Stability analysis method, device and medium for heterogeneous vehicle fleet considering time-distance strategy

Abstract

The present invention belongs to the field of intelligent transportation technology, and discloses a method, device and medium for analyzing the stability of a heterogeneous fleet considering a time distance strategy, wherein the method includes: determining the distribution characteristics of vehicles in the heterogeneous fleet according to the heterogeneity of the fleet; constructing a vehicle following model with a variable headway strategy according to the vehicle distribution characteristics; constructing a transfer function about speed disturbance according to the vehicle following model, and determining the basis for judging the stability of the heterogeneous fleet. On the basis of conventional stability analysis criteria, the acceleration factor of the leading vehicle is introduced, and the stability analysis criteria of homogeneous and heterogeneous fleets under a new type of heterogeneous fleet are derived to analyze the stable state of the fleet under complex heterogeneity. Through numerical simulation, the effects of various index coefficients on the stability of the fleet are deeply analyzed, and the advantages of the improved model and the effectiveness of the stability analysis method are further verified.

Description

Technical Field

[0001] The present invention relates to the field of intelligent transportation technology, and more specifically, to a method, device and medium for analyzing the stability of a heterogeneous vehicle fleet considering a time interval strategy. Background Art

[0002] Autonomous driving and vehicle platooning have great potential in terms of safety, environment, mobility, etc. As CAVs and CVs are continuously deployed in the market, traffic scenarios with mixed platooning of CAVs, CVs, AVs and HVs will inevitably appear due to the differences in autonomous driving and the uncertainty of communication functions.

[0003] In the process of vehicle following, the CACC model and the ACC model are often used to characterize the vehicle following behavior of CAV and AV, and the IDM model is often used to characterize HV, but all three models use a fixed safe headway. When small disturbances continue to propagate and change frequently in a heterogeneous fleet system, it is difficult for the test vehicles to flexibly adjust the headway to ensure the stability of the queue. In the VTH strategy, the safe headway is a nonlinear function of the vehicle speed, which is more suitable for the real traffic environment. Since different types of vehicles have different following behaviors, applying the VTH strategy to the modeling process of the vehicle following model of CAV, CV, AV and HV is a problem that still needs to be solved.

[0004] After the introduction of the VTH strategy, due to the complex heterogeneity of the new heterogeneous fleet, different queue distributions will occur, and the stability of the fleet will also change. The stability criterion of heterogeneous fleets in the existing technology is mainly aimed at the vehicle following model that considers the speed of the ego vehicle, relative speed, and head-to-head distance. When the ego vehicle obtains other information about the preceding vehicle, the stability criterion has certain limitations. Summary of the invention

[0005] The purpose of the present invention is to provide a method, device and medium for analyzing the stability of heterogeneous vehicle fleets taking into account time distance strategies. In the face of the problem that it is difficult for the vehicle to flexibly adjust the headway distance, the differences in variable headway time distance strategies are analyzed based on the characteristics of the networking functions. In view of the differences in different networking environments and vehicle information receiving capabilities, different VTH strategies are adopted to construct vehicle following models for CAV, AV, CV and HV. In order to analyze the stable state of the vehicle fleet under complex heterogeneity, the acceleration factor of the leading vehicle is introduced on the basis of the conventional stability analysis criteria, and the stability analysis criteria for homogeneous and heterogeneous vehicle fleets under the new heterogeneous vehicle fleet are derived. Through numerical simulation, the effects of various index coefficients on the stability of the vehicle fleet are deeply analyzed, and the advantages of the improved model and the effectiveness of the stability analysis method are further verified.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] According to a first aspect of the present invention, a method for analyzing the stability of a heterogeneous fleet considering a time interval strategy is provided, the method comprising:

[0008] According to the heterogeneity of the fleet, determine the distribution characteristics of vehicles in the heterogeneous fleet;

[0009] According to the characteristics of vehicle distribution, a vehicle following model with variable headway strategy is constructed;

[0010] A transfer function for speed disturbance is constructed according to the vehicle following model, and a basis for judging the stability of a heterogeneous vehicle fleet is determined.

