mussoneanalysisurbancollisionsusing1999.md 89 KB
category: literaturenote citekey: mussoneanalysisurbancollisionsusing1999 title: An analysis of urban collisions using an artificial intelligence model authors: "Mussone, Lorenzo; Ferrari, Andrea; Oneta, Marcello" year: 1999 date: 1999-00-00 1999 doi: 10.1016/s0001-4575(99)00031-7 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/s0001-4575(99)00031-7" zotero_key: 6CEGZP49 zotero_storage: MEN8362I collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Mussone, Lorenzo"
status: converted
model
Lorenzo Mussone *, Andrea Ferrari, Marcello Oneta Department of Transport Systems and Mobility, Polytechnic of Milan, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy Received 20 July 1998; received in revised form 23 February 1999; accepted 2 March 1999
Traditional studies on road accidents estimate the effect of variables (such as vehicular flows, road geometry, vehicular characteristics), and the calculation of the number of accidents. A descriptive statistical analysis of the accidents (those used in the model) over the period 1992–1995 is proposed. The paper describes an alternative method based on the use of artificial neural networks (ANN) in order to work out a model that relates to the analysis of vehicular accidents in Milan. The degree of danger of urban intersections using different scenarios is quantified by the ANN model. Methodology is the first result, which allows us to tackle the modelling of urban vehicular accidents by the innovative use of ANN. Other results deal with model outputs: intersection complexity may determine a higher accident index depending on the regulation of intersection. The highest index for running over of pedestrian occurs at non-signalised intersections at night-time. © 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Artificial neural networks; Accidents; Intersections; Safety; Urban environment; Models
A widely used approach in describing accident phenomena involves the creation and calibration of a functional relationship capable of treating the above-mentioned variables. The model is calibrated by samples of accidents which determine both its structure and its forecasting capabilities. The latter one is a fundamental property which a model must possess since intervention policies, aimed at increasing road safety,
The artificial neural network (ANN) model in this paper is the follow up on an approach which we have used before (Mussone and Rinelli, 1996; Ferrari et al., 1997). Though similar to traditional analyses of accidents the ANN has different capabilities and characteristics. The making of accurate predictions depends on the collection and manipulation of accident data and on the choice of variables used in the model structure. Instead of working out an analytical functional relationship, usually a complex and laborious task, the
* Corresponding author. Tel.: +39-2-2399-6612; fax: +39-2-2399-
0001-4575/99/\$ - see front matter © 1999 Elsevier Science Ltd. All rights reserved.
E-mail address: mussone@mail.polimi.it (L. Mussone)
PII: S0001-4575(99)00031-7
depend on the forecasting capabilities.
neural network model reconstructs, simply by learning from the real data of accidents, the weights by which
The study focuses only on accidents that occurred at intersections and not on links which would require a different approach. The data, therefore, have been desegregated in order to have a clear view of the kind and number of accidents at different types of intersections. We examine only superficially accidents on links. In fact, the aim of this paper is to identify the most significant parameters that determine the possibility of an accident occurring at an intersection. Attention has been paid to the identification of possible causes of accidents: roadway conditions; visibility; weather; and the characteristics of vehicles and drivers. On the other hand, a descriptive analysis enables us to clarify the distribution of the values of variables noted by the authorities, but this analysis does not enable us to say anything about the presumed causes of accidents, or the influence of the various factors involved and in general it is not possible to single out any relationships between the causes and effects of accidents. For this purpose it is necessary to use mathematical models in order to quantify the degree of danger linked to particular flow
each variable must be weighed.
and environmental conditions.
An analysis of urban collisions using an artificial intelligence
Abstract
1. Introduction
6606.
There are several assumptions regarding the number of the lines of vehicles turning at intersections and in circulation on the main roads. It is assumed that a single line of vehicles turns 90° at an intersection. Other criteria were used to improve the database which is the basis on which the neural net model is elaborated. The purpose was to integrate the information contained in TABTOT, with the field survey of flow circulation and complexity of intersections.
