Fund
P
roject
:
Op
en
F
und of Chongqing Key Laboratory of Traffic and Transportation Engineering under Grant
NO.2008CQJY006
The
A
uthor: Z
HOU
S
ha (1986

),
F
emale, Xiantao, Hubei. She is a
secon
d

year graduate student in Department
of Tra
nsportation at Chongqing Jiaotong University. Her current research interests are in the field of traffic safety
and ITS. She received the MA degree in Traffic Engineering from Wuhan University of Science and Technology
in 2008. E

mail:
agenlsa@hotmail.com
,
Tel
:
13114058224
,
Fax
:
023

68662112
1
Forecast of Traffic Safety Based on Fuzzy
Generalized Neural Network
Z
HOU
Sha,
J
IANG
Gongliang,
H
UANG
Yong
Chongqing Key Laboratory of Traffic and Transportation Engineering
, Chongqing Jiaotong
University
, P.O. Box 213
Chongqing Jiaotong University
, City,
Chongqing 400074; PH (
8
6)
13114058224; FAX (86) 023

68662112
; email:
agenlsa@hotmail.com
Abstract:
Considering a number of factors
affecting
traffic safety
, t
he
predetermination model for traffic safety of
fuzzy generalized neural network was
built in this paper
.
This was a
combination of neural network
s
with fuzzy
algorithm
s
, through the study of present road safety situation
s
in China
,
and t
he
summary of domestic and broad documents. This method
was
based on
MATLAB
programming
,
and fuzzy revised
generalized learning vector quantization
modeling
;
f
uzzy
g
eneralized
n
eural
n
etwork
s
had
to
be used
to cope with subjective factors in
traffic a
ccident prediction
and
improv
e
the
computations
of
the
predetermination
model for traffic safety. The theoretical
analysis
and experimental results indicate
d
that the model wa
s effective for the good function of nonlinear mapping and
generaliz
ation
，
and
can be applied to
forecast traffic
accident
suitably
.
Key words
: Traffic Safety; Predetermination model
；
Fuzzy Generalized Neural
Network
；
Generalized Learning Vector Quantization
Ⅰ
INTRODUCTION
Road safety is a vague concept, that is to say, it
’
s connotation and ex
tension is
ambiguous,
thus it is difficult to
d
etermine
a
clear and reasonable
boundary
between
security and insecurity
[
3
]
.
U
nsafe matter on the road
s,
k
nown as traffic
accident
s
are
caused by the imbalance of dynamic traffic system
s
composed of people, vehicles,
roads,
the
environment
,
and management,
all of
which are part of
a
particular
traffic environment. P
eople, vehicles, roads, environment
,
and management
,
are t
he
basic factors
of affecting
traffic safety
.
Traffic
accidents are the result of
several
factors.
Only a variety o
f factors
can
be
considered
.
R
easonable measures can be
Fund
P
roject
:
Op
en
F
und of Chongqing Key Laboratory of Traffic and Transportation Engineering under Grant
NO.2008CQJY006
The
A
uthor: Z
HOU
S
ha (1986

),
F
emale, Xiantao, Hubei. She is a
secon
d

year graduate student in Department
of Tra
nsportation at Chongqing Jiaotong University. Her current research interests are in the field of traffic safety
and ITS. She received the MA degree in Traffic Engineering from Wuhan University of Science and Technology
in 2008. E

mail:
agenlsa@hotmail.com
,
Tel
:
13114058224
,
Fax
:
023

68662112
2
established
to prevent road traffic accident
s
.
Artificial neural network as a parallel
settlement model
have
more advantages than
the
previous models
have
.
It
has
achieved remarkable results in many practical fields.
The a
ccuracy
of accident
pr
ediction models
that
used BP network
are
higher than the traditional methods
. BP
neural network
ha
s
been successfully used in many patte
rn prediction problems
[
2
].
The
drawback
of
BP neural network is
the
slow convergence and
the
local minor
.
Hence, t
he result
s
are
not satisfactory when it comes
to
smaller
sample
s
and
noise
problems
.
G
eneralized fuzzy neural network
(GFNN)
was
use
d
to predict road traffic
accident
in this
paper.
GFNN
network
was
trained with
fuzzy
g
eneralized
l
earning
v
ector
q
uantization
(FGLVQ)
algorithm that
made
the training process tend to global
optima
.
The comparative
analyses
of
the various
forecasting methods are presented
in table 1.
Table 1
Comparative
A
nalysis of Road Traffic
A
ccident
F
orecasting
M
ethod
Prediction
Categories
Features
Scope
General
approach
T
he model
is
based
on
causality and
time

