Simulation study of freeway work zone scenes for autonomous driving using Simulink and PreScan

Abstract

To solve the problem of high traffic accident rates in freeway work zones, an in-depth analysis of freeway work zone scenes under an autonomous driving environment was conducted, and traffic conflicts in work zones were analyzed, as were warning areas and upstream transition areas, which are the key road sections where the most potential conflicts occur. Using the National Vehicle Accident In-depth Investigation System (NAIS) database, representative accident cases were selected and studied for various work zones, and specific scenes of the work zone were summarized accordingly. A joint simulation platform was constructed using PreScan and Simulink software, and the behaviors of the main vehicle with lane changes and without lane changes were simulated. The simulation results reveal the main factors influencing of the potential conflict between the warning area and upstream transition area under the condition of no lane change behavior, which is comprehensively analyzed via correlation analysis and the gray correlation analysis method. Specific requirements for the length of the zone and the length of the upstream transition zone are proposed accordingly. In the case of lane change behavior, the analysis identified the key influencing factors for potential conflicts when the target vehicle changes lanes to the front of the main vehicle and when the main vehicle changes lanes to the front of the target vehicle. Based on this foundation, appropriate recommendations are proposed for the speed limit of borrowing from the opposite lane work zone.

Introduction

A freeway work zone is a section of freeway where traffic control is carried out due to the influence of road construction, maintenance, and other methods on traffic operation¹. With the increasing penetration of autonomous driving vehicles on freeways, accidents occasionally occur in freeway work zones. According to the National Vehicle Accident In-depth Survey System (NAIS), due to the complexity of the driving environment in the work area, there is a significant increase in the number of accidents related to the work area, which is 17.3% higher than the accident rate of the normal roadway among injury accidents, and 23.8% higher among non-injury accidents than the accident rate of the normal roadway among non-injury accidents. In cases involving automated vehicles, by searching the keyword "autonomous driving work zone accident" online, multiple accidents involving autonomous driving vehicles in the work zone can be identified. For example, on July 16, 2021, in the direction of Nanjing on the G25 Changshen freeway, a vehicle in assisted driving mode failed to recognize reflective cones behind the working area, and it directly ran into the working area at a speed of 80 km/h and collided with a construction vehicle. The accidents present the complexity and variability of work zone environments, insufficient maturity in autonomous driving technology, impediments in recognition and perception, challenges in planning and decision-making, difficulties in interaction and emergency handling, data and communication security, and attributions of responsibility issues, which are all potential risks in work zones under autonomous driving. This highlights the shortcomings of current technology in handling dynamic environments and complex scenes.

At present, the research of domestic and foreign scholars on freeway work zones has focused on traffic organization, traffic characteristics, safety management, and risk analysis of traditional vehicles, mainly through accident prevention and risk assessment of work zones, to carry out research and propose many methods and models. For example, La Torre et al.² used the Bayesian method to analyze a large amount of accident information in a freeway work zone, and the results revealed that traffic organization planning and facility arrangement in the work zone is critical to safety. Ali et al.³ developed a probit model to study the factors affecting accident severity in freeway work zones and reported that the probability of serious accidents in work zones at dawn and dusk is greater. Heiden et al.⁴ used a random method to assess the impact of freeway work zones on road traffic flow and congestion and estimated traffic flow in work zones to develop a traffic capacity prediction model for short-term and long-term work zones. Ghasemzadeh and Ahmed⁵ used crash data and two modeling approaches, including complementary parametric probit regression and nonparametric classification trees, to identify factors related to the severity of weather-related crashes in work zones. Sze and Song⁶ examined the factors contributing to the seriousness of work zone-related crashes based on crash data from New Zealand. In addition, some studies have started to introduce machine learning and simulation techniques in an attempt to break through the limitations of traditional models. For example, Junhua Wang et al.⁷ introduced a convolutional neural network and a binary logistic regression model to investigate real-time collision prediction in freeway work zones via a machine learning approach. H Ge and Y Yang⁸ proposed a method to determine the length of freeway caution zones via the VISSIM simulation model and an alternative safety assessment model (SSAM). These studies provide new technical tools for risk prediction and traffic organization optimization in work zones. Zhang et al.⁹ used a driving simulator to develop and evaluate an in-vehicle freeway back-of-queue alerting system. Their results demonstrated that such a system significantly reduces driver reaction time and improves safety in scenarios where vehicles approach the tail end of congested traffic. These studies provide new technical tools for risk prediction and traffic organization optimization in work zones, particularly by incorporating advanced simulation techniques and real-time driver response systems.

Despite the important progress made by existing studies, there are still significant limitations. First, most studies focus on single-dimensional analyzes, such as accident severity or traffic flow, and lack a comprehensive exploration of multidimensional factors (eg.time, weather, area characteristics, driving behavior). Second, traditional statistical models have limitations in dealing with high-dimensional nonlinear data and dynamically changing characteristics, while machine learning and simulation technologies, although gradually applied, have yet to be verified for their applicability and generalization ability in real-world scenarios. In addition, current research is mostly based on summarizing the phenomena and descriptive analysis and lacks in-depth comparisons of different modeling approaches as well as critical analyzes of their applicability and limitations.

