- Email: [email protected]
Simulating Traffic Flow Dispersion by Neural Network System Identification
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress ofTFAC
Q-8e-Ol-5
Copyright © 1999 IFAC 14th Triennial World Cungress, Beijing, P.R. China
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWORK SYSTEM IDENTIFICA TION Fengxiang Qiao and Hai Yang Department a/Civil and Structural Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowlool1., Hong Kong, China, fax:852-23581534, email:[email protected], [email protected]
Abstract: Some typical statistical models describe the dispersion of traffic flow on urban road segments: normal distribution model, geometric distribution model and etc. These probabilitybased models fit traffic flow very well under some ideal physical environments but may not be so good under certain complex cases for strict mathematical assumptions. A neural network based system identification approach is used to establish an auto-adaptive model simulating traffic flow dispersion. This model, being feasible to vary kinds of traffic circumstances, can be calibrated online operation and used on forecasting freeway flow. Data simulation shows good performance of the proposed approach. Copyright @ 19991FAC Keywordii;; Traffic Control; Neural Networks; Simulation; ldent(fication; Flow measurement
I.INTRODUCTION
flow by Qiao et al. (l998b), and some neural network methods were used in simulating traffic flow. The neural network methods are good tools in tackling with such transportation problems as the classification of traffic states by Yang et al. (1998), the queue prediction by Chang et al. (1992), and etc. Here in this paper, a neural network based system identification approach is used to establish an autoadaptive model to simulate and forecast the dispersion of traffic flow on road segments. The neural network model used are feasible to varies kinds of traffic circumstances due to their learning and optimization phases, while their structures and linking weights can be calibrated on-line the operation varying with different traffic environments.
Analyzing the dispersion of traffic flow is one of the bases of traffic forecasting, simulation, signal timing and even is one of the cores of some Traffic Control Systems (as such the cases for TRANSYT and SCOOT). There are some typical statistical models for analyzing traffic flow dispersion on urban road segments: the normal distribution model (G. M. Pacey,1956), the geometric distribution model (D. I. Robertson, 1969) and etc. These probability-based models can fit traffic flow very well under some ideal physical environments but may not be so well in certain complex cases since that they are based on some strict mathematical assumptions. It is difficult for these models to fit for varies kinds of traffic flow dispersion on-time the urban road segments, and therefore the limitation of the application of those UTe systems using these models are often occurred in some road areas where the characteristics of traffic flow are quit different from those in the place where the systems were originally produced.
To validate the proposed model, simulation with three data sets have been made. Two sets of them use the classical normal distribution function and the geometric distribution function, while the third set uses the actual data surveyed on one segment in the Nanjing-Hefei freeway in China.
Actually for simulating traffic ±low, apart from the classical probability methods, some other methods have been developed in recent years. The linear program method was used for simulating railway passenger flow by Qiao et a1. (1998a), the dynamic data system method was used for simulating freeway
As traffic moves downstream, the initially tight platoon formed from the departing queue tends to disperse the farther downstream it travels. Because drivers tends to maintain safe headways, or spacing
2. NOTATION OF PLATOON DISPERSION
8357
Copyright 1999 IF AC
ISBN: 008 0432484
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
between vehicles and often travels at different speeds, the platoon tends to spread out - a few moving ahead and some dropping back. Note that the dispersion appears to be to the right because the flow rate is decreasing with time as the platoon reaches each point of observation.
Due to the control of traffic signal, vehicle platoon departed from the stop-line after the beginning of a certain green stage can follow some kinds of rules. Vehicles would depart either with the saturation flow, which occurs at the saturated stage, or with the platoon from up stream, which happens at the unsaturated stage. As dispersion keeping on, the peak of the platoon will become more and more smoothly.
14th World Congress oflFAC
describe the dispersion of platoon. For each time interval (step) t, the arrival flow at the downstream stop-line is found by the following recurrence equation: j-I
qd(i+ t)
=L
.
qo(i)F(l- F)i
11
(3)
i=1
where,
q d (i + t) : predicted fl ow rate (in time interval
(i + t)
of the predicted platoon);
q 0 (i) : flow rate of the initial platoon during step t; F: a smoothing factor that is defined as:
F=(l+a(3T)-1
(4) The analysis of the phenomenon of platoon dispersion is of vital importance in the real time prediction of downstream flow alone the road segment between intersections, and therefore in the on-line signal timing and the Driver Information Systems (DIS).
a is a dispersion factor, which has been found by V.S. when it was set at 0.35; !3 is an empirical factor, generally 0.8.
