TELKOM
NIKA
, Vol.11, No
.3, March 2
0
1
3
, pp. 1683 ~ 1690
ISSN: 2302-4
046
1682
Re
cei
v
ed
No
vem
ber 1
6
, 2012; Re
vi
sed
Jan
uar
y 26, 2
013; Accepte
d
February 9,
2013
Chaotic Prediction for Traffic Flow of Improved BP
Neural Network
Yue Hou
*1
, Yuemei Mai
2
1,2
School of Ele
c
tronic an
d Informatio
n
Engi
n
eeri
ng, La
n Z
hou Jia
o
T
ong Universit
y
,
Lan Z
h
o
u
73
00
70, P.R.Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hou
yu
e@ma
i
l
.lzjtu.cn
*1
, y
u
e
m
eimai
@
16
3.c
o
m
2
A
b
st
r
a
ct
A pred
iction
al
gorith
m
for traf
fic flow
predicti
on
of BP
ne
ural b
a
se
d on
Di
fferential Ev
ol
u
t
ion (D
E
)
is prop
ose
d
to
overco
me the
prob
le
ms suc
h
as lon
g
co
mp
uting ti
me an
d
easy to fal
l
into
local
mini
mu
m by
combi
ng DE
a
nd n
eur
al n
e
tw
ork. In the a
l
go
rithm, DE
is us
ed to
opti
m
i
z
e
the thres
h
o
l
ds
and w
e
i
ghts of
B
P
neur
al netw
o
rk, and the BP n
eura
l
netw
o
rk is used to sear
ch for the optima
l
soluti
on. The efficiency of
the
prop
osed
pre
d
i
c
tion
meth
od i
s
tested by th
e si
mul
a
tio
n
of
tw
o typical ch
aotic ti
me ser
i
es an
d rea
l
tra
ffic
flow
.
T
he simulati
on results
show
that th
e propos
ed method has hi
g
her prec
isi
on
compar
ed w
i
th the
traditio
nal BP n
eura
l
netw
o
rk, so prove it is fe
asibl
e
an
d effe
ctive in the pra
c
tical
prediction of traffic flow.
Ke
y
w
ords
: pre
d
ictio
n
; traffic fl
ow
; BP neural netw
o
rk; differentia
l evol
utio
n
(DE)
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Traffic guid
a
n
ce an
d con
t
rol is the important
pa
rt of the intelligent traffic system.
Real
-time an
d pre
c
i
s
e traffic flow is th
e premi
s
e a
nd the key to the
reali
z
ation of
traffic guid
a
n
c
e
and control [
1
, 2]. Urban t
r
affic flow
system ha
s
si
g
n
ificant chaot
ic ch
ara
c
te
ristic, and its sh
ort-
term traffic flo
w
data is the
cha
o
tic time serie
s
. The tho
ught, based o
n
that fact, is to build a non-
linear
mappi
n
g
, whi
c
h i
s
to
build a
pre
d
i
c
tion mo
del t
o
re
store its
origin
al sy
ste
m
app
roximat
e
ly.
So far, many
schola
r
s h
a
v
e made a l
o
t of research
in this field
and built va
riou
s traffic fl
ow
predi
ction m
o
dels
su
ch a
s
Volterra filte
r
ada
ptive model [3], BP
neural netwo
rk mo
del [4] and
RBF ne
ural
netwo
rk
mod
e
l [5]. Among these mod
e
ls, ne
ural
n
e
twork b
e
co
mes the
hot
spot
becau
se of its great lea
r
ning po
we
r and goo
d g
eneralization
ability. However, values of
threshold
s
a
nd weig
hts o
f
neural network h
a
ve
a greate
r
influen
ce to the performan
ce in the
pra
c
tical u
s
e
[6]. Differential Evolution (DE), pr
o
p
o
s
e
d
in 1995 by Storn, is an algorithm ba
se
d
on gro
up opti
m
ization [7]. The algo
rith
m has great global sea
r
ch
ing ability and simple p
r
in
ciple
with fewe
r controlle
d parameters
to realize easily,
so it’s very
adapta
b
le for neural net
work
para
m
eters o
p
timization.