A common form of freeway is a two-way four-lane road, which usually has a large amount of traffic flow. In many regions, they are the dominant types of freeways, making the study of these road types essential for broader applicability and representation. Through the analysis of such roads, a variety of traffic conditions and conflicts can be captured more effectively, leading to a better understanding and improvement of traffic conditions and safety on these roads.

Based on the above background and review, the objective of this paper is to comprehensively study and analyze traffic conflicts in the Freeway Work Zone by combining “typical accident scenes” and “standard regulatory scenes”. Most of the existing studies focus on one type of scene or a single factor, but this paper tries to combine the real situation of accidents with the regulatory requirements and conducts an in-depth scene analysis, which provides theoretical support for the adaptability of autonomous Driving systems in complex environments.

Characterization of the work zone

Composition of the work zone

The work zone mainly consists of six parts: the warning area, upstream transition area, buffer area, working area, downstream transition area, and termination area ¹⁰. The typical freeway four-lane closure of an outside lane work zone is taken as an example, as shown in Fig. 1.

Fig. 1

Composition of the freeway work zone.

Traffic organization in the work zone

In accordance with the Chinese national standard GB 5768.4–2017 “Road Traffic Signs and Markings Part 4: Work Zone”, four main types of work zones are considered in this study, as shown in Table 1.

Table 1 Classification of freeway work zones.

Traffic characteristics of the work zone

Operational characteristics of the vehicles in the work zone

In the work zone, vehicles experience three main states: the free driving state, the following driving state, and the lane change state. In the free-driving state, vehicles are less disturbed and can drive freely according to the driving task. Their speed and trajectory changes are affected mainly by the traffic organization of the work zone. In the following-driving state, vehicles are affected by the surrounding vehicles, and the speed and trajectory are also affected by other vehicles, particularly during high traffic flows, which need to pay attention to deceleration to avoid traffic conflicts. In the lane change state, owing to the construction of lane reduction, vehicles need to slow down to change lanes, particularly during high traffic flows, which are vulnerable to the influence of the surrounding vehicles; thus, it is necessary to pay attention to the safety and timely completion of lane changes.

Analysis of traffic conflicts in work zones

Traffic conflict in freeway work zones has always been a research focus in the field of freeway traffic safety, and many related studies have focused on traffic conflict by analyzing vehicle trajectories before accidents. The vehicle trajectories in freeway work zones can be divided into two categories: straight along the centerline of the lane and change lanes. The conflicts in freeway work zones can be divided into straight-through conflicts and lane-changing conflicts¹¹. Through an investigation of the number of vehicles in different lanes, Sun Jiahao reported that 92.5% of vehicle lane change behaviors in a freeway work zone occurred in the second half of the warning area to the start of the upstream transition area, and another 7.5% of lane change behaviors occurred after the start of the upstream transition area¹². The traffic conflicts in the work zone mainly occur near the starting point of the warning area and the second half of the warning area to the starting point of the upstream transition area through the summary of relevant research and near the starting point of the warning area of the freeway operation section as the main area of tailgating traffic conflicts and near the starting point of the upstream transition area as the main area of lane change conflicts, so it is necessary to carry out corresponding research on the warning area and upstream transition area. Therefore, this paper analyzes only warning areas and upstream transition areas in the study of freeway work zone scenes for autonomous driving.

Adjacent headway time interval

Based on the research needs of this paper, an analysis of headway in adjacent lanes of same-direction traffic, an analysis of the headway distance between vehicles traveling in adjacent lanes in the same direction is conducted, data collection and analysis of the actual traffic conditions of the freeway are conducted, the operation data of 3309 vehicles in a section of the Chengdu second bypass freeway are obtained via UAV aerial video, and data analysis is performed. According to the principle of statistics, the excluded anomalies accounted for less than 5% of the data, and 3252 valid data points were finally obtained. It can be concluded that the distribution of headways between adjacent lanes is more concentrated, in which the distributions of the largest proportions of the three intervals are 1.0–1.5 s, 1.5–2.0 s, and 2.0–2.5 s. The median value for each interval is selected as the experimental reference data, namely, 1.25 s, 1.75 s, and 2.25 s as the adjacent headway time interval¹³.

Scene element mining and construction

Data sources

The National Vehicle Accident In-Depth Investigation System was established in August 2011 by the Defective Products Management Center of the State Administration of Market Supervision and Administration of the People’s Republic of China (SAMSA) in conjunction with several universities, vehicle accident research institutes, and traffic forensic centers in the United Nations. Its main purpose is to understand the causes, characteristics, and effects of vehicle accidents in detail and to develop more effective transportation safety policies, regulations, and measures to reduce the occurrence and severity of traffic accidents. Based on the case selection criteria and the classification of work zones, one representative typical accident case for each type of work zone was selected for analysis. The case selection is based on the following criteria: first, covering common accident types in the work zone, such as rear-end collisions, side impacts, or collisions with safety facilities, to ensure that a wide range of accident patterns are represented; second, covering diverse environmental conditions, including short-term, long-term, or nighttime work zones, as well as varying weather, traffic flow, and construction layouts; third, giving preference to cases that have complete data and detailed information, such as recording detailed accident time, weather road layout, and traffic flow; fourth, significant consequences that reflect the high-risk characteristics of the operating area (e.g., serious injuries or large-scale congestion); and fifth, ensuring that the cases match the study scenarios, such as four-lane freeway operating areas, to enhance the applicability of the analysis results.

