Using artificial neural network to estimate average speed of vehicles in rural roads

Abbas Mahmoudabadi

PhD Candidate, Technical and Engineering Faculty, Payam-e-Noor University & General Director of Traffic Safety

Department, Road Maintenance and Transportation Organization, Tehran, Iran

E-mail: mahmoudabadi@phd.pnu.ac.ir

Abstract—Average speed of vehicles, one of the main

parameters in traffic engineering, has been widely used

particularly in road and safety equipment designing and road

working. In this paper, an artificial neural network model has

been developed for estimating average speed of vehicles in

rural roads. Road type, day time, traffic volume, and

proportion of heavy vehicles have been considered as the

major effective parameters for estimating average speed of

vehicles. Assuming at least 85 percent of total deviations is

remained, principle component analysis technique has been

used to ensure that input variables have not inter-relation. Two

types of regression models, including simple and weighted

linear regression models have also been developed and

proposed neural network model has been evaluated by

comparing the mean square errors with their performances.

Results showed that artificial neural network with the best

performance measure (least mean square errors) can be used

to estimate the average speed of vehicles regarding to the main

influential parameters in road traffic engineering. Results also

showed that the performance measure of neural network can

be improved when a appropriate network is considered.

Keywords-Estimating models, Average speed, Traffic Volume,

Principle Component Analysis, Artificial Neural Network,

Multiple Regression

I. INTRODUCTION

Traffic parameters are widely used in process of decision making and road designing in urban and rural transportation. Estimating of traffic parameters is main concern of researchers because achieving the survey-based parameters is an expensive activity. Speed is one of traffic parameters witch is widely used in road traffic planning, so it is vital that model must be developed to estimate speed based on achievable parameters and minimum errors.

Statistical models have frequently been used in highway safety studies. They can be utilized for various purposes, including establishing relationships between variables, screening covariates and predicting values [1]. In the recent years, artificial neural network has been used to estimate the several kinds of traffic parameters. Fallah Tafti [2] used an artificial neural network model to simulate traffic flow in the vicinity of merges and estimate the average time of journey. Based on the good results in validation process, he suggested that artificial neural network models can be used to validation of performance in different purposes.

Wa’el and Awad [3] developed a neural network model for estimating the traffic capacity in weaving areas. Geometric design, speed, length, traffic volume, and number

of lanes have been considered as the major effective parameters in traffic capacity analysis. Their results showed that neural networks can be used as appropriate model comparing with linear regression models for analyzing the capacity in weaving areas.

Ngwangwa, Heyns, Labuschagne, and Kululanga [4] utilized an artificial neural network that reconstructs road surface profiles from measured vehicle accelerations for road damage assessment and demonstrated the capabilities of their methodology in the presence of noise, changing vehicle mass, changing vehicle speeds and road defects.

Tong and Hung [5] developed an artificial neural network model for estimating the discharge headway of individual queued vehicle in intersections. By utilizing the back propagation algorithm in training and sensitivity analysis, they concluded that the neural network model performed better than the other models to discharge headway estimates for individual vehicles. Chang and Su [6] also showed the same results by developing artificial neural network models for predicting intersection queue. Their proposed models are capable of providing prediction accuracy more than 90% at 3 time-steps ahead.

Zhang and Forshaw [7] used an artificial neural network model for analyzing traffic volume, speed and traffic direction, where generated data via closed circuit television system was considered as input data. They combined model and CCTV system and showed that combination of image processing techniques and neural network based model have an appropriate ability to be used for traffic analysis concerns.

Srinivasan, Sharma, and Toh [8] presented an artificial neural network model based on multivariate techniques for incident recognition in freeways. They used data reduction techniques for reducing the variables even a non-linear model can be used for incident recognition in freeways.

Dia [9] developed an object-oriented neural network model for predicting short-term traffic conditions on a section of highway and showed that model is capable of predicting speed up to 5 minutes into the future with a high degree of accuracy of 90 to 94%.