From th
e pe
rspe
ctive of n
on-lin
ea
r time se
rie
s
, this article, u
s
in
g ch
aotic
dynamics
theory to anal
yze the sho
r
t-term traffic flow,
puts forwa
r
d a BP neural netwo
rk m
e
thod ba
sed
on
DE (DEBP).
When apply this method
to two typical
chaoti
c
time series and traffic flow time
seri
es, results sh
ow that the
method h
a
s greate
r
no
n-line
a
r fitting
ability and higher p
r
e
d
icating
ac
cur
a
cy
.
2. Basic Di
fferential
Ev
olution Algori
t
hm
Differential e
v
olution (DE
)
algorithm i
s
an improved
algorith
m
ba
sed on group
evolution
with characte
ristics of o
p
timal value of
memori
al in
dividual an
d
grou
p-i
n
information sha
r
i
ng,
whi
c
h is to optimize the
value of
the pr
oble
m
using coop
era
t
ion and co
mpetition am
ong
individual
s in the grou
p [7].
First, get a group of ran
d
o
m
initialed po
pulation:
0
X
=
[
]
,..,
,
0
0
2
0
1
NP
x
x
x
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
o
tic Pre
d
i
c
tion for T
r
affic Flow
of Im
p
r
oved BP Ne
ural Netwo
r
k (Yue Hou)
1683
NP
is the size of the population and D is the
dimen
s
ion
.
Under a se
ries of operation,
evolution of i
ndividual
s of
the t gene
rati
on is
]
,...,
,
[
,
2
,
1
,
t
D
i
t
i
t
i
t
i
x
x
x
x
.The pri
n
cipl
e of algo
rithm
is that the differen
ce vecto
r
obtained by the di
vision b
e
twee
n two random differe
nt individuals
o
f
the pare
n
t generation ad
ded on a ra
ndom sele
cted
individual
create
s
a m
u
tation individual.
Then a
c
cordi
ng to certain
proba
bility, crossove
r pa
rent individual
s and mutati
on individual
s to
cre
a
te a ne
w individual,
which com
p
are
s
with pa
rent individu
als a
c
cordi
n
g to the value of
sufficie
n
cy fu
nction, an
d then sel
e
ct indi
viduals
wi
th the optimal su
fficiency a
s
child gen
eratio
n.
2.1.
Mutation Operation
Mutation op
e
r
ation
can
avoid evolutio
n
falli
ng into p
a
rtial optim
al
value. The
basi
c
mutation part
of DE is the
differen
c
e ve
ctor of
parent
generation a
nd each vect
or pair
contai
ns
two different i
ndividual
s
(
t
r
t
r
x
x
2
1
,
).
With the fact that mutation i
ndividual
s ha
ve different creating
mode
s, variet
ies evolutio
n scena
rio
s
are
fo
rmed an
d the ba
sic mut
a
tion is eq
uat
ion (2
).
)
(
2
1
3
t
r
t
r
t
r
m
x
x
F
x
x
(2)
Whe
r
e
t
r
x
1
and
t
r
x
2
a
r
e differe
nt ra
ndom individ
uals a
n
d
]
2
,
0
[
F
is the zoom fa
ctor.
2.2. Cross
o
v
e
r Opera
t
ion
DE use
s
cro
s
sover op
era
t
ion to maintain gro
up di
versity. Cro
s
sover
strateg
y
is:
makin
g
cro
s
sover ope
ratio
n
betwe
en th
e
i
individual
t
i
x
and
m
x
of the g
r
oup to
cre
a
te a test
individual
T
x
.To guarantee in
dividual evol
ution, firs
t through rand
om
sele
ction, assuri
ng
T
x
is
provide
d
by
at least o
n
e
m
x
and oth
e
r bit
s
are obtai
n
ed by CR. T
he fun
c
tion
of cro
s
sover
operation is e
quation (3).
CR
rand
x
CR
rand
x
x
t
ij
mj
Tj
()
()
D
j
,...,
2
,
1
(3)
whe
r
e
()
rand
is the random val
ue in [0, 1];
CR
[0,1]. The bigger CR is, more ben
efit fo
r
accele
rating
conve
r
ge
nce
speed. Th
e
smaller
CR
is, more b
enefit for maintaining g
r
oup
diversity
and global sea
r
ch
.