Scene element mining

The process of determining scene elements in this paper is as follows: (1) scene analysis of accident cases in the NASI database through four links: analysis of accident sections, analysis of traffic organization in accident work zones, analysis of accident processes, and extraction of scene elements, to excavate key information of the scene in the freeway work zones; (2) reference to the characteristics of the work zones summarized in the existing literature to ensure that the scene elements have a theoretical basis; (3) consult freeway traffic experts and field staff, verify the reasonableness of the selected variables through questionnaires and interviews, and optimize the elements based on the feedback; (4) next, screen the elements that are universally representative of the work area by comparing the contrast of different accident case characteristics. Finally, the scene elements of the four-lane freeway work zone are sorted out by combining the scene theory, and the corresponding scene elements are added on this basis according to the analysis of the characteristics and requirements of autonomous driving, to summarize the scene information of four-lane freeway work zone for autonomous driving. The scene information of a four-lane freeway work zone for autonomous driving is summarized. As shown in Figs. 2, 3, 4, 5.

Fig. 2

Shoulder closure accident scene information.

Fig. 3

Closure of inside-lane accident scene information.

Fig. 4

Closure of outside lane accident scene information.

Fig. 5

Borrow opposite lane accident scene information. A brief explanation of the elements of the scenarios in Figs. 2, 3, 4. Self-vehicle: Location, direction of travel, and whether or not you were speeding. Collision object: Collision object, object, position, state. Roads: Basic roadway information such as speed, number of lanes, lane width, etc. Work areas: work area speed limits, types, traffic facilities. Accident weather: Weather conditions at the time of the accident. Accident time: Time at the time of the accident.

Scene construction

Freeway work zone accident cases are analyzed to derive key information about the work zone scene, which is then organized to obtain the functional scene of the work zone. The scene element depiction parameters are analyzed, and the logical scene of the freeway work zone is identified. Through the actual data and the existing relevant standards to determine the scene element parameters, get the specific scene of the work zone, and scene parameter values and determine the basis for Table 2.

Table 2 Specific scene for the work zone.

The following is an explanation of key factors such as road radius, length of warning area, and Length of upstream transition area:

Description of road radius: Referring to relevant specifications, the design of the minimum radius of a round curve for the freeway should follow Table 3. “General value” is the value adopted under normal conditions; “Extreme value” is the value that can be adopted when the condition is restricted; “Imax” is the maximum value of overheight adopted. Imax” is the maximum value of over-height adopted. When setting the round curve, it should be compatible with the terrain, and it is appropriate to adopt the radius of the round curve corresponding to the over-height of 2–4%, and the values of the minimum radius of the round curve include the general value of 810m and the extreme value of 1000m, respectively.

Table 3 Freeway design specification circular curve.

In this paper, we study the traffic organization of freeway operation zones for automated driving. The traffic organization of the freeway operation area for automated driving mainly considers the length of the warning zone and transition zone. The length of traditional warning zones is mainly considered from the driver reaction time, the inconsistency of speed limit compliance rate due to different driver personalities, and the deceleration of vehicles to the desired speed.The three parts are considered comprehensively, but the self-driving car can not consider its reaction time and obedience rate, when the vehicle receives the sensor signals, the vehicle immediately carries out the corresponding deceleration behavior or lane-changing behavior. Therefore, in this paper, we try to take the value downward to explore the minimum requirements for self-driving cars.Therefore, in this paper, we try to take the values downward to explore the minimum requirements of self-driving cars and preset the length of the warning zone and transition zone as follows in Table 4.

Table 4 Preset length of warning area and upstream transition area.

Simulation model construction

Simulation software

The organized scene information is reorganized into scenes, and the key elements of the work zone are studied via a simulation test. This paper utilizes joint simulations via PreScan and Simulink. PreScan is a simulation platform for developing ADASs and intelligent vehicle systems on the basis of physical models. It supports the development of multiple application functions, including camera, radar, laser radar, GPS, and intervehicle communication. PreScan is based on the MATLAB simulation platform and supports multiple usage modes, such as model-in-the-loop (MIL), real-time software-in-the-loop (SIL), and hardware-in-the-loop (HIL) modes. Simulink is one of the important components in MATLAB and provides an integrated environment for dynamic system modeling, simulation, and comprehensive analysis. Simulink can build a complex system through simple and intuitive mouse operation without writing many programs. There is a close relationship between Simulink and MATLAB, and many analysis and design tools can be used.

Model building

Road modeling

The road type is four lanes, with a lane width of 3.75 m, an emergency lane width of 3 m, a center separation area width of 3 m, and guardrails on both sides of the road as well as in the median, with scene profiles shown in Figs. 6, 7, 8, 9.

Fig. 6

Simulation environment of the shoulder closure work zone.

Fig. 7

Simulation environment of the CIL work zone.

Fig. 8

Simulation environment of the COL work zone.

Fig. 9

Simulation environment for borrowing in the opposite lane work zone.