[0011] According to a second aspect of the present invention, a device for analyzing the stability of a heterogeneous vehicle fleet considering a time interval strategy is provided, the device comprising:

[0012] A distribution characteristic determination unit is configured to determine a distribution characteristic of vehicles in a heterogeneous fleet according to the heterogeneity of the fleet;

[0013] A following model building unit is configured to build a vehicle following model with a variable headway strategy according to vehicle distribution characteristics;

[0014] The judgment basis determination unit is configured to construct a transfer function about speed disturbance according to the vehicle following model and determine the stability judgment basis of the heterogeneous vehicle fleet.

[0015] According to a third aspect of the present invention, there is provided a readable storage medium storing one or more programs, wherein the one or more programs can be executed by one or more processors to implement the method as described above.

[0016] The present invention has at least the following beneficial effects:

[0017] (1) Considering that CAV and CV vehicles will degenerate into AV and HV vehicles respectively when communication fails, and cannot obtain accurate information about the preceding vehicle through the networking function, a new heterogeneous fleet consisting of CAV-AV-CV-HV is defined. Combined with the characteristics of non-networked vehicles, the VTH strategy based on relative speed is considered, and the ACC model and IDM model are improved to characterize the following behavior of AV and HV; according to the characteristics of networked vehicles, the VTH strategy based on relative speed and the acceleration of the preceding vehicle is considered, and the CACC model and IDM model are improved to characterize the following behavior of CAV and CV respectively.

[0018] (2) For the vehicle following model that takes into account the vehicle's own speed, relative speed, headway and acceleration of the leading vehicle, a transfer function of the platoon with respect to speed disturbance is constructed by first-order Taylor linear approximation and Laplace transform, and a platoon stability analysis method is proposed. Based on the constructed new heterogeneous platoon and considering the actual proportional relationship of the vehicles, the chord stability criteria of the homogeneous and heterogeneous queues under the new heterogeneous platoon are derived.

[0019] (3) The VTH strategy enables the fleet to maintain stability within a larger equilibrium speed range; the fleet stability is positively correlated with the ratio of CAV to CV, and negatively correlated with the ratio of AV to HV; the CAV fleet is always stable, while the AV fleet is always unstable; the stability function of the new heterogeneous fleet that introduces the VTH strategy has greater volatility, but the unstable equilibrium speed range is also smaller; at the same time, as the CV ratio increases, the unstable range decreases faster. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flow chart of a method for analyzing the stability of a heterogeneous vehicle fleet considering a time interval strategy according to an embodiment of the present invention is shown.

[0021] Figure 2 A flow chart for constructing a vehicle following model of a variable headway strategy according to an embodiment of the present invention is shown.

[0022] Figure 3 A schematic diagram of a homogeneous fleet stability function under a variable headway strategy according to an embodiment of the present invention is shown.

[0023] Figure 4 : shows a schematic diagram of a stability function of a heterogeneous fleet under a variable headway strategy according to an embodiment of the present invention, wherein P a =0.25, (a) traditional model; (b) improved model.

[0024] Figure 5 : shows a schematic diagram of a stability function of a heterogeneous fleet under a variable headway strategy according to an embodiment of the present invention, wherein P b =0.25, (a) traditional model; (b) improved model.

[0025] Figure 6 shows different P a and P b Lower stability function S m The minimum value S m,min Schematic diagram of .

[0026] Figure 7 A structural diagram of a heterogeneous vehicle fleet stability analysis device considering time interval strategy according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0027] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and specific embodiments, but are not intended to limit the present invention. For the various steps described herein, if there is no necessity for a causal relationship between each other, the order in which they are described as examples herein should not be regarded as a limitation, and those skilled in the art should know that they can be adjusted in order, as long as the logic between them is not destroyed, resulting in the inability to implement the entire process.

[0028] Terminology explanation:

[0029] CAV (connected automated vehicles): intelligent connected vehicles;

[0030] AV (autonomous vehicles): self-driving vehicles;

[0031] CV (connected vehicles): connected vehicles;

[0032] HV (human-driven vehicles): Human-driven vehicles;

[0033] CACC (Cooperative Adaptive Cruise Control): Cooperative Adaptive Cruise Control;

[0034] ACC (Adaptive Cruise Control): Adaptive cruise control;

[0035] IDM (Intelligent Driver Model): Intelligent Driver Model;

[0036] VTH (variable time headway): variable time headway.

[0037] The embodiment of the present invention proposes a method for analyzing the stability of a heterogeneous fleet considering the time interval strategy, such as Figure 1 As shown, it is a flow chart of the method, which includes the following steps S100 to S300, which are described in detail as follows.