2.3. Selectio
n Opera
t
ion.
DE adopts g
r
eedy sea
r
chi
ng strate
gy to sele
ct child
generatio
n with high sufficiency,
and the fun
c
tion of sele
ctio
n operation is equation (4).
)
(
)
(
)
(
)
(
1
t
i
T
t
i
t
i
T
T
t
i
x
f
x
f
x
x
f
x
f
x
x
(4)
3. BP Neural
Net
w
o
r
k
BP neural ne
twork is a kin
d
of multilayer fo
rwa
r
d net
work which contain
s
input
layer,
output layer and implication layer. The
docume
n
t
prese
n
ts a typical 3-laye
r BP neural net
work
[8], and the q
uantity of neu
ron of o
u
tput
layer with
bet
ter predi
ctive effect in chao
tic time se
rie
s
predi
ction is
m
, the quantity of neuron
of selecte
d
implicatio
n layer is
p
, the
quantity of output
layer is 1 so mappin
g
of neural n
e
two
r
k is
1
:
R
R
f
m
and its exp
r
essio
n
is eq
uation (5
).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1682 – 1
690
1684
p
j
j
j
i
i
b
c
X
f
x
1
1
)
exp(
1
1
)
(
(5)
Whe
r
e
j
c
the link wei
ght from implication is layer to output layer;
is the thre
sh
o
l
d of output
layer and
j
b
is the output of n
ode
s of implication layer.
Tran
sition fun
c
tion of BP n
eural n
e
two
r
k is sigmoid fu
nction
x
e
x
f
1
1
)
(
, thus
we
have equ
atio
n (6).
p
j
x
w
b
m
i
j
i
ij
j
,
,
2
,
1
,
)
exp(
1
1
1
(6)
whe
r
e
ij
w
is the
link wei
ght from input layer to implicatio
n layer;
j
is the thresh
old of nodes of
implication layer; link wei
g
ht
ij
w
,
j
c
and thre
shol
d
j
,
can
obtaine
d by
BP neural ne
twork
training so
1
i
x
is predi
cable.
Equation 4 is predi
ction m
odel of chaoti
c
time serie
s
of BP neural
netwo
rk, no
rmally
p
is
1
2
m
.
4. Algorithm Design o
f
BP Neural Ne
tw
o
r
k Based
on DE
4.1. Principle
The pri
n
ci
ple of DEBP is: list the possibl
e existing
neurons in
neural network
and
make th
e po
ssi
ble lin
k weights a
nd th
reshold
s
of these neu
ron
s
befo
r
e trai
ning bin
a
ry code
string
or in
dividual
s rep
r
e
s
ented by re
al cod
e
st
ri
ng, furthe
rmo
r
e ra
ndom g
ene
ra
te populatio
n of
these st
ring
s and enhan
ce the popula
t
ion diversity using ran
d
o
m
selectio
n, mutation and
cro
s
sove
r. Throu
gh mutat
i
on and cro
s
sover ope
ratio
n
, a new tempora
r
y popul
ation is creat
ed.
Usi
ng strate
gy to make
optimized
selectio
n
of individual
s of population,
thereby a new
popul
ation is
cre
a
ted on
ce
again. In accordan
ce
with the pro
c
e
s
s optimal in
dividual wo
uld
be
found. Assig
n
the optimal individual
obt
ained by DE to initial weigh
t
and threshol
d, and then use
BP neural n
e
twork p
r
edi
cti
on mod
e
l to find the be
st
to get predi
ctio
n value of BP neural netwo
rk
with glob
al op
timal value.
4.2. Algorith
m
of BP Neu
r
al Net
w
o
r
k
Bas
e
d on D
E
.
Steps of the algorith
m
are:
(i)
Cod
e
: DE uses re
al cod
e
whi
c
h the len
g
th of
individual cod
e
is e
qual to the numbe
r of its
variable. Thi
s
pape
r co
de
s BP neural n
e
twork’
s pa
ra
meters
ij
w
,
j
c
,
j
and
together
into
one individu
al
and ea
ch ind
i
vidual rep
r
e
s
ents a BP network st
ru
cture.