6.2. The NN methodology
The methodology used to build the model is based on artificial neural networks. We used feed-forward neural networks with a back-propagation learning paradigm. This type of neural network is well known and has been described in Cybenko (1989) paper and in other papers (Hornik et al., 1990; Hornik, 1991; Girosi and Poggio, 1991; Leshno et al., 1993). These papers describe the ANNs capability of approximating with minimum error any function belonging to L2 space (the Lebesgue two space). Applications regarding transport, planning and control fields are numerous (Dougherty, 1995; Mussone, 1995). This approximation capability is a fascinating tool which does not need any a priori assumption on relationships between variables, linear or non linear. In problems where the phenomena are not well known and an analytical approach could be time consuming, NN offers the opportunity to investigate and create the first discriminant analysis.
Essentially the methodology in building an ANN model consists of four phases. The first is a random extraction from the entire data set of a subset. The number may vary from a few 100 to 1000 cases. The subset must satisfy the law of large numbers. A very large subset may slow down the learning procedure. When data are grouped into classes, the model should recognise a particular classification pattern. Data extraction moreover should be as homogenous as possible for each class both for train and test set and an equal number of cases should be randomly extracted for each class. If not, because of the too low number of cases used which don't cover all possible combinations, ANN performance (evaluated on the test set) can worsen; this may happen when many variables are used and data are not homogeneously distributed. Therefore a lesser number of input variables can improve data extraction and case distribution between test and train set.
In the second phase the data subset is randomly subdivided into two sets, the training and test sets, which will be used for the learning and validation of the ANN. The third and fourth phase consist in the learning and testing of the ANN, iteratively until the optimal network is determined. Optimal means that ANN minimises model error. The number of inputs and outputs of models does not have any theoretical limit. However the exact relationships between input/output vectors and the optimal network are not known. Therefore, it is not known how many cases are needed for the learning phase. When the number of inputs and outputs increases the complexity of the process, the more complicated networks require more data.
The heuristic approach in all four phases increases the amount of computational time needed in order to work out the optimal network. If the heuristic procedure fails to recognise certain network configurations that lead to better performance, results obtained by other means may be considered valid. To build our ANN we first used the neural network toolbox in Matlab to single out the optimal network. The best ten network configurations were analysed using Neural-Works (a neural network shell) to single out the best model based on an evaluation of their performance.
The structure of the ANN used to work out the model is drawn in Fig. 3. The input layer has ten neurones for eight variables: in fact the Crash variable is represented by three binary neurones (0 or 1) to consider the six types of accident (Table 3). The hidden layer has four neurones and the output has one neurone. The neurone transfer functions of the input layer are linear, hyperbolic tangent for the hidden layer and sigmoid for the output one. It is not easy to explain why the transfer functions differ from the hidden to the output layer but it is the result of the learning phase aimed at the reduction of RMSE (root mean square error). Other transfer functions such as sine were tried but without success.
Each neurone belonging to the 'outer' layer represents a variable while those on the hidden layers are directly connected to the values of non physical variables, so that they haven't a physical sense. The input variables of the neural network have either a numerical value (generally normalised) or a binary code such as for the Crash variable. In the latter case, if the whole range of the possible values cannot be coded by a unique binary variable (0/1), it is necessary to use more
Fig. 3. Structure of the model.
Table 3 Characteristics of the input neurones of the model
| Number | Variable name | Binary/numerical code | | | | | | |--------|---------------------------------------------------------------|------------------------------------------------------------------------|--|--|--|--|--| | 1 | Day or night | 0, night; 1, day | | | | | | | 2 | Flows circulating in the intersection | Numerical value (normalisation flow 10 000 [v/h]) | | | | | | | 3 | Number of virtual conflict points | Numerical value (normalisation value 40) | | | | | | | 4 | Number of real conflict points | Numerical value (normalisation value 60) | | | | | | | 5 | Type of intersection | 0, not signalised; 1, signalised | | | | | | | 6 | Crash 1 | 0/1 | | | | | | | 7 | Crash 2 | 0/1 | | | | | | | 8 | Crash 3 | 0/1 | | | | | | | | Type of accident (combination of the three variables crash 1, | 1-0-0, frontal impact; 1-1-0, frontal/side impact; 0-1-0, side impact; | | | | | | | | 2 and 3) | 0-0-1, bump; 0-0-0, pedestrian running over; 1-1-1, other types | | | | | | | 9 | Road bed | 0, dry; 1, wet | | | | | | | 10 | Weather conditions | 0, clear; 1, cloudy or rainy | | | | | |
than one neurone. In general with n binary neurones, 2n values of a variable can be represented. The variables related to the ten neurones of the input layer, are described in detail in Table 3. The output layer of the model has one neurone representing the Accident Index (AI) as described by Eq. (1).