3.CURRENT M.ETHODS
Since traffic situation varies from place to place, the idea probability-based models may not actual1y fit for the real traffic states, which may be one of the po,~sibJc explanations for why some traffic control systems timed based on these models can not work well on some urban traffic control systems. So, a more auto-adaptive approach may be developed to simulate the trai'fic flow dynamically on time operations.
Quan (1989) summarized that there are currently two kinds of probability based mathematical models describing the dispersion of platoon. One is the normal distribution model that was proposed by G. M. Pacey in 1956, the another one is the geometric distribution model that wa" proposed by D. l. Robertson in 1969. Both supposed that the frequency of the occurring of journal time alone a certain road segment fits for the corresponding random distribution.
3.3
Comments· on Methods
the
Classical
Mathematical
4. NEURAL NETWORK BASED SYSTEM IDENTIFICA TION APPROACH
3.1. Normal Distribution Mudel 4.1. Basic idea According to the normal distribution model, the arrival flow at the downstream stop-line is found by the following equation: }
q,,(i):;
L
qo(i)gU - i)
i==
0)
(2) where, q D (i) : upstream flow rate at time i; q d (j) : downstream flow rate at time j; T: travel time; a: distance; v : average speed ; S: standard deviatjon; g(T): special normal distribution function.
3.2 Geometric Distribution Model
Some famous traffic control systems such as TRANSYT and SCOOT use the geometric model to
The topics of artificial neural networks (NNs) for identification is at present one of the key research areas in the field of traffic system. NNs have been proposed by information and neural science as a result of the study of the mechanisms and structures of the brain. This has led to the development of new computational models, based on this biological background, for solving complex problems like pattern recognition, fast information processing, predicting, controlling, learning and adaptation. Here, we shall investigate a one-layer recurrent network that can be described with the following state equations: y(t + 1) == l(y(t),u(t») (5)
where r is a non-linear mapping and u is the control input. Fig.1 presents a block diagram of the system that can be described by Eq. (5), where, N is the feed forward multilayer neural network, Z-l is the time shift operator.
8358
Copyright 1999 IFAC
ISBN: 0 08 043248 4
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress ofTFAC
4.2. Stages
Y(t+J)
The neural network based system identification may be realized by four stages: Choose Of Nonlinear Model Structure: For comparison. a model structure similar to Fig.2 can be established. Initially, a fully connected network architecture is selected;
Fig. I. Block Diagram of a Neural Network The idea of back-propagation through time is to unfold the network through time, i.e. replace the onelayer recurrent network with a feed-forward one with multi-layers represented by the same neural network mode.ling the mapping r . The class of multi-layer networks considered here is
Validation Of Trained Network: The function of this part is to validate the generated neural network; Improving Performance By Pruning: In order to remove the superfluous weights from the network, it is necessary to determine the optimal network architecture by pruning the network;
furthermore confined to those having only one hidden
layer, and the hyperbolic tangent and linear activation functions (f, F) can be written like this:
y~ (w, W) = F,(i W,;hj (w) + Wi~) pI
=
F{ ~ Wiif{ t
wj1u,
+
Wjn
4.3. Block Diagram of Computer Sim.ulation
J+ w,~ J (6)
The
weights
alternatively
(specified by the
by
the
matrices
!!,
vector
w,
W)
Validation of the final network: Start by re-scaling the weights so that the validation can be performed on un-scaled data.
are
or
All the above approaches and theories have been compiled into computer program in MATLAB language. Fig.2 is the block diagram for computer simulation.
the
adjustable parameters of the network and they are determined from a set of examples (or realizations) through the process ca1led training.
Start
Specify the training set by: ZN
=
{[u(t),y(t)]lt
= \, ...