[0038] Step S100, determining the distribution characteristics of vehicles in the heterogeneous fleet according to the heterogeneity of the fleet.

[0039] It should be noted that the heterogeneous fleet described in this article is a new type of heterogeneous fleet, which includes CAV, AV, CV and HV. CAV and CV result in AV and HV with networked equipment due to communication failure. CAV is defined as an autonomous driving vehicle using the CACC driving mode, and AV is defined as a CAV that degenerates into an AV when it cannot obtain the information of the vehicle in front through V2V communication using the CACC driving mode. CV is defined as a manually driven vehicle with V2V communication equipment. HV is defined as not only including traditional manually driven vehicles, but also including CVs that have networked functions but cannot communicate when they are the rear vehicles of HVs. According to the vehicle definition, the vehicle types in the new heterogeneous fleet are shown in Table 1.

[0040] Table 1 Vehicle types of heterogeneous fleets

[0041]

[0042] The vehicle proportions of CAV, AV, CV and HV in a heterogeneous fleet are calculated based on probability theory. Assuming the number of vehicles in the fleet is N, and the market penetration rate of CAV is p a (0≤p a ≤1), the market penetration rate of CV is p b (0≤p b ≤1), then the permeability of HV is p c =1-p a -p b , the value range is [0,1]. The number of CAV, AV, CV and HV vehicles in the fleet N CAV , N AV , N CV and N HV The expression is:

[0043]

[0044] The actual ratio of CAVs, AVs, CVs and HVs in the fleet CAV ,P AV ,P CV and P HV The expression is:

[0045]

[0046] Step S200: constructing a vehicle following model with a variable headway strategy according to the vehicle distribution characteristics.

[0047] like Figure 2 As shown, according to the vehicle distribution characteristics, constructing a vehicle following model with a variable headway strategy includes the following steps S201 to S203.

[0048] Step S201, setting variable headway strategies under non-networked conditions and networked conditions.

[0049] Specifically, considering the PF information topology and the vehicle's information acquisition capability, the VTH strategy is analyzed. If the headway is defined as a function of relative speed, that is, the vehicle can obtain the speed information of the vehicle ahead, then a VTH strategy under non-connected conditions is defined, and the expression is:

[0050]

[0051] In the formula, represents the variable headway under non-connected conditions, represents a fixed time interval, c v represents the weight coefficient of relative speed, represents the relative speed of vehicle i, v i-1 represents the speed of vehicle i-1, v i represents the speed of vehicle i.

[0052] If the headway is defined as a function of the relative speed and the acceleration of the preceding vehicle, that is, the vehicle can obtain the speed and acceleration information of the preceding vehicle, then a VTH strategy under networked conditions is defined to reflect the changing trend of the preceding vehicle’s acceleration. The expression is:

[0053]

[0054] In the formula, represents the variable headway under network conditions, c a represents the weight coefficient of the acceleration of vehicle i-1, a i-1 represents the acceleration of vehicle i-1.

[0055] Step S202: constructing a vehicle following model of a variable headway strategy based on the variable headway strategy under the non-networked condition and the networked condition.

[0056] Specifically, the traditional IDM model, CACC model, and ACC model use a constant headway. Considering the connected characteristics of CAV and CV vehicles, the acceleration information of the leading vehicle can be accurately obtained. Therefore, the VTH strategy under connected conditions is introduced into the CACC model to characterize the following behavior of CAV. The expression is as follows:

[0057]

[0058] In the formula, x i represents the position of vehicle i, x i-1 represents the position of vehicle i-1, v i represents the speed of vehicle i, v i-1 represents the speed of vehicle i-1, ei represents the error of the headway distance, k1 represents the headway distance control coefficient, k2 represents the control coefficient of the relative speed, and k3 represents the control coefficient of the acceleration of vehicle i-1.

[0059] The IDM model after the improvement of VTH strategy under the network connection condition represents the following behavior of CV, and the expression is:

[0060]

[0061] In the formula, represents the expected acceleration of the vehicle; represents the maximum acceleration of vehicle i; represents the relative speed of vehicle i; b i Indicates the comfortable deceleration of the vehicle; v f represents the free flow speed; represents the desired spacing between vehicles; represents the actual distance between vehicles i, represents the headway of vehicle i, L represents the vehicle length; θ is the free acceleration index.

