Evaluation and prediction of free driving behavior type based on fuzzy comprehensive support vector machine

The SVM is based on the principle of structural risk minimization and the dimension theory in statistics. Based on the limited sample information, the SVM seeks the best compromise between the complexity of the model and the learning ability, which can be applied to classification problems and can have unique advantages in solving small sample, nonlinear and high-dimensional pattern recognition [37]. In FC-SVM, SVM reduces the influence of subjective factors on the weight of FC. The free driving behavior score and free driving behavior evaluation type of FC-EM constitute the input of SVM (I _z , y _{m Z} ). I _z is the free driving behavior score after the z-th group fuzzy comprehensive analysis, and y _mz is the z-group driving behavior evaluation type (z = 1, 2, ⋯; m = 1, 2, 3, 4, 5).

In the case of linear separability, the SVM is proposed to obtain the optimal classification plane. For a linearly separable sample set, there is a hyperplane w ^T x _i  + b = 0, by determining the positive and negative of g (x _i ) = w ^T x _i  + b to confirm which class x_i in the sample set belongs to. w is the normal vector of the hyperplane, T stands for transpose, and b is the offset, which determines the distance of the hyperplane from the origin. When some sample points in the sample are linearly inseparable, the relaxation variable ξ_i (ξ_i≥0, i = 1, 2, ⋯, n) is introduced, but not all sample points have slack variables. ξ_i does just apply to outliers in the sample, in which case the hyperplane must meet the conditions: y i ( w T x i + b ) ⩾ 1 - ξ i(10)

When ξ_i <1, the sample points can still be correctly classified. When ξ_i≥1, the classification surface cannot classify the samples correctly, so the following function is introduced. φ ( w , ξ ) = 1 2 w T w + C ∑ i = 1 n ξ i(11)

Among them, C is a penalty factor, which indicates the trade-off between good generalization ability and minimum training error. At this time, SVM is realized by quadratic programming as follows [38, 39]. { max ∑ i = 1 n a i - 1 2 ∑ i = 1 n ∑ j = 1 n a i a j y i y j ( x i T x j ) s . t . a i ⩾ 0 , i = 1 , 2 , ⋯ , n ∑ i = 1 n a i y i = 0(12)

Substituting the kernel function K (x_i, x_j) for x i T x j is equivalent to mapping the original sample to a high-dimensional space. This process makes the linear indivisible problem linearly separable, and finally obtains the classification function: f ( x ) = sgn ( ∑ i = 1 n a i y i K ( x i · x ) + b )(13) where a_i is the lagrange multiplier, b is the threshold, and K(x_i, x_j) is the kernel function. Commonly used kernel functions are polynomial kernel function, RBF kernel function and Sigmoid kernel function.

There are currently two ways for SVM linear classifiers to solve multi-classification problems: (1) One-versus-one (OVO SVMs), which is used to design an SVM between any two types of samples, so samples of k categories need to design k(k-1)/2 SVMs. (2) One-versus-rest (OVR SVMs) training classifies samples of one category into one class in turn, and other remaining (k-1) class samples are classified into another class. When classified, the unknown sample is classified as the one with the largest classification function value. Comparing these two methods, OVO SVMs are computationally intensive and complex in structure, and are used less in practical applications. Therefore, OVR SVMs are used in the classification prediction of driving behavior types.

According to the given training set where T = { (x₁, y₁) , ⋯ , (x _L , y _L ) } ∈ (X × Y)  ^L , x _i  ∈ X = R ⁿ , y _i ∈ Y = { 1, 2 ⋯ , M } (i = 1, 2 ⋯ L), a decision function is looked for.

To get a multi-class classifier, a series of two-class classifiers is needed to be constructed. Firstly, a certain type of free driving behavior is taken as a category, and the remaining free driving behavior types are used as a class to construct a classifier to classify driving behaviors. In this way, multiple classifiers are designed to classify and predict driving behavior types. Next, it is presumed to judge the attribution of a certain input x. The specific description is as follows.

