Forecast of Traffic Safety Based on Fuzzy Generalized Neural Network

haremboingAI and Robotics

Oct 20, 2013 (3 years and 5 months ago)

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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



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).


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].




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



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



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
.



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.



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