Forecasting the risk of traffic accidents by using the artificial neural networks/Eismo ivykio rizikos prognozavimas naudojant dirbtinius neuroninius tinklus/Celu satiksmes negadijumu riska prognozesana ar maksligajiem neiralajiem tikliem/Liiklusonnetuste prognoos kasutades kunstlikke narvivorke.

Sliupas, Tomas ; Bazaras, Zilvinas

1. Introduction

Traffic accident risk is defined as a relative probability to have a traffic accident resulting in death (fatal accident) or injury on a particular road section while driving the distance of 1 km. The definition of traffic accident risk makes it easier to compare safety characteristics of different road sections withdrawing the influence of a distance (length of a road section) and traffic volume (measured by calculating AADT--Annual Average Daily Traffic, vehicles per day). The traffic accident risk level of a road section is affected by the quality of road surface and road infrastructure in general, social composition of drivers which might be different in distinct areas of a country, different speed and other traffic limitations (established by road signs), meteorological conditions, etc. The goal of this research is to find out if and how the traffic accident risk is related to the aforementioned factors by using the Artificial Neural Networks (ANN).

Earlier attempts to forecast the number of traffic accidents on Lithuanian roads were taken by a relatively small number of Lithuanian researchers. Scientific methods applied to achieve this goal included the use of: linear regression equations (Ratkeviciute 2009), different types of regression equations (Sliupas 2009b), and other research models (Jasiuniene 2012). Using ANN for traffic accident forecasting is not a common practice abroad (Maher, Summersgill 1996). Factors influencing traffic accidents (based on the Lithuanian road data) are analysed in various sources: Miskinis, Valuntaite (2010), Sliupas (2009a), Ratkeviciute et al. (2011a), Ratkeviciute (2010). Feasibility of traffic accident prediction in Lithuania was studied by Ratkeviciute et al. (2011b). One of the most complex and systematic studies on traffic accident factors carried out abroad was conducted by Elvik and Vaa (2004). The use of Geographic information system (GIS) data for the forecasting of accident risk is described by Andrey and Lister (1999).

2. Research data

State roads of Lithuania are subdivided into 3 parts: main, national and regional road networks. The objects of this research are the main and national roads. Merely fatal and injury-incurring traffic accidents are analysed in the study. All accidents which were registered on the LAKIS database (abr. from Lithuanian--Lietuvos automobiliu keliu informacine sistema) and occurred during the period of 2002-2006 were selected for the analysis. The analysed roads are divided into 341 sections. These road sections were formed by excluding the road intervals with the same AADT value. Normally they start after one more significant intersection and end by another and always contain an AADT measuring post. Sections of roads that cross small towns and highly populated areas are excluded from the study because they are much different from the rest of road sections and are more likely to resemble streets by their characteristics. An average length of a road section is 18.77 km. The total length of these road sections amounts to approx 6.401 km. As it is indicated by The Lithuanian Road Administration under the Ministry of Transport and Communications of the Republic of Lithuania, the total length of the main and national road network is 6.722.80 km. These 341 sections cover 30.10% of the Lithuanian state roads.

After the primary research, the following data on the parameters affecting the traffic accident risk was collected:

--number of inhabitants within 17.00 km radius from a road section;

--road section class variable;

--weighted average of road pavement width, m;

--quantity of 3-way junctions in a road section;

--quantity of 4-way junctions in a road section;

--number of bus stop grounds;

--number of rest grounds;

--number of large long time rest grounds;

--number of gasoline stations;

--ratio of pavement length, bicycle path length or bicycle/pedestrian path length along a road section and length of a road section;

--ratio of guardrail length in a road section and road section length;

--ratio of illuminated road section length and total road section length.

All of these 12 parameters were used to forecast the accident risk by using the ANNs described below. A more comprehensive research dedicated to the influence of population density (within a chosen radius from a road section) on the number of traffic accidents and traffic volume in particular road sections could be found in the following sources: Sliupas et al. (2006) and Sliupas (2009b). The road section class variable defines the class of a road following the official state classification as described in Road Technical Regulation of Lithuania KTR 1.01:2008. The road section class variable is helpful when there is a case of different road classes on the same road section. A detailed description on how the aforementioned calculations are made is given by Sliupas (2009). The rest of the road parameter information for the analysis was extracted from the LAKIS (2008) database, which is located at The Road and Transport Research Institute, Lithuania. Classified traffic volume information of each road section was collected from the annual volume research reports of the same institute.

