8/12/2019 05362817

1/4

Traffic Flow Prediction Based on Wavelet Analysis,

Genetic Algorithm and Artificial Neural Network

Lu Baichuan

Transport School, Chongqing Jiaotong University

No. 66, Xuefu Road, Chongqing 400074, China

Emails: baichlu@gmail.com

Huang Meiling

Transport School, Chongqing Jiaotong University

No. 66, Xuefu Road, Chongqing 400074, China

Emails: humeli317@163.com

AbstractBased on the analysis of the characteristics of

nonlinearity and strong interference of traffic flow due to the

complex and uncertainty of time variance in real traffic system, a

new approach has been proposed for traffic flow prediction. First,

wavelet transform is used to eliminate the noise of original traffic

data. Then it decomposes the traffic flow sequence into the low and

high frequencies in the multi- scale analysis and restores the trendcomponents. The artificial neural network is used in multi-scale

forecasting of these coefficients, in which gene algorithm is used to

optimize the artificial neural network. Finally, the real detected

traffic data are used to testify the precision of the model, and the

results show that the model can produce more accurate predictions

than that of traditional artificial neural network model.

Keywords: traffic flow prediction; wavelet analysis; denoise;

multi-scale analysis; artificial neural network; genetic algorithm

I. INTRODUCTIONTraffic flow prediction is to accurately estimate traffic flow

situations during the next period with a prediction algorithm by

analyzing the traffic flow data. It is important to prerequisite indeveloping the right measures for traffic control and inducedtraffic, also now widely carried out for intelligent transportationsystems. There have been many ways for short-term traffic flowprediction, like Kalman filtering method, linear regression model,time series method, non-parameter regression model, ANNmodel etc. As every method has its advantage and also limitation,it is impossible to use only one measure to predict the traffic dueto its complexity, randomness and uncertainty, therefore it needsto develop new measures.

This paper presents a new method of traffic flow prediction-traffic flow prediction based on wavelet analysis, geneticalgorithm and artificial neural network. Wavelet transform has

good time-frequency analysis capability. Wavelet theory ofmulti-scale analysis can describe the characteristics of thephenomenon or process properties in different scale and theperformance of the essential characteristic of these phenomena orprocess; Neural network has a strong nonlinear mapping ability,learning and self-adaptive characteristics. Genetic algorithms can

find the global optimal solution in a complex, multi-peak, non-linear and non-differentiable space, which make up the neuralnetwork easy to fall into a local minimum situation.

II. MULTI-SCALE ANALYSISThe basic ideal of multi-scale analysis is to divide the chosen

signals into different scales. The part being divided into coarsescale is called smoothing signals and the other part is calleddetailed signal. The wavelet transform is a tie to connect signalsin different scale.

The three level wavelet decomposition of signal A0 is shownas Fig. 1, in which A is low frequency, D is high frequency, andserial number is the level of wavelet decomposition.

It is now known from Fig.1 that, in multi-scale analysis, lowfrequency can be further decomposed, and the decomposition canbe represented as, A0=A3+D1+D2+D3. For the next step, it isdecomposed to A4 and D4.

Figure 1. Three level multi-scale analysis tree

III. ELIMINATION OF TRAFFIC FLOW NOISE WITH WAVELETANALYSIS

Normally, there are three steps in the process of de-noisingwith wavelet threshold:

Step 1, wavelet decomposition of one dimension signal. Tochoose a suitable wavelet and a level, then to decompose X(k)

978-1-4244-4994-1/09/$25.00 2009 IEEE

8/12/2019 05362817

2/4

into j levels, finally to make wavelet decomposition andreconstruction with Mallat algorithm. The signal can bedecomposed in following formula:

( ) ( 1)

0

( ) ( 1)

1

( 2 ) , 0,

( 2 ) , 0,

j j

k n

n

j j

k n

n

h n k x j j Z

d h n k x j j Z

+

+

=

=

(1)

Where,( )j

kd is discrete detail coefficients,( )j

kx is discrete

approximation coefficients, 0 ( )k n is low-pass filter coefficients,

1( )k n is high-pass filter coefficients, with

1 0( ) ( 1) ( )nk n h N n= (2)

In which N is the length of filter.

Step 2, Coefficients processing after the signaldecomposition. It uses the soft threshold function for quantitativedisposal at each level of wavelet coefficients.

The soft threshold function is chosen with,

sgn( )(| | ),| |( , )0 | |

ht tx T t

t

= =

8/12/2019 05362817

3/4

VI. SIMULATION RESULTSHere about 570 traffic flow data are used, which were

detected every 2 minutes from 5:00 to 24:00 on a road inChongqing. The errors and fitting are chosen with,

Mean absolute error

( ) ( )1

| |( )

pred real

t real

Y t Y t

maerr N Y t

= (5)Max absolute errors

( ) ( )max | |

( )

pred real

real

Y t Y t mxaerr

Y t

= (6)

Root-mean-square error

2( ( ) ( ))pred realt

Y t Y t

rmserrN

=

(7)

Fitting degree

2

2 2

( ( ) ( ))

1( ) ( )

pred real

t

pred real

t t

Y t Y t

ECY t Y t

=

(8)

In whichrealY is the real traffic flow data, and predY is their

prediction.