Traffic parameters have complicated effects in speed that drivers chose to drive vehicles [10]. This characteristics and the concept behind of neural network modeling known as black box are the same so speed may be results of some parameters which have direct or indirect effects in each other via linear or non-linear models [10].

Conductive loops are widely used for data gathering in urban and rural road and comparing their stored data and the results of output models would be considered in validation process of developing traffic models because conductive

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loops have appropriate role in data gathering for traffic measures [11]. Because collecting reliable length data from single and dual loop detectors has been considered impossible due to the noisy speed estimates provided by conventional data aggregation at single-loop detectors, Coifman and kim [12] presented a methodology to use single-loop detector to classify vehicles and speed estimation in freeways.

In this paper, an artificial neural network model has been developed to estimate the average speed of vehicles, in which traffic volume, daytime, road geometric design, and the proportion of heavy vehicles are considered as input variables. Because neural network models have a sensitive reaction regarding to training data [13], a data analyzing has been proposed to check the validity of model based on different set of training, validation, and testing data. Principle component analysis, a well-known statistical technique, has also been used to be confident that input variables do not have inter-relations. %85 of variation had been considered to be remained and existing of all variables in proposed models has been checked. Two kinds of widely used statistical models including simple and weighted linear regression models have been developed to validate the performance of proposed neural network model.

II. ESTIMATING MODELS

There are various kinds of models that are used for estimating parameters in road safety. Regression models are known as common, because of simplicity. In this section a brief discussion of simple and weighted linear regression and artificial neural network models are presented.

A. Simple linear regression

Minimizing the mean square errors between observations

and model outputs is the main concern behind the setting

parameters of simple linear regression models [14]. Two

kinds of variables including independent and dependent

variables are used in modeling named multivariate linear

regression mode if there are more than one variable as

independent variables [14]. Therefore, model set relationship

between independent variables X1, X2, . . . Xn, and dependent

variable Y by the equation (1). In the equation (1),

coefficients β0, β1, β2, β3 . . . and βn must be set based on

minimizing the mean square errors between observations and

model outputs.

)1(...3322110 nn XXXXY βββββ +++++=

B. Weighted Regression model

When it is considered that the effects of independent

variables on dependent variable are power-based, the model

called weighted linear regression. Parameters are being

calculated based on the minimum of mean or total square

errors between observations and model outputs [15]. It is

obvious that multivariate regression model can be defined

when independent variables X1, X2, . . . Xn and dependent

variable Y are defined as equation (2) shows.

)2(...321

3322110

Pn

nn

PPP XXXXY βββββ +++++=

In equation (2) coefficients β0, β1, β2, β3 . . . and βn and p1, p2, p3… and pn are being estimated regarding to the minimizing the mean or total square errors between observations and the model outputs.

C. Artificial neural network model

In the neural network model, the neuron is the basic component [16]. Each neuron of a layer is connected to each neuron of the next layer from the input layer to the output layer through the hidden layers as shown in figure 1 [16].

In this structure the output Yi of each neuron of the nth layer is defined by a derivable non-linear function F by equation (3) where F is the non-linear activation function, wji are the weights of the connection between the neuron Nj and Ni, yi is the output of the neuron of the (n−1)th layer [16]. The most common used of validation criteria is mean or sum square errors between observations and model outputs.

Figure 1. General view of neural network model

)3(∑ ⎟⎟⎠⎞

⎜⎜⎝⎛

=j

jjii ywFy

III. DATA GATHERING

Input data including average speed, traffic volume, road geometric design, daytime, and proportion of heave vehicles in 461 days have been gathered in different months and different topography. Freeway, highway, and main road are three types of geometric design roads are considered as input parameters 1, 2, and 3 respectively. Daytime has been calculated based on the length of day from sunrise to sunset divided to 24. Traffic volume, the proportion of heavy vehicles, and average speed of vehicles have been collected via conductive loops installed in rural roads.