,N}
(7) Then the objective of training is to determine a mapping from the set of training data to the set of possible weights: (8)
" so that the network will produce predictions y(t),
Simulating The Rest Data
which is in some sense "close" to the true outputs yet). The prediction error approach, which is the strategy applied here, is based on the introduction of a measure of closeness in terms of a mean square error criterion:
VN (8,ZN)
eJo
N( y(t)- y(tI8») " ~T(y(t)- y(tI8») " ~ = -1L 2Nt~1
(9)
The weights are then found as:
e" =- arg
a
min VN CS, z'v )
Fig.2. Block Diagram of Computer Simulation (10)
by some kind of iterative minimization scheme:
e
e(1)
f+l
=
e
i
+ /-l (i) j ( i )
specifies the current iterate (number 'I'),
the search direction and fl (i) is the step size.
(11) is
f(i)
The programs for generating and reading data are specially compiled with convenient man-machine dialogue menu, while the programs relating with the network training and data simulating are based on some MATLAB Toolbox.es on Neural Networks, Signal Processing, System Identification and etc.
8359
Copyright 1999 IF AC
ISBN: 008 0432484
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress oflFAC
5. DATA SIMULATION
N-method
2000
'~"'i800
To compare the neural network based system identification approach with the classical probabilitybased method, data simulations are conducted. There are three sets of data used for simulation;;. The first one is generated from the normal distribution model; the second one is generated from the geometric distribution model, while the third one is surveyed from the actual freeway segment.
1600 -.::J400 Cl>
U
= 58.6 -
0.465D (12)
\
~) 2()()
:
!
\
\
o
, '.' *
wL ,
g ..
)()
._ .
Tinfi\sec)
20
.
40
j
60
50
Fig. 4.Simulating down flow by NN and Ndistribution method 5.2. Simulation Using Data Geometric Distribution Model
Generated
From
Similar to the above, the simulated data of traffic flow followed the geometric distribution is shown in Fig.5. 2000
r
-"i::' 1500
(
!
~
~
1000
" S ::I
.....
,
c
500
\ \ \
\
. .
,
.,
\
\
\
0 0
40
20
60
BD 100 120 140 160 180 Time(sec)
Fig.5. Simulated Data of Traffic Flow by Gdistribution
~ 1500
.
"'::"1000
"
.
i
500
,
Q
~
\
.,J
"
. =
2000
... S ::I
\
j
~~~O L··~"~~·~~'~~~~~\~-~~~~A~ul.~~~~~"-..J. / / \
'0
The simulated data of traffic flow followed the normal distribution is shown in Fig.3.
\
I
~ 600
...."I.
(
I
j
§JOOO :;800
5 . 1. Simulation Using Data Generated From Normal Distribution Model The physical and flow condition for generating the data set is as below: • the distance between the upstream and downstream flow is 150 meters; • the average vehicle velocity is 25km/hr; • the standard deviation of vehicle velocity is 6 km/hr; • time interval for statistical is 2 sec.; • the relationship between velocity U and density D is :
,::7N-ethod
f '
0
o
M
~
00
The lagged platoon stands for the downstream !low. Also , the first pair of platoon is used for training the neural network while the other two used for predicting.
00 1001~1~1W100 Time (sec) 'C2000
The Jagged platoon stands for the downstream flow. There are totally three pairs of upstream-downstream flows, the first one of which is used fOT training the neural network (to determine the network structure and calibrate all the linking weights) while the other two pairs used for predicting. FigA shows the simulation results by neural network approach together with the upstream flow and the downstream flow generated foHowing normal distribution (corresponding to the second and the third platoon in Fig.3). From FigA we may find that the down stream now simulated by the neural network approach fit very well with that generated by the normal distribution model.
~-m"bOd
~,1500
Fig.3. Simulated Data of Traffic Flow by Ndistribution
I \
~
~ lOOO
-S
I
I
500
J
o o
I~
I
\ ."j!
!