series,
main
ly.
It
cannot reflect the
inherent and complex properties of the
forecasting dynamic data
roundly and
constitutionally
.
It
will
lose the amount of
information
easily
.
W
hen a small amount of
investigation was added, it
was
able to
be forecasted.
Then
these methods could be
considered.
ANN
I
t
had
an excellent
n
onlinear mapping
ab
ility
and
low e
xpectation of
the
structure, parameters
,
and dyna
mic
characteristics related to
m
odeling
objects
.
It
just
needed
the object input and
output data
;
it can be finished through the
learning function
of the completion of the
network itself.
It
was
better with
continuous
urban transport development
policies when there
was
complete historical data.
3
Artificial neural network and fuzzy systems
are
based on fuzzy theory
;
b
oth have
used
numerical method
s
to estimate nonlinear mapping relationship between the
input and output.
None of them
used
m
athematical modeling
.
Different
to the
traditional
s
ymbol
method
s
and
m
odeling
method
s
,
they obtain
ed
certain nonlinea
r
dynamic control solution
s
by
the
adaptive dynamic method.
The membership
functions and fuzzy weights
had to
be precisely established in fuzzy algorithm, and
thi
s process
was
completed
adaptively in neural network
.
BP
algorithm
,
b
ased on
t
he rules of
gradient descent
,
received
local minimization too easily and
converged
slowly
.
S
olving global minimum
s
of complex nonlinear equations
was
regarded as
the target in BP algorithm.
This
a
lgorithm itself
was
a method i
n local optimum
searching
.
The
training process
was to
essentially
get
the minima of a nonlinear
function
.
The
training
would have failed
because of the local optimization.
The
training
strengthenin
g
and
learning ability may
have
be
en
decreased
.
Over fitting
may have occurred as well.
In
regard
to
the
research
method
,
this
paper
dealt
with
the
accuracy improvement of
traffic accident
prediction
by GFNN,
combining
fuzzy
system
theory
and
neural
network
.
T
he learning algorithm
of this combined model
ing
is fuzzy generalized
learning vector quantization algorithm
(FGLVQ).
Ⅱ
FGLVQ
S
tructure
of FGLVQ
A
neuron is defined as follows:
If
X
i
i
s
input
of
the
i
th
fuzzy logic
neuron
, and
is
corresponding
weight,
where
i=1,2,
…
,n,
and
is
a
threshold value
.
Function
f
is
defined
by
(
1
)
Sample vector
,
is t
he current cluster
ing
center
. T
he
weighted error function
and
mathematical expectation
[6
]
are
4
defined
respectively
by
（
2
）
（
3
）
W
here
ur
=
ur(x)
，
r=1,2,…c
. It
is
the weight of sample
X
which belongs to the Rth
c
ategory
.
f(x)
is the probability distribution density
function
when
X
belongs to space
R
n
.
If
x
belongs to
X
and
,
V
r
will be called
winning
unit.
Usually
t
he
corresponding weight
of the w
inning unit
V
r
is
set
to
one
, and
the
n
on

winning unit
u
i
is a
non

negative number less than
one.
F
ig.1 shows
the
structure of
a fuzzy logic neuron.
Figure 1:
A fuzzy logic neuron
The structure block diagram of
GFNN
is
given in
Fig.
2.
Input vector
X
is a factor set
in
layer 1
.
Input
of
layer
2 equals to fuzzy membership degr
ee of input in
layer 1
,
and it
indicate
s
the membership degree of of
i
th
factors.
, between layer
2 and
layer 3, is the
required weight
.
The
fourth
l
ayer is a fuzzy logic operation
, and
the
last layer is
the output
b
j
,
j=1,2,
…
c
.
.
5
Figure
2
:
The structure block diagram of
GFNN
Fuzzy
membership function
Let us first consider the simplified case
.
A simple and effective membership function
will b
e defined in order to reduce
calculations
. Non