A. Normalized Data

Data have been converted to normal type by equation (4), which is commonly used to normalize data, where n is the number of observations [17]. The above equation convert data in to a closed interval of [0 1]. Tables I and II

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respectively show the experimental and normalized data of all variables that are considered in modeling process. As shown in table II, the minimum and maximum of standard types of all variables zero and one respectively.

)4((min)(max)

(min))()(

ii

iii

xx

xoldxnewx =

TABLE I. EXPERIMENTAL DATA

Variable Experimental Data

Max. Min. Mean STD

Road Type (R_T) 3 1 1.99 0.816

Day Time (D_T) 0.617 0.424 0.518 0.071

Traffic Volume (T_V) 59768 800 9793 6356

Heavy Vehicle (H_V) 0.72 0.015 0.259 0.154

Average Speed (A_S) 111 22.5 85 12.6

TABLE II. NORMALISED DATA

Variable Normalized Data

Max. Min. Mean STD

Road Type (R_T) 1 0 0.496 0.408

Day Time (D_T) 1 0 0.485 0.369

Traffic Volume (T_V) 1 0 0.153 0.108

Heavy Vehicle (H_V) 1 0 0.345 0.219

Average Speed (A_S) 1 0 0.710 0.141

IV. PRINCIPLE COMPONENT ANALYSIS

Principle component analysis (PCA) is a statistical process categorized in data reduction techniques. The PCs are the uncorrelated (orthogonal) variables, obtained by multiplying the original correlated variables with the eigenvector, which is a list of coefficients [17]. Thus, the PCs are weighted linear combinations of the original variables. It is a powerful technique for pattern recognition that attempts to explain the variance of a large set of inter-correlated variables and transforming into a smaller set of independent (uncorrelated) variables (principal components). Factor analysis further reduces the contribution of less significant variables obtained from PCA and the new group of variables, known as vari-factors, is extracted through rotating the axis defined by PCA [18]. Selecting the first n PCs is regarding to eigen-values grater than one or obtaining enough deviations mostly 85 percent of whole deviations [17]. The high proportion of deviation, consist of large dimensioned variables, so variables should be homogenous in the process of PCA [18]. In this paper, standardized data is used for analyzing the PCA process.

A. Standardizing data

As it is mentioned briefly in the last section, in PCA analysis, dimension of variables must be homogenous. Standardizing data is one of the well known methods to homogenize data in normal function. Equation (5) converts original data in different dimension to normal distribution function with the average of zero and standard deviation of one, where x(new) is standardized data and x(old) is original data.

( ))5(

1-

-

-)()(

∑

1

2

n

xx

xoldxnewx

n

i

i

i

i

=

=

Table III shows the standardized data which have been converted from original data by equation (5).

TABLE III. STANDARDIZED DATA

Variable Normalized Data

Max. Min. Mean STD

Road Type (R_T) 1.237 -1.216 0 1

Day Time (D_T) 1.396 -1.316 0 1

Traffic Volume (T_V) 7.862 -1.415 0 1

Heavy Vehicle (H_V) 2.993 -1.576 0 1

Average Speed (A_S) 2.057 -5.029 0 1

B. Eigenvalues

Calculating eigen-values is the second stage of PCA. Each score has specific eigen-value ordered descending shown in table IV. PCs are uncorrelated so if 85 percent of variation is assumed to be remained PC1, PC2, and PC3 with cumulative percent of deviation more than eighty five percent, must be considered to the next stage of PCA process and PC4 can be ignored.

TABLE IV. PRINCIPLE COMPONENTS

Score Eigen-

value

Variation

percent

Cumulative

percent

PC1 1.9606 49% 49%

PC2 1.0220 25% 74%

PC3 0.7864 20% 94%

PC4 0.2310 6% 100%

C. Loading

The simple correlation between original variables and scores, is loading [17]. As shown in table V, correlation between traffic volume (T_V) and the first score is high, means that variation of traffic volume is more influential in the first score.