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3. Method of the analysis

The forecasts of road traffic accident risk are calculated by using ANN and following the procedure displayed in Fig. 1.

The dataset used in the research is multidimensional. One of many ways to display such kind of data is a matrix of scatter plots (Medvedev 2007). Visual analysis did not reveal strict dependency patterns. A more interesting dataset view fragments are displayed in Figs 2 and 3.

As it can be noted from Fig. 2, the accidents are concentrated in two lager spots: around the roads with a 9 meter-width pavement and roads with a 22 meter-width pavement. Dots are not distributed all over the scale because of road width standards. The same figure also shows that wider roads are safer than narrow, but that presumption may not be correct. Wider roads that were represented in the study are the best roads (highways) of the country having the best upkeep and traffic safety financing. Also, these roads have high traffic volumes. Most of them have grade separated intersections, limited U-round opportunities, etc., that is why the presumption that wider roads are safer might not be a universal rule. Elvik and Vaa (2004) note that road widening improves traffic safety in unpopulated areas; however, this makes it worse in densely populated territories.

Fig. 3 reveals that road sections having a larger distance of guardrails are a little bit safer than the opposite case. That seems logical because guardrails prevent the front to front collisions and road departing accidents. Positive effects of guardrails were noted by Hunter et al. (2001), Short and Robertson (1998), Griffith (1999), etc. However, Fig. 3 shows a large dispersion of dots and the pattern is not clearly expressed.

ANNs are usually applied to model complex relationships between inputs and outputs or to find patterns in the data. As ANNs are non-linear statistical data modelling tools, in this case they might show better results than other methods.

4. ANN types applied and the process of calculation

3 types of ANN were used in the research:

1. Feedforward two-layer ANN (its scheme is displayed in Fig. 4). The variables displayed in Fig. 4 are: [p.sub.1] - [p.sub.n] --traffic accident risk affecting parameters; m--number of neurons in the first layer; [w'.sub.1,1] - [w'.sub.m,n]--network weights of the first layer neurons; f--function of hyperbolic tangent; [a'.sub.1] - [a'.sub.m]--outputs of the first layer neurons; [w'.sub.1] - [w".sub.m]--weight vector of the second layer neuron; b--bias; f"--linear function; a" or r--output of the second layer neuron or forecasted result of neural network.

2. Feedforward ANN of one neuron, using hyperbolic tangent function (Fig. 5). [w.sub.1] - [w.sub.n]--weight vector of the neuron; f--function of hyperbolic tangent.

3. Feedforward ANN of one neuron, using linear function.

These three types of ANN were used to forecast accident risks on the main and national road networks separately using the scheme displayed in Fig. 1. Quantity of analysed data was not large; therefore, data splitting into training and testing datasets was performed three times. This is reflected in Table 1 as a test number. The data was sorted and every tenth data unit was taken to the testing dataset of test No. 1. Later on the process was repeated twice by using different dataset row numbers. Such a process made the distribution of datasets compounds accidental. After that the arithmetic mean of the forecast error was calculated. As a result, the estimate of a forecast error has become more reliable than it would have been if it was evaluated just once.

Before performing calculations the dataset values were modified by multiplying them with one or another constant to avoid the excesses in the amplitude of values (that is, very small and very big values). This process had no effect to the relation of accident risk and affecting parameters, however, it helped to improve the calculation result. Adapted digits, while calculated with the computing program MATLAB by MathWorks, provide more exact results.

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In all the three ANN types same network training function, which updates the weight and bias (a part of the numerical representation used to interpret a fixed-point number) values according to Levenberg-Marquardt optimization ("trainbr"), was used. It minimizes the combinations of squared errors and weights, and then determines the correct combination so as to produce the network that grants a satisfactory generalisation.

In the first ANN configuration, the number of neurons m in the first layer of the network was changed from 1 to 15 (Fig. 4). The aim of this process was to get the optimal network configuration. As it was mentioned above, the process was repeated three times. Hereby the first ANN type (Fig. 4) performed 45 calculations using different inputs and ANN configuration with the main roads only. Same process was repeated with the national roads. The second and the third ANN types were significantly less time and effort-consuming, as they differ by transfer function only.

