Analysis of historical road accident data supporting autonomous vehicle control strategies

Black spot identification

Black spot management (identification, analysis, and treatment of black spots in the public road network) is one of the most important tasks of road safety engineers. The identification of these extremely hazardous sections is the first step to prevent further accidents or to decrease the seriousness of these. It is a heavily researched area, and there are several theoretical methods for this purpose.

However it has a long tradition in traffic engineering; interestingly, there is not any generally accepted definition of road accident black spots (also known as hot spots), the official definition varies by country. It follows that the method used to find these hazardous locations also varies by country. For example, by the definition of the Hungarian government, outside built-up area black spots are defined as road sections no longer than 100 meters where the number of accidents during the last three years is at least 3. According to this, road safety engineers use simple threshold-based methods (for example, the traditional sliding window technique) to find these areas. Switzerland uses a significantly different definition as black spots are sections of the road network (or intersections) where the number of accidents is “well above” the number of accidents at comparable sites. The key difference is the term “comparable sites” because these advanced comparative methods do not try to classify all road segments by itself but try to compare to similar areas.

There are some general attributes of accident black spots to overcome the conceptual confusion. These are usually well-defined sections or intersections of the public road network, where road accidents are historically concentrated (Elvik, 2008; Delorme & Lassarre, 2014; Murray, White & Ison, 2012; Montella et al., 2013; Hegyi, Borsos & Koren, 2017). Nowadays, road accidents are monitored by the governments and all data about accidents are stored in large, reliable and partially public databases (without any personal information about the participants). Much data about the road network is also available (road layout, speed limits, tables, etc.). As a result, road safety engineers can use several procedures from various fields (statistics, data mining, pattern recognition) to localize accident black spots in these databases.

It is a common assumption that the number of accidents is significantly higher at these locations compared to other sections of the road network. However, this alone is neither a necessary nor sufficient condition. The variation of the average yearly accident count of road sections is relatively high compared to the number of accidents. Because of this, the regression to the mean effect can distort the historical data. A given section with more accidents than average is not necessarily an accident black spot. The converse is also true, as there may be true black spots with relatively few accidents for a given year. However, this deficiency is already theoretically proven as most black spot identification methods are based on the accident numbers of the last few years, simply because this is the best place to start a detailed analysis.

Nevertheless, it is always worth keeping in mind that these locations are just black spot candidates, but it needs further examination to make the right decision concerning them. The best way to do this is via a detailed scene investigation, but it is very expensive and time-consuming. Another theoretical approach can be the analysis of accident data to find some irregular patterns and identify one or more risk factors causing these accidents. Without these, it is possible that the higher frequency of accidents is purely coincidental at a given location and time.

To localize potential accident black spots, the most traditional procedure is the sliding window method (Lee & Lee, 2013; Elvik, 2008; Geurts et al., 2006). The input parameters of the process are the section length and a threshold value. The method is based on the following:

1. Divide the selected road into small uniform sized sections;

2. Count the number of accidents that have occurred in the last few years for each section;

3. Flag the segments where this number is higher than a given threshold as potential black spots.

There are many variants of the proposed traditional sliding window method (Anderson, 2009; Szénási & Jankó, 2007). A potential alternative is to use variable window length. One of its advantages is that it is unnecessary to set the appropriate parameter, but sufficient to give a minimal and maximal value. The method can try several window lengths to find the largest black spots possible. Due to this modification, it can find small local black spots and larger ones too. The traditional sliding window method uses non-overlapping segments, but it is also possible to slide the window with smaller steps than the window size. This leads to a more sensitive method, which can find more black spot candidates. However, it is also necessary to manage the overlapping black spots (considering these as one big cluster, or multiple distinct ones). It is worth mentioning that the method has some additional advantages: it has very low computational demand (compared to the alternatives) and is based only on the road accident database.

The sliding window method is one of the first widely used procedures; therefore, it is based on the traditional road number + section number positioning system (for example, the accident location is Road 66, 12+450 kilometer+meter). This traditional positioning system was the only real alternative in the past. However, in the last decades, the spreading of GPS technology makes it possible to collect spatial coordinates of accidents. This step has several benefits (faster and more accurate localization) but also requires the rethinking of the already existing methods. It is possible to extend the sliding window method to a two-dimensional procedure, but it is not widely used. It is better to seek out better and more applicable methods fitting to the spatial systems given by the GPS coordinates.