Under the training set of Equation (14), the following operations are performed like that the j class is denoted as “1”, and the remaining (M-1) classes are denoted as “–1”, and decision function is found by SVM Equation (12): f j ( x ) = sgn ( g j ( x ) )(14) where gj(x) determines that input x belongs to j-th category, and j is the largest value between 1 and M.

4.1 Experimental description

Prescan and Matlab/Simulink joint simulation is used to build the simulation platform shown in Fig. 3. Through Prescan, the driving road of the typical 3 km section of Zhihui Avenue in Jingkou District of Zhenjiang was built to simulate the free driving situation of the road in real scene, and the road ratio was 1:1. Using Sketchup to build a driving participation scene around the road, the driving environment simulates the real environment, avoiding large errors in the simulation results due to changes in the driving environment. Various vehicles, traffic lights, marking rods, sensors and other modules are added to the traffic scene. Although the experimental scenario was designed to be as close to the real world as possible, there are still some differences between them. Fortunately, some differences in the external environment do not have much impact on the vehicle, driving simulation experiments focus on the current road vehicles and the driver himself. The driving simulator controls the vehicle Audi_A8_1, and the driver manipulates the simulator to simulate the real free driving scene.

OPEN IN VIEWER

Fig. 3

Prescan simulation platform.

In the typical driving simulation scenario built by Prescan, the driver simulates the real driving vehicle, and collects the throttle and brake pedal opening, steering wheel angle and gear position of the vehicle. At the same time, the relative distance between the simulated vehicle and the front or rear vehicles in the traffic environment is collected. Besides, the vehicle speed and intersection traffic light status are collected. The parameters that can be collected by the vehicle are converted into parameters related to driving behavior by Matlab/Simulink. Because there are some differences between the driving simulator simulation and real vehicle test to some degree, experiments done in the following are all based on the improved driving platform, which can improve the fidelity of simulators and be closer to real vehicle.

We used accumulated mileage to distinguish the driving experience of participants in this study by reference to two studies [40, 41]. Accumulated mileage is the total number of driving mileage by the data of statistics. The drivers with accumulated mileage less than 3000 km are novices. The drivers with accumulated mileage between 3000 km and 100,000 km are medium experienced. The drivers with accumulated mileage more than 100,000 km are experienced. The participants that took part in our experiments are divided into medium experienced drivers and experienced drivers, as shown in supplementary Table 4. Specific experiments (Experiment 1–5) are described in the following sections.

Free driving behavior evaluation adopts three control strategies. The three control strategies are as follows: 1) Driving behavior score was obtained by weighted synthesis method (WE-SY); 2) Analytic hierarchy process (AHP) was used to obtain driving behavior score; 3) The Matlab fuzzy toolbox was used to establish the corresponding fuzzy rules and set the basic parameters of the fuzzy module of Simulink. The driving behavior evaluation model based on established FC-EM above was used to obtain the driving behavior evaluation score.

Experiment 1: Simulation test: A male driver aged 30 that are experienced was selected to participate in the simulation experiment of driving behavior based on Prescan. In the built simulation scenario, the driver performs a single driving simulation, and Prescan collects simulation data in real time to obtain different driving behavior scores under different environmental complexity (different environmental complexity is achieved by adding the number of surrounding vehicles and pedestrians), as shown in Fig. 4. “L₁ = 0.25” and “L₂ = 0.5” represent respectively lower environment complexity and higher environment complexity. The reason why we choose the two kinds of case instead of other kinds is that the road traffic will become congested under higher environment complexity than 0.5. This experiment aims to evaluate the driving behavior type, while the driver will form his own unique free driving behavior type during the long-term driving process [8], so our evaluation experiment set can derive the driver’s accurate free driving behavior type in the two kinds of cases.

OPEN IN VIEWER

Fig. 4

Comparison of the same driver’s single driving score.

Available from Fig. 4: (1) When L₁ = 0.25, the driving score curve obtained by FC-EM tends to be fixed after short-time simulation, while the simulations of the other methods are still large at the end of simulation. L₂ = 0.5 is also like this. (2) Whether L₁ = 0.25 or L₂ = 0.5, using the FC-EM to obtain the driving behavior score, due to the environmental complexity in the model, the scoring curve fluctuates greatly at the beginning of the simulation. With the increase of the simulation time, the evaluation can be performed within a few minutes without sudden traffic conditions. A stable driving behavior score can be obtained, thereby obtaining a stable type of free driving behavior.