The AI, that the model furnishes as an answer, represents the degree of danger associated with a particular set of variables described by the input layer. The value *N*max in Eq. (1) is the number of accidents that occurred at the most dangerous intersection of the zone under examination (69 accidents rounded up to 70). This means that, if the AI for a certain set of input values is, for instance 0.5, the degree of danger is about 35 accidents in four years. The safety of intersections with the same conditions can be estimated with a certain margin of error.
It can be noted that, along with the descriptive variables in the input layer, there is also the accident index in the output layer. This is a characteristic of the type of ANN used. Back-propagation provides a solution to the problem of learning with a feed-forward ANN. This type of ANN has the capacity to reconstruct any continuous function regardless of whether the input–output sequence is known.
The process of iterative learning used many sets of data that represent the real associations between the causes and effects of intersection collisions. The whole set of data is divided in two equal subsets: one for training and another for testing. The reduction in the number of variables in comparison to those contained in the TABTOT was essential for performance. By increasing the number of variables, local minima points increase. Therefore error, which is minimised by searching along an n-dimensional surface stopping where reliability of the results obtained by the simulations increases, can be higher. The smaller the number of variables used, the better the generalisation of the results. The loss of information of those dropped variables simplify the overall execution of the ANN.
The number of cases used for the process of learning of the net is 2073 of which 1037 cases were used for the phase of training and 1036 for the testing phase. The best solution which minimises the RMSE calculated on the testing set was found after 50 000 cycles of learning; RMSE is equal to 18.24% equal to an error on AI of about 3.2 accidents per year. The course of the RMSE in relation to the number of learning cycles is shown in Fig. 4; it is also possible to notice the phenomenon of 'overfitting' that occurs when the number of learning cycles exceeds the zone of least error. An example of the test results is reported in Table 4. Each case is characterised by an input data vector, the real AI value and that obtained by the model; the last column is the error. The table shows also how the NN model can be used to obtain answers for a specific input data vector.
The particular choice of the variable involves a good fit of the model to reality. It remains difficult to simulate an AI closer to the unit. This is a consequence of the 'distance' of such values from the middle value of the index in relation to all accidents. Since the ANN minimises the RMSE for all accidents simultaneously, certain isolated cases cannot be accurately estimated.
6.3. Application of techniques other than NN
Other techniques are applied to the same data, used in the above-mentioned model, to compare achievable performance. In particular multiple linear and exponential regressions are tested by using tools in Excel7 software. Exponential regression is in the form: y= bmi xi . where b is a coefficient, xi are the dependent variables and mi the coefficient calculated by the regression.