[0062] Considering that CAV and CV degenerate into AV and HV when they cannot communicate with the preceding vehicle, the VTH strategy under non-connected conditions is introduced into the ACC model to characterize the following behavior of AV. The expression is:

[0063]

[0064] The VTH strategy under non-connected conditions is used to improve the IDM model to characterize the following behavior of HV. The expression is:

[0065]

[0066] Step S203, determining a state equation of the convoy system according to the vehicle following model of the variable headway strategy.

[0067] The vehicle following model considering the variable time interval strategy is defined as an abstract function, and the expression is:

[0068]

[0069] In the formula, represents the headway distance of vehicle i.

[0070] When the convoy remains stable, the vehicle following model at the equilibrium point is expressed as:

[0071]

[0072] In the formula, represents the expected headway of vehicle i, Represents the desired speed of the vehicle.

[0073] Assuming that a slight disturbance occurs during the driving of the convoy, the speed and distance between vehicles i will change, so the speed disturbance and spacing disturbance To define,

[0074]

[0075] Derivative the spacing disturbance to obtain the relationship between the headway and speed:

[0076]

[0077] In the formula, x i-1 represents the position of vehicle i-1, x i represents the position of vehicle i.

[0078] The equilibrium point expression of the vehicle following model is linearly approximated by first-order Taylor expansion, and the expression is:

[0079]

[0080] In the formula, represents the speed v of vehicle i i The first derivative with respect to time, a i-1 (t) represents the acceleration of vehicle i-1 at time t, and represents the partial derivatives of vehicle i with respect to velocity, relative velocity and headway. Represents the partial derivative of vehicle i-1 with respect to acceleration. They are respectively expressed as:

[0081]

[0082] The expression of the vehicle following model at the equilibrium point can be further transformed into:

[0083]

[0084] Therefore, the state equation of the fleet system is expressed as:

[0085]

[0086] In the formula, Represents the first-order derivative of the speed disturbance experienced by vehicle i-1 at time t with respect to time t.

[0087] Step S300: constructing a transfer function for speed disturbance according to the car-following model, and determining a basis for determining the stability of the heterogeneous vehicle fleet.

[0088] The stability of the convoy is analyzed by the transfer function method. Based on the definition of the transfer function and the first-order Taylor expansion of the vehicle following model at the equilibrium point when the convoy is in a stable state, the differential equation about the disturbance term is Laplace transformed. After derivation, the transfer function of speed disturbance between two adjacent vehicles is:

[0089]

[0090] Among them, G i (z) represents the transfer function of velocity disturbance, represents the speed disturbance of vehicle i The Laplace transform of represents the speed disturbance of vehicle i-1 Laplace transform of , z represents a complex variable, represents the Laplace transform symbol, represents the vehicle i spacing disturbance The Laplace transform of .

[0091] By setting z = Jω, the transfer function of the velocity disturbance is converted from the Laplace domain to the frequency domain.

[0092]

[0093] In the formula, J represents the imaginary unit, ω represents the frequency, G i (Jω) represents the transfer function of the speed disturbance of vehicle i in the frequency domain.

[0094] Assume that the number of vehicles in the fleet is N, the number of vehicle types is n, and the probability of each vehicle type appearing is p1, p2, ..., p k ..,p n , p k Represents the proportion of the kth type of vehicle, and the transfer function expression of the fleet regarding speed disturbance in the frequency domain is:

[0095]

[0096] In the formula, G(Jω) represents the transfer function of the speed disturbance of the fleet in the frequency domain, Represents the speed disturbance of the Nth vehicle in the frequency domain The Laplace transform of Represents the speed disturbance of the first vehicle in the frequency domain The Laplace transform of It represents the product of the speed disturbance transfer function from the first type of vehicle to the nth type of vehicle in the frequency domain.

[0097] If the fleet maintains overall linear stability, according to the transfer function theory, the following expression needs to be satisfied:

[0098]

[0099] Where n represents the number of vehicle types, p k represents the proportion of the k-th type of vehicles.

[0100] If the fleet contains only one type of vehicle, the fleet is a homogeneous fleet. In this case, formula (20) is transformed into formula (21),

[0101]

[0102] Where G(Jω) represents the transfer function of the speed disturbance of the fleet in the frequency domain.