Vehicle modeling

The standard Audi A8 model that uses PreScan software was chosen as the model for the main and target vehicles and employs 2D dynamic models and driver models. 2D vehicle dynamics models are widely used in transportation research, and their simulation of longitudinal and transverse vehicle motion can accurately capture key behaviors such as acceleration, deceleration, and lane change, which is a core tool for analyzing the safety of the work zone. Mingze Xu et al.¹⁴ established a vehicle two-degree-of-freedom dynamics model combined with a lateral LQR control algorithm and a longitudinal dual PID control algorithm for the study of intelligent vehicle trajectory tracking control. Although the study mainly focuses on trajectory tracking of intelligent vehicles, the validated 2D model is also applicable to areas such as traffic conflict analysis and safety assessment. In addition, since the operation area is usually a flat roadway with limited influence of vertical dynamics on safety analysis, the simplified 2D model is sufficient to meet the current research objectives, while significantly reducing modeling and simulation complexity and ensuring that the research focuses on the analysis of critical traffic behaviors in the work zone.

The model parameters of the main vehicle are set as shown in Table 5.

Table 5 Main vehicle model parameters,

The model parameters of the target vehicle are set as shown in Table 6.

Table 6 Target vehicle model parameters.

On the basis of the determined transverse acceleration of 3.6 m/s², since the system comes with the model only sets the maximum steering angle of the vehicle’s steering wheel and the ratio of the steering wheel angle to the front wheel angle, the maximum steering angle of the steering wheel is 500°, the ratio of the steering wheel angle to the front wheel angle is 20, the formula can be used to calculate the size of the steering wheel turning angle of the target vehicle when the vehicle changes lanes and is input into the steering control system.

$$a=v2 sin(\theta /k)/l$$

(1)

where a represents the transverse acceleration of the target vehicle; v represents the current speed of the target vehicle; θ represents the steering wheel angle of the target vehicle; k represents the ratio of the steering wheel angle to the front wheel angle, which is 20; l represents the wheelbase of the vehicle; and the wheelbase of the vehicle model is 2.94 m.

Sensor and AEB system configuration

According to the test requirements for the main vehicle to add TIS sensors and V2I sensors, the traffic environment roadside equipment should add V2I sensors, and the sensor parameters should be debugged. The AEB system uses two TIS sensors: long-range radar and short-range radar. The detection length of long-range radar is 150 m, and the detection angle is 9°; the detection length of short-range radar is 35 m, and the detection angle is 50°, as shown in Fig. 10.

Fig. 10

TIS sensor configuration.

The V2I sensor communication model is divided into an effective domain, a statistical model, and a model that is based on physical principles. In this work, the effective domain model is selected as the V2I communication model within the signal coverage area, without considering the phenomena of signal loss, signal delay, and manually setting the signal coverage, in which the V2I sensors on the main vehicle only have signal receiving functionality, whereas the V2I sensors on the roadside equipment only have signal transmitting functionality, as shown in Fig. 11.

Fig. 11

V2I sensor configuration.

This paper adopts the TTC algorithm as the AEB control system algorithm. The algorithm is configured such that a collision warning is issued when the TTC equals 2.6 s; partial braking is applied when the TTC equals 1.6 s; and full braking is applied when the TTC equals 0.6 s.

Simulation simulation

The sensor detection signals are input into the corresponding control algorithm after being processed in the PreScan scene, and the calculation results are output to the dynamics control module, allowing Simulink to control the vehicle’s deceleration and steering based on preset commands; when the TIS sensor detects a target signal, it is input into the AEB control algorithm. Simulink can also add the signal output module, which is very convenient for reading and using the simulation results. Simulink can also add a signal output module, configure the simulation strategy set for the simulation running time, obtain the test results, and analyze them through simulation.

Experimental design

All the elements are parameterized according to the logical scenes, and specific scenes are generated through different combinations of parameters. Then, batch simulation is carried out via a simulation platform. There are 21 elements in 5 categories, 13 of which have multiple parameters, and the method of permutation and combination is needed to generate different specific scenes. According to the results of the conflict analysis of the work zone in the previous section, the driving trajectory of the main vehicle in the work zone is chosen as the classification standard of the experimental design, and the relevant indicators are selected as the objects of analysis.

Without the lane change behavior of the main vehicle

When the main vehicle is in the unclosed lane, there is no lane change behavior of the vehicle at this time. The type of traffic organization in a work zone can be divided into three categories, as shown in Table 7.

Table 7 Type of work zone without lane-changing behavior of the main vehicle.

When the main vehicle is located in the shoulder closure work zone, it needs to actively decelerate upon receiving the speed limit signal at the beginning of the warning zone until it reaches the speed limit standard and completes the deceleration behavior before the warning area ends. When the length of the warning area is not long enough, the speed of the main vehicle before it reaches the end of the warning area may conflict with the speed limit requirement of the work zone. Therefore, the length of the warning zone directly affects whether the main vehicle conflicts with the speed limit of the work zone. Research has been conducted on the initial velocities of different vehicles and the speed limit requirements.

For the main vehicle in an unclosed lane in a closure of the inside lane or closure of the outside lane work zone, only the speed limit requirements need to be met, and the length of the warning area is the same as that of the shoulder closure work zone. In addition, if the target vehicle is located in front of the main vehicle in the adjacent lane when the target vehicle is located at the beginning of the upstream transition area of the traditional work zone, it must perform lane change behavior, which may result in a lane change conflict with the main vehicle. Under the assumption that the main vehicle and the target vehicle have completed the speed limit requirements, the longitudinal distance between the main vehicle and the target vehicle in the road direction at the instant of lane change is combined with the speed limit of the work zone to calculate the headway spacing reference value. The longitudinal distance between the main vehicle and the target vehicle in different speed limit work zones is shown in Table 8.