TABLE V. LOADING

Score PC1 PC2 PC3

Variable

R_T 0.8795 -0.1882 -0.2898

D_T 0.5410 0.9791 -0.1864

T_V 0.9123 0.0149 -0.2211

L_V -0.5932 -0.1668 -0.7866

D. Extracting variables

Extracting variables, last stage of principle component analysis, is based on loadings that are shown in table V. In this stage Selected PCs must be considered with loading either more than 0.7 or less that -0.7 [18]. For the first PC it can be concluded that variables R_T and T_V must be considered as input variables, by considering PC2 variable D_T, by considering the PC3 variable L_V would be added to inputs. In this case it is concluded that all of the variables R_T, D_T, T_V, and L_V must be considered as input variables. All of desired loading in table V, which have been

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used in decision process are shown in bold marked style. It is concluded that all input variables must be considered as input variables by considering at least 85 percent of variations.

V. DEVELOPING OF THE MODEL

As mentioned briefly in section II.C, the neural network model is consisting of input layer, hidden layer, and output layer. In this case, with three input and one output variables, neural network model must be formed of three neurons in input and one neuron in output layer. Hidden layer will be different based on the number of observation. If it’s assumed that the number of observation should not be exceeded than ten times of necessary parameters, the maximum number of hidden neurons in model was calculated as 8. Well-known software of MATLAB has been used for modeling. Figures 2 shows artificial neural network model of average speed of vehicles and five times of running models have been considered with stop criteria of 1e-5.

Figure 2. Structure of Artificial Neural Network

In order to evaluate the model, four structures of networks with different numbers of neuron in hidden layers have been analyzed. Four structures including (4-4-1-1), (4-5-1-1), (4-6-1-1), (4-8-1-1) have been analyzed and (4-8-1-1) structure is the best one based on mean square errors.

TABLE VI. CATEGORIZING DATA

Sample

Code

Sample Size (Percent)

Training Validation Testing

A 323(70) 69(15) 69(15)

B 369(80) 46(10) 46(10)

C 415(90) 23(5) 23(5)

The numbers of data that are assigned in each category of

training, validating, and testing process have significant effect in the process of model development and network measures [19]. Three types of categorizing data defined as sample codes A, B, and C shown in table VI have been considered in data analysis. The proposed model has been run five times, using different sample size and network structure and the average of two criteria measures of correlation coefficient and mean square errors have been calculated and shown in table VII.

TABLE VII. MEAN SQUARE ERRORS AND CORRELATION COEFFICIENT

Network

Structure

Sample

Code

Correlation Coefficient Mean Square Error (e-4) Iterations Stopping

Iteration Train Validate Test Train Validate Test

4-4-1-1

A 0.943 0.956 0.931 22 18 28 39 33

B 0.963 0.957 0.888 14 30 37 59 59

C 0.917 0.867 0.944 32 53 15 24 18

4-5-1-1

A 0.980 0.958 0.936 8 12 26 37 31

B 0.983 0.976 0.951 6 21 18 64 59

C 0.968 0.899 0.961 13 16 16 12 6

4-6-1-1

A 0.983 0.954 0.962 7 11 12 25 19

B 0.974 0.980 0.980 16 12 9 12 6

C 0.960 0.945 0.943 15 20 38 14 8

4-8-1-1

A 0.990 0.915 0.963 4 57 15 23 17

B 0.970 0.950 0.977 10 30 14 15 9

C 0.972 0.984 0.971 14 7 17 12 6

4-8-1-1 Total 0.9889 4.4 16 10

According to the measures in table VII, it can be

concluded that if the number of neurons in hidden layer is increased, the number of iterations will be decreased and network parameters will be improved. When there is no improvement in mean square errors, iterative calculations are stopped and network is reached in steady state. Network measures in three stages of training, validation, and testing have a reverse behavior depending on the number of data in each category. It means that network measures will be improved (mean square errors will be decreased and correlation coefficient is getting to be close of one) when the number of data in each category is increased. Figure 3 illustrates a kind of improvement process when mean square errors have not improvement after 6 iterations.