The main difficulties to include into a regression model some variables arise with class variables such as day/night, intersection, road-bed, weather and, above all, with type of accident. The latter is resolved dividing data according to each class present in type of accident; this can lead to a greater computing effort but, above
Table 4Examples of model outputs for some cases of the test file
| Da ig ht y o r n |
F low in he in- t ion ter t sec no r- l ise d t ma o 1 0 0 0 0 [ve / h] t |
V irt l c f l ict ua on int po s n or- l ise d t 4 0 ma o |
Re l c f l ict a on int po s n or- l ise d t 6 0 ma o |
Ty f int pe o er- ion t sec |
Ty f a i- pe o cc de nt |
Ro d s fac a ur e d it ion co n s |
M log ica l ete oro d it ion co n s |
Ac l n be tua um r f a i de nt o cc no r- l ise d t 7 0 ma o |
Ca lcu lat d n e um - be f a i de nts r o cc l ise d t no rm a o 7 0 |
Er ror |
|---|---|---|---|---|---|---|---|---|---|---|
| Da y |
0. 4 6 1 |
0. 2 25 |
0. 0 5 0 |
ign l ise d S a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 2 2 9 |
0. 2 3 7 8 |
0. 0 0 8 8 |
| Da y |
0. 6 7 4 |
0. 17 5 |
0. 0 5 0 |
ign l ise d S a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 1 2 9 |
0. 1 2 6 9 |
−0 0 0 2 1 |
| ig ht N |
1 8 1 0. |
0. 2 25 |
0. 0 5 0 |
S ign l ise d a |
Ot he r |
Dr y |
C lea r |
0. 25 7 |
6 0. 2 3 0 |
6 0. 0 0 0 |
| ig ht N |
0. 1 8 6 |
0. 2 25 |
0. 0 0 5 |
S ign l ise d a |
Ot he r |
Dr y |
C lea r |
0. 27 1 |
0. 2 6 2 1 |
−0 0 0 8 9 |
| Da y |
0. 6 17 |
0. 3 7 5 |
0. 0 6 7 |
S ign l ise d a |
l /s i de Fr ta on |
Dr y |
C lea r |
0. 45 7 |
0. 4 6 6 1 |
0. 0 0 9 1 |
| Da y |
0. 3 4 3 |
0. 0 0 0 |
0. 0 8 3 |
No ign l ise d t s a |
Pe de ian str ru n- ing n ov er |
Dr y |
C lea r |
0. 1 1 4 |
0. 1 1 8 4 |
0 0 0 4 4 |
| Da y |
0. 1 8 8 |
0. 0 0 0 |
0. 0 8 3 |
No ign l ise d t s a |
Pe de ian str ru n- ing n ov er |
Dr y |
C lea r |
0. 1 2 9 |
0. 1 2 8 9 |
−0 0 0 0 1 |
| Da y |
0. 9 6 4 |
0. 25 0 |
0. 0 8 3 |
S ign l ise d a |
Bu mp |
W et |
C lea r |
0. 1 0 0 |
0 0 9 6 4 |
−0 0 0 3 6 |
| Da y |
0. 2 2 9 |
0. 0 0 0 |
0. 0 8 3 |
No ign l ise d t s a |
Bu mp |
Dr y |
C lea r |
0. 1 1 4 |
0. 1 2 0 6 |
0. 0 0 6 6 |
| Da y |
0. 0 1 3 |
0. 0 0 0 |
0. 0 8 3 |
No ign l ise d t s a |
Bu mp |
Dr y |
C lea r |
0. 1 1 4 |
0. 1 2 3 0 |
0. 0 0 9 0 |
| Da y |
0. 2 8 8 |
0. 0 0 0 |
0. 0 8 3 |
No ign l ise d t s a |
S i de |
Dr y |
C lea r |
0. 1 1 4 |
0. 1 1 3 7 |
−0 0 0 0 3 |
| Da y |
0. 15 7 |
0. 0 0 0 |
0. 0 8 3 |
No ign l ise d t s a |
Fr l ta on |
Dr y |
C lea r |
0. 15 7 |
0. 1 6 25 |
0. 0 0 5 5 |
| ig N ht |
0. 15 6 |
0. 0 0 0 |
0. 0 8 3 |
ign ise No l d t s a |
i Fr l /s de ta on |
W et |
C lea r |
0. 1 4 3 |
0. 1 3 7 7 |
0. 0 0 5 3 |
| Da y |
0. 2 3 8 |
0. 0 0 0 |
0. 0 8 3 |
ign l ise d No t s a |
l i de Fr /s ta on |
Dr y |
lea C r |
0. 1 4 3 |
0. 1 4 17 |
−0 0 0 1 3 |
| Da y |
0. 1 2 2 |
0. 0 0 0 |
0. 0 8 3 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 15 7 |
0. 15 6 4 |
−0 0 0 0 6 |
| Da y |
0. 2 9 9 |
0. 0 0 0 |
0. 0 8 3 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 1 4 3 |
0. 1 3 4 9 |
−0 0 0 8 1 |
| Da y |
0. 6 9 5 |
0. 4 25 |
0. 1 0 0 |