Table 8 Longitudinal distance between the main vehicle and the target vehicle.

The main vehicle has lane change behavior

When the main vehicle is in a closed lane, the speed limit needs to be completed before the warning area ends, and the lane change needs to be completed before the upstream transition area ends.

Assuming that the target vehicle is behind the adjacent lane of the main vehicle, the main vehicle does not find a safe lane change time in the warning area, and when the main vehicle drives to the beginning of the upstream transition area to force a lane change, the insufficient length of the upstream transition area may lead to a conflict between the main vehicle and upstream transition area. At the same time, the main vehicle may experience a lane change conflict with the target vehicle behind the adjacent lane. On this basis, this paper studies the headway and length of the upstream transition area for safe lane changes in the main vehicle. Assuming that the target vehicle maintains a constant speed during the main vehicle lane change process and that the target vehicle speed meets the speed limit requirements in the work zone, when the main vehicle completes lane change behavior, the spacing between the two vehicles changes with different speed limit requirements as well as the initial longitudinal distance. Here, we introduce the minimum safe following distance (MFD) on the freeway ¹⁸:

$$MFD \, = \, 0.0029*3.6^{2} *v^{2} + \, 0.3049*3.6*v$$

(2)

MFD is the minimum safe freeway following distance; V refers to the target vehicle speed.

According to the different speed limits in the work zone, the MFD is calculated via formula (2), as shown in Table 9.

Table 9 MFD.

According to the traffic organization of the work zone, the work zones where there is a need for lane changes when the main vehicle is driving in the work zone are divided into three categories, as shown in Table 10.

Table 10 Type of work zone with lane-changing behavior of the main vehicle.

The spacing between the target vehicle and the main vehicle in adjacent lanes of the CIL work zone and COL work zone is shown in Table 8. The traffic organization of the warning area and upstream transition area of the borrow opposite lane work zone is the same as that of the closure of the outside lane work zone. Therefore, this paper only simulates and analyzes the potential traffic conflicts at the opening of the central separation area.

Methods of analysis

Correlation analysis

Simple correlation analysis directly calculates the degree of correlation between two variables, which is suitable for the research in this paper. The Kolmogorov‒Smirnov method was used to test the normal distribution of the variables, and the Spearman correlation coefficient was chosen for the correlation analysis in this study¹⁸.

Gray correlation analysis

The gray correlation analysis method does not require a specific number of samples or sample data to meet the correlation law; it has a small computational burden and is convenient to use. There are essentially no cases where the quantitative results do not match the results of the qualitative analyzes. The fundamental idea of gray correlation analysis is to judge the closeness of the connection on the basis of the similarity of the geometric shapes of the sequence curves.

On the basis of the experimental design, warning area length, upstream transition area length, TTC, minimum safe distance, and whether there is a collision as the evaluation index to analyze the scene of the freeway work zone for autonomous driving. Independence verification of parameters such as weather, time, headway, speed limit, road radius, and type of work zone. We verified the theoretical and statistical independence of the key variables in our study (e.g., speed limit, weather, and headway). By definition, these variables come from different sources, e.g., the speed limit is determined by roadway design, while the weather is determined by natural conditions and is independent of each other. In addition, we found through chi-square independence tests and correlation analyzes that the variables did not exhibit significant associations with each other, further supporting the independence hypothesis. As the study employs correlation analysis to investigate the impact of various variables on the evaluation indicators, it is necessary to numerically encode non-numeric variables to meet the requirements of data calculation for correlation analysis, as shown in Table 11.

Table 11 Experimental variable coding table.

Nonlinear regression and parameter interaction analysis

In order to explore the potential nonlinear relationships and interaction effects between variables, we introduced nonlinear regression analysis and interaction term analysis. By constructing nonlinear regression models, we evaluated the nonlinear effects of speed, headway, and other variables on system output. Specifically, we used polynomial regression and support vector regression (SVR) to model complex relationships that linear methods could not capture.

To evaluate the interaction effects between variables, we employed a systematic ANOVA approach. Full factorial experiments were designed to observe the combined effects of different parameter combinations on system output, and the significance of these interactions (p-value) was calculated. Detailed results of the interaction effects are presented in the Results and Discussion section.

Sample size and power analysis

In this study, sample size determination was based on existing literature and experimental design. Statistical power analysis (using G*Power software) was conducted to ensure that at a significance level of α = 0.05, the statistical power (1 − β) would exceed 0.8 to meet the analysis requirements. This ensures that the study has sufficient power to detect meaningful effects and that the results are reliable and statistically valid.

Results and discussion

Warning area length analysis

The main vehicle without lane change behavior work zone scene is selected to analyze the length of the warning area, assuming that no target vehicle cuts in front of the main vehicle, the displacement of the main vehicle when the speed limit is completed is output, and the traffic organization requirements of the warning area are determined through the analysis of the main vehicle’s displacement at the speed limit. The correlation analysis method is used to analyze the displacement of the main vehicle when the speed limit is reached, and the relevant parameters are selected. The calculation results are shown in Table 12.

