Continuous traffic flow state deduction method under influence of intelligent network connection vehicle

Abstract

The invention discloses a continuous traffic flow state deduction method under the influence of an intelligent network connection vehicle, and relates to the technical field of traffic flow state evolution models. Comprising the following steps: S1, establishing a road state evolution model on the basis of a first-order macroscopic traffic flow model without considering CAV, and solving the established road state evolution model to obtain a basic framework of an HV and CAV mixed traffic flow state evolution model; and S2, modeling CAVs at different speeds based on a mobile bottleneck theory, calculating the influence of the CAVs on the road traffic evolution process, and combining with the basic framework of the HV and CAV mixed traffic flow state evolution model in the S1 to establish a state evolution model considering the combined action of the road bottleneck and the CAVs. According to the method, factors such as lane changing behaviors and acceleration behaviors of road vehicles and speeds of moving bottleneck vehicles are fully considered, and the vehicle passing rate can be accurately calculated; and on the premise of giving the initial condition of the road, the road state evolution result of the road under the mutual influence of one or more CAVs can be efficiently and accurately calculated, the road state of a certain space-time position or a certain space-time region can be accurately solved, and the result can be used for traffic management and control.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic flow state evolution models, and in particular to a method for deducing continuous traffic flow states under the influence of intelligent networked vehicles. Background Art

[0002] By controlling the Connected and Automated Vehicle (CAV), the behavior of the surrounding human-driven vehicles (HV) can be affected, achieving the effect of "controlling flow with particles". However, in the existing macro-modeling research on the evolution of continuous flow states, there are limitations in the analysis of road state evolution under the influence of different numbers of CAVs, and it is difficult to flexibly calculate the interaction and influence between different vehicles on the road. The existing macro-model based on the basic graph has low flexibility and is difficult to reflect the behavior of CAVs under different permeability rates in the road and to dynamically analyze the mutual influence between CAVs on the road; the method based on probability theory and acceptable gap theory can analyze various interactions between CAVs, but requires preset trajectories; the existing research on modeling CAVs using the mobile bottleneck theory adopts a fixed pass rate, which will produce large errors when predicting the evolution of road states and cannot effectively analyze the impact of CAVs on mixed traffic flows.

[0003] Therefore, it is an urgent problem for technical personnel in this field to propose a method for deducing continuous traffic flow states under the influence of intelligent connected vehicles to solve the difficulties existing in the prior art. Summary of the invention

[0004] In view of this, the present invention provides a method for deducing continuous traffic flow states under the influence of intelligent connected vehicles, which solves the technical problem that large errors will be generated when predicting road state evolution and the impact of CAV on mixed traffic flow cannot be effectively analyzed.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for deducing continuous traffic flow state under the influence of intelligent networked vehicles comprises the following steps:

[0007] S1. Without considering the CAV, a road state evolution model is established based on the first-order macro traffic flow model, and the established road state evolution model is solved to obtain the basic framework of the mixed traffic flow state evolution model of human-driven vehicles HV and CAV;

[0008] S2. Based on the mobile bottleneck theory, networked autonomous driving vehicles (CAV) of different speeds are modeled, and their impact on the road traffic evolution process is calculated. Combined with the basic framework of the mixed traffic flow state evolution model of manually driven vehicles HV and networked autonomous driving vehicles CAV in S1, a state evolution model considering the joint effects of road bottlenecks and networked autonomous driving vehicles CAV is established.

[0009] In the above method, optionally, the basic framework of the mixed traffic flow state evolution model of the manually driven vehicle HV and the connected autonomous driving vehicle CAV in S1 is determined according to the conservation rate, the LWR model and the Hamilton-Jacobi equation, including the following steps:

[0010] S111. Calculation of conservation rate:

[0011] In the basic section of the highway 1 to x 2 In the area, the road section has no entrance or exit, and the vehicle travels normally for Δt time and Δt = t 2 -t 1 , let N 1 , N 2 They are respectively passing through the section x in the time Δt 1 , x 2 The number of vehicles, q 1 ,q 2 They are respectively passing through the section x in the time Δt 1 , x 2 The average flow rate is Area [x 1 ,x 2 ]The number of vehicle changes in Δt time is ΔN = N 2 -N 1 =ΔqΔt, where ΔN is greater than 0, indicating that the number of vehicles exiting the road section is greater than the number of vehicles entering the road section;

[0012] Assume that the region [x 1 ,x 2 ] in the section of t 1 , t 2 The average vehicle density at each time is k 1 , k 2 , since there is no entrance or exit on the road section, let Δx = x 2 -x 1 , then the area [x 1 ,x 2 The cumulative number of vehicle changes ΔN within Δt is expressed as: ΔN = k 1 Δx-k 2 Δx=-ΔkΔx; we get ΔkΔx+ΔqΔt=0, and further we get: If we set Δt→0, Δx→0, we get the following conservation equation, also called conservation rate: Where k(t,x) and q(t,x) represent the instantaneous density and instantaneous flow of the road at position x at time t, respectively;

[0013] S112. Determine the state evolution model using the LWR model and Hamilton-Jacobi equation:

[0014] In the LWR model, it is assumed that the basic traffic map exists, that is, q = Q (k), where Q is a function of the flow and density in the basic traffic map. Substituting the above formula into the conservation rate formula, we get: Let N(t,x) represent the cumulative number of vehicles passing through position x at time t. By default, the function numbers the vehicles in ascending order according to their appearance. When the vehicle numbered n passes through the road position x at time t, then N(t,x)=n, and N(t,x)>0, which increases monotonically for the time variable t. According to the definition of flow, the instantaneous flow of the road section at a certain time and the instantaneous density of the road section at a certain time are obtained as follows:

[0015]

[0016] Assuming that N(t,x) is second-order differentiable, the Hamilton-Jacobi equation is obtained as follows. Among them, the flow-density function Q is the Hamiltonian operator of the equation. By solving this equation, the road state parameters at any spatiotemporal position of the road can be obtained, and then the spatiotemporal evolution of the road state can be analyzed at the macro level.