(ii)
Initial popul
ation an
d pa
ra
meters of al
g
o
rithm: given
the si
ze
of po
pulation
as
NP
, the initial
popul
ation ra
ndom create
d
NP
individuals a
s
T
p
W
W
W
W
)
,
,
,
(
2
1
, zoom factor as
M
and
initial value of crosso
ver probability factor
CR
. Setting the biggest
iteration of algorithm
k
,
get a real vector
t
w
w
w
,
,
,
2
1
of individual
i
W
as a chro
moso
me of DE.
(iii)
Sufficiency fu
nction:
suffici
ency i
s
the
main
ind
e
x d
e
scribi
ng me
rit degre
e
of i
ndividual
s in
popul
ation in
DE. This p
a
p
e
r, we
adopt
mean
sq
u
a
re
error a
s
sufficien
cy functi
on and th
e
expre
ssi
on is
equatio
n (7
).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
o
tic Pre
d
i
c
tion for T
r
affic Flow
of Im
p
r
oved BP Ne
ural Netwo
r
k (Yue Hou)
1685
2
1
)
(
1
p
N
p
p
y
t
N
G
(7)
Whe
r
e
N
i
s
the total sum
of training sa
mples;
p
t
is the expectatio
n
value of the
p
sampl
e
;
p
y
is
the actual o
u
t
put of the
p
sampl
e
. Cal
c
ulate the suffi
cien
cy
of each individual a
nd re
se
rve the
individual wit
h
the minimu
m sufficien
cy.
(iv)
Mutation: ma
ke mutation
operation to individual
i
W
accordin
g to eq
uation (2
) to create
mutation indi
vidual
'
i
W
.
(v) Cro
s
sove
r: make
crosso
ver ope
ratio
n
to mutation individual
s
i
W
and
'
i
W
according to
equatio
n (3
), and then
cre
a
t
e new individ
ual
T
W
.
(vi)
Selection: su
bstitute and into object fun
c
tion and a
c
cordin
g to equation (4) sele
ct individual
with s
m
all value of s
u
ffic
i
enc
y
func
tion
'
T
W
as individ
uals of new pop
ul
ation.
Separate the
individual o
b
tained by
DE in
to the link
weight a
n
d
thre
shol
d
of BP
neural net
wo
rk which al
so
worke
d
a
s
th
e initial weigh
t
and thresho
l
d of predi
ction model. M
a
ke
training of BP neural net
wo
rk p
r
edi
ction
netwo
rk to
ge
t the optimal
value of chao
tic time serie
s
predi
ction.
5. Simulation Experimen
t
Apply DEBP prediction
model to
prediction
of real traffic flow time
series then
comp
are with
BP neural ne
twork predi
ction model
to confirm the val
i
dity of the method.
5.1. Prediction Ass
essm
ent Sta
ndard
s
Erro
r asse
ssment of experime
n
t main
ly uses RMS
E
, NRMSE and Re, whi
c
h are
expre
s
sed in
equatio
n (8
) to (11
)
.
2
/
1
1
2
)
(
)
(
ˆ
1
1
S
t
t
y
t
y
S
RMSE
(8)
2
/
1
1
2
2
)
(
)
(
ˆ
)
1
(
1
S
t
t
y
t
y
S
NRMSE
(9)
S
t
S
t
t
y
t
y
t
y
1
2
1
2
)
(
)
(
)
(
ˆ
Re
(10
)
Whe
r
e
S
the numbe
r of pre
d
iction is sa
mples;
)
(
t
y
and
)
(
t
y
a
r
e se
parately predi
ction a
n
d
expectatio
n
value;
re
pre
s
ents
stand
ards vari
an
ce
of object t
i
me se
rie
s
. Apply follow
expre
ssi
on to
make no
rmal
ization to time seri
es d
a
ta of experime
n
t and then ma
ke ph
ase sp
a
c
e
recons
truc
tion [9].
)
min(
)
max(
1
1
i
i
n
i
i
i
i
x
x
x
n
x
x
(11
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1682 – 1
690
1686
Whe
r
e
i
x
is ori
g
i
nal time se
rie
s
and
i
x
is norm
a
lizatio
n time seri
es.