li
near membership function is
defin
ed
as
(4)
, and
linear membership function is defined by
(5)
F
uzzy membership
functi
on
ur(x)
is defined
as
(
6
)
, where
the equation for agsigning the values of D is
(
7
)
Rep
resents
generalized
fuzzy membership degree
correspond
ing
to
current input vector
Vr
.
p(z) is a monotonically decreasing function of z.
p(z)
meets
conditions
: P(0)=1
,
p(z) =1 /z,
p(z)=0
.
It can be
defined by
[1] [3
]
.
At this time quantization
error function
[6
]
is
defined by
6
(8
)
The
Input vector
is mapped into
interval [0,1)
via
generalized
fuzzy
membership
function
.
The
I
nput
vector is converted into
fuzzy membership degree
via f
uzzy set
membership function
.
Then
the precise
input is changed in
to
fuzzy
quantity.
That is
the
fuzzying input vector.
Afterward, the
v
ague language
will be
converted into
precise numeri
cal
values
.
That is
anti

fuzzy
ing
output vector
.
T
he iteration coefficients of FGLVQ have a good upper and lower bounds
. It can
solve the "Scale" problem
of
generalized learning vector quantization algorithm
(
GLVQ
).
T
he fuzzy learning vector quantization
algorithm
(FLVQ) is
sensitive to the
initial learning rate
, however, FGLVQ
is
not. The learning of reference vectors by
FGLVQ can avoid these problems [5]. L
earning then ensues
, as defined in [5].
Ⅲ
T
HE
PROCESS
OF
T
RAFFIC
ACCIDENT
P
REDICTION
Using the met
hod of
F
GLVQ
,
by establishing
the
China
traffic
safety
model,
and
adapting the data
coming from
China
statistical year
book
(19
9
5

200
8
),
the number
of traffic accidents
can
be predicted.
S
even factors related
to
road traffic accident
that
stored
in the
matrix
X
are
the
input
variable
s
, and
the number of traffic accidents is
output
variable
s
.
The
fuzzy rule database is established according to the rule table
.
This
provide
s
numerous
learning sample
s
for
F
GLVQ.
In summary,
the
combi
ned
p
redetermination
model
GFNN
via
FGLVQ
learning
algorithm
is a
six

step process
.
(1)
Select
ing
an input pattern. T
he target forecast
ed
area
and
the prediction
y
ear
should be confirmed
first.
(2)
C
ollect
ing
traffic data
.
T
he factors related
to
road t
raffic accidents
are d
etermin
ed
.
If
the historian
accident
data can be
obtained
,
more
information
can be received
.
G
enerally
,
appropriate data
will
be
collected
when
the acquisition cost
i
s taken into
account
.
(3)
Applying the
combination mo
del
.
E
ach parameter
is
unitize
d
f
irst
ly,
and then
it is
hazed
.
(4)
L
earning
the
parameters
with
F
GLVQ.
Afterward,
the weights
will be revised
until they are
stable
.
(5)
A
nti

fuzzy output.
(6)
S
ubmit
ing
the forecast
ed
results
.
7
F
igure
3
: The
process of
traffic saftey
prediction
Ⅳ
R
ESULTS
AND
D
ISCUSSION
Using the above combination method
,
GFNN
,
in the
specific calculation of
traffic
safety
prediction.
The target region is China.
T
he following seven historical statistical data
are
regarded as
impact factors
,
according to
the
analy
sis of the above factors results
:
p
opulation, number of motor vehicles, highway mileage,
passen
ger and freight
transport
,
passenger
turnovers
,
and
freight turnovers
.
The num
ber of road traffic
accidents
is
the output factor
.
GFNN is
construct
ed.
T
he output of
G
FNN
function
represents
function
S
.
E
ach parameter
is
unitize
d
and
hazed
before the
imitative learning
because of
the
output value
s
ranging between
zero
and one
.
MATLAB
was
used
for debug
ging in this paper. T
he maximum
numbe
r of
learning
was
2,000
times, and the
rate of
l
earning
was
0.05
.
The
learning
goal
was
t
he sum of
squares of errors
, which
was
0.001.
T
he initial value of the network connection
weight
was
a
random number
that
belonged
to the space
[

