cy seq
u
e
n
ce
s a
c
qui
rin
g
by
wavelet decompo
sitio
n
and re
co
nstruction
of the time seri
es
ca
n be se
en a
s
the stat
ion
a
ry time se
ries with
stro
ng ra
ndom
n
e
ss,
whi
c
h refle
c
t the
lo
cal muta
tion
ch
ara
c
te
ristics
of
the d
a
ta. Therefore, we b
u
ild A
R
MA predi
ction
model
and
correct th
e
de
viation of th
e
predi
ct
ed va
lue by
the
M
a
rkov
corre
c
ti
on m
e
thod.
T
h
e
spe
c
ific
step
s can be d
e
scribed a
s
follows:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Com
b
ine Mul
t
i-pre
d
icto
r of Gas
Con
c
e
n
tration Pre
d
icti
on Base
d on
Wa
velet…
(Wu Xiang
)
7365
(1) Build the ARMA(
p
，
q
) model
for
j
D
and
use the
existing
seq
uen
ce val
u
e
s
to
estimate the
para
m
eters where
1,
j
Ji
M
.
(2) With adaptive tes
t
ing for the ARMA
(
p
，
q
) mod
e
l a
n
d
AIC
criterio
n meth
od
app
lied fo
r
the orde
r det
ermin
a
tion of the model, the model pa
ra
meters
p
and
q
are obtai
ne
d.
(3) T
he predi
cted value
,
ˆ
j
Nk
d
of
,
j
Nk
d
can be obtai
ned by the ARMA(
p
，
q
) m
odel.
(4) G
r
id meth
od is ap
plied
to param
eter
opt
imizatio
n of the weight
ed Markov co
rre
ction
method
whe
r
e the state
d
i
vided wi
ndo
w
[,
]
s
ss
Wa
b
and the p
r
oba
bility cal
c
ulatio
n wi
nd
ow
[,
]
cc
c
Wa
b
and the minimum cla
s
sification error ra
te is applied
as the criteri
on to obtain the
optimum pa
ra
meters
s
W
and
c
W
.
(5) With the optimum parameters
s
W
and
c
W
and the e
quatio
n (5
), the
ga
s co
nce
n
tratio
n
time seri
es i
s
transfo
rme
d
to the state se
quen
ce.
(6) The predi
cted state
val
ue
,
j
Nk
s
is e
s
timated de
pen
d o
n
the p
r
e
s
ent
values of th
e
state sequence and
the possi
bility transi
t
ion matrix.
(7)Cal
cul
a
te the state valu
e
,
ˆ
j
Nk
s
for the pre
d
i
cted value
,
ˆ
j
Nk
d
wi
th equation (5
).
(8) T
he final correcte
d pre
d
i
cted value
,
ˆ
ˆ
j
Nk
d
is obtained by the equ
ation (6).
The lo
w-freq
uen
cy detail
seq
uen
ce
with nonlin
ea
rity reflec
t
s
the bas
i
c characte
ristics of
the gas
co
ncentration tim
e
se
rie
s
. The
r
efore,
we u
s
e the SVM model for it
s predi
ction. T
he
spe
c
ific
step
s can be d
e
scribed a
s
follows:
(1)
C-C meth
od is ap
plied
to get the opt
imum delaye
d
time and e
m
beddi
ng di
mensi
on
of
,1
,
2
,
{,
,
,
}
.
JJ
J
J
N
Aa
a
a
(2) Th
e inp
u
t and
outp
u
t
vectors
of th
e SVM mo
de
l is
obtain
ed
throug
h p
h
a
s
e spa
c
e
recon
s
tru
c
tio
n
with the del
ayed time an
d embed
ding
dimen
s
ion.
(3) T
he pa
ra
meters of SVM are optimi
z
ed by the P
S
O(Parti
c
le
Swarm
Opti
mization
)
[10, 11].
(4) T
he predi
cted value
,
J
Nk
a
of the detail se
quen
ce i
s
obt
ained by trai
n
ed SVM mod
e
l
[12].
The final
predicte
d
valu
e of the ga
s co
n
c
ent
rati
on time
seri
es i
s
obtai
n
ed by
sup
e
rim
p
o
s
in
g the predi
cte
d
values of all
compo
nent
s.
