Networked vehicle following model and traffic flow stability analysis method

Abstract

The invention discloses a networked vehicle following model and traffic flow stability analysis method, and relates to the technical field of intelligent traffic systems, and the method comprises the steps: introducing a time-varying expected interval based on an adaptive cruise control model ACC and a collaborative adaptive cruise control model CACC, and obtaining a TV-ACC and a TV-CACC following model; based on the TV-ACC car-following model and the TV-CACC car-following model, respectively obtaining a homogeneous traffic flow stability constraint discriminant value and a heterogeneous traffic flow stability discriminant value; analyzing the stability of the mixed traffic flow according to the homogeneous traffic flow stability constraint discriminant value and the heterogeneous traffic flow stability discriminant value; by overcoming the defects of collision, reversing, large speed fluctuation amplitude and the like of an original model, the speed of a subsequent vehicle is more gentle and more practical.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent transportation systems, and in particular to a connected vehicle following model and a traffic flow stability analysis method. Background Art

[0002] With the rapid development of vehicle automation and communication technology, many vehicles have been equipped with driver assistance systems (ADAS). Manually driven vehicles can no longer meet social needs, which has made adaptive cruise control (ACC) gradually become mainstream. Through ACC technology, vehicles can automatically adjust speed and maintain a safe following distance based on data obtained by on-board sensors. In ACC vehicle following, it is crucial to maintain a stable distance between the front and rear vehicles. The intelligent driver model (IDM) just contains this parameter. By adjusting the headway time parameter in the model, the traditional vehicle following model can be transformed into an ACC vehicle following model. Therefore, IDM is widely used to describe ACC vehicle following. Later, PATH Laboratory proposed an ACC following model based on the ACC control characteristics. The model has a simple structure and clear physical meaning of parameters. It is widely used to analyze the traffic capacity of ACC traffic. The parameters of the ACC following model were calibrated using measured data, which improved the reliability of the model in analyzing the traffic capacity of ACC traffic. In view of the shortcomings of the ACC vehicle following model, some scholars proposed an ACC following model based on nonlinear dynamic headway. This improved model can effectively improve road capacity. Based on the ACC following model, some scholars have established an improved ACC model, taking into account the differences in driving behaviors of different drivers. The established model makes the acceleration and headway distance curves smoother, which can effectively improve the following efficiency and driving safety.

[0003] However, in practice, ACC vehicles cannot achieve coordinated actions with other vehicles, making their impact on traffic flow relatively limited. In order to overcome the shortcomings of ACC, the Cooperative Adaptive Cruise Control (CACC) system was proposed. CACC can combine the assisted driving system with vehicle-to-vehicle (V2V) communication technology to shorten the headway time between following vehicles, reduce the driving burden, and thus improve the stability and safety of traffic flow. Some scholars proposed a CACC following model based on the CACC control characteristics. In order to improve the traffic capacity of CACC, the parameters of the CACC following model were calibrated using measured data, which enhanced the reliability of the model analysis of CACC traffic capacity. However, the model uses a constant headway time, which makes the CACC traffic flow characteristics greatly affected by the headway time value, and it is difficult to determine the headway time value that can weigh the impact of various traffic flow characteristics. In order to make up for the defects of the CACC vehicle following model, a CACC following model based on a nonlinear dynamic headway strategy was established to improve the traffic capacity. Under normal traffic conditions, the expected headway should be an increasing function of vehicle speed. Some scholars have analyzed the changing characteristics of the expected headway under different traffic flow conditions, proposed the general function form of the expected headway in the process of vehicle following, and constructed a following queue, indicating that the improved CA CC model has advantages in following efficiency. As a special case of intelligent connected vehicles (CAVs), CACC vehicles have led many scholars to use the CACC model to simulate the following characteristics of CAVs. Studies have shown that CAVs equipped with advanced communication and automation capabilities can improve traffic capacity, increase traffic flow stability, improve traffic safety and basic map impact, and reduce energy consumption and carbon emissions.

[0004] However, many scholars have only considered two types of vehicles, HDVs and CAVs, while there are often mixed driving situations of multiple types of vehicles on actual roads. Therefore, these research results may not fully reflect the actual traffic conditions. Although some scholars have considered three types of vehicles, HDVs, AVs and CAVs, they use the same following model to describe the driving behavior of AVs and CAVs. This method fails to effectively reflect the following characteristics of actual vehicles. At the same time, although some scholars have chosen different models to describe the driving behavior of AVs and CAVs, they mainly describe the following characteristics of different vehicles based on the ACC and CACC following models proposed by the PATH laboratory, and pay less attention to the rationality of the model itself. When proposing the ACC and CACC following models, the PATH laboratory mainly analyzed the trajectories in the speed range of 22-33.3m / s, pointing out that the ACC model will have oscillation problems, and the CACC model is more stable when following the leading vehicle. However, these studies did not comprehensively explore the rationality of the trajectory in the full speed domain, resulting in certain deficiencies in the research content. From the perspective of trajectory simulation in the full speed range, by analyzing the trajectories of the ACC and CACC models proposed by the PATH laboratory under different working conditions, it was found that the ACC and CACC models had unrealistic collisions, reversing behaviors, and large speed fluctuations. Summary of the invention

[0005] Aiming at the shortcomings of ACC and CACC models in the prior art, such as unrealistic collision and reversing behaviors and large speed fluctuation, which lead to poor vehicle driving stability, the present invention provides a connected vehicle following model and a traffic flow stability analysis method, and improves ACC and CACC models by using time-varying expected spacing to obtain TV-ACC and TV-CACC models, thereby solving the problems in the prior art, such as unrealistic collision and reversing behaviors and large speed fluctuation, which lead to poor vehicle driving stability.

[0006] A connected vehicle following model and a traffic flow stability analysis method, comprising the following steps:

[0007] Obtain the vehicle speed, the speed difference between the front and rear vehicles, and the head-to-head distance in the following state;

[0008] Based on the adaptive cruise control model ACC, the time-varying expected distance is introduced, and the expected distance between vehicles in ACC is replaced to obtain the TV-ACC following model.

[0009] Based on the cooperative adaptive cruise control model CACC, the time-varying expected distance is introduced, and the expected vehicle distance in CACC is replaced to obtain the TV-CACC following model.

[0010] According to the first-order partial derivative of vehicle speed, front and rear vehicle speed difference and headway, the homogeneous traffic flow stability constraint discriminant values ​​of TV-ACC following model and TV-CACC following model are obtained respectively.

[0011] The partial differential terms of vehicle speed, front and rear vehicle speed difference, and headway are calculated respectively, and the heterogeneous traffic flow stability discrimination values ​​of TV-ACC and TV-CACC following models under different speeds, different CAV penetration rates, and maximum queues are obtained.

[0012] The stability of mixed traffic flow is analyzed based on the homogeneous traffic flow stability constraint discriminant value and heterogeneous traffic flow stability discriminant value of the TV-ACC following model and the TV-CACC following model.

[0013] Furthermore, the calculation formula of the time-varying expected spacing is:

[0014]

[0015] Among them, s0 is the minimum distance allowed between the following car and the leading car after stopping, l is the body length of the leading car, τ is the driver's reaction time, is the speed of the front and rear vehicles, a n-1 、a n is the maximum deceleration of the front and rear vehicles.