[0103] Simplifying, we get:

[0104]

[0105] The stability criterion of a homogeneous fleet is shown in formula (23):

[0106]

[0107] Formula (20) can be transformed into:

[0108]

[0109] Therefore, the string stability criterion of the new heterogeneous fleet is as follows:

[0110]

[0111] Furthermore, the stability judgment basis of a homogeneous fleet can be specifically expressed as:

[0112] Combined with formula (23), the stability criterion of a homogeneous fleet is:

[0113]

[0114] In the formula, S CAV , S AV , S CV , S HV They represent the homogeneous fleet stability functions of CAV, AV, CV, and AV, respectively. They represent the CAV vehicle following model at the equilibrium point The partial derivatives of vehicle i’s speed, headway, and relative speed are: Indicates that the CAV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 is They represent the AV vehicle following model at the equilibrium point The partial derivatives of vehicle i’s speed, headway, and relative speed; Indicates that the AV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 is They represent the CV vehicle following model at the equilibrium point The partial derivatives of vehicle i’s speed, headway, and relative speed are: Indicates that the CV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 at They represent the HV vehicle following model at the equilibrium point The partial derivatives of vehicle i's speed, headway, and relative speed are, Indicates that the HV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1.

[0115] Combining formulas (14) and (4)–(7), the vehicle following models of CAV, AV, CV, and HV are at the equilibrium point The partial differential expressions for velocity, relative velocity, headway and acceleration of the preceding vehicle are as follows:

[0116]

[0117] The stability criterion of heterogeneous fleet is as follows:

[0118] According to formula (25), the stability criterion of heterogeneous fleet is:

[0119] S m =P CAV S m,CAV +P AV S m,AV +P CV S m,CV +P HV S m,HV ≥0, (31)

[0120] In the formula,

[0121]

[0122] In the formula, S m represents the stability function of the heterogeneous fleet, S m,CAV represents the stability function of CAVs in a heterogeneous fleet, S m,AV represents the stability function of AVs in a heterogeneous fleet, S m,CV represents the stability function of CV in heterogeneous fleet, S m,HV represents the stability function of HVs in a heterogeneous fleet.

[0123] The partial differential expressions of various vehicle stability functions with respect to speed, relative speed, headway and front vehicle acceleration are shown in equations (27)–(30).

[0124] The following embodiments of the present invention will specifically introduce an example of implementing stability judgment according to the stability criterion given above.

[0125] The left side of formula (26) is defined as the homogeneous fleet stability function S of different vehicle types CAV , S AV , S CV , S HV When the stability function is greater than zero, it means that the current homogeneous fleet is stable. Therefore, the stability curves of the four homogeneous fleets at different equilibrium speeds are plotted, as shown in Figure 3 When the fleet is homogeneous, the stability of the fleet is S CAV >S CV >S HV >S AV The stability of the CAV fleet and the AV fleet is positively correlated with the equilibrium speed, and the CAV fleet is constant and stable, while the AV fleet is constant and unstable.

[0126] The left side of formula (31) is defined as the heterogeneous fleet stability function S m , when S m When ≥0, it means that the heterogeneous fleet is stable. The VTH strategy significantly improves the stability of the heterogeneous fleet, and the unstable equilibrium speed range is smaller. At the same time, the initial penetration rate of CAV and CV also shows a positive correlation with the stability of the heterogeneous fleet, such as Figure 4 and Figure 5 shown.

[0127] Considering the variation of single vehicle penetration, when the initial penetration of CV is 65% or when the initial penetration of CAV is 55%, the heterogeneous fleet will maintain a constant stable state, such as Figure 6 shown.

[0128] The embodiment of the present invention also provides a heterogeneous vehicle fleet stability analysis device considering the time interval strategy, such as Figure 7 As shown, the device comprises:

[0129] The distribution characteristic determination unit 701 is configured to determine the distribution characteristics of vehicles in the heterogeneous vehicle fleet according to the heterogeneity of the vehicle fleet;

[0130] A following model building unit 702 is configured to build a vehicle following model with a variable headway strategy according to vehicle distribution characteristics;

[0131] The judgment basis determination unit 703 is configured to construct a transfer function about speed disturbance according to the vehicle following model and determine a judgment basis for the stability of the heterogeneous vehicle fleet.

[0132] It should be noted that the device structure described in this embodiment and the method described previously belong to the same technical concept, and achieve the same technical effect through the same principle, which will not be repeated here.

[0133] An embodiment of the present invention further provides a readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the method described in any of the above embodiments.