4. Experiment Re
sults a
nd Discu
ssi
ons
We te
st the p
r
opo
se
d mod
e
l with 86
0 g
a
s
con
c
e
n
trat
ion sample
s
comin
g
from t
he II826
Coal Fa
ce of
Luling coal m
i
ne of Huaib
e
i
Mini
ng Gro
u
p
Comp
any in Anhui Provi
n
ce. We sel
e
c
t
the first
720
data a
s
th
e e
x
perime
n
tal
sample
s a
nd t
he la
st 1
40 d
a
ta a
s
the
predictive
sam
p
les.
Firstly, the ga
s con
c
ent
rati
on time
seri
e
s
is
re
co
nstru
c
ted to th
ree
seq
uen
ce
s
wi
th 3 level
sca
l
e
wavelet b
a
se
db3
by the
wavelet
de
co
mpositio
n an
d re
co
nstruct
i
on of the
ori
g
inal d
a
ta. T
he
recon
s
tru
c
ted
sequ
en
ce
s a
r
e sh
own in F
i
gure 2.
Figure 2. Wa
velet Decomp
osition a
nd Reco
nstruc
tio
n
of the Origin
al Gas
Con
c
e
n
tration Time
Series
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ISSN: 23
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TELKOM
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KA
Vol. 12, No. 10, Octobe
r 2014: 736
1
– 7368
7366
We build the
ARMA model
for the high-f
r
equ
en
cy seq
uen
ce
s D1, D2, and D3 while the
AIC crite
r
io
n
method i
s
use
d
for
ord
e
r d
e
termi
n
a
t
ion. The n
e
w con
s
tru
c
te
d mod
e
ls
are
ARMA(2
，
9),
ARMA(9
，
8
)
and A
R
MA(7
，
10
). Th
en
we
co
rrect
the predi
cted
value by th
e
weig
hted Markov co
rre
ctio
n
meth
od an
d
obtai
n
the
optimum pa
rameters
s
W
and
c
W
by the
grid
method whe
r
e
[
1
,
100]
s
W
and
[
1
,
2
00]
c
W
. The optimum pa
ra
meters obtain
ed by the ARMA
model with
weighted Ma
rkov corre
c
tion
method a
r
e show a
s
the T
able 1.
Table 1. Mod
e
l Paramete
rs of Detail Se
quen
ce
s
Reconstructe
d Sequence
p q
Ws Wc
D1 2
9
64
197
D2 9
8
100
169
D3 7
10
72
193
We
cal
c
ulate
the larg
est L
y
apunov exp
onent
by
sm
all data sets
for the lo
w-freque
ncy
approximate seq
uen
ce an
d the result is
0.1
146
.
It indicates that the sequ
ence has
cha
o
ti
c
c
h
arac
teris
t
ic. With the optimum delayed time
2
an
d the emb
e
d
d
ing dim
e
n
s
i
on
5
m
obtaine
d by C-C metho
d
, we re
co
nst
r
uct pha
se
sp
ace of the
se
quen
ce a
nd
get the input
and
output vecto
r
s of the SVM model. With
radial b
a
si
s f
unctio
n
as th
e ke
rnel fun
c
tion of the SVM
model, the pa
ramete
rs of S
V
M optimized
by the PSO
are
241
.
944
1
c
，
0.
01
，
0.
1
．
For co
mpa
r
i
s
on, we
cho
o
se
fou
r
eva
l
uation crite
r
i
ons
MAE(M
ean
A
b
sol
u
te
Error),
MAPE (Mean Absolute
Percentag
e Error), RMS
E
(R
oot Mean Square E
rror) and NRMSE
(No
r
mali
ze
d root mean squ
a
re e
rro
r).
Expressio
n
s of
these criteri
o
ns are sh
ow
as follo
w:
，
(7)
，
(8)
，
(9)
，
(
1
0
)
Whe
r
e
is th
e
index of th
e d
a
ta,
is th
e p
r
e
d
icte
d
value
of the d
a
ta,
i
s
the true
value
,
is the
averag
e valu
e and is
is the total numbe
r of the data.
In orde
r to verify the pre
c
ision of the fi
tted model, u
s
e the al
go
rithm propo
sed
in this
pape
r to
pre
d
ict the
la
st
140
ga
s
con
c
entration
val
ues.