Table 12 Correlation analysis of the main vehicle speed limit displacement.

According to Cohen’s criterion (0.1 = small effect, 0.3 = moderate effect, and 0.5 = large effect), initial speed exhibits a great effect, suggesting that it has a significant positive effect on speed limit displacement and is a central factor in optimizing the design of the length of the warning area. This suggests that controlling the initial speed of entry into the work zone is critical for enhancing traffic safety. The moderately strong negative correlation between speed limit and speed limit displacement supports a stricter speed limit policy, but its actual effect may be moderated by other variables (e.g., initial speed), and the interaction effect needs to be further explored. The low and non-significant correlations for road radius, type of work zone, time, and weather may indicate that these factors have limited influence on the current scene or that their potential role needs to be further revealed through non-linear analyzes or interaction effects. Research should focus on the moderating role of initial speed and speed limits and optimize their application in the safe management of work zones, the degree of relationship between the initial speed, speed limit, road radius type of the work zone, and main vehicle speed limit displacement is analyzed, and the degree of relationship results are shown in Table 13.

Table 13 Relational degree of the main vehicle speed limit displacement.

Table 11 shows that initial speed has the highest correlation with main vehicle speed limit displacement, followed by speed limit, while road radius has the lowest correlation. This indicates that initial speed and speed limit are the key factors affecting the main vehicle’s speed limit displacement, which determines the dynamic behavior of the vehicle when it enters the work zone. The theoretical analysis further supports the conclusion that since the primary vehicle has no lane-changing behavior, its speed limit displacement is less affected by the road radius and type of work zone. The high correlation of initial speed suggests that speed management of vehicles before entering the work zone is crucial for traffic conflict prevention. The second-highest correlation of speed limit emphasizes the necessity of reasonable speed limit signs and control measures to ensure the safe operation of vehicles in the work zone. Based on the experimental output and analysis results, the length of warning area requirements that meet the experimental conditions of this paper are compiled, as shown in Table 14.

Table 14 Warning area length.

Upstream transition area length analysis

The scene of the work zone when the main vehicle changes lanes is chosen for analysis. When the main vehicle starts to change lanes at the beginning of the upstream transition area, the lane change displacement of the main vehicle is recorded upon completion. The traffic organization requirements of the upstream transition area are determined by analyzing the lane change displacement of the main vehicle. The correlation analysis method is used to analyze the relevant variables of the experiment and the lane change displacement of the main vehicle. The calculation results are shown in Table 15.

Table 15 Correlation analysis of the lane change displacement of the main vehicle.

According to Cohen’s criterion, the analysis results show that the speed limit shows a great positive correlation and is the core factor influencing the displacement of main vehicle lane change. The reasonable setting of speed limit policy can effectively control lane-changing behavior and reduce the risk of traffic conflict, which should be the focus of optimizing the design of the length of the upstream transition area. The effects of road radius and type of work zone were small and insignificant and may need to be further revealed by interaction analysis for potential impacts. Time and weather did not show a significant effect, suggesting that their independent effects on lane-changing behavior are limited and may be considered for redesign or evaluation of their effects in more complex scenes. The study should focus on the core role and practical significance of speed limits, while expanding the understanding of other factors through nonlinear and interaction analyzes, to provide a more comprehensive basis for the safe design of work zones, the correlations of the speed limit, road radius, and type of work zone with the lane change displacement are analyzed, and the relational degree results are shown in Table 16.

Table 16 Relational degree of the lane change displacement of the main vehicle.

Table 16 shows that speed limit has the highest correlation with main vehicle lane change displacement, followed by type of work zone, while road radius has the lowest correlation. This indicates that the speed limit is the most critical factor affecting the main vehicle lane change displacement, which directly determines the lane change behavior of the vehicle when entering the work zone. The next highest correlation of Type of work zone indicates that the design of the work zone has a more significant role in guiding vehicle lane-changing behavior, whereas the effect of road radius on the main vehicle lane-changing displacement is relatively weak, probably because the main vehicle lane-changing behavior is mainly determined by the lateral control strategy, which is less correlated with curvature changes. In practical applications, this ranking result emphasizes the importance of setting reasonable speed limits and optimizing the type of work zones to effectively guide vehicles to change lanes smoothly and reduce the risk of traffic conflicts. The length of the upstream transition area that satisfies the experimental conditions of this paper is organized according to the experimental output and analysis results as shown in Table 17.

Table 17 Length of the upstream transition area.

Analysis of lane change conflict

When the main vehicle has no lane change behavior, the minimum TTC value of the main vehicle’s AEB system is output when the target vehicle changes lanes to the front of the main vehicle; when the main vehicle has lane change behavior, the distance between the two vehicles is output when the main vehicle changes lanes to the front of the target vehicle.

TTC analysis

When the type of work zone is a CIL work zone or a COL work zone, the minimum TTC value of the main vehicle during lane change from the target vehicle lane to the main vehicle lane is output and analyzed. According to the experimental design, a total of six variables, including the speed limit, headway, road radius, type of work zone, time, and weather, are selected to analyze the correlation with the TTC, and the calculation results are shown in Table 18.

Table 18 Correlation analysis of TTC.

