RESULTS: ESTIMATION OF INCIDENT PROBABILITY

EIP Fuzzy Logic Model

Summary of Testing Performance

The fuzzy logic model was not tested with data from the Barcelona test site. Instead, two test data sets were constructed for two typical situations frequently occurring on Dutch motorways.

Two tests were performed:

1. Test EIP FL1: Adverse weather conditions, and
2. Test EIP FL2: Shock-wave of a moving jam.

Test EIP FL1 covers 150 (fictional) minutes. Test EIP FL2 covers 30 (fictional) minutes.

The test results for Test EIP FL1 are given in the form of the risk of an individual driver, per minute and per kilometre. For EIP FL2, this was supplemented with the overall risk of all drivers, per kilometre. The results are presented in a graphical form, which shows the development of the risk over time.

Test EIP FL1: Adverse weather conditions
The data from Figure 1 formed the input for the testing of this example in the fuzzy logic model. Suppose it has been dry for two weeks after which it starts to rain. The precipitation intensity is depicted in Figure 1(a). In the first two hours the rain is light followed by a severe cloudburst at time t = 120 min. Other variables associated with weather or traffic conditions were kept constant.

Fig 1: (a) Precipitation intensity over time and (b) the incident risk per vehicle estimated by the Fuzzy Knowledge-based EIP

Experts were unanimous about this kind of situation, stating that the mixture of water with residues of oil and rubber (accumulated during the long, dry period) make the road surface very slippery, especially when the soap-like pellicle is not immediately washed away by heavy rainfall. Therefore a very dangerous situation will develop in the first minutes after the rain has started to fall. This statement is reflected in the weather rule base as follows:

IF dry_period_before_today IS long AND pavement IS wet AND change_in_weather_type IS very_recent THEN risk_increase IS very_large_and_positive;

Fig 2: Membership functions for the variable "change_in_weather_type"

In the example of Figure 1(a) the expression "dry_period_before_today IS long" is certainly true for Dutch conditions. Due to the rainfall the "pavement IS wet". These two expressions combine to the value 'true' with a degree of familiarity (DOF) equal to 1. The DOF for the expression "change_in_weather_type IS very_recent" will change over time after it has started to rain. Since it cannot be decisively said when the change in weather type is still recent, the boolean logic of 'true' and 'false' does not suffice anymore. This is where the real fuzzy logic comes in. The fuzzy set for this variable is defined with membership functions for the linguistic classes 'very_recent', 'today', 'yesterday', and 'many_days_ago' that define how 'true' the value is depending on the continuous time since the last weather change (see Figure 2). Therefore the 'very_large_and_positive" risk increase contributes only temporarily to the incident risk, which explains the declining curve between t = 30 and t = 80 in figure 3(b). Note how the cloudburst at t = 120 again increases the incident risk significantly due to another rule in the rule base that accounts for this situations.

Test EIP FL2: Shock-wave of a moving jam
The second example represents the observation of a shock wave associated with a moving jam. Suppose detectors recorded the speed and density time series of Figure 3(a) and Figure 3(b). Other weather and time-related variables in the fuzzy rule base were kept constant in this example. Drivers moving into the upstream jam front are suddenly confronted with severe braking manoeuvres, which leads to a high risk at the onset of the jam (see period around t = 10 in Figure 3(c)). In the body of the jam the congestion is rather homogeneous which is a relatively safe situation (between t = 13 and t = 20). The nervous maneuvering when moving out of the jam at the downstream jam front again increases the incident risk but not as high as during the deceleration. (t > 20). When multiplied with the density the total incident risk is found in Figure 3(d).

Fig 3: : Traverse of a shock-wave. (a) Speed measurement, (b) density measurement, (c) risk incurred by individual drivers and (d) risk aggregated over all vehicles.

Note how the relatively low incident risk per driver in the jam body incurred by a large number of drivers apparently leads to worse conditions than in the downstream jam front where the lower density 'dilutes' the total incident risk.

Note that the results presented in the two examples were generated using the first draft of the model, for which no calibration has been carried out yet. Fictional data has been used. Encouragingly, the results appeal rather well to what is intuitively expected.

The fuzzy logic EIP model requires less detailed data to construct it than the Logit model, but detailed, minute-by-minute data, including weather variables, is still required to test it quantitatively. However, for this quantification a reliable incident database is necessary, together with simultaneous recordings of all values of variables in the fuzzy rule base. The PRIME project accounts for such a database for traffic, road geometry and time data. A database containing also detailed weather conditions is unfortunately not yet available. Therefore, a comparison with the performance of the other EIP models was impossible. However, improvement of the fuzzy logic based EIP model is still possible by further structuring of the rule base, by including research results from literature in the rule base, and by calibrating the model. The latter would allow to quantitatively estimate the incident probability instead of the qualitative indicator that we have denoted with the term 'risk'.