Tabl
e 2
sh
ows the
p
r
edi
ction
erro
r of
each se
que
n
c
e. It shows
that the high
er level
the wavelet de
co
mpositio
n an
d recon
s
tru
c
t
i
on
rea
c
he
s, the
stron
g
e
r
the
rand
omn
e
ss
and noi
se of
these det
ail seq
uen
ce
s b
e
com
e
an
d the
lowe
r the
pre
c
isi
on of A
R
MA pre
d
ictio
n
mod
e
l
get.
And Ma
rkov con
s
traint correctio
n
met
hod
can
greatly correct th
e de
viation
of the
predi
cted
val
ue du
e to
ran
domne
ss. Ho
wever, fo
r the
D3
seq
uen
ce
with small
ran
d
o
mne
ss, A
R
MA predi
ct
io
n model
can
get a high
predictive p
r
e
c
i
s
ion
and M
a
rkov
corre
c
tion
m
e
thod
do n
o
t
have a
rem
a
rkabl
e result. Experiment
result
s
sho
w
t
hat
for the gas concentratio
n
time serie
s
with str
ength v
o
latility, the c
o
mbinatio
n of ARMA model
1
1
ˆ
n
ii
i
M
AE
y
y
n
1
ˆ
1
n
ii
i
i
yy
MA
P
E
ny
2
1
1
ˆ
()
n
ii
i
RM
S
E
y
y
n
2
1
1
ˆ
()
1
()
n
ii
i
n
i
i
yy
NR
M
S
E
n
yy
i
ˆ
i
y
ˆ
i
y
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Com
b
ine Mul
t
i-pre
d
icto
r of Gas
Con
c
e
n
tration Pre
d
icti
on Base
d on
Wa
velet…
(Wu Xiang
)
7367
and the
Markov modificati
on st
rategie
s
can ta
ke
adv
antage
of the
pre
d
ictive a
b
ility of the linear
model an
d st
atistical mo
de
l.
Table 2. Pred
iction Error of
Wavelet De
compo
s
ition S
eque
nce
Reconstructed
Sequence
Method
MAE
MAPE
RMSE
NRMSE
D1
ARMA
0.0303
31.4719
0.0632
0.2574
ARMA-MCM
0.0137
17.0502
0.0232
0.0944
D2
ARMA
0.014
3.8727
0.0295
0.1193
ARMA-MCM
0.0111
3.0899
0.0249
0.1006
D3
ARMA
0.0076
0.8507
0.0137
0.0431
ARMA-MCM
0.0078
0.864
0.0133
0.0418
A3
SVM
0.0131
0.0363
0.019
0.0349
Figure 3 sh
ows the cha
r
t of the final pr
e
d
icte
d
value su
pe
rimpo
s
e
d
up
on every
sub
s
e
que
nce
and the a
c
tu
al data. Fro
m
the Figure,
It can b
e
seen
that the final predi
cted d
a
ta
of the propo
sed method
ca
n fit the
actual gas con
c
ent
ration data
well.
Figure 3. Actual Value (th
e
solid lin
e) a
nd M
odel O
u
tput (the da
sh
ed line) of Ch
ecking Sam
p
l
e
s
To verify the
effectivene
ss
of the p
r
o
posed
meth
od,
routine m
e
tho
d
s
are
u
s
ed
t
o
p
r
edi
ct
the ga
s
co
n
c
entration
sa
mples for co
mpari
s
o
n
. Th
ese
metho
d
s incl
ude
BP
neural n
e
two
r
k
predi
ction
mo
del, SVM p
r
e
d
iction
mo
del
, SVM predi
ction m
odel
ba
sed
on
BP
(W-BP) an
d S
V
M
predi
ction
mo
del b
a
sed
on
wavel
e
t d
e
compo
s
itio
n
(W-SVM
). Th
e
predi
cted
re
sults comp
ari
s
on
sho
w
a
s
the Table 3.