S ign l ise d a |
l /s i de Fr ta on |
Dr y |
C lea r |
0. 47 1 |
0. 47 4 2 |
0. 0 0 3 2 |
| Da y |
0. 6 9 5 |
0. 4 25 |
0. 1 0 0 |
S ign l ise d a |
de ian Pe str ru n- ing n ov er |
Dr y |
C lea r |
0. 47 1 |
0. 4 6 47 |
−0 0 0 6 3 |
| Da y |
0. 7 5 0 |
0. 27 5 |
0. 1 0 0 |
S ign l ise d a |
Fr l ta on |
Dr y |
C lea r |
0. 2 8 6 |
0. 2 9 3 9 |
0. 0 0 7 9 |
| Da y |
0. 2 6 9 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l ta on |
W et |
C lou dy /ra iny |
0. 1 4 3 |
0. 1 4 8 4 |
0. 0 0 5 4 |
| Da y |
0. 6 8 2 |
0. 4 25 |
0. 1 0 0 |
S ign l ise d a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 47 1 |
0. 47 3 8 |
0. 0 0 2 8 |
| N ig ht |
0. 0 1 0 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 1 8 6 |
0. 1 8 9 3 |
0. 0 0 3 3 |
| N ig ht |
0. 0 0 7 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 1 8 6 |
0. 1 8 9 8 |
0. 0 0 3 8 |
| N ig ht |
0. 1 0 4 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
W et |
C lou dy /ra iny |
0. 17 1 |
0. 17 27 |
0. 0 0 17 |
| Da y |
0. 2 9 9 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 1 4 3 |
0. 1 3 5 7 |
−0 0 0 7 3 |
| Da y |
0. 47 1 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lou dy /ra iny |
0. 1 2 9 |
0. 1 3 8 5 |
0. 0 0 9 5 |
| N ig ht |
0. 0 0 4 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 2 0 0 |
0. 1 9 0 3 |
−0 0 0 9 7 |
| Da y |
0. 6 8 2 |
0. 4 25 |
0. 1 0 0 |
ign l ise d S a |
l i de Fr /s ta on |
Dr y |
lea C r |
0. 47 1 |
0. 47 3 8 |
0. 0 0 2 8 |
| Da y |
0. 2 3 4 |
0. 0 0 0 |
0. 1 0 0 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 1 4 3 |
0. 1 4 3 1 |
0. 0 0 0 1 |
| ig ht N |
0. 1 4 2 |
0. 0 0 0 |
0. 1 0 0 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 17 1 |
0. 1 6 8 3 |
−0 0 0 27 |
| ig ht N |
1 0. 0 3 |
0. 0 0 0 |
1 0. 0 0 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
C lea r |
1 8 6 0. |
1 8 8 9 0. |
9 0. 0 0 2 |
| b le 4 ( Co inu d ) Ta nt e |
||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Da ig ht y o r n |
F low in he in- t ion ter t sec no r- l ise d t ma o 1 0 0 0 0 [ve / h] t |
V irt l c f l ict ua on int po s n or- l ise d t 4 0 ma o |
Re l c f l ict a on int po s n or- l ise d t 6 0 ma o |
Ty f int pe o er- ion t sec |
Ty f a i- pe o cc de nt |
Ro d s fac a ur e d it ion co n s |
M log ica l ete oro d it ion co n s |
Ac l n be tua um r f a i de nt o cc no r- l ise d t 7 0 ma o |
Ca lcu lat d n e um - be f a i de nts r o cc l ise d t no rm a o 7 0 |
Er ror |
| Da y |
0. 2 25 |
0. 0 0 0 |
0. 1 0 0 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 1 4 3 |
0. 1 4 4 1 |
0. 0 0 1 1 |
| Da y |
0. 5 3 1 |
0. 4 25 |
0. 1 0 0 |
S ign l ise d a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 47 1 |
0. 4 6 9 9 |
−0 0 0 1 1 |
| Da y |
0. 4 0 2 |
0. 1 0 0 |
0. 1 3 3 |
S ign l ise d a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 15 7 |
0. 1 6 5 7 |
0. 0 0 8 6 |
| ig N ht |
0. 3 4 0 |
0. 1 0 0 |
0. 1 3 3 |
ign ise No l d t s a |
i Fr l /s de ta on |
Dr y |
C lea r |
0. 15 7 |
0. 15 2 2 |
−0 0 0 4 8 |
| Da y |
0. 3 8 1 |
0. 1 0 0 |
0. 1 3 3 |
ign l ise d S a |
l i de Fr /s ta on |
W et |
lou dy iny C /ra |
0. 15 7 |
0. 1 6 0 0 |
0. 0 0 3 0 |
| Da y |
0. 3 8 1 |
0. 1 0 0 |
0. 1 3 3 |
ign l ise d S a |
l /s i de Fr ta on |
W et |
lou dy /ra iny C |
0. 15 7 |
0. 1 6 0 0 |