From this field, Kernel Density Estimation (KDE) methods are one of the most popular spatial data analysis techniques (Bíl, Andrášik & Janoška, 2013; Flahaut et al., 2003; Anderson, 2009; Yu et al., 2014; Toran & Moridpour, 2015). These have been employed in many research projects to analyze road accidents. KDE methods have the advantages of simple implementation and easy understanding. These also have the benefit to naturally handle the noise of the data (caused by inaccuracy of GPS devices). In general, KDE is used as an estimation of the Probability Random Function of a random variable. From the safety experts’ point of view, the result of the KDE method is the accident density estimation at a given reference point. The procedure has several parameters, like the search radius distance from the reference point (bandwidth or kernel size) and the kernel function.

Several researchers recommend the use of empirical Bayesian methods combining the benefits of the predicted and historical accident frequencies. These models usually analyze the distributions of the already existing historical data from several aspects, and give predictions about the expected accident state. In the Empirical Bayesian method, the existing historical accident count and the expected accident count predicted by the model are added using different weights (Ghadi & Török, 2019). Because of this, this process requires an accurate accident prediction model.

Another group of already available methods is based on clustering techniques. These procedures are from the field of data mining, where clustering is one of the widely used unsupervised learning methods. In this context, a cluster is a group of items, which are similar to each other and differ from items outside the cluster. Accidents with similar attributes (where properties can be the location and/or another risk factor(s)) can be considered as one cluster, using this concept in the field of black spot searching. Most studies use the basic K-means clustering method (Mauro, De Luca & Dell’Acqua, 2013), but there are also some fuzzy-based C-means solutions.

As already mentioned, the results of the proposed methods are just a set of black spot candidates. It needs further analysis to make a final, valid decision as to whether it is a real accident black spot or not. Furthermore, whether or not it requires any actions. This is the point where our research turns away from traditional road safety management work (identification and elimination of black spots). Based on the collected clusters, road safety engineers must select the black spot candidates having the largest safety potential, which is based on the prediction of the effect of the best available preventive action (cost of the local improvement activity compared to the expected befits in the number and severity of further accidents). From the perspective of autonomous car control, the role of this safety potential is essential. The self-driven car has no options to solve road safety problems. The only important information is the existence of accident black spots and the potential safety mechanisms, which may help to avoid further crashes. As a second difference, from the road safety engineers’ point of view, it is not necessary that the accidents of a given black spot have common characteristics. The hot spot definition of this paper assumes that accidents of a given cluster have similar attributes because this pattern will be the basis of the preventive actions.

The localization of accident black spot candidates is a heavily researched area and there are several fully-automated methods to find these. Nevertheless, the further automatic pattern analysis of these is not as well developed. This phase usually needs a great deal of manual work by human road safety experts (they must travel to the scene and investigate the environment to support their decisions about recommended actions). However, this process is supportable by some general rules but is mostly done manually using the pattern matching capability of the human mind. To fully automate it, it is necessary to make this method applicable to self-driven cars.

According to this objective, this paper focuses on the help for autonomous vehicles to take the appropriate preventive actions to avoid accidents:

• Localize black spot candidates using historical accident database;

• Make assumptions about the common risk factors and patterns of these accidents;

• According to these preliminary results, the autonomous device will know where the dangerous areas are and what preventive actions to take.

Automated accident prevention

Autonomous vehicles will have several ways to avoid accidents and, therefore, is a hot, widely researched topic. Nevertheless, most papers deal with options existing only in the far future when autonomous devices will be a part of a densely connected network without any human interferences. Real-world implementations are far from this point, but some technologies already exist, although they are not closely related to autonomous vehicles. Currently, implemented accident prevention systems are built into traditional cars as braking assistants, etc. However, it is worth considering these because such methods will be the predecessor of the future techniques applicable to self-driven vehicles.