[0016] Furthermore, the adaptive cruise control model ACC introduces a time-varying expected distance, replaces the expected vehicle distance in the ACC, and obtains a TV-ACC following model, which specifically includes the following steps:

[0017] The ACC model is expressed as:

[0018]

[0019] Among them, v n (t) are the speed and acceleration of the nth vehicle at time t; Δv n (t) is the speed difference between the nth vehicle and the preceding vehicle at time t; x n-1 (t), x n (t) are the displacements of vehicles n and n-1 at time t; l is the vehicle length; s0 is the minimum safe stopping distance; k1 and k2 are the vehicle spacing error control coefficient and speed difference control coefficient respectively; T a is the expected inter-vehicle time distance of ACC vehicles;

[0020] The time-varying expected distance is introduced into the ACC model to replace the expected vehicle distance, and the TV-ACC following model is obtained, which is expressed as:

[0021]

[0022] Since the optimal model parameters vary with different following scenarios, the present invention sets k2 as follows:

[0023]

[0024] Furthermore, the collaborative adaptive cruise control model CACC introduces a time-varying expected distance, replaces the expected vehicle distance in CACC, and obtains a TV-CACC following model, which specifically includes the following steps:

[0025]

[0026] in, is the target output acceleration of vehicle n at time t; is the acceleration of the preceding vehicle n-1 at time t; k3, k4 and k5 are coefficients; T c is the expected workshop time interval of CACC;

[0027] The time-varying expected distance is introduced into the CACC model to replace the expected vehicle distance, and the TV-CACC following model is obtained, which is expressed as:

[0028]

[0029] in, is the acceleration of the front vehicle; m is the number of front vehicles that can communicate with the current CACC vehicle, which is 3; β1 and β2 are the driver's attention to the speed of the adjacent vehicle in front and the average speed of the multiple vehicles in front, respectively, where β1+β2=1; is the average speed of the vehicles ahead.

[0030] Furthermore, the homogeneous traffic flow stability condition is expressed as:

[0031]

[0032] Among them, f v 、f Δv and f Δx They represent the first-order partial derivatives of the following model with respect to vehicle speed, speed difference between front and rear vehicles, and head-to-head distance.

[0033] Furthermore, the homogeneous traffic flow stability constraint discrimination values ​​of the TV-ACC following model and the TV-CACC following model are obtained according to the first-order partial derivative of the vehicle speed, the front and rear vehicle speed difference, and the headway distance, respectively; wherein the homogeneous traffic flow stability constraint discrimination value of the TV-ACC following model is obtained by the steps of:

[0034] The f v 、fΔv and f Δx The specific formula is:

[0035]

[0036] Among them, v * is the velocity in equilibrium; Δx * is the headway distance in equilibrium;

[0037] and as well as

[0038] Then the stability constraint discriminant value of the TV-ACC car-following model is expressed as:

[0039]

[0040] The stability constraint discriminant value of the TV-CACC car-following model is expressed as:

[0041]

[0042] Furthermore, the heterogeneous traffic flow stability condition is expressed as:

[0043]

[0044] Among them, n and m are the vehicle numbers; It is the partial differential term of the following model of the nth vehicle with respect to vehicle speed, speed difference and headway between vehicles.

[0045] Furthermore, the heterogeneous traffic flow includes four following modes, and their spatial distribution probabilities are expressed as follows:

[0046]

[0047] Where p is the penetration rate of CAVs in heterogeneous traffic flow; N is the maximum fleet size of CAVs; P H , P A , P P With P C are the spatial distribution probabilities of the four following modes, and P H +P A +P P +P C =1.

[0048] Furthermore, the stability discrimination values ​​of heterogeneous traffic flows under different speeds, different CAV penetration rates and maximum queues of the TV-ACC and TV-CACC following models are:

[0049]

[0050] Simplified to:

[0051]

[0052] Furthermore, it also includes using the comfort index CI of the international ISO standard to determine the driving comfort level of the TV-ACC following model and the TV-CACC following model at different CAVs penetration rates p, and the calculation formula of the index CI is:

[0053]

[0054] Among them, a i is the i-th acceleration value counted; m is the total amount counted.

[0055] The present invention provides a connected vehicle following model and a traffic flow stability analysis method, which has the following beneficial effects:

[0056] The present invention improves the ACC and CACC models based on the time-varying expected distance to obtain TV-ACC and TV-CACC models. According to the vehicle speed of the networked vehicle, the speed difference between the front and rear vehicles, the head distance, and the head distance of other networked vehicles except the networked vehicle, the homogeneous traffic flow stability constraint discrimination value and the heterogeneous traffic flow stability discrimination value of the TV-ACC following model and the TV-CACC following model can be obtained, and then the traffic flow stability of the TV-ACC and TV-CACC following models of the networked vehicle is analyzed, so as to overcome the shortcomings of the original model such as collision, reversing and large speed fluctuation, so that the subsequent The vehicle speed is smoother and more realistic; the TV-ACC and TV-CACC models make the vehicle more sensitive to the speed changes of the vehicle in front and maintain a reasonable distance, thereby improving the driving stability of the following vehicles; the stability of the TV-ACC and TV-CACC models is also better than that of the ACC and CACC models, and their stability judgment values ​​change with speed; the traffic flow stability of the TV-ACC and TV-CACC models is better than that of the ACC and CACC models as a whole, and with the increase in the penetration rate of CAVs, the stability of the mixed traffic flow and the driving comfort show a trend of first deteriorating, then improving and finally stabilizing. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A vehicle distribution diagram in an embodiment of the present invention;

[0058] Figure 2 The driving data under different working conditions collected in the embodiment of the present invention;

[0059] Figure 3 Schematic diagram of the trajectory under ACC acceleration condition in an embodiment of the present invention;

[0060] Figure 4 Schematic diagram of the trajectory of the ACC deceleration condition in an embodiment of the present invention;

[0061] Figure 5 Schematic diagram of the trajectory of ACC in congested conditions in an embodiment of the present invention;

[0062] Figure 6 A schematic diagram of the trajectory of an ACC signalized intersection in an embodiment of the present invention;

[0063] Figure 7 Schematic diagram of the trajectory under the CACC acceleration condition in an embodiment of the present invention;

[0064] Figure 8 Schematic diagram of the trajectory under the CACC deceleration condition in an embodiment of the present invention;

[0065] Fig. 9 Schematic diagram of the trajectory of CACC under congestion conditions in an embodiment of the present invention;

[0066] Fig.10 A schematic diagram of a trajectory of a CACC signalized intersection in an embodiment of the present invention;

[0067] Fig.11 Schematic diagram of the trajectory of the TV-ACC under the acceleration condition in the embodiment of the present invention;

[0068] Fig.12 Schematic diagram of the trajectory of the TV-ACC deceleration condition in an embodiment of the present invention;

[0069] Fig.13 Schematic diagram of the trajectory of TV-ACC in congested conditions in an embodiment of the present invention;

[0070] Fig.14 A schematic diagram of the trajectory of a TV-ACC signalized intersection in an embodiment of the present invention;

[0071] Fig.15 is the comparison result between the ACC and TV-ACC models in the embodiment of the present invention;

[0072] Fig.16 Schematic diagram of the trajectory under the TV-CACC acceleration condition in an embodiment of the present invention;