~
/N-method
20
Tim~o(sec)
\
\
~.',.~~~~....J 60
80
Fig. 6. Simulating down flow by NN and Gdistribution method Fig.6 shows the simulation results by neural network approach together with the upstream flow and the downstream flow generated following geometric distribution (corresponding to the second and the third platoon in Fig.5). From Fig.6 we may find that the down stream flow simulated by the neural
8360
Copyright 1999 IFAC
ISBN: 0 08 043248 4
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
network approach also fit rather well with that generated by the geometric distribution model. 5.3 Simulation Using the Actual Freeway Data A test using the aforementioned approach has been made to simulate and forecast traffic flow. The road segment for test is located on Nanjing-He(fei Freeway in Anhui Province of China, which links two provincial capitals (Nanjing and Heifei) and is part of the longest national highway (corded G312). The road-band width of the freeway is 26 meters with two lanes in each direction. A sub-control center is nearby the selected road segment to detect and monitor the flow according to the message from the loop detectors embedded beneath road pavement. Fig.7 is the schematic illustration for the survey of the actual data on the segment of part of the chosen freeway.
119f+SOO
118KiOOO
Tp_]II~_iliglL_~
--..,..',..,
14th World Congress ofTFAC
downstream flow (from a certain past time point to the point just one step ahead before the present time), while the output is the down stream flow at present time. The total time period for analysis is 72 min. The first 40 min are chosen for training, the rest ones are then used for forecasting. Fig.8 s.hows the simulation result, from which we may see that the simulated curve can basically follow the actual situation. 500 ~400
~
300
~200
e""'::I
~
117k+SOO
lOO
0
o
20
40
Time (min)
60
80
Fig.8. Predicting freeway flow using NN method
____________________ l ________ _____ _ ~
+--
6. SUMMARY (1) Upstream Section (2) Downstream Section (3) Validating Section
r:;;oCameral Loop
o
Fig. 7 Illustration of test arrangement The test was focu:.ed on flow direction from Nanjing to Hefei with time period from 15:00 to 16:20 ep.m.) on one typical traffic day on April 1995. The upstream section was chosen on 119K+500 while the downstream section was chosen on 117k+SOO, and therefor the total length of the testing segment is 2km. Data of traffic variables on the upstream section and the downstream section were collected once a minute from LOOP detector:. locating on road pavement with TV camera monitoring the whole operation of flow system. Besides, to validate the surveyed data, a manual counting of corresponding tlow variables was made on 118K+OOO between the surveyed segment. Time interval for collecting data is 1 minute. The input to the system are chosen as upc."fream velocity, upstream flow (both are time series from a certain past time point to the present time point), and
This paper proposes a neural network based system identification approach to simulate the traffic platoon dispersion on urban road segments, which has also been proved to be applicable to the situation of freeway systems. Table 1 gives a comparison between the classical mathematical methods and the proposed approach, from which we may see that the neural network approach can fit for more physical conditions, with no deterministic probability assumption. The results of data simulation may possibly give us such an evident of the good performance for the proposed neural network based system identification approach, especially for the simulation to flow platoon on urban road segments. This might provide a possible way for dynamic traffic systems, such as on-line signal control system, dynamic route auto-guide system, freeway dynamic traffic control system and etc., to simulate and predict traffic flow more efficiency and more autoadaptively.
8361
Copyright 1999 IF AC
ISBN: 008 0432484
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress ofIFAC
Table I Comparison Between the Classical Mathematical Method and the Proposed Neural Network Approach Methods
Mathematical Methods
Physical Conditions Assumptions
Between intersections (with distances about 150 meters or less) Following some deterministic probability based distribution function
Result Applications
Rather smoothly Normally in signal control system
Neural Network System Identification Approach Between Intersections For freeway flow forecasting Both model type and all parameters generated from input data can fit for varies kinds of traffic conditions Smoothly but wl slight variation Signal control system Freeway flow forecasting Auto-guide system, etc.
REFERENCES Chang G.-L. & C. -co Su (1995). Predicting Intersection Queue with Neural Network Models. Transportation Research, 3c, 175-19 I. Qiao F. & H. Yang (l998a). A Transit Passenger Flow Control Model on KCR In: Traffic and Transportation Studies (Z. Yang, K. C. P. Wang, and B. Mao, Bd.). pp.427-435. ASCE, Reston, Virginia. Qiao F. & H. Yang (1998b). A Dynamic Data System Approach to Simulate Freeway Traffic Flow In: Proceedings of the 8-th World Conference on Transportation Research. Antwerp, BeJgium. Quan Y. (1989). Urban Traffk Control, The People's Transportation Publishing House. Beijing, China. Yang H. & F. Qiao (1998). Neural Network Approach to Classification of Traffic Flow States. Journal a/Transportation Engineering, 124,521525.