5.2. T
w
o
Ty
p
i
cal Chao
tic Time Series
Hen
o
n
chaoti
c
time se
rie
s
:
The mathem
atical mod
e
l of chaoti
c
time seri
es i
s
eq
uation (1
2).
)
(
)
1
(
)
(
)
(
1
)
1
(
2
k
bx
k
y
k
ax
k
y
k
x
(12
)
Whe
n
,
4
.
1
a
,
3
.
0
b
，
system is in cha
o
tic co
ndition,
the powe
r
sy
stem thro
ugh
pha
se
spa
c
e recon
s
truction afte
r the iteration i
s
sho
w
n in Fig
u
re 1.
Lore
n
z
cha
o
tic time se
rie
s
predi
ction.
The mathem
atical mod
e
l of chaoti
c
time seri
es i
s
eq
uation (1
3).
bz
xy
dt
dz
y
x
z
c
dt
dy
x
y
a
dt
dx
)
(
)
(
(13
)
Whe
n
10
a
,
3
/
8
b
,
28
c
, system is in
cha
o
tic co
ndition
, three dime
n
s
ion
a
l pha
se
spa
c
e
trajecto
ry an
d the two-di
mensi
onal p
h
a
se pla
ne attracto
r thro
ug
h pha
se sp
a
c
e re
co
nst
r
u
c
tion
are sho
w
n in
Figure 2.
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
-0
.
4
-0
.
3
-0
.
2
-0
.
1
0
0.
1
0.
2
0.
3
0.
4
x
n
y
n
Figure 1. Hen
on syste
m
it
erative of a=1.
4 and b
=
0.3
In experime
n
t, BP neural net
wo
rk stru
cture
sel
e
cts
1
-
5
-
m
typic
a
l three-layer
stru
cture, the step si
ze of
int
egral time
of two typical cha
o
tic time se
rie
s
is 0.1, embed
ded
dimen
s
ion
m
is 4, 4, 2 separately an
d delay time
is 1. The nu
mber of train
i
ng is 1
0
,000
,
training o
b
je
ct error i
s
0.01 and le
arn
i
ng rate i
s
0
.
1. DE para
m
eters ar
e: set the si
ze
of
popul
ation a
s
10, the number of evolution gene
rat
i
on as 100, cro
s
sove
r rat
e
as 0.4 an
d
mutation rate
as 0.2. Take forme
r
1,500
data of cha
o
tic time se
rie
s
as traini
ng sa
mples a
nd lat
e
r
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TELKOM
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046
Cha
o
tic Pre
d
i
c
tion for T
r
affic Flow
of Im
p
r
oved BP Ne
ural Netwo
r
k (Yue Hou)
1687
500 d
a
ta a
s
predi
ction
test sampl
e
s. Fi
gure
3-Figu
re
4 sho
w
s
sin
g
le-step
pre
d
i
c
tion im
pre
ssion
dra
w
ing of Lo
ren
z
sy
stem and Tabl
e 1 shows predi
ct
ion error of two typical ch
ao
tic time seri
es.
-20
-1
0
0
10
20
-40
-20
0
20
40
0
10
20
30
40
50
x
L
o
r
e
n
z
a
ttr
a
c
to
r
y
z
-20
-15
-1
0
-5
0
5
10
15
20
-30
-20
-10
0
10
20
30
x
y
Lorenz
a
t
t
r
ac
t
o
r
-3
0
-20
-1
0
0
10
20
30
0
5
10
15
20
25
30
35
40
45
50
y
z
Lo
r
e
nz
at
t
r
ac
t
o
r
-2
0
-15
-1
0
-5
0
5
10
15
20
0
5
10
15
20
25
30
35
40
45
50
x
z
Lo
r
e
n
z
at
t
r
ac
t
o
r
Figure 2. Lorenz attracto
rs through p
h
a
s
e spa
c
e reco
nstru
c
tion
0
10
20
30
40
50
60
70
80
90
100
-2
-1
0
1
2
n
x
(
n,
t
r
u
e
)
,
x
(
n
,
pr
ed
)
t
r
ue
(
-
)
an
d pr
ed(
.