[0134] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some or all of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for analyzing the stability of heterogeneous fleets considering time-to-distance strategies, characterized in that: The method comprises: According to the heterogeneity of the fleet, determine the distribution characteristics of vehicles in the heterogeneous fleet; According to the characteristics of vehicle distribution, a vehicle following model with variable headway strategy is constructed; A transfer function of speed disturbance is constructed according to the vehicle following model, and a basis for determining the stability of a heterogeneous vehicle fleet is determined; According to the vehicle distribution characteristics, a vehicle following model with variable headway strategy is constructed, which includes: Set variable headway strategies under non-connected and connected conditions; Based on the variable headway time strategy under the non-connected condition and the connected condition, a vehicle following model of the variable headway time strategy is constructed; The state equation of the convoy system is determined according to the vehicle following model of the variable headway strategy. Based on the variable headway strategy under the non-connected condition and the connected condition, a vehicle following model of the variable headway strategy is constructed, specifically including: The variable headway strategy under networked conditions is introduced, and the improved CACC model is used to characterize the following behavior of CAV. The expression is as follows: In the formula, x i represents the position of vehicle i, x i-1 represents the position of vehicle i-1, e i represents the error of the headway distance, k1 represents the headway distance control coefficient, k2 represents the relative speed control coefficient, k3 represents the acceleration control coefficient of vehicle i-1, v i represents the speed of vehicle i, v i-1 represents the speed of vehicle i-1, a i represents the acceleration of vehicle i; The variable headway strategy under networked conditions is introduced, and the improved IDM model is used to characterize the following behavior of CV, which is expressed as: In the formula, represents the expected acceleration of vehicle i; represents the maximum acceleration of vehicle i; represents the relative speed of vehicle i; b i Indicates the comfortable deceleration of the vehicle; v f represents the free flow speed; represents the desired distance between vehicles, Indicates the minimum distance between vehicles; represents the actual distance between vehicles i, L represents the length of the vehicle; θ represents the free acceleration index; The variable headway strategy under non-connected conditions is introduced, and the improved ACC model is used to characterize the AV's following behavior. The expression is: The variable headway strategy under non-connected conditions is used to improve the IDM model and characterize the following behavior of HV. The expression is: The state equation of the convoy system is determined according to the vehicle following model of the variable headway strategy, specifically including: The vehicle following model of the variable headway strategy is defined as an abstract function, expressed as: In the formula, f represents the abstract function, t represents the time, represents the headway of vehicle i; When the heterogeneous fleet maintains a stable state, the equilibrium point expression of the vehicle following model is determined as: In the formula, represents the expected headway of vehicle i, represents the expected speed of vehicle i; When a heterogeneous fleet experiences slight disturbance during driving, the speed disturbance of vehicle i at time t is determined by the following formula: and spacing disturbance In the formula, v i (t) represents the speed of vehicle i at time t, represents the headway of vehicle i at time t; Derivative the spacing disturbance to obtain the relationship between the headway and speed: In the formula, represents the result after derivation of the spacing disturbance, represents the first-order derivative of the headway distance of vehicle i with respect to time, and represents the first-order derivative of the displacement of vehicle i-1 and vehicle i with respect to time, v i-1 (t) represents the speed of vehicle i-1 at time t, represents the speed disturbance of vehicle i-1 at time t; The equilibrium point expression of the vehicle following model is linearly approximated by first-order Taylor expansion, and the expression is: In the formula, represents the speed v of vehicle i i The first derivative with respect to time, a i-1 (t) represents the acceleration of vehicle i-1 at time t, f i (v) , and represents the partial derivative of vehicle i with respect to speed, relative speed and headway, Represents the partial derivatives of vehicle i-1 with respect to acceleration, respectively: The equilibrium point expression of the vehicle following model is further transformed into: The expression for determining the state equation of the fleet system is: In the formula, Represents the first-order derivative of the speed disturbance experienced by vehicle i-1 at time t with respect to time t.

2. The method according to claim 1, characterized in that According to the heterogeneity of the fleet, the distribution characteristics of vehicles in the heterogeneous fleet are determined, including: According to the heterogeneity of vehicles in the fleet, the proportion of each type of vehicle in the heterogeneous fleet is calculated by the following formula: Where P CAV , P AV , P CV and P HV They represent the proportions of CAV, AV, CV and HV in the heterogeneous fleet, and p a represents the initial penetration rate of CAV, p b represents the initial permeability of CV.