According to Cohen’s criterion, the analysis shows that speed limit has a great positive correlation with TTC, which is a core factor and should be the focus of safety optimization in the work zone. Headway shows a moderate effect, significantly affects TTC and is closely related to traffic safety and flow control, suggesting the importance of optimizing the combination of headway management and speed limit policy. The road radius and type of work zone effects are small and insignificant, with limited practical significance, but may indirectly influence the results through interaction. Time and weather had no significant effect on TTC, possibly due to inadequate variable definition or data coverage. The study should focus on the key roles of speed limit and headway time distance, combined with nonlinear and interaction analyzes, to further optimize the safety design strategy for the work zone. Under the results of the correlation analysis, the gray correlation method is used to analyze the minimum TTC value in the process of speed limit, headway, road radius type of work zone, and target vehicle lane change. The relational degrees are shown in Table 19.

Table 19 Relational degree of the TTC.

Table 19 shows that speed limit has the highest correlation with TTC, followed by headway, while road radius has the lowest correlation with the type of work zone. This indicates that speed limit and headway are the key factors affecting the minimum TTC. The high correlation of speed limit suggests that a higher speed limit in the work zone helps to increase the minimum TTC and thus the safety margin between vehicles. The second-highest correlation of headway indicates that maintaining a reasonable headway is an effective means to avoid triggering the main vehicle AEB system. The experimental data show that when the headway of neighboring lanes is greater than 1.25 s, the target vehicle will not trigger the AEB system when changing lanes from the neighboring lane to the front of the main vehicle, which indicates that under the experimental conditions of this paper, maintaining sufficient headway between vehicles is crucial to the safety of lane changing. In addition, the minimum TTC value increases with the increase of speed limit and headway, while it is basically independent of the change of road radius and type of work zone. This further validates the central influence of speed limit and headway time distance on the safety of lane-changing behavior. In practical applications, the findings highlight the need to optimize speed limit settings in work zones and guide vehicles to maintain safe headway. These measures can help reduce the triggering of emergency braking and improve traffic safety and operational efficiency in the work zone.

Follow-up distance analysis

The type of work zone involves the closure of the inside lane and the closure of the outside lane. When the main vehicle is located in the closed lane and needs to change lanes to the unclosed lane, the main vehicle is located in front of the target vehicle, and the minimum distance between the two vehicles during the lane change process of the main vehicle is exported. The correlation analysis method is adopted to analyze the impact of six parameters, including the speed limit, headway, road radius, type of work zone, time, and weather, on the two-vehicle spacing. The calculation results are illustrated in Table 20.

Table 20 Correlation analysis of follow-up distance analysis.

According to Cohen’s criterion, speed limit and headway have a large positive correlation on the distance between followers, which are the key factors affecting the following behavior, and are directly related to speed control and safety spacing management, respectively, and should be prioritized to optimize the speed limit policy and spacing management strategy. The correlation between road radius and type of work zone was weak and insignificant, time and weather had no significant effect, probably due to insufficient data or variable design limitations. The study should focus on the central role of speed limit and headway to provide a scientific basis for optimizing traffic safety in the work zone, the gray correlation method is used to analyze the relationship between the closure of the inside lane work zone and the closure of the outside lane work zone and between the follow-up distance of the two vehicles and the scene elements when the main vehicle exhibits lane change behavior. Only the speed limit, headway, road radius, and type of work zone are analyzed here. The results of the correlation analysis are shown in Table 21.

Table 21 Relational degree of follow-up distance.

Table 21 shows that speed limit has the highest correlation with the following vehicle distance, followed by headway, while the correlation between the type of work zone and road radius and the two-vehicle spacing is relatively low. This indicates that speed limit and headway are the key factors affecting the following vehicle distance during main vehicle lane change. The high correlation of speed limit reflects the important role of speed management in ensuring a safe distance between vehicles; the second-highest correlation of headway suggests that appropriate headway helps to alleviate the safety pressure during vehicle lane-changing. The simulation results show that when the headway between neighboring lanes is 1.25 s and 1.75 s, under different speed limits, the distance between the two vehicles during the main vehicle lane change does not reach the minimum safe following distance. Only when the headway reaches 2.25 s, the distance between the two vehicles can meet the safety requirement. This further suggests that maintaining sufficient headway is crucial for the safety of lane-changing. In practice, this result emphasizes the importance of optimizing speed limit settings and guiding vehicles to maintain reasonable headway. Especially in the work zone environment, speed limit management and driving behavior guidance should be used as key interventions to ensure safety margins when vehicles change lanes and reduce the occurrence of potential traffic conflicts.

Conflict analysis of the central separation area opening

According to the principle of experimental design, the potential conflict between the main vehicle and the central separation area opening under different speed limit conditions is analyzed, and the collision detection results of the main vehicle under different experimental conditions when the work zone is borrowed opposite the lane in the work zone are analyzed. Owing to the low volume of simulation experiments, the results can be analyzed simply and intuitively. The analysis of the raw simulation data reveals that the main vehicle collides with the end of the center separation area opening on the basis of the experimental design conditions of this paper when the speed is greater than or equal to 70 km/h, and the results are not affected by the time, weather or road radius. Therefore, the speed limit in the work zone should be less than or equal to 60 km/h when the central separation area opening in the work zone of the borrow opposite lane is 40 m, on the basis of the experimental conditions of this paper.