0. 0 0 3 0 |
| Da y |
0. 1 1 9 |
0. 0 0 0 |
0. 15 0 |
ign l ise d No t s a |
de ian Pe str ru n- ing n ov er |
Dr y |
lea C r |
0. 1 2 9 |
0. 1 3 8 3 |
0. 0 0 9 3 |
| Da y |
0. 1 2 0 |
0. 0 0 0 |
0. 15 0 |
ign l ise d No t s a |
de ian Pe str ru n- ing n ov er |
Dr y |
C lea r |
0. 1 4 3 |
0. 1 3 8 2 |
0. 0 0 4 8 |
| N ig ht |
0. 27 3 |
0. 5 25 |
0. 15 0 |
S ign l ise d a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 3 5 7 |
0. 3 4 8 7 |
−0 0 0 8 3 |
| Da y |
0. 17 5 |
0. 0 0 0 |
0. 1 6 7 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 15 7 |
0. 15 7 1 |
0. 0 0 0 1 |
| Da y |
0. 1 6 6 |
0. 0 0 0 |
0. 1 6 7 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 15 7 |
0. 15 8 4 |
0. 0 0 1 4 |
| Da y |
0. 17 1 |
0. 0 0 0 |
0. 1 8 3 |
No ign l ise d t s a |
Pe de ian str ru n- ing n ov er |
W et |
C lou dy /ra iny |
0. 1 2 9 |
0. 1 3 0 9 |
0. 0 0 1 9 |
| Da y |
0. 7 0 1 |
0. 5 7 5 |
0. 1 8 3 |
S ign l ise d a |
Bu mp |
Dr y |
C lea r |
0. 3 1 4 |
0. 3 1 3 8 |
−0 0 0 0 2 |
| N ig ht |
0. 7 8 2 |
0. 5 7 5 |
0. 1 8 3 |
S ign l ise d a |
Bu mp |
Dr y |
C lea r |
0. 3 1 4 |
0. 3 1 3 7 |
0. 0 0 0 3 |
| Da y |
0. 2 3 4 |
0. 0 0 0 |
0. 1 8 3 |
No ign l ise d t s a |
S i de |
Dr y |
C lea r |
0. 1 1 4 |
0. 1 2 0 8 |
0. 0 0 8 8 |
| Da y |
0. 3 4 4 |
0. 5 0 0 |
0. 2 0 0 |
S ign l ise d a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 4 2 9 |
0. 4 2 15 |
−0 0 0 7 5 |
| Da y |
0. 3 6 4 |
0. 0 0 0 |
0. 2 0 0 |
ign l ise d No t s a |
l i de Fr /s ta on |
Dr y |
lea C r |
0. 1 4 3 |
0. 1 3 6 7 |
−0 0 0 6 3 |
| Da y |
0. 3 5 7 |
0. 0 0 0 |
0. 2 0 0 |
ign l ise d No t s a |
l i de Fr /s ta on |
Dr y |
lea C r |
0. 1 4 3 |
0. 1 3 7 5 |
−0 0 0 5 5 |
| Da y |
0. 3 3 2 |
0. 5 0 0 |
0. 2 0 0 |
ign l ise d S a |
l /s i de Fr ta on |
Dr y |
lea C r |
0. 4 2 9 |
0. 4 1 9 8 |
0. 0 0 9 2 |
| Da y |
9 0. 0 0 |
0. 0 0 0 |
17 0. 2 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
C lea r |
1 8 6 0. |
1 8 0. 7 4 |
1 0. 0 0 4 |
| Da y |
0. 1 0 2 |
0. 0 0 0 |
0. 2 17 |
ign l ise d No t s a |
l /s i de Fr ta on |
W et |
C lou dy /ra iny |
0. 1 8 6 |
0. 1 8 2 9 |
−0 0 0 3 1 |
| Da y |
0. 1 1 3 |
0. 0 0 0 |
0. 2 17 |
ign l ise d No t s a |
l /s i de Fr ta on |
Dr y |
C lea r |
0. 1 8 6 |
0. 1 8 25 |
0. 0 0 3 5 |
| Da y |
0. 0 9 5 |
0. 0 0 0 |
0. 2 17 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 1 8 6 |
0. 1 8 6 3 |
0. 0 0 0 3 |
| Da y |
0. 1 9 6 |
0. 0 0 0 |
0. 2 17 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 17 1 |
0. 1 6 6 0 |
0. 0 0 5 0 |
| Da y |
0. 3 3 0 |
0. 0 0 0 |
0. 2 8 3 |
No ign l ise d t s a |
Fr l /s i de ta on |
Dr y |
C lea r |
0. 17 1 |
0. 17 6 6 |
0. 0 0 5 6 |
| Da y |
0. 4 0 6 |
0. 0 0 0 |
0. 8 6 7 |
S ign l ise d a |
Fr l /s i de ta on |
W et |
C lou dy /ra iny |
0. 5 5 7 |
0. 5 5 3 1 |
−0 0 0 3 9 |
all, in some cases to a reduction of statistical significance. The remaining variables are transformed into a binary variable. For example, the day/night variable is transformed into two variables: day becomes a variable which is 1 when the accident occurred in the daytime, and night becomes another variable which is 1 when the accident occurred at night time. Output is the accident index as previously calculated in Eq. (1). Only some results are reported but they are sufficient to evaluate model performance.