The two main classes of accident prevention systems are passive and active methods. Passive systems send notifications to the driver about their warnings but do not perform any active operations. On the contrary, active methods have the right to perform interventions (braking, steering, etc.) to avoid accidents. It seems obvious that these prevention systems have a large positive impact on accident prevention, and it has already been proven by Jermakian (2011) that passive methods have significant benefits. There are more than one million vehicle crashes prevented in the USA each year. As Harpen proved (Harper, Hendrickson & Samaras, 2016), the cost-benefit ratio of these systems is also positive.

Brake assist systems are one of the most researched active systems, where the potential benefits are the lower risk of injury, and the less serious injuries of the pedestrians (Rosén et al., 2010). Current forward-looking crash avoidance systems are usually continuously scanning the space in front of the vehicle using various devices (camera, radar, LIDAR, etc.). If any of these detects an unexpected vehicle or pedestrian, the brake assistant system takes the appropriate (preliminary) actions, which can be the enforcement of the braking system or direct autonomous emergency braking. Bálint, Fagerlind & Kullgren (2013) presented very promising results with a test-based methodology for the assessment of braking and pre-crash warning systems. These typically are only using the real-time information given by the vehicle sensors without any knowledge extracted from historical accident data.

Run-time crash prediction models are also related to the topic of this paper. Hossain et al. (2019) presented a comprehensive comparison and review of existing real-time crash prediction models. The basic assumption of these systems is that the probability of a crash situation within a short time window is predictable by the current environmental parameters measured by the sensors. Therefore, most of the already existing methods use only the acquired sensor data to make real-time decisions about potential crash situations. According to this assumption, authors do not use the already existing accident databases as an input to fine-tune the system’s predictions.

The work of Lenard, Badea-Romero & Danton (2014) is closer to the research presented in this paper. They analyzed the common accident scenarios to support the development of autonomous emergency braking protocols. Based on the hierarchical ascending method in two British accident databases filtered by some previously defined conditions (they use only the urban pedestrian accidents that occurred in daylight and with fine weather conditions), attributes of the most common accident scenarios were presented. This paper defines the major accident scenarios and classifies all existing pedestrian accidents into one of these categories. The results of this research would be useful in the training phase of a self-driven vehicle to introduce all possible scenarios to the algorithm.

The objective of Nitsche et al. (2017) is similar, which proposes a novel data analysis method to detect pre-crash situations at various (T- and four-legged) intersections. The purpose of this work is also to support the safety tests of autonomous devices. They clustered accident data into several distinct partitions with the well-known k-medoids procedure. Based on these clusters, an association rules algorithm was applied to each cluster to specify the driving scenarios. The input was a crash database from the UK (containing one thousand junction crashes). The result of the paper contains thirteen crash clusters, describing the main pre-accident situations.

Black spot candidate localization

Analysis of black spot candidates

The result of the various black spot localization algorithms (sliding window, clustering, etc.) is a list of potential hot spots. However, having some accidents in a cluster does not mean that the hazard of accidents is significantly higher here. It is usually accepted by researchers that the number of accidents in a given area (section) of the road network fits the Poisson distribution. A special feature of road accident distribution is that the number of accidents is relatively low (compared to the size of the road network), and the variance is high. Therefore, the volatility of the accident number is very high, which means that a given cluster where the number of accidents is above the average is not inevitably a hot spot. The list given by the previous methods needs further examination to find the real hazardous sites.

At this point, the methodology of this paper significantly differs from the work of road safety engineers. Their objective is to find hazardous sites and take the appropriate actions to decrease the probability of further accidents. They must select the sites having the largest safety potential where the best cost-effective actions can be taken to decrease the number and severity of accidents. It is a very complex procedure based on the data of historical accidents, the expected number of accidents, the environmental conditions and the cost/expected benefits of different safety actions. Contrary to this, the objective of a self-driven car is not the elimination of road safety problems. As an ordinary participant of traffic, it has no chance to make the road network better. Nevertheless, as a passive participant, it should be able to localize the problematic areas, analyze these, and take the necessary preliminary steps to avoid further accidents.

Another difference between the methods of these fields is that from the perspective of road safety engineers, it is not necessary that the accidents of a given black spot have any special patterns or common characteristics. For the self-driven car, the localization of high-risk areas where the number of accidents is significantly higher than expected is not enough because this fact does not help to take the appropriate preliminary steps. This is the reason why this paper focuses on the identification of accident reasons.