8362
Copyright 1999 IF AC
ISBN: 0 08 043248 4
14th World Congress ofTFAC
Q-8e-Ol-5
Copyright © 1999 IFAC 14th Triennial World Cungress, Beijing, P.R. China
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWORK SYSTEM IDENTIFICA TION Fengxiang Qiao and Hai Yang Department a/Civil and Structural Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowlool1., Hong Kong, China, fax:852-23581534, email:[email protected], [email protected]
Abstract: Some typical statistical models describe the dispersion of traffic flow on urban road segments: normal distribution model, geometric distribution model and etc. These probabilitybased models fit traffic flow very well under some ideal physical environments but may not be so good under certain complex cases for strict mathematical assumptions. A neural network based system identification approach is used to establish an auto-adaptive model simulating traffic flow dispersion. This model, being feasible to vary kinds of traffic circumstances, can be calibrated online operation and used on forecasting freeway flow. Data simulation shows good performance of the proposed approach. Copyright @ 19991FAC Keywordii;; Traffic Control; Neural Networks; Simulation; ldent(fication; Flow measurement
I.INTRODUCTION
flow by Qiao et al. (l998b), and some neural network methods were used in simulating traffic flow. The neural network methods are good tools in tackling with such transportation problems as the classification of traffic states by Yang et al. (1998), the queue prediction by Chang et al. (1992), and etc. Here in this paper, a neural network based system identification approach is used to establish an autoadaptive model to simulate and forecast the dispersion of traffic flow on road segments. The neural network model used are feasible to varies kinds of traffic circumstances due to their learning and optimization phases, while their structures and linking weights can be calibrated on-line the operation varying with different traffic environments.
Analyzing the dispersion of traffic flow is one of the bases of traffic forecasting, simulation, signal timing and even is one of the cores of some Traffic Control Systems (as such the cases for TRANSYT and SCOOT). There are some typical statistical models for analyzing traffic flow dispersion on urban road segments: the normal distribution model (G. M. Pacey,1956), the geometric distribution model (D. I. Robertson, 1969) and etc. These probability-based models can fit traffic flow very well under some ideal physical environments but may not be so well in certain complex cases since that they are based on some strict mathematical assumptions. It is difficult for these models to fit for varies kinds of traffic flow dispersion on-time the urban road segments, and therefore the limitation of the application of those UTe systems using these models are often occurred in some road areas where the characteristics of traffic flow are quit different from those in the place where the systems were originally produced.
To validate the proposed model, simulation with three data sets have been made. Two sets of them use the classical normal distribution function and the geometric distribution function, while the third set uses the actual data surveyed on one segment in the Nanjing-Hefei freeway in China.
Actually for simulating traffic ±low, apart from the classical probability methods, some other methods have been developed in recent years. The linear program method was used for simulating railway passenger flow by Qiao et a1. (1998a), the dynamic data system method was used for simulating freeway
As traffic moves downstream, the initially tight platoon formed from the departing queue tends to disperse the farther downstream it travels. Because drivers tends to maintain safe headways, or spacing
2. NOTATION OF PLATOON DISPERSION
8357
Copyright 1999 IF AC
ISBN: 008 0432484
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
between vehicles and often travels at different speeds, the platoon tends to spread out - a few moving ahead and some dropping back. Note that the dispersion appears to be to the right because the flow rate is decreasing with time as the platoon reaches each point of observation.
Due to the control of traffic signal, vehicle platoon departed from the stop-line after the beginning of a certain green stage can follow some kinds of rules. Vehicles would depart either with the saturation flow, which occurs at the saturated stage, or with the platoon from up stream, which happens at the unsaturated stage. As dispersion keeping on, the peak of the platoon will become more and more smoothly.