3. The method according to claim 2, characterized in that The expression of the variable headway strategy under non-connected conditions is: In the formula, represents the variable headway under non-connected conditions, represents a fixed time interval, c v represents the weight coefficient of relative speed, represents the relative speed of vehicle i, v i-1 represents the speed of vehicle i-1, v i represents the speed of vehicle i; The expression of the variable headway strategy under network conditions is: In the formula, represents the variable headway under network conditions, c a represents the weight coefficient of the acceleration of vehicle i-1, a i-1 represents the acceleration of vehicle i-1.

4. The method according to claim 3, characterized in that According to the vehicle following model, a transfer function of speed disturbance is constructed, and a stability judgment basis of a heterogeneous vehicle fleet is determined, including: Based on the first-order Taylor expansion of the vehicle following model at the equilibrium point when the convoy is in a stable state, the Laplace transform of the differential equation about the disturbance term is performed The transfer function between two adjacent vehicles regarding speed disturbance is determined as: Among them, G i (z) represents the transfer function of velocity disturbance, represents the speed disturbance of vehicle i The Laplace transform of represents the speed disturbance of vehicle i-1 Laplace transform of , z represents a complex variable, L represents the Laplace transform symbol, represents the vehicle i spacing disturbance The Laplace transform of Set z = Jω and convert the transfer function of the velocity disturbance from the Laplace domain to the frequency domain: In the formula, J represents the imaginary unit, ω represents the frequency, G i (Jω) represents the transfer function of the speed disturbance of vehicle i in the frequency domain; Assume that the number of vehicles in the fleet is N, the number of vehicle types is n, and the probability of each vehicle type appearing is p1, p2, ..., p k ..,p n , p k Represents the proportion of the kth type of vehicle, and the transfer function expression of the fleet regarding speed disturbance in the frequency domain is: In the formula, G(Jω) represents the transfer function of the speed disturbance of the fleet in the frequency domain, Represents the speed disturbance of the Nth vehicle in the frequency domain The Laplace transform of Represents the speed disturbance of the first vehicle in the frequency domain The Laplace transform of It represents the product of the speed disturbance transfer function from the first type of vehicle to the nth type of vehicle in the frequency domain; The convoy maintains overall linear stability when the following expression is satisfied: Where n represents the number of vehicle types, p k represents the proportion of the k-th type of vehicles; If the fleet contains only one type of vehicle, the fleet is a homogeneous fleet, and formula (20) is transformed into formula (21): Where, |G(Jω)| represents the transfer function of the speed disturbance of the fleet in the frequency domain; Simplifying formula (21) we can obtain: The stability criterion for determining a homogeneous fleet is shown in formula (23): Transform formula (20) into: The criterion for determining the string stability of the new heterogeneous fleet is as follows:

5. The method according to claim 4, characterized in that According to the vehicle following model, a transfer function of speed disturbance is constructed, and a basis for determining the stability of a heterogeneous vehicle fleet is determined, which also includes: Based on formula (23), the stability criterion of the homogeneous fleet is updated as: In the formula, S CAV , S AV , S CV , S HV They represent the homogeneous fleet stability functions of CAV, AV, CV, and AV, respectively. They represent the CAV vehicle following model at the equilibrium point The partial derivatives of vehicle i’s speed, headway, and relative speed are: Indicates that the CAV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 is They represent the AV vehicle following model at the equilibrium point The partial derivatives of vehicle i’s speed, headway, and relative speed; Indicates that the AV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 is They represent the CV vehicle following model at the equilibrium point The partial derivatives of vehicle i’s speed, headway, and relative speed are: Indicates that the CV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 at They represent the HV vehicle following model at the equilibrium point The partial derivatives of vehicle i's speed, headway, and relative speed are, Indicates that the HV vehicle following model is at the equilibrium point The partial derivative of the acceleration of vehicle i-1 at The vehicle following models of CAV, AV, CV and HV at the equilibrium point The partial differential expressions for speed, relative speed, headway and front vehicle acceleration are as follows: According to formula (25), the stability criterion of the heterogeneous fleet is determined as: S m =P CAV S m,CAV +P AV S m,AV +P CV S m,CV +P HV S m,HV ≥0, (31) In the formula, In the formula, S m represents the stability function of the heterogeneous fleet, S m,CAV represents the stability function of CAVs in a heterogeneous fleet, S m,AV represents the stability function of AVs in a heterogeneous fleet, S m,CV represents the stability function of CV in heterogeneous fleet, S m,HV represents the stability function of HVs in a heterogeneous fleet.