[0073] Fig.17 Schematic diagram of the trajectory of the TV-CACC deceleration condition in an embodiment of the present invention;

[0074] Fig.18 Schematic diagram of the trajectory of TV-CACC under congestion conditions in an embodiment of the present invention;

[0075] Fig.19 A schematic diagram of the trajectory of a TV-CACC signalized intersection in an embodiment of the present invention;

[0076] Fig. 20 is the comparison result between the CACC and TV-CACC models in the embodiment of the present invention;

[0077] Fig.21 Schematic diagram of stability analysis of homogeneous traffic flow in an embodiment of the present invention;

[0078] Fig. 22 Schematic diagram of the stability analysis result of heterogeneous traffic flow in an embodiment of the present invention;

[0079] Fig.23 Schematic diagram of mixed traffic flow stability analysis results in an embodiment of the present invention;

[0080] Fig.24 Schematic diagram of mixed traffic flow stability in an embodiment of the present invention. DETAILED DESCRIPTION

[0081] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0082] The networked vehicles referred to in the present invention are adaptive cruise control (ACC) vehicles and collaborative adaptive cruise control (CACC) vehicles; based on the time-varying expected spacing, improved ACC and CACC models are proposed, namely TV-ACC and TV-CACC models. Numerical simulation results show that compared with the original model, the TV-ACC and TV-CACC models can overcome the shortcomings of the ACC and CACC models, such as collision, reversing and large speed fluctuation, and show better performance, making the speed of the following vehicles smoother and more realistic. The full speed difference (EFVD) model improved by predecessors, TV-ACC and TV-CACC models are used to describe the following characteristics of HDVs, intelligent vehicles (AVs) and CAVs, respectively, and the stability conditions and driving comfort under homogeneous traffic flow and heterogeneous traffic flow are analyzed. The results show that the improved model can effectively improve the stability of traffic flow, and with the increase of CAVs penetration rate, the stability and driving comfort of mixed traffic flow show a trend of first deteriorating, then improving and finally stabilizing. Compared with the existing research, the main contributions of the present invention are:

[0083] (1) The measured data is used as the driving trajectory data of the leading vehicle, and the ACC and CACC models are used to simulate the following vehicle behavior. The trajectory simulation shows that the ACC and CACC models will cause problems such as collision, reversing, and large speed fluctuations.

[0084] (2) Improve the ACC model based on the time-varying desired headway to obtain the TV-ACC model, which overcomes the deficiencies of the original model such as collisions, reverse driving, and large speed fluctuations, making the speed of the following vehicle smoother and more in line with reality.

[0085] (3) Aiming at the differences between CACC and ACC, introduce the time-varying desired headway and the speed and acceleration information of multiple leading vehicles to improve the CACC model, obtaining the TV-CACC model, which can overcome the deficiencies of the original model such as collisions, reverse driving, and large speed fluctuations, making the speed of the following vehicle stable and more in line with the actual situation.

[0086] (4) Theoretical derivations and numerical simulations show that the traffic flow stability of the TV-ACC and TV-CACC models is generally better than that of the ACC and CACC models, and with the increase in the CAVs penetration rate, the stability and ride comfort of the mixed traffic flow show a trend of first deteriorating, then improving, and finally stabilizing.

[0087] Under the condition of mixed traffic flow, it is assumed that there are only three types of vehicles in the mixed traffic flow, namely HDVs, AVs, and CAVs. According to the following order of vehicles, there are 9 different following types, namely CAV-CAV (C-C), CAV-AV (C-A), CAV-HDV (C-H), AV-CAV (A-C), AV-AV (A-A), AV-HDV (A-H), HDV-CAV (H-C), HDV-AV (H-A), and HDV-HDV (H-H). If the maximum CAVs queue size is considered, the following type CAV-CAV can be divided into two situations: the CAV in the queue follows the CAV in the following vehicle queue and the CAV that follows the CAV queue when the size of the front row reaches the maximum, that is, C-C (in the vehicle queue) and C-P (between vehicle queues), as shown in Figure 1 the innermost lane in the figure. Therefore, there are a total of 10 vehicle following types in this mixed traffic flow.

[0088] From Figure 1 it can be seen that when M CAVs form a queue, if the maximum queue size is N (N < M), a new queue will be formed from vehicle N + 1. Therefore, according to the characteristics of different following methods, the vehicles driving on the road can be divided into the following four types.

[0089] (1) Case 1: The following vehicle is an AV or a degraded CAV. The following types corresponding to this case are A-C, H-C, H-A, A-A, and C-A.

[0090] (2) Case 2: The following vehicle is an HDV. The following types corresponding to this case are A-H, C-H, and H-H.

[0091] (3) Scenario 3: When the leading convoy reaches the maximum, the CAV follows another CAV convoy, i.e., convoy following. Therefore, the following type corresponding to this situation is CP.

[0092] (4) Scenario 4: The CAV is not the leading vehicle in the same platoon, but a following vehicle in the platoon. Unlike Scenario 1, the CAV in this scenario can communicate with the CAV in front of it, and the following vehicle type corresponding to this scenario is CC.

[0093] In summary, in mixed traffic flow, considering different sorting methods between vehicles, there are four situations, and their spatial distribution probability distributions are expressed as P H , P A , P P and P C .

[0094] The present invention adopts a car-following model to describe the car-following behavior between vehicles, and selects the EFVD model, ACC model and CACC model to analyze the driving trajectories of HDVs, AVs and CAVs respectively.

[0095] Currently, there are many following models that can be applied to the analysis of driving characteristics of manually driven vehicles. Among them, the FVD model can better reflect the driving characteristics of traditional drivers who perform longitudinal driving control based on the head-to-head distance and speed difference of the preceding vehicle. Therefore, the FVD model is used to describe the following characteristics of manually driven vehicles. The predecessors comprehensively considered the head-to-head distance and speed difference, and further proposed an improved FVD model to make it more realistic. In order to more conveniently describe the model, the improved FVD model is referred to as the EFVD model. The present invention uses the EF VD model as the following model for manually driven vehicles, and its formula is as follows (1):

[0096]

[0097] In formula (1), is the derivative of vehicle speed, m / s 2 ; k and λ are the sensitivity coefficients of the model; Δx is the headway between the vehicle and the vehicle in front, m; v is the speed, m / s; L is the vehicle length, m; Δv is the speed difference between the vehicle and the vehicle in front, m / s; V(Δx) is the optimized speed function, that is:

[0098]

[0099] In formula (2), v f is the free flow velocity, m / s; α is the sensitivity coefficient; s0 is the minimum safety distance, m.

[0100] The parameter values ​​of the EFVD model are: k = 0.629s -1 ,λ=4.10s -1, α=1.26s -1 , v f =33.0m / s, s0=2.46m, L=5m.