Multiple linear regression, applied to the sets of data, gives an r 2 (r is the coefficient of correlation) ranging from 0.20 to 0.40. RMSE (root mean square error) calculated on real data and data calculated by the regression model ranges from 0.5 to 0.6. In some cases when output must be close to zero, the regression model gives negative values, too.
Multiple exponential regression gives an r 2 ranging from 0.17 to 0.41. RMSE calculated on real data and data calculated by of the regression model ranges from 0.5 to 0.7.
Therefore, considering the low level of these results no further analysis was carried out using these methods.
7. Results and discussion
The ANN model can include all possible permutations of variables, discrete or continuous. For continuous variables a classification is carried out only in order to reduce the number of possible values and to lessen computational time. As previously mentioned, Table 4 represents a set of possible enquires and outputs. If these enquires are organised by type, certain particular graphs can be obtained. Some of these examples are drawn in Figs. 5 and 6.
The following results are most significant for the discussion:
- 1. the degree of danger is the highest in night-time collisions, for any type of accident, at signalised intersections;
- 2. the degree of danger is the highest, with respect to all types of accident, for the running over of pedestrians at night-time at non-signalised intersections;
- 3. meteorological conditions and the state of the road surface are not determinant in the number of the accidents of each intersection; that is, at the level of analysis of a single intersection there is no statistically relevant correlation between the accident index and meteorological conditions or the state of the road surface but this doesn't mean that grouping together the accident data of some intersections a significant relationship cannot be singled out;
- 4. the accident index is greater for an intersection of average complexity (number of real and virtual points) if not signalised, compared to a signalised one with the same complexity; on the other hand, for signalised intersections of average complexity at night-time it is smaller than at non-signalised ones or ones with flashing yellow intersections;
Fig. 4. Learning cycles necessary to minimise the root mean square error.
Fig. 5. Accident Index for different types of intersection and regulation.
- 5. the accident index is greater for an intersection of average dimensions compared to more or less complex ones;
- 6. the accident index is greater for a small intersection if signalised compared to a small intersection that is not signalised;
- 7. real conflict points (that do not depend on trafficlights) are more important than virtual conflict points;
- 8. the accident index of a single intersection does not depend on accident type;
- 9. the rate of increase of average flow at a single intersection has no influence on the accident index; this means that in average in the same intersection accidents occurred both with high and low flow so that no rule can be singled out. It can usually be observed that by increasing the average flow (hourly flow for example) on a road network the number of accidents increases; but it is rather difficult to understand whether the accidents occurred with precisely those flow conditions or not.
In general the ability of the ANN to simulate road accidents can be attributed, like any other deterministic or statistical models, to the following factors:
- the choice and number of the variables used. The ANN requires a classification of the variables to be used. The choice is both theoretical (supported by analogous studies already conducted), and is linked to the availability of data already gathered. For instance, it may be easy to survey an intersection or obtain data on climatic conditions, but the same cannot be said for many human factors. The reduction of the number of variables used to describe the problem leads to an increase in the potential error of the model. Simple ANNs cannot fully explain multi-dimensional phenomena.
- 2. data collection factors. Once the variables for the ANN are chosen, the collection of these can frequently introduce other biases and errors. The data collection errors impinge in an unpredictable manner on the ANN model results;
- 3. stochastic aspect of the phenomenon. Though all the variables necessary to describe the process are employed and collected with a minimal degree of bias, the deterministic nature of the ANN does not assure irrelevance of model error when variables have a great stochastic component.