Sensitivity analysis

In this paper, speed limit and headway distance were identified as key factors affecting traffic conflicts, and the effects of small changes in these parameters on the results were evaluated through single- and multi-parameter sensitivity analyzes. The speed limit range was set to 40–80 km/h (in steps of 10 km/h) and the headway distance range was set to 1.25–2.25 s (in steps of 0.5 s), and the parameters were adjusted step by step and the changes of each index were recorded using PreScan and Simulink simulation platforms. The single-parameter analysis shows that the speed limit has the most significant effect on the length of the warning zone and the minimum value of the TTC, followed by the headway; while the headway has a more prominent effect on the following distance. The joint multi-parameter analysis found that the combination of higher speed limit and smaller headway spacing leads to a significant decrease in TTC minima and increases the risk of collision; while the combination of lower speed limit and larger headway spacing helps to improve the safety of each indicator. Specifically, when speed increases by 10%, crash risk increases by 15%, while roadway radius has a smaller effect with a change of only 2%. In addition, the interaction effects between the parameters were systematically evaluated through ANOVA methods. The results showed that there was a significant interaction between speed and headway distance (p < 0.05), and the effect of the change in headway distance on collision risk was more significant when the speed was higher. This suggests that the joint effects of vehicle speed and headway time distance need to be considered in order to optimize system performance in practical applications. Detailed results are shown in Table 22.The results of the nonlinear regression analysis show that the effect of vehicle speed on the collision risk presents obvious nonlinear characteristics (as shown in Fig. 12). When the vehicle speed exceeds a certain threshold, the collision risk increases significantly. In addition, the ANOVA results showed that there was a significant interaction effect between vehicle speed and headway time distance (p < 0.05). When the vehicle speed was higher, the effect of the change in headway time distance on the collision risk was more significant (as shown in Fig. 13).

Table 22 Sensitivity analysis results.

Fig. 12

Nonlinear regression curves of vehicle speed on crash risk.

Fig. 13

Plot of the interaction between vehicle speed and headway time distance.

Although the sample size of this study meets the requirements of statistical efficacy analysis, the small sample size of some variables due to data limitations may affect the generalizability of the results. Future studies will further expand the sample size to verify the robustness of the findings of this study.Future research will further extend the parameter range to include influences such as weather conditions, lighting conditions, etc. in order to evaluate the dynamic characteristics of the system output more comprehensively.

Conclusions

This study analyzes the composition of work zones, traffic organization, and traffic characteristics and proposes warning areas and upstream transition areas as the sections with the highest potential for conflicts. A simulation experiment scheme was designed as a result. Through an analysis of typical cases in the NAIS database, specific information about work zone scenes is obtained, and scenes are constructed via PreScan and Simulink software to simulate two scenes of the main vehicle with lane changes and no lane changes. By employing correlation analysis and gray correlation analysis, this study determines the relationships among the initial speed, speed limit, adjacent headway time interval, road radius, type of work zone, time and weather, and evaluation indices. The results of the study show that the analysis identifies the main factors influencing the potential conflicts between the warning area and the upstream transition area under different lane-changing behavioral conditions, and based on this, design recommendations for the length of the warning area and the length of the upstream transition area are made. However, these conclusions may be oversimplified and do not fully consider the complex interactions among various factors under lane-changing behavior conditions. Further research should explore the interactions of these influencing factors and their applicability in different roadway environments. In addition, the study did not provide an in-depth discussion of methodological and data limitations, especially sample representativeness and generalizability of the results to real-world scenarios, which need to be supplemented in subsequent studies. Also, the key influencing factors of potential conflicts when the target vehicle changes lanes to the front of the main vehicle and when the main vehicle changes lanes to the front of the target vehicle are identified under the condition of lane change behaviors, and recommendations for borrowing speed limits from the work zone in the opposite lane are presented. Although this study provides valuable insights into the optimal design of freeway work zones an autonomous driving environment, it is mainly based on simulation experiments, which may not fully reflect the complexity of real scenes. Future research should validate the simulation results through field tests or naturalistic driving studies, especially under complex conditions such as high traffic densities, mixed traffic flows, and inclement weather. In addition, extending the study to more road types and complex scenes will further enhance the generalizability of the findings.

Although this study focuses on four-lane freeway work zones, future research should extend to six-lane or eight-lane freeways to enhance the generalizability of the findings. Roads with different numbers of lanes may lead to different traffic flow and behavior patterns, especially as the number of lanes increases, where traffic volume and lane-changing behavior may become more complex, potentially affecting the applicability of the current conclusions. For six-lane or eight-lane freeways, future research should focus on factors such as the number of lanes, traffic flow density, geometric characteristics of road sections (e.g., road radius and lane width), and the complexity of lane-changing behavior. These factors should be validated through field tests and larger-scale simulations to assess their impact on work zone safety management and traffic organization. Additionally, it is necessary to explore how to adapt the design recommendations from this study (e.g., the lengths of warning and transition zones) to more complex road configurations, ensuring that work zone optimization solutions can be widely applied to different freeway environments. Through these improvements, future research can provide a more comprehensive understanding of the factors influencing work zone safety management and traffic organization, thereby offering a scientific basis for the design of work zones in various road configurations.