14th World Congress oflFAC
describe the dispersion of platoon. For each time interval (step) t, the arrival flow at the downstream stop-line is found by the following recurrence equation: j-I
qd(i+ t)
=L
.
qo(i)F(l- F)i
11
(3)
i=1
where,
q d (i + t) : predicted fl ow rate (in time interval
(i + t)
of the predicted platoon);
q 0 (i) : flow rate of the initial platoon during step t; F: a smoothing factor that is defined as:
F=(l+a(3T)-1
(4) The analysis of the phenomenon of platoon dispersion is of vital importance in the real time prediction of downstream flow alone the road segment between intersections, and therefore in the on-line signal timing and the Driver Information Systems (DIS).
a is a dispersion factor, which has been found by V.S. when it was set at 0.35; !3 is an empirical factor, generally 0.8.
3.CURRENT M.ETHODS
Since traffic situation varies from place to place, the idea probability-based models may not actual1y fit for the real traffic states, which may be one of the po,~sibJc explanations for why some traffic control systems timed based on these models can not work well on some urban traffic control systems. So, a more auto-adaptive approach may be developed to simulate the trai'fic flow dynamically on time operations.
Quan (1989) summarized that there are currently two kinds of probability based mathematical models describing the dispersion of platoon. One is the normal distribution model that was proposed by G. M. Pacey in 1956, the another one is the geometric distribution model that wa" proposed by D. l. Robertson in 1969. Both supposed that the frequency of the occurring of journal time alone a certain road segment fits for the corresponding random distribution.
3.3
Comments· on Methods
the
Classical
Mathematical
4. NEURAL NETWORK BASED SYSTEM IDENTIFICA TION APPROACH
3.1. Normal Distribution Mudel 4.1. Basic idea According to the normal distribution model, the arrival flow at the downstream stop-line is found by the following equation: }
q,,(i):;
L
qo(i)gU - i)
i==
0)
(2) where, q D (i) : upstream flow rate at time i; q d (j) : downstream flow rate at time j; T: travel time; a: distance; v : average speed ; S: standard deviatjon; g(T): special normal distribution function.
3.2 Geometric Distribution Model
Some famous traffic control systems such as TRANSYT and SCOOT use the geometric model to
The topics of artificial neural networks (NNs) for identification is at present one of the key research areas in the field of traffic system. NNs have been proposed by information and neural science as a result of the study of the mechanisms and structures of the brain. This has led to the development of new computational models, based on this biological background, for solving complex problems like pattern recognition, fast information processing, predicting, controlling, learning and adaptation. Here, we shall investigate a one-layer recurrent network that can be described with the following state equations: y(t + 1) == l(y(t),u(t») (5)
where r is a non-linear mapping and u is the control input. Fig.1 presents a block diagram of the system that can be described by Eq. (5), where, N is the feed forward multilayer neural network, Z-l is the time shift operator.
8358
Copyright 1999 IFAC
ISBN: 0 08 043248 4
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress ofTFAC
4.2. Stages
Y(t+J)
The neural network based system identification may be realized by four stages: Choose Of Nonlinear Model Structure: For comparison. a model structure similar to Fig.2 can be established. Initially, a fully connected network architecture is selected;
Fig. I. Block Diagram of a Neural Network The idea of back-propagation through time is to unfold the network through time, i.e. replace the onelayer recurrent network with a feed-forward one with multi-layers represented by the same neural network mode.ling the mapping r . The class of multi-layer networks considered here is
Validation Of Trained Network: The function of this part is to validate the generated neural network; Improving Performance By Pruning: In order to remove the superfluous weights from the network, it is necessary to determine the optimal network architecture by pruning the network;
furthermore confined to those having only one hidden
layer, and the hyperbolic tangent and linear activation functions (f, F) can be written like this:
y~ (w, W) = F,(i W,;hj (w) + Wi~) pI
=
F{ ~ Wiif{ t
wj1u,
+
Wjn
4.3. Block Diagram of Computer Sim.ulation
J+ w,~ J (6)
The
weights
alternatively
(specified by the
by
the
matrices
!!,
vector
w,
W)
Validation of the final network: Start by re-scaling the weights so that the validation can be performed on un-scaled data.
are
or
All the above approaches and theories have been compiled into computer program in MATLAB language. Fig.2 is the block diagram for computer simulation.
the
adjustable parameters of the network and they are determined from a set of examples (or realizations) through the process ca1led training.