This last factor needs further clarification. When an ANN model is used it learns from realty expressed by the use of real data. The accident index associated with the particular set of values of variables that describe the accident is heavily influenced by the distribution of values in the actual set of accidents the ANN receives for the learning process. If a particular value of one variable in the learning set has a high accident index value the ANN will assign a higher link to this factor than to one with a lower value. Whether this link is randomly high or low the ANN will output an average value.
In order to solve a statistical problem of large values, it is necessary to make an appropriate extraction from real data to guarantee an equal distribution to all factors. For this purpose a database that represents every learning process should be built which contains a uniform distribution for the different values of the most meaningful variables.
For example, accidents that occurred in daytime are around 70% of the total. The consequence of this imbalance may be that a greater index is associated by the model to daytime cases. Regardless of whether a uniform database was constituted, the ANN classifies the most dangerous conditions only at those places where crashes most frequently occur. Such a selection of data would lead to a reduction of the available sets of real data for learning and consequently a reduced capacity to understand the nature of collisions. For the purposes of this paper it was not possible to satisfy a similar requirement because it would have been necessary to increase the number of intersections.
The fact that the model does not work perfectly (that is the variance the model actually explains better than stochastic character of the output as shown in Section 6.2) is due to the possibility that other variables should have been used. Intuitively this effect may be more serious in those cases exhibiting accident indexes with low values. This explains the apparently random nature of certain situations. For instance, during the nighttimes of festive occasions elevated speeds are adopted by young drivers. Unfortunately speed and flow data were not collected for all collisions at all times. The absence of these variables has contributed to making the daytime cases less 'clear'. They are more linked to a factor that varies in ways our ANN cannot understand. All these aspects help to explain some of the discrepancies between real values and those estimated by our ANN.
Another way of testing the validity of results is to apply the findings to other situations. This is to establish whether a certain model, trained with a certain set of data, is capable of carrying out reliable solutions for contexts different from those where data are collected. Generally the greater the quantity of data used for learning, the better the possibility of generalising the results and extending them to other urban contexts. It is necessary to emphasise, however, that if we want to extend the results of the simulations on a model 'educated' with data from a certain urban context, the similarity of the contexts must be evaluated since:
- 1. the association of the same variables do not necessarily give rise to the same results when a different context is examined; it is probable that in another city or environment the same variable may have a different weight as regards the actual number of accidents at intersections;
- 2. not using variables considered not fundamental for the designing of the model in some contexts, could lead to errors in model of other places. If, for instance driving in rainy weather represents a normal condition in one city, the same ANN cannot be used for a city where rain is rare.
If we want to extend our generalisation to other urban realities the results obtained by the ANN used in a specific context, attention should be paid to the choice of a 'similar' context. This applies not only to the values of variables used in the ANN model, but also in terms of those variables that were discarded during the learning phase. Another approach is to create a large database containing descriptions of all possible cases. Such a database is more likely to have a similar distribution of values across variables.
8. Conclusions
To understand which of the three subset factors, human, vehicular or road, is the most important and
Fig. 6. Accident Index for intersections of average dimensions and not signalised at night-time according to the type of accident.
which one it is necessary to intervene on, is not a simple task. We need to create tools of investigation capable of answering this question with a reasonably low margin of error.
Our paper shows one method to follow in the use of the ANN. Thanks to the clarity of the results, in terms of which factors explain accidents and which factors contribute to a higher degree of danger, the capability of extracting information from data, exhibited by neural networks, makes the proposed methodology of analysis still more interesting, above all for the possibility of using databases that already exist or have been built for other purposes.
It is necessary to continue work on these types of models, to tackle and solve problems connected to the distribution of data with a low average value. In order to make this factor less preponderant, we suggest a procedure that envisages an extraction of preliminary data (for example by a cluster analysis) so as to improve the training phase of ANNs.
Another problem not yet resolved in technical papers concerns the different recurrence of phenomena which may cause an accident; this can lead to the collection data that are not homogenous in time and affect results in an unpredictable way. To avoid these difficulties studies on driver behaviour and peculiarities have already been carried out in order to understand what is the best (minimum) sample interval for the various accident scenarios.
The use of the accident index to compare the degree of danger of the intersections may be criticised. It is a macroscopic value which could lead to a misunderstanding of microscopic effects occurring at the intersection.
Acknowledgements
Thanks are due to the City Hall for providing data and other help. This paper is partially funded by CNR (Murst 40%).
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