)
0
10
20
30
40
50
60
70
80
90
100
-0
.
1
0
0.
1
0.
2
0.
3
n
Pr
e
d
i
c
t
i
o
n
Er
r
o
r
a. The fore
ca
sting re
sult b
a
se
d on BP
neural network model
0
10
20
30
40
50
60
70
80
90
100
-2
-1
0
1
2
n
x
(
n
,
tr
u
e
)
,x
(
n
,p
r
e
d
)
t
r
ue
(
-) a
nd
pred(.
)
0
10
20
30
40
50
60
70
80
90
100
-0.
1
0
0.
1
0.
2
0.
3
n
P
r
edi
c
t
i
on E
r
r
o
r
b. The fore
ca
sting re
sult b
a
se
d on DEB
P
neural
netwo
rk m
o
d
e
l
Figure 3. The
foreca
sting
result ba
se
d o
n
Hen
on cha
o
tic time se
ri
es
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ISSN: 2302-4
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TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1682 – 1
690
1688
0
50
100
150
200
250
300
35
0
400
45
0
500
-20
-10
0
10
20
n
x
(
n
,tr
u
e
)
,x
(
n
,p
r
e
d
)
t
r
u
e
(-)
and pr
ed
(.
)
0
50
100
150
200
250
300
35
0
400
45
0
500
-0
.
1
0
0.
1
0.
2
0.
3
n
P
r
edi
c
t
i
on E
r
r
o
r
0
50
100
150
200
250
300
350
400
450
500
-2
0
-1
0
0
10
20
n
x
(
n,
t
r
ue)
,
x
(
n
,
p
r
ed)
t
r
ue(
-)
and
pr
ed(
:
)
0
50
100
150
200
250
300
350
400
450
500
-0
.
1
0
0.
1
0.
2
0.
3
n
P
r
e
d
i
c
t
i
on E
r
r
o
r
a
.
Th
e f
o
r
e
c
a
s
t
in
g
r
e
su
lt ba
se
d
o
n
BP n
e
u
r
a
l ne
t
w
o
r
k
mo
d
e
l b.
Th
e
f
o
r
e
ca
s
t
in
g re
su
lt
b
a
s
e
d
on
DEBP me
u
r
al n
e
t
w
o
r
k
mod
e
l
Figure 4. The
foreca
sting
result ba
se
d o
n
Lore
n
z
cha
o
tic time se
ri
es
Table 1. Fo
re
ca
sting erro
rs of
two typical nonline
a
r sy
stem
s
sy
stem
Henon
Lorenz
training steps
BP 4580
560
DEBP 8
2
RMSE
BP 0.1019
0.1038
DEBP 0.0512
0.0233
NRMSE
BP 0.1380
0.2250
DEBP 0.0778
0.0504
Re
BP 0.0193
0.0585
DEBP 0.0049
0.0025
5.3. Prediction of Re
al Traffic Flo
w
Ti
me Series
The traffic flow data in the simulatio
n
ca
me
from the traffic data in March, 2011
of the
Britain Tran
sport Bureau.
Observation t
i
me is 6:
0
0
-2
0:00 an
d the
traffic flow d
a
ta is record
ed
and cal
c
ulate
d
every 15
minutes. In this pape
r,
5
days’ data (3
36 grou
ps) was taken a
s
the
resea
r
ch object and the improve
d
algorithm
cal
c
ul
ating the maximum Lyapunov index wa
s
adopte
d
[10]. The re
sult
s sho
w
that the
delay time
is
1, embed
ding
dimen
s
ion
m
is 3 and the
maximum Lyapun
ov index is 0.3754 which illust
rate
that
this tim
e
serie
s
of traffic flow is the
c
h
aotic
time series
.
In the experiment, the number of network tr
ai
ning is 5,000, train
i
ng object error is
0.01, and learning rate is 0.1 and other param
et
ers remain unch
ange
d. Take the former 2
36
data of traffic flow se
rie
s
as trai
ning
sample
s an
d the later 1
00
as te
sting sa
mples to m
a
ke
predi
ction usi
ng DEBP and BP models. Figure 5 shows the prediction result
s when
=1,
m
=3.