Experiment 2: Under different environmental complexity, the same driver mentioned in Experiment 1 performs 20 simulations for the three control strategies on the same simulation scenario. The reason for choosing the same driver is keeping other influencing factors unchanged except his own condition. The final result is shown in Fig. 5.

OPEN IN VIEWER

Fig. 5

Comparison of the same driver’s multiple driving behavior scores.

Variance (VA) is used to measure the discreteness of driving behavior evaluation results, as shown in Equation (15). Besides, Standard Deviation (SD) [42] is used as an analysis index for driving behavior evaluation, as shown in Equation (16). VA = 1 / N ∑ i = 1 N ( x i - u ¯ ) 2(15) SD = 1 / N ∑ i = 1 N ( x i - u ¯ ) 2(16)

u ¯ represents the average value of the data. The calculated results are shown in Fig. 6 (a) and (b) respectively, which is used to measure the dispersion degree of the driving score value itself. The smaller the SD and VA, the better the stability.

OPEN IN VIEWER

Fig. 6

Analysis of driving behavior scores.

Available from Figs. 5 6:

Under L₁ = 0.25 or L₂ = 0.5, the driving behavior scores using FC-EM are lower than the other methods’ scores, and the FC-EM driving behavior score curve is smaller than other methods, and the analysis index SD and VA are also small, which proves that FC-EM has good stability.

Based on the Experiment 1 and Experiment 2 comprehensively, the evaluation of driving behavior based on FC-EM can more specifically evaluate the driver’s personalized driving.

Experiment 3: Select 10 drivers (5 males and 5 females) consisting of 5 medium experienced drivers and 5 experienced drivers, and each driver alternately simulates 20 complete driving processes in the simulated scene (selecting L₁ = 0.25). After using FC-EM, the final 200 groups of driving behavior scores and the respective driving type m are obtained, where number Z is from 1 to 200 and the range of input IZ is [0,100]. 120 groups of the sample data (1–120) are shown in Table 5, of which each parameter has been explained in section 3, and the rest 80 groups (121–200) are used as test set data to predict the free driving behavior.

There are many types of kernel functions, such as Linear kernel, Polynomial kernel, Sigmoid kernel and RBF kernel. Because the RBF kernel can map the sample to a higher dimensional space, it can handle the example when the relationship between class labels and features is non-linear. In addition, compared with Polynomial Kernel, RBF kernel has the advantage of fewer parameters, so RBF kernel has lower complexity of model selection. Also, it is important to note that the sigmoid kernel is incorrect for some parameters, such as no inner product of two vectors. Therefore, in the FC-SVM method, the classification experiments are carried out by selecting RBF kernel function as the optimal kernel function. The training and prediction of the model are carried out by using the SVM toolbox of Matlab.

After using the FC-SVM method to predict the type of free driving behavior, the following evaluation indicators can be used for analysis [43, 44]:

Accuracy rate of class m driving behavior (P_m): P m = l m M m(17)

M_m is the number of the m-th class output by the classification system, and l_m is the correct classification number in M_m.

Recall rate of class m driving behavior (R_m): R m = l m N m(18)

N_m is the number of all the test data belonging to the m-th class, and l_m is the number with the correct result of the m-class output through the classification system.

Comprehensive classification rate of class m driving behavior (F1 _m): F 1 m = 2 P m R m P m + R m(19)

P_m is the accuracy of the m-th class, and R_m is the recall rate of the m-th class.

Macro average precision (MacropP) M ac roP = 1 w ∑ t = 1 w P t(20)

P_t is the accuracy of the t-th class and w is the total number of all categories. After predicting the free driving behavior type by Decision Tree (ID3), Random Forest and SVM, the Equation (17)–(20) are used to analyze, and the evaluation results are shown in Table 6.