1,1]
.
F
GLVQ
was
used in
the
network learning algorithm, and then GFNN
was
used to
simulat
e.
The relative
predict
ed
error
was
0.01%
.
Consequently, these were satisfying results.
8
The
data from 199
5
to 2003
was
the
training sample
of
network
.
The
sample data
from 2004 to 2008
was
e
xtrapolate
d in
the
prediction test
. The s
ample
d
ata
is
shown
in Table
2.
Table
2
The S
ample
D
ata
Year
P
opulation
N
umber
of
V
ehicles
H
ighway
M
i
leage
Passenger
T
ransport
F
reight
T
ransport
P
assenger
T
urnovers
F
reight
T
urnovers
N
um
ber
of
R
oad
T
raffic
A
ccidents
units
million
million
million
miles
billion
billion
tons
billion
person

kilometers
billion
ton

kilometers
thousand
1995
1211.21
25.35
1.1
6
11.73
12.35
900.19
3590.90
271.84
1996
1223.89
28.73
1.19
12.45
12.98
916.48
3659.00
287.69
1997
1236.26
34.34
1.23
13.26
12.78
1005.55
3838.50
304.22
1998
1247.61
40.90
1.28
13.79
12.67
1063.67
3808.90
346.13
1999
1257.86
49.10
1.35
13.9
4
12.93
1129.98
4056.80
412.86
2000
1267.43
57.77
1.40
14.79
13.59
1226.10
4432.10
616.97
2001
1276.27
65.26
1.70
15.34
14.02
1315.51
4771.00
755.00
2002
1284.53
82.27
1.77
16.08
14.83
1412.57
5068.60
773.00
2003
1292.27
94.92
1.81
15.88
15
.65
1381.05
5385.90
667.51
2004
1299.88
104.79
1.87
17.68
17.06
1630.91
6944.50
567.75
2005
1307.56
117.55
3.35
18.47
18.62
1746.67
8025.80
450.25
2006
1314.48
124.95
3.46
20.24
20.37
1919.72
8884.00
378.78
2007
1321.29
137.92
3.58
22.28
22
.76
2159.26
10141.90
327.21
2008
1328.02
169.89
3.73
2
3
.
96
24
.
45
23
3
0
.
47
1
0345
.
35
265.20
Source:
NBS, China statistical Yearbook, various years.
Fig.4 shows the
network training process.
Inspection of Fig. 5

7 indicate
s
the results
of fit training
,
residual
,
and
relative error respectively.
The
predictive
absolute
value of the maximum relative error is
5.2755*10

7
, and
the
average of absolute
relative deviation (AARD) is 2.6021*10

9
in the road traffic accident
predetermination model.
9
Fig.
4
the n
etwork training process
Fig.
5
T
he output value compared with
original data
Fig.
6
Residual curve
Fig.
7
relative error
curve
The above figure
s
illustrate
that
GFNN
has
a
great
learning ability
.
The prediction
re
s
ults and the actual
data
ar
e compared
,
and the accuracy of
prediction
s
is
assessed. It
i
s found that the
GFNN
model g
i
ve
s
a
n
accurate prediction
.
The
estimation results
approximately
approach detective values.
The results of tra
i
ning
and
extrapolation prediction
via GFNN
,
indicates that the forecasted value has a
better fit with
the
actual value, and the e
rror rate
i
s only 0.01%
.
The comparison of
the simulated results with the o
riginal
data shows that the model
GFNN
has good
generalizatio
n ability
, and
the error
mee
ts prediction accuracy
.
Therefore
, GFNN
can
be used to forecast
traffic accident
.
10
Ⅴ
CONCLUSION
Fuzzy logic system is easy to understand,
and n
eural network
has
very strong
adaptive
abilities
.
A hybrid of Fuzzy and GLVQ m
odeling
GFNN
for forecasting
traffic
safety
has been
put forward
in
this
paper.
T
he ambiguity of road traffic safety
was
taken
into account
in m
embership degree of fuzzy mathematics
.
T
he maximum
membership degree has two fundamental flaws
:
only extremes are considered
, and
it is
easy to lose the middle of the information
.
Comprehensive consideration of
various factors on the impact of road traffic accident
can
overcome the deficiencies
.
Moreover, n
etwork training
via
GFN
N
requires neither
a large number of samples
,
nor many m
an
ual
adjustable parameters
. T
he Gaussian smoothing factor
only
need
be
estimate
d i
n the training
.
Thus
,
p
rediction
is
more objective
,
accurate
,
and
faster
than
the
ordinary
approach
.
In
conclusion
,
the combination of
Fuzzy logic system
and neural model
GFNN
is
feasible in
traffic safety
prediction
s
,
with
high precision
,
s
trong fault tolerance
,
and
strong self

adap
ting characte
ristic
s
.
GFNN provides a new approach for forecasting
road accident, which has strong practical significance
.
Ⅵ
ACKNOWLEDGMENT
The authors would like to acknowledge the helpful comments
by the anonymous
referees and the editorial comments which contributed
to the improvement of the
final version
of the paper.
Ⅶ
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