Take NRMS
E as the evaluation inde
x, Table 2
p
r
esents p
r
edi
ction errors of two prediction
model
s un
de
r different d
e
la
y time and e
m
beddi
ng di
mensi
on. Fig
u
re
5 an
d Ta
ble 2 expl
ain
that
the predi
ction
result
s of the two model
s are abl
e to
predict the tend
ency of
the chang
e of traffic
flow prope
rly, and that the
predi
ctabl
e accuracy
of
optimize
d
DE
BP model is
highe
r than
BP
model
whi
c
h
explain
s
tha
t
using
DEB
P
predi
ction
model to
pre
d
ict real- traf
fic flow
se
rie
s
is
valid. Seen from Tabl
e 2,
we
can
co
ncl
ude that
the
predi
ction
re
sults rea
c
h th
e be
st wh
en
and
m
valued the best opti
m
al delay time and emb
e
d
d
ing dime
nsi
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
o
tic Pre
d
i
c
tion for T
r
affic Flow
of Im
p
r
oved BP Ne
ural Netwo
r
k (Yue Hou)
1689
0
10
20
30
40
50
60
70
80
90
10
0
20
40
60
80
10
0
12
0
14
0
16
0
18
0
20
0
n
t
r
ue,
pr
ed
T
r
u
e
v
a
l
ue an
d pr
e
d
i
c
t
e
d
v
a
l
u
e f
o
r
B
P
m
o
de
l
tr
u
e
pr
e
d
a.The fore
ca
sting result ba
sed o
n
BP neural net
wo
rk
model
0
10
20
30
40
50
60
70
80
90
10
0
20
40
60
80
10
0
12
0
14
0
16
0
18
0
20
0
n
t
r
ue,
p
r
ed
T
r
ue
v
a
l
u
e an
d pre
d
i
c
t
e
d v
a
l
u
e
f
o
r
D
E
B
P
m
o
de
l
tr
u
e
pr
ed
b.The forecasting resu
lt based on DEBP meural network m
odel
Figure 5. Actual mea
s
u
r
e the fore
ca
st re
su
lts
of traffic flow c
h
aotic
s
e
quenc
e
Table 2. Traf
fic flow fore
ca
sting erro
rs b
a
se
d on different delay time and emb
e
d
d
ing dime
nsi
on
Method
Ty
p
e
4,
1
m
3,
2
m
3,
1
m
BP
0.8815
0.7799
0.7735
DEBP 0.5920
0.5868
0.4470
Comp
ared with typical chaotic time seri
es p
r
edi
ction, the advance
d
extent o
f
predi
ction precisi
on of DEBP model acted on traffic fl
ow time series is less whi
c
h explains that
urba
n traffic flow sy
stem ha
s high
er com
p
lexity.
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ISSN: 2302-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1682 – 1
690
1690
6. Conclusio
n
Aiming at hig
h
deman
d on
real time of traffic guid
a
n
c
e and control
and its indi
cated
non-li
nea
r an
d unce
r
tainty, this paper, started from
no
n-line
a
r time seri
es, provid
es an improved
cha
o
tic time
seri
es
pre
d
ict
i
on of BP neu
ral net
work b
a
se
d on
DE and ap
plie
s the metho
d
to
the
predi
ction of
real traffic flow sy
stem, and then ma
ke
s com
p
a
r
ison
with BP neural n
e
twork
predi
ction m
o
del on p
r
edi
ct
ion preci
s
ion.
Results
sho
w
that the ne
w mod
e
l ha
s better no
n-lin
ear
fitting ability a
nd high
er p
r
e
d
iction p
r
e
c
isi
on on typical
cha
o
tic time serie
s
and traffic flow.
Ackn
o
w
l
e
dg
ements
This
wo
rk
wa
s finan
cia
lly supp
orte
d by the n
a
tional
so
cia
l
sci
en
ce fo
undatio
n
(12
C
GL
004
)
and Ga
nsu provincial n
a
tura
l sci
en
ce fou
ndation (111
2
R
JZA051
).
Referen
ces
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JM.
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plica
b
l
e
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e
rm T
r
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l
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r
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r
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g
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a
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he
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