Among them, MacropP is up to 89.2%, and the comprehensive classification rate F1 _m of each category is not less than 88.3% for using SVM. Obviously, compared with other methods [45, 46], prediction using SVM has highest MacroP, which verifies the accuracy of FC-SVM classification prediction based on SVM. Besides, when m = 4 (that is aggressive driving behavior), its P_m, R_m and F1 _m are all highest. It can be seen that the type of aggressive driving is more distinct from other types.

Experiment 4: In order to further verify the environmental adaptability of the prediction method, 20 drivers consisting of 10 medium experienced drivers and 10 experienced drivers were selected (10 males and 10 females), each of which simulates 15 complete free driving processes on the L₁ = 0.25 and L₂ = 0.5 simulation scenes, respectively, as Group1. Among them, the ratio of test set to verification set is 3:2. After predicting the free driving behavior type by FC-SVM method, different types of P_m, R_m and Fl_m are calculated respectively. One week apart, the previous 20 drivers performed the same experiment and the result was recorded as Group2. Similarly, Group3 to Group10 is generated accordingly, and the statistical results of the three types of evaluation indicators on prediction are shown in Fig. 7. For example, every data point in Fig. 7(a) represents P_m value corresponding to m value under the current experiment ID, where m represents free driving behavior type and P_m is accuracy rate of class m.

OPEN IN VIEWER

Fig. 7

Statistical results of different evaluation indexes.

In Fig. 7, the free driving behaviors of the 20 drivers are concentrated in m = 3, m = 4, and m = 5, and the results of the evaluation of free driving behavior are relatively stable. In the same Group ID experiment, when the environment is more complicated, the larger the corresponding P_m, R_m and F_lm, the more accurate the FC-SVM classification prediction, and the stronger the environmental adaptability of the prediction method. When the driver’s driving type is certain, the fluctuations of different evaluation indexes are not large compared with different groups. Especially when m = 4 (that is aggressive driving behavior), the fluctuations of P_m, R_m and F_lm are smaller and more stable.

Experiment 5: The urban expressway simulation scenario is constructed as Fig. 8(a). There are two types of vehicles. One is manual vehicle (MV), and the other is connected automatic vehicle (CV). Among these vehicles, the MV is controlled by driving simulator considered as free driving behavior, the other various CVs are added on the way. Five people representing different free behavior types are selected to manipulate simulator in planned path. Each person completed a driving simulation along a planned route in Fig. 8(a) and Table 7. Specific simulation scenario is described as Fig. 8(b). The vehicle exchanges information with outside world through V2X which is key technologies for intelligent transportation systems.

OPEN IN VIEWER

Fig. 8

Method applied in an experiment scenario.

Accordingly, one kind of the method’s application examples is depicted in Fig. 8(c). When current MV free driving behavior type result is cower(m = 1) after applying FC-SVM method, nearby cars obtaining this behavior information will change current driving pattern. For example, CV₂ following MV will choose to overtake it on the left. Meanwhile, the back right CV₁ will speed up on the right. Relative minimum time headway ratio and relative to the time taken are used to separately evaluate the application’s safety and efficiency. Time headway (TH) represents the time difference between the front ends of two vehicles passing through the same location. Relative minimum time headway ratio means the relative rate of the minimal TH after using this method in strongly following state. These results are shown in Table 7. Relative minimum time headway ratio is used to judge road safety, and relative to the total time is used to evaluate road efficiency. It is obvious to see that using this method makes minimum time headway increase and makes total driving time decrease. Whatever type the current driver is, the road safety and efficiency are improved. For example, comparing m = 1 with m = 5, the planned path and distance are the same, but relative minimum time headway ratio of m = 5 is larger and decreased time is smaller. The reason for this is that after applying FC-SVM surrounding vehicles stay away from impulsive driving behavior(m = 5) and this kind of impulsive driver can pass fast. Besides, when m = 4 (that is aggressive free driving behavior), the application effect of the method is the most obvious, compared with other free driving behavior types, which is consistent with the discovery mentioned above. The mixed traffic flow composed of aggressive driver has a higher traffic efficiency in basic sections.