6. A device for analyzing the stability of heterogeneous fleets considering time-distance strategies, characterized in that: The device comprises: A distribution characteristic determination unit is configured to determine a distribution characteristic of vehicles in a heterogeneous fleet according to the heterogeneity of the fleet; A following model building unit is configured to build a vehicle following model with a variable headway strategy according to vehicle distribution characteristics; A judgment basis determination unit is configured to construct a transfer function about speed disturbance according to the vehicle following model and determine a judgment basis for stability of the heterogeneous vehicle fleet; The car-following model building unit is further configured as follows: Set variable headway strategies under non-connected and connected conditions; Based on the variable headway time strategy under the non-connected condition and the connected condition, a vehicle following model of the variable headway time strategy is constructed; The state equation of the convoy system is determined according to the vehicle following model of the variable headway strategy. Based on the variable headway strategy under the non-connected condition and the connected condition, a vehicle following model of the variable headway strategy is constructed, specifically including: The variable headway strategy under networked conditions is introduced, and the improved CACC model is used to characterize the following behavior of CAV. The expression is as follows: In the formula, x i represents the position of vehicle i, x i-1 represents the position of vehicle i-1, e i represents the error of the headway distance, k1 represents the headway distance control coefficient, k2 represents the relative speed control coefficient, k3 represents the acceleration control coefficient of vehicle i-1, v i represents the speed of vehicle i, v i-1 represents the speed of vehicle i-1, a i represents the acceleration of vehicle i; The variable headway strategy under networked conditions is introduced, and the improved IDM model is used to characterize the following behavior of CV, which is expressed as: In the formula, represents the expected acceleration of vehicle i; represents the maximum acceleration of vehicle i; represents the relative speed of vehicle i; b i Indicates the comfortable deceleration of the vehicle; v f represents the free flow speed; represents the desired distance between vehicles, Indicates the minimum distance between vehicles; represents the actual distance between vehicles i, represents the headway of vehicle i, L represents the vehicle length; θ represents the free acceleration index; The variable headway strategy under non-connected conditions is introduced, and the improved ACC model is used to characterize the AV's following behavior. The expression is: The variable headway strategy under non-connected conditions is used to improve the IDM model and characterize the following behavior of HV. The expression is: The state equation of the convoy system is determined according to the vehicle following model of the variable headway strategy, specifically including: The vehicle following model of the variable headway strategy is defined as an abstract function, expressed as: In the formula, f represents the abstract function, and t represents the time; When the heterogeneous fleet maintains a stable state, the equilibrium point expression of the vehicle following model is determined as: In the formula, represents the expected headway of vehicle i, represents the expected speed of vehicle i; When a heterogeneous fleet experiences slight disturbance during driving, the speed disturbance of vehicle i at time t is determined by the following formula: and spacing disturbance In the formula, v i (t) represents the speed of vehicle i at time t, represents the headway of vehicle i at time t; Derivative the spacing disturbance to obtain the relationship between the headway and speed: In the formula, represents the result after derivation of the spacing disturbance, represents the first-order derivative of the headway distance of vehicle i with respect to time, and represents the first-order derivative of the displacement of vehicle i-1 and vehicle i with respect to time, v i-1 (t) represents the speed of vehicle i-1 at time t, represents the speed disturbance of vehicle i-1 at time t; The equilibrium point expression of the vehicle following model is linearly approximated by first-order Taylor expansion, and the expression is: In the formula, represents the speed v of vehicle i i The first derivative with respect to time, a i-1 (t) represents the acceleration of vehicle i-1 at time t, f i (v) , and represents the partial derivative of vehicle i with respect to speed, relative speed and headway, Represents the partial derivatives of vehicle i-1 with respect to acceleration, respectively: The equilibrium point expression of the vehicle following model is further transformed into: The expression for determining the state equation of the fleet system is: In the formula, Represents the first-order derivative of the speed disturbance experienced by vehicle i-1 at time t with respect to time t. 7 . A non-transitory computer-readable storage medium storing instructions, which, when executed by a processor, executes the method according to claim 1 .

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