Here DB3 is chosen as wavelet, in which there are threelevels and four series. At the first decomposition, high frequencycomponent D1 is obtained; then at the second and thirddecomposition, to get D2, D3, and A3 for the denoise and

reconstruction.

The prediction of every component is with BP NeuralNetwork in three levels. At input level, there are 8 vectors,

corresponding to 8 detected traffic data. At the hide layer, thereare 15 nodes, mapping to the hyperbolic tangent function tansig.At output level, there is only one node in purelin mapping, whichis the traffic flow within one time interval. Target error of A (3)is set as 1e-6, with maximum training number of 2000. Targeerror of D (1) ~D (3) is set as 1e-5, with maximum trainingnumber of 1000. In the parameters of Genetic Algorithm

population size with 60crossover rate with 0.2mutation rate

with 0.05

evolving algebra with 500.300 existing data are first used for the network learning, and

to predict the vehicle number in the next 10 Intervals. Then theexisting data and 10 new data are used to train network againand to predict the vehicles in another 10 intervals. The process isrepeated until all 270 intervals are predicted. The predictions anderror are shown in Fig. 3.

With similar neural network structure and input, the obtainedpredicting results with single neural network are shown in Fig. 4the predicting results with multi-scale neural networks are shownin Fig. 5.

The comparisons of errors with three neural networkpredictions are shown in table 1.

Through evaluating the three effects of the three methodswith different evaluation targets, it is known that the result withmulti-scale and neural network optimized by genetic algorithmmodel is better. It can evidently decrease prediction error andimprove the forecasting veracity compared with typical neuralnetwork.

Flow(veh/2min)

Figure 3. Traffic flow prediction based on multi-scale analysis and neural network optimized by genetic algorithm

8/12/2019 05362817

4/4

Flow(veh/2min)

Figure 4. Traffic flow prediction with single neural network

Flow(veh/2min)

Figure 5. Traffic flow prediction with multi-scale analysis and neural networks

TABLE I. THE COMPARISON OF ERRORS WITH THREE NEURAL NETWORK PREDICTIONS

measuresMean absolute

errors (%)Max absolute

errors (%)Root-mean-square

errorfitting

degree

single neural network 4.6041 52.5129 6.6701 0.9737

multi-scale analysis and neural networks 0.8461 6.2835 0.8625 0.9943multi-scale analysis and neural network

optimized by genetic algorithm0.3986 3.1219 0.5807 0.9975

VII. CONCLUSIONSThis paper has briefly introduced a new approach for the

traffic flow prediction. The real detected traffic data are used totest the accuracy of the model. The results show that the model ofmulti-scale and neural network optimized by genetic algorithmhas advantages over the traditional neural network inqualification-rate of prediction, and good adaptability to thedynamic traffic flow environment. It could be an efficient method

to the prediction of the real-time dynamic traffic flow

VIII.

ACKNOWLEDGEMENTSThe authors wish to acknowledge the financial support of the

Foundation of Ministry of communications of China (2008-319-

814-060) and 2008 Research Projects for Returned Experts of

Ministry of Human Resources and Social Security of China.

IX. REFERENCES[1] Stephane G. Mallat. A Theory for Multiresolution Signa

Decomposition:The Wavelet Representation[J], IEEE Transactions onPattern Analysis and Machine intelligence, 1989.11(7):674~693.

[2] Maniezzo V. Genetic evolution of the topology and weigh t distribution ofneural networks [J]. IEEE Trans On Neural Networks, 1994, 5 (1) : 39253.

[3] TAN Manchun ,LI Yingjun,XU Jianmin. A Hybrid ARIMA and SVMModel for Traffic Flow Prediction Based on Wavelet Denoising[J],Computer Engineering and Applications,2009,26(7):127-131. (inChinese)

[4] MA Jun,Li Xiaodong,MENG Ying. Research of Urban Traffic FlowForecasting Based on Neural Network [J],Acta ElectronicaSinica,2009,37(5):1092-1093. (in Chinese)

[5] Skander Soltani ,On the use of the wavelet decomposition for time seriesprediction[J] , Neurocomputing , 2002 :267277.

[6] CHANG Jianxia, YU Xingjie, HUANG Qiang.Water demand for ecastingbased on multi-scales analysis and neural network[J],Computer Engineering and Applications, 2008, 44( 17) : 219- 221. (in Chinese)