Start
Specify the training set by: ZN
=
{[u(t),y(t)]lt
= \, ...
,N}
(7) Then the objective of training is to determine a mapping from the set of training data to the set of possible weights: (8)
" so that the network will produce predictions y(t),
Simulating The Rest Data
which is in some sense "close" to the true outputs yet). The prediction error approach, which is the strategy applied here, is based on the introduction of a measure of closeness in terms of a mean square error criterion:
VN (8,ZN)
eJo
N( y(t)- y(tI8») " ~T(y(t)- y(tI8») " ~ = -1L 2Nt~1
(9)
The weights are then found as:
e" =- arg
a
min VN CS, z'v )
Fig.2. Block Diagram of Computer Simulation (10)
by some kind of iterative minimization scheme:
e
e(1)
f+l
=
e
i
+ /-l (i) j ( i )
specifies the current iterate (number 'I'),
the search direction and fl (i) is the step size.
(11) is
f(i)
The programs for generating and reading data are specially compiled with convenient man-machine dialogue menu, while the programs relating with the network training and data simulating are based on some MATLAB Toolbox.es on Neural Networks, Signal Processing, System Identification and etc.
8359
Copyright 1999 IF AC
ISBN: 008 0432484
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress oflFAC
5. DATA SIMULATION
N-method
2000
'~"'i800
To compare the neural network based system identification approach with the classical probabilitybased method, data simulations are conducted. There are three sets of data used for simulation;;. The first one is generated from the normal distribution model; the second one is generated from the geometric distribution model, while the third one is surveyed from the actual freeway segment.
1600 -.::J400 Cl>
U
= 58.6 -
0.465D (12)
\
~) 2()()
:
!
\
\
o
, '.' *
wL ,
g ..
)()
._ .
Tinfi\sec)
20
.
40
j
60
50
Fig. 4.Simulating down flow by NN and Ndistribution method 5.2. Simulation Using Data Geometric Distribution Model
Generated
From
Similar to the above, the simulated data of traffic flow followed the geometric distribution is shown in Fig.5. 2000
r
-"i::' 1500
(
!
~
~
1000
" S ::I
.....
,
c
500
\ \ \
\
. .
,
.,
\
\
\
0 0
40
20
60
BD 100 120 140 160 180 Time(sec)
Fig.5. Simulated Data of Traffic Flow by Gdistribution
~ 1500
.
"'::"1000
"
.
i
500
,
Q
~
\
.,J
"
. =
2000
... S ::I
\
j
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5 . 1. Simulation Using Data Generated From Normal Distribution Model The physical and flow condition for generating the data set is as below: • the distance between the upstream and downstream flow is 150 meters; • the average vehicle velocity is 25km/hr; • the standard deviation of vehicle velocity is 6 km/hr; • time interval for statistical is 2 sec.; • the relationship between velocity U and density D is :
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The lagged platoon stands for the downstream !low. Also , the first pair of platoon is used for training the neural network while the other two used for predicting.
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The Jagged platoon stands for the downstream flow. There are totally three pairs of upstream-downstream flows, the first one of which is used fOT training the neural network (to determine the network structure and calibrate all the linking weights) while the other two pairs used for predicting. FigA shows the simulation results by neural network approach together with the upstream flow and the downstream flow generated foHowing normal distribution (corresponding to the second and the third platoon in Fig.3). From FigA we may find that the down stream now simulated by the neural network approach fit very well with that generated by the normal distribution model.