The result of this further investigation can be one of the following:

• If it is not possible to identify any unexpected pattern in the accident attributes then the cluster cannot be considered as an accident black spot. The high number of accidents is just a coincidence and there are no suggestions to avoid further crashes.

• In contrast, if there is a special pattern in the accident attributes then this cluster has the potential to decrease the probability of further crashes. These reasons for similar accidents would be related to the road network, weather, lighting conditions or human errors (drivers and pedestrians).

In the second case, the knowledge of this special pattern (the common reasons for accidents in the same cluster) can be essential. It is presumable that it is possible to avoid accidents caused by the car itself. For example, if it is visible from the accident database that the number of accidents caused by slippery road is significantly higher than expected in a given area, the self-driven car should decrease the speed or change its trajectory to reduce the probability of this event. However, it is also worth noting that the preliminary actions can be very useful to decrease the probability of accidents caused by other drivers or pedestrians. For example, if the historical accident data contains patterns that the number of accidents caused by pedestrians is higher than expected, then the self-driven car would proactively try to decrease this negative potential using some type of visual or auditory warning or decreasing speed.

Scoring factors

The practical evaluation presented by this paper focuses on one specific accident reason (N = 1) the slippery road condition factor (R₁).

The used accident database contains more than two hundred fields, in four categories:

• general accident attributes (date and time, location, nature, etc.);

• general environmental attributes (weather conditions, visibility, etc.);

• data about participants (was it a vehicle or pedestrian, speed, direction, etc.);

• data about injured persons (age of the injured person, etc.).

Weighting tables have been developed to estimate the effect of a given accident reason factor on the occurrence of the accident. It is possible to distinguish the following three type of accident properties, focusing on the slippery road condition accident factor:

• Some fields directly contain information about the examined factor. In this case, the “Road surface” property (abbreviated as roadsrf) of an accident has an option of “4-oily, slippery”. This is taken as the basis for further weights; the score value of this attribute is 1.0 (W¹_{roadsrf = 4} = 1.0), showing that the accident is highly affected by the slippery road condition factor. It is worth noting that it is not efficient making a binary decision about the examined factor based on this value because there are other values (“3-snowy”, “5-another staining”) having similar effects. This is reflected in the weight values.

• In some cases, there are no such direct fields, but it is possible to deduce information about a given factor from the already existing data. For example, in the case of the slippery road condition factor, the weather conditions (wthr property in the database) can help this process. In these cases, the score values assigned to different weather condition cases show an estimation of how much the given factor affected the occurrence of the accident. In the case of snowing (“6-snowy”), it would be higher (W¹_{wthr = 4} = 0.3) than for ideal conditions like “1-sunny” (W¹_{wthr = 1} = 0). It is also considered that in the case of accident nature “31-Slipping, carving, overturning on the road”, the slippery road factor influenced the results (W¹_{accnat = 32} = 0.2)

• The last group contains the fields without any relation to the examined factor. For example, fields like “Age of the driver” do not affect the results. The weights for all values of these fields are consequently zero.

The Supplemental File “Scoring tables” contains the given weight values for the affected fields. Weight values are based on a comprehensive literature review from the fields of road safety and road friction measurements (Wallman & Åström, 2001; Andersson et al., 2007; Sokolovskij, 2010; Colomb, Duthon & Laukkanen, 2017). However, some of the values are affected by the subjective experiments of the authors. It should take some further research to determine the most efficient weights.

Accident database

This paper uses the official road accident database of Hungary, where data regarding accidents with personal injury are collected by the police. After some conversion and corrections, this dataset is handled by the Central Statistics Department. The completeness of the database is ensured by legislation, and participants of public road accidents with personal injury are obliged to report it to the police. A police officer starts the data collection on the spot by recording the most relevant data about the location and the main attributes of the accidents (participants, casualties, etc.). After 30 days, it is possible to refine the final injury level for all participants. After that finalization step, the Central Statistics Department collects and rechecks all records. Road safety engineers and researchers can use this database for their work.