Figure 3. Stopping Iteration After 6 Iterations

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A. Fitness measure of observations and model outputs

In order to check the fitness measures between observations and model outputs, four kinds of regression equations training, validation, test, and all data models can be analyzed. Results show that the four equations 6 to 9 represent the compatibility between experimental data and model outputs, which O = output and T = target.

)6(963.0057.092.0: =+×= RTOTraining

)7(976.0055.092.0: =+×= RTOValidation

)8(98.0034.096.0: =+×= RTOTest

)9(967.0054.093.0: =+×= RTOAll

The coefficients between outputs and observation are more than 0.85 and distance from origin is less than 0.05, in all linear regression models based on standardized data, so the compatibility of data and model is good enough.

VI. REGRESSION MODELS

Proposed model can be validated with the other models, which may be used for prediction. Simple and weighted linear regression models have been selected for validation and well-known software of MATLAB was used for generating fitness equations. Input and output variables are defined as below:

R_T: Road geometric design (Road type)

D_T: Daytime

T_V: Traffic volume

L_V: Proportion of heavy vehicles

A_S: Average speed of vehicles The simple and weighted linear regression models are

fitted as equations (10) and (11) respectively.

A_S= 0.5995 + 0.0913*R_T + 0.0307*D_T - 0.2150*T_V -

0.1366*L_V (10)

A_S= 0.3992 + 0.5080*(R_T)0.052 + 0.1491*(D_T)0.0442 -

0.0652*(T_V)1.3581 - 0.3310*(L_V)9.2510 (11)

In the equation (10), when power coefficient is getting to raised means the effect of input variable is low because all data is set in closed interval [0 1] so it means that the proportion of heavy vehicles in traffic volume has not significant effect on average speed. Road type and daytime have direct effects in average speed means that when the grade of road improved to the next level, average speed will be increased and vice versa. Traffic volume has reverse effect, means that when traffic volume is getting to raise average speed will be decreased and vice versa. The proportion of heavy vehicle traffic has a reverse effect in average speed of vehicles means that when it is increased the average speed will be decreased.

VII. COMPARING THE MODELS

Mean square errors measure is one of the most applicable measures which can be used to compare the efficiency of prediction models [14]. Mean square errors have been calculated in different types of models and results showed in table VIII.

TABLE VIII. MEAN SQUARE ERRORS

Model Mean Square errors (e-4)

Artificial Neural Network 4.4

Simple Linear Regression 1316.2

Weighted Linear Regression 145.5

Results in table VIII show that artificial neural model is

the best model with minimum mean square errors as 4.4e-4 and weighted and simple regressions follows that on the second and third step respectively.

VIII. SUMMARY AND CONCLUSION

Because of wide application of average speed in road designing and safety equipments, in this paper an artificial neural network model has been developed based on effective parameters data, which collected in 461 days in different roads and different months. Four main parameters including road geometric type, daytime, traffic volume, and proportion of heavy vehicles have been considered as input and average speed of vehicles as output and data have been converted to closed interval [0 1]. By assuming at least 85 percent of total deviations must be remained, principle component analysis technique has been used to ensure that input variables have not inter-relation and results show that four assumed variable must be considered as input variables in modeling. Mean square errors has been considered as criteria measure for evaluation and artificial neural network has been evaluated with simple and weighted linear regression models and results show that artificial neural network has the best performance in estimation of average speed. It can be concluded that road type and daytime have direct effects in average speed means that when the grade of road improved to the next level, average speed will be increased and vice versa. Traffic volume has reverse effect, means that when traffic volume is getting to raise average speed will be decreased and vice versa. The proportion of heavy vehicle traffic has a reverse effect in average speed of vehicles means that when it is increased the average speed will be decreased. Results show that artificial neural network model can be applied for prediction of average speed with a significant compatibility. For the further studies, it can be suggested that researchers should be focused on the other parameters influencing on average speed such as level of enforcement and roadside facilities located near the roads.

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