[0101] PATH laboratory has carried out a lot of research work on the ACC vehicle traffic flow model, and the ACC vehicle following model proposed by it has been widely recognized and applied. Based on this, the present invention adopts this model to describe the ACC vehicle following behavior. The ACC model formula is as follows:

[0102]

[0103] In formula (3), v n (t) are the speed (m / s) and acceleration (m / s) of the nth vehicle at time t. 2 );Δv n (t) is the speed difference between the nth vehicle and the preceding vehicle at time t, m / s; x n-1 (t), x n 9t) are the displacements of vehicles n and n-1 at time t, m; l is the vehicle length, which is 5 m; s0 is the minimum safe stopping distance, which is 2 m; k1 and k2 are the vehicle spacing error control coefficient and speed difference control coefficient, which are k1 = 0.23 s -1 , k2=0.07s -1 ; T a is the expected inter-vehicle time distance of ACC vehicles, with a value of 1.1-2.2s. After testing, it was found that T a When the value is 1.1-2.2s, the model will show unrealistic collision and reversing behaviors and large speed fluctuations. a The value of is also 1.5s.

[0104] Like the ACC model, the collaborative adaptive cruise control (CACC) model proposed by the PATH laboratory has a simple structure and clear physical meaning of parameters, and is widely used to analyze the traffic capacity of CAVs. Based on this, the present invention adopts the CACC model proposed by the PATH laboratory to analyze the characteristics of CAVs in mixed traffic flow. The CACC model formula is as follows (4):

[0105]

[0106] In formula (4), is the target output acceleration of vehicle n at time t, m / s 2 ; is the acceleration of the front vehicle n-1 at time t, m / s 2; k3, k4 and k5 are coefficients, and their values ​​are k3=1s -1 , k4=0.2s -1 , k5=3s -1 ; T c is the CACC expected headway time, with a value of 0.6-1.1s. After testing, it was found that when the value is 0.6-1.1s, the model will have unrealistic collision and reverse behaviors. c Take it as 0.6s, and the other parameters are the same as above.

[0107] In order to study the rationality of the trajectory of the ACC and CACC models, real vehicle data is collected as the lead vehicle (leading vehicle) data to simulate the following trajectory of the ACC and CACC models. This method aims to verify the rationality of the model. It should be emphasized that the lead vehicle acts as the leading vehicle in the fleet, and the subsequent vehicles will follow the trajectory of the lead vehicle to ensure the authenticity and effectiveness of the trajectory simulation. In order to collect real following data, the present invention uses a real vehicle collection method to collect the driving trajectory data of the lead vehicle. The present invention mainly collects driving data under various road environments such as branch roads, secondary trunk roads, main roads, expressways, mountain roads, highways and intersections. These data cover situations under different driving conditions. In order to better analyze the driving conditions of the vehicle, the trajectories under the four most typical conditions of acceleration, deceleration, traffic jams and signal intersections are selected for analysis, and the data sets are as follows. Figure 2 (a)-(d) are shown in Figure 2 The measured data sets of (a)-(d) are used as the driving trajectory data of the leading vehicle.

[0108] The simulation experiment of the present invention is carried out in the Matlab software environment. A following vehicle fleet consisting of 10 ACC vehicles (or CACC vehicles) is designed in a single-lane environment to evaluate their performance when following the lead vehicle. In order to fully demonstrate the performance of the ACC and CACC models under different working conditions, the measured data collected under different working conditions are used as the driving data of the lead vehicle, and the ACC model (or CACC model) proposed by the PATH laboratory is used to describe the following behavior of the subsequent 10 vehicles. It should be noted that the lead vehicle is a manually driven vehicle, and when the following vehicle is a CACC vehicle, the following vehicle 1 will degenerate into an ACC vehicle.

[0109] The trajectory simulation results of the ACC model under different working conditions are as follows: Figure 3-6 shown.

[0110] For acceleration conditions, Figure 3 (a) It can be seen that the vehicle can follow the leading vehicle normally, but starting from the following vehicle 8, the displacement trajectory of the following vehicles fluctuates; Figure 3 (b) and Figure 3(c) It can be found that between 35-60s and 100-140s, the acceleration and deceleration of the vehicle changed too quickly, resulting in unreasonable oscillation of the vehicle speed, which in turn caused fluctuations in the displacement trajectory.

[0111] For deceleration conditions, Figure 4 (a) It can be seen that at 28 seconds, the displacement difference between the following car 10 and the following car 9 is less than 5 meters (the length of the car body is 5 meters), which leads to a collision between the vehicles. After 38 seconds, the 4th to 10th cars also collided one after another. Figure 4 (b) and Figure 4 (c) It can be found that between 18-40s and 45-60s, starting from the following car 6, the vehicle acceleration reaches 3m / s 2 , the acceleration of the following car 10 is -6m / s 2 and 6m / s 2 In addition, after 38 seconds, starting from the following car 1, the following cars have negative speeds (reversing phenomenon), especially starting from the following car 8, the speed of the vehicle is lower than -10m / s, and the acceleration and deceleration oscillation of the vehicle is more severe.

[0112] For congested conditions, Figure 5 (a) It can be seen that the vehicles follow the leading vehicle, and the displacement fluctuates. The following vehicle 6 begins to collide with other vehicles. Figure 5 (b) and Figure 5 (c) It can be seen that between 100 and 130 seconds, the speeds of following car 9 and following car 10 became negative, indicating reverse behavior. At this time, the acceleration and deceleration of the vehicles changed too much, and the acceleration of following car 10 first reached 3.5 m / s. 2 , and then quickly dropped to -3.8m / s 2 , which does not conform to the actual driving situation.

[0113] For signalized intersections, Figure 6 (a) It can be seen that the leading car stopped at the red light between 27 and 68 seconds, but the following car 2 collided with the following car 1 at 30 seconds, causing the following cars to reverse one after another. Figure 6 (b) and Figure 6 (c) It can be found that at 27s, when the first car slowed down to a stop after passing the red light, the 1st to 10th cars successively showed large negative speeds, showing obvious reversing behavior. Between 36s and 70s, the 8th to 10th cars showed large changes in acceleration and deceleration, with acceleration reaching even 4m / s 2 , which is obviously inconsistent with actual driving behavior.

[0114] In summary, during the deceleration, congestion, and signalized intersection stages, vehicles collided and reversed. During the acceleration, deceleration, congestion, and signalized intersection stages, the vehicle speed showed oscillation due to large changes in acceleration / deceleration, and this oscillation gradually intensified as the number of vehicles increased. The reason for this is that the ACC model over-relies on constant headway, so that the distance between vehicles cannot be properly adjusted according to the dynamic changes in speed, resulting in the failure of the following vehicles to effectively follow the leading vehicle.

[0115] Furthermore, the CACC model’s trajectory is analyzed under the same experimental conditions. The trajectory simulation results of the CACC model under different working conditions are shown in the figure below. Figure 7-10 shown.

[0116] For acceleration conditions, Figure 7 (a) It can be seen that the following vehicle can effectively follow the leading vehicle to accelerate. Figure 7 (b) and Figure 7 (c) It can be seen that from 0s, when the leading vehicle gradually accelerates, the 7th to 10th vehicles show rapid oscillation behavior, accelerating rapidly from 0 to 4m / s, and then quickly decelerating to 1m / s, which is inconsistent with the gradual acceleration of the leading vehicle. At this time, the acceleration and deceleration of the 7th to 10th vehicles change too quickly. Between 85-120s, starting from the following vehicle 6, the acceleration and deceleration of the vehicles change rapidly, causing the speed to fluctuate.