The evaluation part of this paper is based on the accidents of this database from 1 January 2011 to 31 December 2018. It contains 128,767 accidents with personal injury classified into three categories: fatal, serious and slight. There are no accidents in the database without personal injury. Because of the high number of accidents and high computational demand of the clustering algorithm, this paper deals with two counties of Hungary: accidents of “Győr-Moson-Sopron” county was used to find the optimal parameters of the algorithm and “Heves” county was used as a control dataset.

DBSCAN clustering

The input database for the clustering was the personal injury accidents of a given county of Hungary (“Győr-Moson-Sopron” county). This experiment was performed twice at two consecutive time intervals to measure the robustness of the method. The examined t interval contains the accidents which occurred in 1 January 2011–31 December 2014. and the $\hat{t}$ validation interval was 1 January 2015–1 December 2018. The number of accidents was 3,256 in the t interval (the D set contains these accidents) and 3,011 in the $\hat{t}$ interval (the $\hat{D}$ set contains these accidents).

In the hot spot search phase, the following DBSCAN parameters were used:

• ε value: 100 m;

• minimum accident count: five accidents;

• minimum accident density: 0.0001 accident/m².

The result of this raw DBSCAN clustering method was 165 black spot candidates in the t interval and 152 black spot candidates in the $\hat{t}$ interval.

Statistical test

Unlike traditional black spot searching methods, the next step is not the calculation of some safety potential index, but the determination of the different accident reason factors using the scoring method presented in Section. Considering the R₁ slippery road condition factor, the S₁(x) value is calculated for all x accidents. Most of these are not related to a slippery road surface reasons; so, S₁ value for these is 0.

As a prerequisite for the Welch-test, a population of S_i(y) values is generated where y stands for all accidents in the database. The main parameters of this sample are:

• number of items (n₁): 3,256

• mean ( ${\overline{x}}_1$): 0.2438

• variance (v₁): 0.1115

It is possible to calculate these values for all of them, iterating the overall black spot candidates. Based on the whole population comparison and the black spot candidates, the Welch-test was applied to get the statistical result values. According to the Welch-test, it is possible to use the Student distribution with these parameters and the given level of significance (α = 0.05) to reject the null hypothesis or not.

Table 1 shows the black spot candidates of the t interval where the null hypothesis was rejected because the mean of the R₁ score for the given black spot candidate was significantly higher than the expected average. It can be assumed that these black spots are affected by the examined R₁ factor.

Figure 1 shows the environment and the accidents of the first black spot from this list. As is visible in the satellite image, it is a part of a long straight road; consequently, there is no reason for the autonomous car to decrease its speed. From the historical database, Table 2 contains detailed information about the accidents. As is visible, there is a high number of accidents affected by one or more slippery road-related attributes. This pattern significantly differs from the expectations; hence, there should be some environmental issues at this location. The examination and elimination of these reasons is the task of road safety experts (Orosz et al., 2015). Nevertheless, until then, it is worth taking preventive steps to decrease the chance of further accidents. The autonomous vehicle should adapt its control to this situation (speed reduction, using safer trajectory, etc.).

Site consistency test

This test assumes that any site identified as a black spot in the t time period should also reveal high risk in the subsequent $\hat{t}$ time period.

Let π(C) the convex boundary polygon of the C cluster given by the algorithm presented in Section, and π is the union of these regions identified in the t time period (10).

(10) $$\mathrm{\Pi }=\bigcup _{i=1}^n\mathrm{\Pi }(C_i)$$As the next step, we collect all accidents for the consecutive $\hat{t}$ time period, which are inside the clusters identified by the prior t time period. The T₁ attribute shows the number of these accidents divided by the summarized area of these clusters. Thus, this is the accident density of these clusters in the consecutive time period Eq. (11).

Accident reason factor consistency test

As this paper goes further, revealing the accident reason factors, it is also worth checking if the accidents in the $\hat{t}$ time period inside the region identified by the t time period have the same attributes or not. This leads to the introduction of the T′₁ value, which shows the average score value for these accidents Eq. (12).