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Fig.3. Simulated Data of Traffic Flow by Ndistribution
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Fig. 6. Simulating down flow by NN and Gdistribution method Fig.6 shows the simulation results by neural network approach together with the upstream flow and the downstream flow generated following geometric distribution (corresponding to the second and the third platoon in Fig.5). From Fig.6 we may find that the down stream flow simulated by the neural
8360
Copyright 1999 IFAC
ISBN: 0 08 043248 4
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
network approach also fit rather well with that generated by the geometric distribution model. 5.3 Simulation Using the Actual Freeway Data A test using the aforementioned approach has been made to simulate and forecast traffic flow. The road segment for test is located on Nanjing-He(fei Freeway in Anhui Province of China, which links two provincial capitals (Nanjing and Heifei) and is part of the longest national highway (corded G312). The road-band width of the freeway is 26 meters with two lanes in each direction. A sub-control center is nearby the selected road segment to detect and monitor the flow according to the message from the loop detectors embedded beneath road pavement. Fig.7 is the schematic illustration for the survey of the actual data on the segment of part of the chosen freeway.
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14th World Congress ofTFAC
downstream flow (from a certain past time point to the point just one step ahead before the present time), while the output is the down stream flow at present time. The total time period for analysis is 72 min. The first 40 min are chosen for training, the rest ones are then used for forecasting. Fig.8 s.hows the simulation result, from which we may see that the simulated curve can basically follow the actual situation. 500 ~400
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Fig.8. Predicting freeway flow using NN method
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6. SUMMARY (1) Upstream Section (2) Downstream Section (3) Validating Section
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Fig. 7 Illustration of test arrangement The test was focu:.ed on flow direction from Nanjing to Hefei with time period from 15:00 to 16:20 ep.m.) on one typical traffic day on April 1995. The upstream section was chosen on 119K+500 while the downstream section was chosen on 117k+SOO, and therefor the total length of the testing segment is 2km. Data of traffic variables on the upstream section and the downstream section were collected once a minute from LOOP detector:. locating on road pavement with TV camera monitoring the whole operation of flow system. Besides, to validate the surveyed data, a manual counting of corresponding tlow variables was made on 118K+OOO between the surveyed segment. Time interval for collecting data is 1 minute. The input to the system are chosen as upc."fream velocity, upstream flow (both are time series from a certain past time point to the present time point), and
This paper proposes a neural network based system identification approach to simulate the traffic platoon dispersion on urban road segments, which has also been proved to be applicable to the situation of freeway systems. Table 1 gives a comparison between the classical mathematical methods and the proposed approach, from which we may see that the neural network approach can fit for more physical conditions, with no deterministic probability assumption. The results of data simulation may possibly give us such an evident of the good performance for the proposed neural network based system identification approach, especially for the simulation to flow platoon on urban road segments. This might provide a possible way for dynamic traffic systems, such as on-line signal control system, dynamic route auto-guide system, freeway dynamic traffic control system and etc., to simulate and predict traffic flow more efficiency and more autoadaptively.
8361
Copyright 1999 IF AC
ISBN: 008 0432484
SIMULATING TRAFFIC FLOW DISPERSION BY NEURAL NETWO ...
14th World Congress ofIFAC
Table I Comparison Between the Classical Mathematical Method and the Proposed Neural Network Approach Methods
Mathematical Methods
Physical Conditions Assumptions
Between intersections (with distances about 150 meters or less) Following some deterministic probability based distribution function
Result Applications
Rather smoothly Normally in signal control system
Neural Network System Identification Approach Between Intersections For freeway flow forecasting Both model type and all parameters generated from input data can fit for varies kinds of traffic conditions Smoothly but wl slight variation Signal control system Freeway flow forecasting Auto-guide system, etc.
REFERENCES Chang G.-L. & C. -co Su (1995). Predicting Intersection Queue with Neural Network Models. Transportation Research, 3c, 175-19 I. Qiao F. & H. Yang (l998a). A Transit Passenger Flow Control Model on KCR In: Traffic and Transportation Studies (Z. Yang, K. C. P. Wang, and B. Mao, Bd.). pp.427-435. ASCE, Reston, Virginia. Qiao F. & H. Yang (1998b). A Dynamic Data System Approach to Simulate Freeway Traffic Flow In: Proceedings of the 8-th World Conference on Transportation Research. Antwerp, BeJgium. Quan Y. (1989). Urban Traffk Control, The People's Transportation Publishing House. Beijing, China. Yang H. & F. Qiao (1998). Neural Network Approach to Classification of Traffic Flow States. Journal a/Transportation Engineering, 124,521525.
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Copyright 1999 IF AC
ISBN: 0 08 043248 4