[0117] For deceleration conditions, Figure 8 (a) It can be seen that the vehicles can follow the lead vehicle well and decelerate. However, the following vehicle 1 collided with the lead vehicle at 58s, causing it to reverse at 61s. The 2nd to 10th vehicles also showed the same reverse behavior. Figure 8 (b) and Figure 8 (c) It can be seen that the leading vehicle decelerated to zero at 61s, but starting from the following vehicle 1, the speeds of the following vehicles gradually became negative, and the acceleration and deceleration of the vehicles oscillated.

[0118] For congested conditions, Fig. 9 (a) and Fig. 9 (c) shows that the following vehicles can relatively stably follow the leading vehicle in the congested road section with speed fluctuations, without any unrealistic reversing or collision behavior or large speed fluctuations.

[0119] For signalized intersections, Fig.10 (a) It can be seen that the following car can follow the leading car normally at the beginning. However, at 22 seconds, the displacement of the following car 6 is smaller than that at 20 seconds, and it appears to be reversing. The 7th to 10th cars also have the same reversing phenomenon. Fig.10 (b) and Fig.10 (c) It can be found that between 47-67s and 94-114s, the speed of the first car slowed down to 0, while the speeds of the 6th to 10th cars became negative and their accelerations also oscillated. The oscillation of the 10th car was the most obvious, with its acceleration increasing from -2.5m / s to -1.5m / s. 2 Rapidly changes to 3.5m / s 2 .

[0120] In summary, the speed of the vehicle showed negative values ​​under deceleration and signalized intersection conditions; the speed of the vehicle oscillated when accelerating, decelerating, in congestion, and passing through signalized intersections. This oscillation phenomenon gradually intensified with the increase in the number of vehicles. The reason is that the CACC model over-relies on the fixed headway and does not adjust the distance according to the dynamic change of speed, resulting in the inability of the following vehicle to effectively follow the front vehicle. Compared with the ACC model, the CACC model introduces the acceleration information of the front vehicle, which improves the problem of negative speed under acceleration and congestion conditions, but there are still unrealistic collisions, reversing behaviors and large speed fluctuations, especially under deceleration and signalized intersection conditions. This is because the rear vehicle failed to respond to the speed change of the front vehicle in time, resulting in a small distance between the vehicles, resulting in a collision. As the collision occurred, the following vehicles began to decelerate and reversed.

[0121] Therefore, in order to overcome the above defects, it is necessary to improve the ACC and CACC following models. By comprehensively considering other relevant factors to improve the model, the performance and stability of the model in the equilibrium and non-equilibrium state of traffic flow can be improved. This will provide a more reliable basis for the modeling and control of actual traffic flow. To this end, the present invention proposes a networked car following model and a traffic flow stability analysis method, which specifically includes the following steps:

[0122] Obtain the vehicle speed, the speed difference between the front and rear vehicles, and the distance between the front of the vehicle in the connected vehicle following state.

[0123] Based on the adaptive cruise control model ACC, the time-varying expected distance is introduced, and the expected vehicle distance in ACC is replaced to obtain the TV-ACC following model.

[0124] Based on the collaborative adaptive cruise control model CACC, a time-varying expected distance is introduced, and the expected vehicle distance in CACC is replaced to obtain the TV-CACC following model.

[0125] The first-order partial derivatives of the vehicle speed, the speed difference between the front and rear vehicles, and the headway between the vehicles are calculated, and the homogeneous traffic flow stability conditions are set based on the calculation results.

[0126] According to the homogeneous traffic flow stability conditions, the homogeneous traffic flow stability constraint discrimination values ​​of the TV-ACC following model and the TV-CACC following model of the connected vehicle are calculated respectively. When the value is greater than 0, the homogeneous traffic flow is stable, and when the value is less than 0, the homogeneous traffic flow is unstable.

[0127] The vehicle speed of the connected vehicle, the speed difference between the front and rear vehicles, the headway between the vehicles, and the partial differential of the headway between the connected vehicles other than the connected vehicle are calculated, and the stability conditions of the heterogeneous traffic flow are set according to the calculation results.

[0128] According to the stability conditions of heterogeneous traffic flow, the stability discrimination values ​​of heterogeneous traffic flow of the connected vehicle TV-ACC following model and TV-CACC following model at different speeds, different CAV penetration rates and maximum queues are calculated respectively. When the value is greater than 0, the heterogeneous traffic flow is stable, and when the value is less than 0, the heterogeneous traffic flow is unstable.

[0129] According to the heterogeneous traffic flow stability conditions, the heterogeneous traffic flow stability judgment values ​​of the TV-ACC following model and the TV-CACC following model of the connected vehicle are calculated respectively under different speeds, different CAV penetration rates and maximum queues.

[0130] Improved ACC model: Vehicles need to maintain a certain distance during the car-following behavior to avoid collision. In order to better simulate the actual traffic conditions, the time-varying expected distance is introduced to improve the car-following model. This improved model is closer to the actual traffic conditions. Therefore, the present invention adopts the time-varying expected distance to improve the adaptive cruise control (ACC) model.

[0131] The proposed formula for calculating the expected vehicle spacing is as follows:

[0132]

[0133] In formula (5), s0 is the minimum distance allowed between the following vehicle and the leading vehicle after parking, m; l is the body length of the leading vehicle, m; τ is the driver's reaction time, s; is the speed of the front and rear vehicles, m / s; a n-1 、a n is the maximum deceleration of the front and rear vehicles, both of which are -8m / s 2 .

[0134] The present invention aims at the defects of the ACC model in formula (3) and establishes an improved ACC following model based on time-varying expected distance. Substituting formula (5) into formula (3), the improved ACC model (TV-ACC model) of the present invention is obtained as formula (6):

[0135]

[0136] Since the optimal model parameters vary with different following scenarios, the present invention sets k2 as follows:

[0137]

[0138] In formula (6), the other parameters are the same as above.

[0139] It can be seen from formula (6) that the TV-ACC model retains the simple structure of the ACC model, but the expected headway of the TV-ACC model is no longer constant, but changes with the speed, which makes the characteristics of the model more realistic.

[0140] TV-ACC model trajectory simulation: In order to verify the effectiveness of the improvement of the ACC model, the present invention first analyzes from the perspective of trajectory simulation. The experimental conditions are consistent with the above. The trajectory simulation results of the TV-ACC model under different working conditions are as follows: Figure 11-Figure 14 shown.

[0141] from Figure 11-Figure 14 It can be seen that the TV-ACC model enables the vehicle to effectively follow the leading vehicle under four conditions: acceleration, deceleration, congestion, and signalized intersections, without any unreasonable collision, reversing behavior, or large speed fluctuations. This is because the TV-ACC model introduces a time-varying expected distance, and the distance between vehicles is dynamically adjusted with speed, so that the vehicle-following distance is kept within a reasonable range, thereby avoiding unrealistic collisions and reversing behaviors and speed oscillations, and improving driving stability.

[0142] The TV-ACC model not only eliminates the unrealistic reversing and collision behaviors and large speed fluctuations caused by the ACC model, but also enables the following vehicles to better respond to the driving of the leading vehicle. Fig.11 (c)-14(c) It can be seen that when the speed of the leading vehicle fluctuates, due to the introduction of the time-varying expected spacing by the TV-ACC model, the acceleration of the following vehicle will not produce large oscillations, but will be able to better respond to the driving of the leading vehicle, and the driving speed is smoother than that of the ACC model and the leading vehicle.