Table 3. Co
m
pari
s
on of Dif
f
erent Predi
ct
ion Method
s
BP
SVM
W-BP
W-SVM
Multi-predictor
MAE
0.0372
0.0317
0.0282
0.0158
0.0131
MAPE
0.1035
0.0681
0.0778
0.0426
0.0363
RMSE
0.0477
0.0279
0.0389
0.023
0.019
NRMSE 0.0878
0.09
0.0716
0.0424
0.0349
In the BP neural
network predi
ction
model,
we g
e
t the avera
ge value of
ten time
indep
ende
nt
predi
ction as the
final
pre
d
i
cted
val
ue. T
he network hi
dden laye
r transfe
r fun
c
tio
n
is Sigmod fun
c
tion, the tran
spo
r
t layer transfe
r fun
c
tio
n
is Purelin fu
nction, the tra
i
ning alg
o
rith
m
is variabl
e le
arnin
g
rate m
o
mentum a
n
d
gradi
ent
de
scent algo
rith
m and the le
arnin
g
rate i
s
0.1
.
In
the
SVM model, we chose
radial basi
s
fun
c
tio
n
a
s
the
ke
rnel fun
c
tion
and o
p
timize
the
para
m
eters
with the PSO
method. F
r
o
m
Tabl
e 3, it
can
be
se
en
that the p
r
e
c
i
s
ion
of the
m
u
lti-
74
0
760
780
800
820
84
0
860
0.
2
0.
3
0.
4
0.
5
0.
6
t /
m
i
n
(C
H
4
)/
%
O
r
i
g
i
n
dat
a
P
r
edi
c
t
dat
a
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 736
1
– 7368
7368
predi
cto
r
mod
e
l pro
p
o
s
ed i
n
this pa
per i
s
obviou
s
ly
superi
o
r to
the
single
-
p
r
edi
ctor model
s, such
as BP a
nd
SVM. And the predi
ction
error i
s
smal
ler tha
n
that
of the supe
r po
sition
of
the
predi
cted val
ues of the wavelet deco
m
positio
n an
d recon
s
tru
c
tion seq
uen
ces ba
sed o
n
the
singl
e-p
r
edi
ct
or BP
or SVM. The
expe
riment
re
sult
s sh
ow that th
e combi
natio
n of m
u
lti-scale
wavelet
de
co
mpositio
n a
n
d
multi-pre
d
i
c
tor
ca
n im
p
r
ove the
p
r
e
d
iction
preci
s
ion a
nd h
a
ve a
strong practi
cability.
5. Conclusio
n
This p
ape
r
d
i
scusse
s the
multi-pre
d
ict
o
r combi
nati
on predi
ctio
n method f
o
r ga
s
con
c
e
n
tration
and buil
d
s t
he multi-p
r
e
d
i
ctor p
r
edi
ctio
n model
with
wavelet tra
n
sform, Ma
rkov
corre
c
tion
model, A
R
MA and
SVM. Acco
rding
to t
he the
o
reti
cal analy
s
is and
experim
ental
results, the fo
llowing
con
c
l
u
sio
n
s
can b
e
dra
w
n.
(1) The
wa
velet de
com
positio
n a
n
d
re
con
s
tructi
on
can
de
comp
ose th
e ga
s
con
c
e
n
tration
information i
n
to different
seq
uen
ce
s.
Acco
rdi
ng to
the ch
ara
c
te
ristics of different
seq
uen
ce
s, we apply different pre
d
ictio
n
model
s fo
r di
fferent se
que
nce
s
a
nd take advantag
es of
each pre
d
icto
r to effectively improve the
predi
ction p
r
eci
s
ion.
(2) Fo
r the
hi
gh-frequ
en
cy detail
se
que
nce
s
ha
s a
st
rong
rand
om
ness,
we
co
mbine th
e
ARMR mo
del
and Markov
con
s
trai
nts correctio
n
method an
d take
full advantage of the line
a
r
fitting ability o
f
the ARMR model an
d the statistical a
b
ility of Markov model.
(3) T
he
singl
e-p
r
edi
ctor m
odel
s have
some di
s
adva
n
tage
s, su
ch
as a g
r
e
a
t volatility of
the result, susceptibl
e
interfere
n
ce caused
by unce
r
taintie
s
and un
wa
rra
nted pre
d
icti
on
pre
c
isi
on. In this pap
er, we
propo
se
d a multi-
predi
cto
r
combi
nation
predi
ction m
e
thod ba
sed
on
wavelet tran
sform. Comp
ared with the ro
uti
ne singl
e-p
r
edi
ctor mo
de
l BP and SVM, and wavel
e
t-
based
single
-
predi
cto
r
mod
e
l W-BP a
nd
W-SVM, Th
e prop
osed met
hod imp
r
oved
the pre
d
ictio
n
pre
c
isi
on.
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