Method consistency test

It is also assumable that a black spot area identified in the t time period will also be identified as black spot in the consecutive $\hat{t}$ time period. A given black spot searching method can be considered consistent if the number of a black spots identified in both periods is large. Meanwhile, that of black spots identified only in one of the examined periods is small. It is possible to use Eq. (13) to calculate this method consistency: (13) $$T_2={\displaystyle \frac{|\{C_1,C_2,\dots C_n\}\cap \{{\hat{C}}_1,{\hat{C}}_2,\dots {\hat{C}}_{\hat{n}}\}|}{|\{C_1,C_2,\dots C_n\}\mathrm{\Delta }\{{\hat{C}}_1,{\hat{C}}_2,\dots {\hat{C}}_{\hat{n}}\}|}}$$where T₂ is the ratio of the number of clusters existing in both search results and the number of clusters given by only the search in t or only in $\hat{t}$ time period (△ stands for the symmetric difference of sets). A pair of clusters from the t and $\hat{t}$ period considered identical if the distance between these is less than 300 m.

Rank difference test

The rank difference test is based on black spots identified in both the t and $\hat{t}$ periods. The black spots of both periods are sorted by accident density, and the rank difference test shows the difference in the positions of the same cluster in the two lists. The smaller the value, the more consistent the examined method is, because the sequence of clusters is similar. Large numbers shows that the examined method was able to identify the same black spot in both intervals but with a different severity related to each other.

Let O and $\hat{O}$ the sequences of black spots identified in both periods (both sequences contain the items of the $\{C_1,C_2,\dots C_n\}\cap \{{\hat{C}}_1,{\hat{C}}_2,\dots {\hat{C}}_{\hat{n}}\}$ set) ordered by accident density in the t time period (O) and in the $\hat{t}$ time period ( $\hat{O}$). The T₃ will show the rank difference of the examined method Eq. (14). Obviously $|O|=|\hat{O}|$.

(14) $$T_3={\displaystyle \frac{\sum _{c\in O}|Rank(c,O)-Rank(c,\hat{O})|}{|O|}}$$where Rank(x, Y) is the rank of the x black spot in the Y sequence.

Evaluation results

First, the proposed method was compared to the traditional Sliding Window method (SW) using dynamic window length. The minimal window length parameter was 250 m, the minimal accident number was 5, and the minimal accident density was 0.01 accidents/m. As a further step, the novel method was also compared to the raw DBSCAN based clustering (without the accident factor scoring). The parameters of this were the same as presented above. The proposed method is presented in the comparison under the DARF (DBSCAN with Accident Reason Factor determination) name.

Table 3 shows the overall results for “Győr-Moson-Sopron” county. As visible, the number of black spots recognized by the DARF method is significantly less than by its alternatives. It was expected because the SW and DBSCAN methods list all clusters where the accident density is higher than a given threshold. In contrast, the DARF method results in only black spots affected by the R₁ accident factor. The difference between the SW and DBSCAN is also significant and is caused by the fact that the SW uses road name + road section positioning which is not available in built-up areas. In comparison, the DBSCAN method is based on GPS coordinates and can find the black spots of municipal roads (which is one advantage of this approach).

The T₁ result is similar in the case of DBSCAN and DARF methods and it is significantly less in the case of SW. The T₂ results are almost the same for all algorithms. The third general metric shows that the proposed method performs very well on the rank difference test. However, it is worth noting that the number of black spots is significantly less in this case, which can be an advantage.

The T′₁ metric shows the real strength of the proposed method. As expected, black spots identified by the SW and DBSCAN contain a mixture of various accidents. Consequently, the average of the R₁ score is near to the mean of the population (0.2159 and 0.1922 compared to 0.2438). Contrary to this, the score number for the accidents of the $\hat{t}$ time interval placed inside the clusters located by the data of the t interval is 0.62, which is significantly higher than the average.

These results confirm that the proposed method has very similar characteristics to the already existing methods. The slightly lower T₂ value shows that as a raw black spot searching algorithm, it is not as robust as the alternatives. Nonetheless, the T′₁ result shows that it is satisfactory for our purpose. It can localize areas when the expected number of accidents with given accident reasons is significantly higher than the average.

Table 4 shows the same values for another county (“Heves”) as a control dataset to check the robustness of the method. As visible, the main characteristics of the results are very similar. In this case, the T₁ and T₃ results are better compared to the alternatives. However, the T′₁ value is slightly lower, but still significantly higher than the population average.