[0143] In order to better demonstrate the superiority of the TV-ACC model, the experimental results were compared with those of the ACC model under the same experimental conditions in the PATH laboratory. Fig.15 shown.

[0144] from Fig.15 It can be seen that compared with the ACC model, the TV-ACC model does not produce large speed fluctuations and can follow the vehicle in front more smoothly. This shows that the TV-ACC model can better simulate the vehicle's following behavior and make its following trajectory smoother.

[0145] Improved CACC model: By introducing the improved PATH laboratory ACC model with time-varying expected spacing, the original ACC model can overcome the problems of unrealistic collision, reversing and large speed fluctuation caused by the large influence of the headway, so that the model can more accurately reflect the vehicle's following characteristics. Therefore, the present invention still introduces the time-varying expected spacing to improve the CACC following model proposed by the PATH laboratory. The improved CACC model (TV-CACC model) is as shown in formula (8):

[0146]

[0147] In formula (8): is the acceleration of the front vehicle; m is the number of front vehicles that can communicate with the current CACC vehicle, which is generally 3; β1 and β2 are the driver's attention to the speed of the adjacent vehicle in front and the average speed of multiple vehicles in front, respectively, where β1+β2=1; is the average speed of the vehicles ahead; the other parameters are the same as above.

[0148] It can be seen from formula (8) that the TV-CACC model retains the characteristics of the CACC model, such as simple structure and clear physical meaning of parameters. However, the expected headway of the TV-CACC model is no longer a constant value, but will change according to the change of speed, making the characteristics of the model more realistic.

[0149] The trajectory simulation results of the TV-CACC model under different working conditions are shown in Figure 16-Figure 19 shown; from Figure 16-Figure 19 It can be seen that the TV-CACC model enables the following vehicle to follow the leading vehicle well under acceleration, deceleration, congestion and signalized intersection conditions, and does not cause unrealistic collisions, reversing and large speed fluctuations as in the CACC model. This is because the TV-CACC model introduces a time-varying expected distance, and the distance between vehicles can be adjusted with the dynamic changes in speed, so that the distance between vehicles is always maintained in a reasonable range, and can respond more sensitively to the speed fluctuations of the leading vehicle, thereby avoiding the occurrence of unrealistic driving behaviors.

[0150] Combination Figure 11-Figure 14 and Figure 16-Figure 19It can be seen that the TV-CACC model makes the speed change trend of the vehicle close to that of the leading vehicle, and the speed change is smoother than that of the following vehicle controlled by the TV-ACC model. At the same time, the following vehicle controlled by the TV-ACC model needs a certain amount of time to adjust its speed to be consistent with the speed change trend of the leading vehicle, while the TV-CACC model enables the vehicle to respond quickly to the driving of the leading vehicle. This shows that the TV-CACC model is more sensitive to the speed change of the leading vehicle than the TV-ACC model, can respond quickly to the driving of the leading vehicle, keep a reasonable distance between it and the leading vehicle, and can better simulate the following behavior of the vehicle.

[0151] In order to better demonstrate the superiority of the TV-CACC model, the experimental results of the TV-CACC model are compared with those of the CACC model under the same experimental conditions of the PATH experiment. The specific comparison results are as follows: Fig. 20 shown.

[0152] from Fig. 20 It can be seen that although the CACC model can follow the leading vehicle well, there will be small disturbances when the leading vehicle enters a constant speed, while the TV-CACC model can better follow the leading vehicle in acceleration and deceleration behavior, and can follow the leading vehicle more smoothly. This shows that the TV-CACC model can better simulate the vehicle's following behavior and make its following trajectory smoother.

[0153] In summary, the TV-ACC model and TV-CACC model not only do not undermine the advantages of the ACC and CACC models, but also avoid the unrealistic collisions, reversing behaviors, and large speed fluctuations that occur in the original models. At the same time, the TV-ACC model and TV-CACC model can make the vehicle speed change more smoothly and can more accurately simulate the vehicle's following behavior. This improvement is expected to improve the stability and driving comfort of the fleet and have a positive impact on the development of autonomous vehicle technology.

[0154] In order to further analyze the advantages and rationality of the improved model, the stability analysis of the TV-ACC model and the TV-CACC model is carried out. This part theoretically derives the stability conditions of the two following models under homogeneous and heterogeneous traffic flows, analyzes the influence of CAVs penetration rate and maximum fleet size on the stability of mixed traffic flow, and the driving comfort level under different CAVs penetration rates.

[0155] The stability condition of homogeneous traffic flow is as follows:

[0156]

[0157] In formula (9), f v 、f Δv and f ΔxThey represent the first-order partial derivatives of the following model with respect to vehicle speed, front and rear vehicle speed difference, and vehicle head distance, respectively. The specific formula is shown in formula (10).

[0158]

[0159] In formula (10): v * is the velocity in equilibrium, m / s; Δx * is the headway distance in equilibrium, m.

[0160] in, as well as

[0161]

[0162] In formulas (11)-(12), F A With F C are the stability constraint discriminant values ​​of TV-ACC and TV-CACC models respectively.

[0163] Similarly, the stability constraint discriminant values ​​of the ACC model and the CACC model can be obtained as follows: and

[0164] Based on formulas (11)-(12), the stability of homogeneous traffic flow can be obtained, such as Fig.21 As shown; Fig.21 shows how the stability of homogeneous traffic flow changes with speed. If the value is greater than 0, the homogeneous traffic flow is stable at that speed. Fig.21 It can be seen that for AVs traffic flow, the stability judgment value of the ACC model is always less than 0, and the traffic flow is unstable. However, for the TV-ACC model, its stability judgment value decreases at 3s. The reason for this phenomenon is that the value of k2 is discontinuous; when the speed is greater than 9.28m / s, the stability judgment value is greater than 0, the AVs traffic flow is stable, and its stability judgment value changes with the speed. This shows that the stability of the TV-ACC model is better than that of the ACC model. For CAVs traffic flow, the stability judgment value of the TV-CACC model and the CACC model are always greater than 0, and are better than the CACC model after the speed is greater than 13.96m / s. This phenomenon shows that the application of CAVs can improve the stability of traffic flow; although the application of AVs is not conducive to the stability of traffic flow when the speed is less than 9.28m / s, it is generally helpful to improve the stability of traffic flow.

[0165] The stability condition of heterogeneous traffic flow is as follows:

[0166]

[0167] In formula (13): n, m are the vehicle numbers; The following model formula for the nth vehicle is the partial differential term with respect to vehicle speed, speed difference and headway between vehicles.

[0168] The mixed traffic flow studied in this paper includes four following modes. Assuming that the maximum number of vehicle queues in the heterogeneous traffic flow is N and the CAVs penetration rate is p, the spatial distribution probability of the following modes under the four following conditions can be obtained as shown in formula (14).

[0169]

[0170] In formula (14), p is the penetration rate of CAVs in mixed traffic flow; N is the maximum fleet size of CAVs; P H , P A , P P With P C are the spatial distribution probabilities of the following modes under following scenarios 1-4, and P H +P A +P P +P C =1.

[0171] Therefore, the stability judgment values ​​of the three types of vehicles can be obtained as shown in formula (15).