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5. Results

The results of traffic accident risk forecasting derived by using the ANN types described above are displayed in Fig. 6 and Table 1. 12 parameters describing the road sections were applied, however, the results show large forecasting errors. In a well-developed road network accidents befall accidentally. Road sections which are subject to more road accidents than are common are called the "black spots". Traffic safety engineers endeavour to decrease or eliminate these spots, thus they usually do not exist for a long period of time. In this way it can be presumed that the forecasting method is suitable and enables to derive satisfactory results when it provides more exact results than could be obtained by calculating the average traffic accident density in a network and then applying it to a road section.

Large errors not necessarily show that the application of the method is not suitable. The accuracy of the results will be improved after collecting more accurate data. The average annual number of road accidents per road section was low in the analysed road networks during the chosen period of time. There were approx 46% of road sections with 3 or less road accidents per year, and only 54% with more than 3. The most recent data available in Lithuania was used in the study; however, it is possible that it was not sufficient. In some road sections 1 accident tends to change the result significantly. Moreover, the impact of single factors on the accident risk is tiny. The method is supposed to provide more weighty results by evaluating the complex of these factors.

It is suggested to apply the method while evaluating traffic accident risk on newly built roads, road sections or bypasses where there are no historic data of traffic accidents. Traffic accident risk is considered as one of the determining factors while calculating the profit of road infrastructure investment projects, the time period of their buy-off and net present value.

Also, it is possible to use other mathematical methods while forecasting accident risk using the same or similar data (Sliupas 2011). The aforementioned source describes a method which permits to forecast the accident risk by evaluating the impact of a bicycle/pedestrian trail, traffic barriers and illuminated road length in the analysed road section. The impact extent is calculated by using "before and after" method. Also, road category, number of intersections, grounds and inhabitants in the road section area are evaluated. The application of the method gives a 53.60% forecast error which is similar to the results displayed in Fig. 6 and Table 1.

6. Conclusions

1. The best traffic accident risk forecasting results for the main roads are obtained using type 1 of ANN with 9 neurons in the first layer (45.86%).

2. The best traffic accident risk forecasting results for the national roads are obtained using type 1 of ANN with 2 neurons in the first layer (45.38%).

3. The application of the method reveals large forecasting errors, but the result was obtained using a relatively small quantity of data. More accurate data, as well as larger volumes of data may change the result. It was not available at the time the study was being carried out in Lithuania.

Caption: Fig. 1. Structural scheme of traffic accident risk forecasting by using ANN

Caption: Fig. 2. Weighted average of road pavement width in a road section and traffic accident risk of a road section for all the main road network sections

Caption: Fig. 3. Ratio of guardrail length in a road section and road section length, and traffic accident risk for all the main road network sections

Caption: Fig. 4. Scheme of a two-layer feedforward neural network which was used for forecasting the traffic accident risk

Caption: Fig. 5. Feedforward ANN of one neuron used in the forecasting of the accident risk

doi: 10.3846/bjrbe.2013.37

Received 14 October 2011; accepted 6 December 2011

References

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Received 19 October June 2011; accepted 28 September 2012

Tomas Sliupas (1) [mail], Zilvinas Bazaras (2)

(1) PE Road and Transport Research Institute, I. Kanto g. 23, P.O. Box 2082, 44009 Kaunas, Lithuania

(2) Dept of Transport Engineering, Kaunas University of Technology, Kestucio g. 27, 44312 Kaunas, Lithuania

E-mails: (1) t.sliupas@ktti.lt; (2) zilvinas.bazaras@ktu.lt

Table 1. Error of traffic accident risk forecasting
with the application of ANN

ANN type               Test No.

             I        II      III     Average

Main roads

2          52.48%   53.53%   74.50%   60.17%
3          46.74%   49.01%   70.92%   55.55%

National roads

2          39.46%   59.34%   60.15%   52.98%
3          36.76%   53.29%   49.11%   46.39%

Fig. 6. Change of forecasting accuracy when the number of
neurons in the first layer of ANN type 1 is changing3

     Main roads   National roads

1    49.0         55.1
2    46.0         45.4
3    52.6         52.0
4    57.3         50.4
5    59.8         53.1
6    55.5         50.4
7    66.5         54.0
8    54.9         45.7
9    45.9         48.5
10   57.2         49.5
11   55.1         53.4
12   63.6         49.2
13   56.3         53.0
14   60.1         57.2
15   56.3         49.5

Note: Table made from bar graph.