[0172]

[0173] Formula (15) can be simplified as:

[0174]

[0175] Based on formula (16), the stability discrimination value of heterogeneous traffic flow under different speeds, different CAVs penetration rates and maximum queue sizes is obtained, as follows: Fig. 22 shown.

[0176] from Fig. 22 (a)- Fig. 22 (d) It can be seen that when the vehicle speed is less than the critical speed, the higher the penetration rate of CAVs, the stronger its stability. At this time, increasing the penetration rate of CAVs can improve the stability of mixed traffic flow at the critical speed, and when the vehicle speed is greater than the critical speed, the stability of mixed traffic flow decreases with the increase of CAVs penetration rate. When the maximum queue size is N = 2, 4, 6 and 8, the corresponding critical speeds are 30.5m / s, 29.9m / s, 29.5m / s and 29.3m / s, respectively, which shows that the critical speed decreases with the increase of the maximum fleet size N.

[0177] In order to further study the impact of CAVs penetration, maximum platoon size, and equilibrium speed on the stability of mixed traffic flow, the analysis results of different CAVs penetration and maximum platoon size N are shown in Figure 2. Fig.23 shown.

[0178] exist Fig.23 In the figure, different color depths represent the F value of mixed traffic flow stability, and the black curve is the stability baseline (F = 0). The unstable condition of mixed traffic flow is F < 0. Fig.23 It can be seen that when the maximum fleet size of CAVs is fixed, the unstable speed range of mixed traffic flow gradually expands with the increase of CAVs penetration rate. This is because the present invention takes into account the functional degradation of CAVs, that is, CAVs will degenerate into AVs in some cases. As the penetration rate of CAVs increases, AVs gradually increase, resulting in a gradual expansion of the unstable speed range of mixed traffic flow. However, Fig.23 (a) shows that when the penetration rate of CAVs is greater than 0.9340, no unstable speed region appears in the mixed traffic flow. This means that when the penetration rate of CAVs reaches a high level, the number of vehicles that degenerate from CAVs to AVs gradually decreases, and the mixed traffic flow returns to a stable state. Fig.23 (a)-(d) show that as the maximum platoon size of CAVs increases, the area covered by the black curve gradually becomes more prominent. The stability of mixed traffic flow shows a trend of first deteriorating, then improving, and finally stabilizing with the penetration rate of CAVs, and gradually weakens with the increase of the maximum platoon size, which is consistent with Fig. 22 The results are consistent.

[0179] In order to verify the stability analysis results of heterogeneous traffic flow, the mixed traffic flow composed of EFVD model, TV-ACC and TV-CACC models was numerically simulated in Matlab. The experimental condition is a heterogeneous fleet consisting of 100 vehicles. The positions of HDVs, AVs and CAVs are randomly determined, and the number is determined by the CAVs penetration rate p. The vehicles in the fleet follow the vehicle according to the collected data of the lead vehicle. In order to intuitively see the operation of the fleet, the data from 1700-1900s in the collected data were selected for numerical simulation. This is because in this time period, the lead vehicle undergoes a certain acceleration and deceleration to gradually stabilize the speed from 0 to 33.4m / s, which is of research significance. The experimental results are as follows Fig.24 shown.

[0180] from Fig.24 It can be seen that with the increase of CAVs penetration rate, the stability of mixed traffic flow gradually improves. Fig.24In the case of no CAVs or a low proportion of CAVs in the convoy, the disturbance propagation of the convoy gradually increases. At this time, the convoy speed is in an oscillating state and has a tendency to expand, which eventually makes the data appear infinite or infinitesimal. Fig.24 Results of (a)-(c). Fig.24 (a)-(c) are partial images, from which it can be clearly seen that when the disturbance is transmitted to a certain vehicle, the speed begins to become uncontrollable. Fig.24 From (a)-(c), it can be concluded that when the proportion of CAVs is low, increasing the proportion of CAVs may not necessarily improve the stability of traffic flow, and may even reduce the stability. This is because when the CAVs penetration rate is 0, the traffic flow is composed of pure HDVs, and the traffic flow is unstable; when the CAVs penetration rate reaches 0.2 and 0.4, the disturbance of the vehicle in front gradually increases, causing the speed of the convoy to oscillate and the heterogeneous traffic flow to be unstable. Fig.24 It can be concluded from (e)-(f) that when the proportion of CAVs reaches 0.6 and above, CAVs have a significant positive effect on the stability of heterogeneous traffic flow. At this time, as the proportion of CAVs increases, the speed oscillation of the fleet gradually decreases. When the proportion of CAVs reaches 0.8, the propagation of disturbances is well suppressed. As the proportion increases further, the fleet is stable as a whole, which shows that CAVs can maintain the stability of traffic flow. This is because when the penetration rate of CAVs is low, the proportion of HDVs in the fleet is high. Due to the randomness of the vehicle position distribution, CAVs will be scattered among HDVs, causing many CAVs to degenerate into AVs, further reducing the stability of heterogeneous traffic flow. As the penetration rate of CAVs increases, the probability of CAVs degenerating into AVs decreases, thereby improving the instability of mixed traffic flow. The simulation results show that the stability of traffic flow has been significantly improved. The calculation results are consistent with the conclusions of theoretical analysis. In order to better evaluate the traffic flow comfort under different CAVs penetration rates, the comfort index CI (Comfort Index) based on the international ISO standard is used to determine the mixed traffic flow comfort level under different CAVs penetration rates p. The lower the value, the better the comfort. In the simulation test of the present invention, the lateral movement of the vehicle is not considered. The calculation of the CI index in the document G S.PADDAN, M J.GRIFFIN, Evaluation of whole-body vibration in vehicles, Journal of Sound and Vibration 253 (1) (2002) 195-213 can be simplified to formula (17):

[0181]

[0182] In formula (17), a iis the i-th acceleration value counted; m is the total amount counted.

[0183] Based on the above simulation experiments and the calculation formula of the comfort index CI (17), the driving comfort analysis results of the original model and the improved model under different CAVs penetration rates p are shown in Table 1.

[0184] Table 1 Comfort analysis results

[0185]

[0186] As can be seen from Table 1, with the increase of CAVs penetration rate p, the comfort CI index shows a trend of increasing first and then decreasing, indicating that the comfort gradually deteriorates, and then gradually recovers and improves. Compared with the original model, the improved model shows better comfort at each CAVs penetration rate, and the value of its comfort index CI is reduced by an average of 9.08%. This is consistent with the discussion results of the trajectory results and stability analysis, and further verifies the effectiveness of the improved model in improving driving comfort.

[0187] From the perspective of trajectory simulation, the present invention studies and analyzes the ACC and CACC models proposed by the PATH laboratory. It is found that the original model has problems such as collision, reversing behavior and large speed fluctuation when simulating vehicle driving trajectories, especially under deceleration and signal intersection conditions. In order to improve these shortcomings, the present invention introduces a time-varying expected distance and proposes an improved ACC model (TV-ACC model). Taking into account the differences between the CACC and ACC models, the time-varying expected distance and the speed and acceleration information of multiple leading vehicles are introduced, and an improved CACC model (TV-CACC model) is proposed. The following vehicle distance can be adjusted with the dynamic changes of vehicle speed, which is closer to the actual situation. The EFVD model and the TV-ACC and TV-CACC models are used to describe the following characteristics of HDVs, AVs and CAVs respectively, and numerical simulations and theoretical derivations are carried out to verify the performance of the improved model in terms of stability and driving comfort of mixed traffic flow. The results show that the TV-ACC and TV-CACC models can overcome the problems of the ACC and CACC models, which are greatly affected by the constant headway, resulting in unrealistic collisions, reversing behaviors and large speed fluctuations, and thus show better performance. The TV-ACC and TV-CACC models make vehicles more sensitive to the speed changes of the leading vehicle and maintain a reasonable distance, thereby improving the driving stability of the following vehicles. The stability of the TV-ACC and TV-CACC models is also better than that of the ACC and CACC models, and their stability judgment values ​​change with speed, which is more in line with the actual situation. In addition, with the increase in the penetration rate of CAVs, the stability and driving comfort of mixed traffic flow show a trend of first deteriorating, then improving and finally stabilizing.

[0188] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A connected vehicle following model and traffic flow stability analysis method, characterized in that: The following steps are involved: Obtain the vehicle speed, the speed difference between the front and rear vehicles, and the head-to-head distance of the connected vehicle in the following state; Based on the adaptive cruise control model ACC, the time-varying expected distance is introduced, and the expected distance between vehicles in ACC is replaced to obtain the TV-ACC following model. Based on the cooperative adaptive cruise control model CACC, the time-varying expected distance is introduced, and the expected distance between vehicles in CACC is replaced to obtain the TV-CACC following model. Calculate the first-order partial derivative of the vehicle speed, the speed difference between the front and rear vehicles, and the headway between the vehicles, and set the homogeneous traffic flow stability condition based on the calculation results; According to the homogeneous traffic flow stability condition, the homogeneous traffic flow stability constraint discrimination values ​​of the TV-ACC following model and the TV-CACC following model of the networked vehicle are calculated respectively; Calculate the vehicle speed of the connected vehicle, the speed difference between the front and rear vehicles, the headway between the vehicles, and the partial differential of the headways between the connected vehicles other than the connected vehicle, and set the stability conditions of the heterogeneous traffic flow according to the calculation results; According to the stability conditions of heterogeneous traffic flow, the stability discrimination values ​​of the TV-ACC following model and the TV-CACC following model of the connected vehicle under different speeds, different CAV penetration rates and maximum queues are calculated respectively; According to the homogeneous traffic flow stability constraint discrimination value and heterogeneous traffic flow stability discrimination value of the TV-ACC following model and the TV-CACC following model, the traffic flow stability of the connected vehicle TV-ACC and TV-CACC following models is analyzed.

2. A connected vehicle following model and traffic flow stability analysis method according to claim 1, characterized in that: The calculation formula of the time-varying expected spacing is: Among them, s0 is the minimum distance allowed between the following car and the leading car after stopping, l is the body length of the leading car, τ is the driver's reaction time, is the speed of the front and rear vehicles, a n-1 、a n is the maximum deceleration of the front and rear vehicles.

3. A connected vehicle following model and traffic flow stability analysis method according to claim 2, characterized in that: The time-varying expected distance is introduced based on the adaptive cruise control model ACC, and the expected vehicle distance in the ACC is replaced to obtain the TV-ACC following model, which specifically includes the following steps: The ACC model is expressed as: The time-varying expected distance is introduced into the ACC model to replace the expected vehicle distance, and the TV-ACC following model is obtained, which is expressed as: Among them, v n (t) are the speed and acceleration of the nth vehicle at time t; Δv n (t) is the speed difference between the nth vehicle and the preceding vehicle at time t; x n-1 (t), x n (t) are the displacements of vehicles n-1 and n at time t; l is the vehicle length; s0 is the minimum safe stopping distance; k1 and k2 are the control coefficients of the inter-vehicle distance error and speed difference, respectively; T a is the expected headway between ACC vehicles.

4. A connected vehicle following model and traffic flow stability analysis method according to claim 3, characterized in that: The collaborative adaptive cruise control model CACC introduces a time-varying expected distance, replaces the expected vehicle distance in CACC, and obtains a TV-CACC following model, which specifically includes the following steps: in, is the acceleration of the preceding vehicle n-1 at time t; k3, k4 and k5 are coefficients; T c is the expected inter-vehicle time distance of CACC vehicles; The time-varying expected distance and the acceleration and speed information of the multiple vehicles ahead are introduced into the CACC model to replace the expected vehicle distance and the acceleration of the leading vehicle, and the TV-CACC following model is obtained, which is expressed as: Where m is the number of vehicles ahead that can communicate with the current CACC vehicle, and its value is 3; β1 and β2 are the driver’s attention to the speed of the adjacent vehicle ahead and the average speed of the multiple vehicles ahead, respectively, where β1+β2=1; is the average speed of the vehicles ahead.

5. A connected vehicle following model and traffic flow stability analysis method according to claim 4, characterized in that: The homogeneous traffic flow stability condition is expressed as: Among them, f v 、f Δv and f Δx They represent the first-order partial derivatives of the following model with respect to vehicle speed, speed difference between front and rear vehicles, and head-to-head distance.

6. A connected vehicle following model and traffic flow stability analysis method according to claim 5, characterized in that: The homogeneous traffic flow stability constraint discrimination values ​​of the TV-ACC following model and the TV-CACC following model of the networked vehicle are calculated according to the homogeneous traffic flow stability condition, and the specific steps include: The f v 、f Δv and f Δx The specific formula is: Among them, v * is the velocity in equilibrium; Δx * is the headway distance in equilibrium; and as well as Among them, α is the sensitivity coefficient, Δx is the distance between the front and rear vehicles, and H represents a manually driven vehicle; Then the stability constraint discriminant value of the TV-ACC car-following model is expressed as: The stability constraint discriminant value of the TV-CACC car-following model is expressed as: Where A represents the ACC vehicle, v represents the vehicle speed, and a k represents the parameter a of the TV-ACC model n ; C stands for CACC vehicle.

7. The connected vehicle following model and traffic flow stability analysis method according to claim 1, characterized in that: The heterogeneous traffic flow stability condition is expressed as: Among them, n and m are the vehicle numbers; It is the partial differential term of the following model of the nth vehicle with respect to vehicle speed, speed difference and headway between vehicles.

8. The connected vehicle following model and traffic flow stability analysis method according to claim 6, characterized in that: The heterogeneous traffic flow includes four following modes, and their spatial distribution probabilities are expressed as: Where p is the penetration rate of CAVs in heterogeneous traffic flow; N is the maximum fleet size of CAVs; P H , P A , P P With P C are the spatial distribution probabilities of the four following modes, and P H +P A +P P +P C =1.

9. A connected vehicle following model and traffic flow stability analysis method according to claim 8, characterized in that: The heterogeneous traffic flow stability discrimination values ​​of the TV-ACC following model and the TV-CACC following model of the networked vehicle under different speeds, different CAV penetration rates and maximum queues are calculated according to the heterogeneous traffic flow stability conditions, and the calculation steps include: Simplified to:

10. A connected vehicle following model and traffic flow stability analysis method according to claim 9, characterized in that: It also includes using the comfort index CI of the international ISO standard to determine the driving comfort level of the TV-ACC following model and the TV-CACC following model at different CAVs penetration rates p, and the calculation formula of the index CI is: Among them, a i is the i-th acceleration value counted; m is the total amount counted.

Images