[0017]

[0018] The above method is optional. In S1, the road state evolution model established by using the boundary condition, the Hopf-Lax formula and the triangle basic diagram in the absence of a networked autonomous driving vehicle CAV mainly includes the following steps:

[0019] S121. Consider the solution conditions:

[0020] Establish a coordinate system, where the horizontal axis represents time, the vertical axis represents distance, and the origin of the coordinate represents the time t=0 and the starting point x of the road 0 ; Consider the following problem of solving the Hamilton-Jacobi equation:

[0021]

[0022] in, Represents the road space-time region boundary: g(r,y) represents the solution condition, which consists of three parts: Road upstream input flow function and the maximum downstream output flow function of the road The formula is as follows:

[0023]

[0024] S122. Use the Hopf-Lax formula to solve the Hamilton-Jacobi equation:

[0025] First, we introduce the Legendre transform: for smooth convex functions and any definition: Q * (p) is the Legendre transformation induced by the function Q; the Hopf-Lax formula means that for the well-defined problem of the Hamilton-Jacobi equation, the Hamilton operator Q that satisfies the convex function condition is used to define the function L and the solution u(t,x) of the equation, which can be expressed as:

[0026]

[0027]

[0028] Among them, g(r,y) represents the solution condition, r and y represent the initial time and initial position respectively;

[0029] S123. Model solution based on triangle basic graph:

[0030] The flow-density function Q in the triangular basic graph is defined as follows, where v f is the free flow speed and the characteristic wave speed in non-congested conditions, k c is the critical density, k is the blocking density, -ω is the characteristic wave speed during congestion; let C = k c v f , Substituting Q(k) into the previous equation and performing Legendre transformation on it, we can obtain L(u), where u∈[ω,v f ],C=k c v f Substituting L(u) into the Hopf-Lax formula, we get the final result N(t,x):

[0031]

[0032] S124. Solve the general well-defined problem by solving the algorithm:

[0033] Let the initial road density be a piecewise linear function, divide the road into multiple small sections, and the density of each section at the initial moment is a linear function, expressed as: Similarly, the flow input at the starting point of the road at the future moment is expressed as a piecewise linear function, which is expressed as: Where i and j are the segment numbers of position and time respectively, k(t 0 ,x) represents the road at the initial time t 0 , the density at position x, q(t,x 0 ) and q(t,x n ) represent the starting point x of the road 0 At time t, the flow input and the road end point x n The maximum passable flow at time t; the corresponding cumulative vehicle number function is calculated and used as the initial condition and boundary condition, expressed as:

[0034]

[0035] in, are all piecewise linear functions, i and j are the segment numbers of position and time respectively. It represents the cumulative number of vehicles at the road section position x at the initial time, with the subscript t 0 represents the initial time, is the initial condition, Represents the initial position x of the road segment 0 The cumulative number of vehicles at the location is denoted by the subscript t 0 represents the initial moment, is the boundary condition, Indicates the end position x of the road segment 0 The cumulative number of vehicles at the location is denoted by the subscript t 0 represents the initial time, is the boundary condition, and the function Together they form the solution condition of the equation, corresponding to the previous N(r,y);

[0036] S125. Substitute the flow-density function Q in the basic triangular traffic diagram and calculate the solutions under its individual action respectively; the solution results can be divided into four types:

[0037] (1) Consider only the initial conditions When in effect:

[0038] Let x∈[x i ,x i+1 ) When 0≤k i ≤k c , and get N i (t,x), where D 1 , D 2 Represents a specified area on a plane. The density k is obtained according to the definition i (t,x).

[0039]

[0040] (2) Consider only the initial conditions When in effect:

[0041] Let x∈[x i ,x i+1 ) When k c ≤k i When ≤κ:

[0042]

[0043] (3) Consider only boundary conditions When in effect:

[0044] Let t∈[t j ,t j+1 ) is the road upstream flow input: Assume that in the flow-density function, The two solutions of f ,k b , where k f ≤k b ,available:

[0045]

[0046] 4) Consider only boundary conditions When in effect:

[0047] Let t∈[t j ,t j+1 ) is the maximum output of the road end flow rate. Assume that in the flow-density function, The two solutions of f ,k b , where k f ≤k b ,available:

[0048]

[0049]

[0050] S126. According to the Hopf-Lax formula, for any point (t, x) in the solution region, the solution under the complete solution condition is as follows, where N i represents the i-th initial / boundary condition, i min Indicates the number corresponding to the minimum value.

[0051]

[0052] In the above method, optionally, in S2, modeling of connected autonomous driving vehicles CAVs of different speeds based on the mobility bottleneck theory is performed to calculate their impact on the road traffic evolution process, including the following steps:

[0053] S211 establishes internal boundary conditions:

[0054] When the speed of CAV and the passing rate of CAV are known, the flow-density relationship in the basic graph of the road is expressed as q = min{Q(k),q r +kv mb}express.

[0055] There is a CAV with a constant speed on the multi-lane road. Its appearance time on the road is t s , the position of occurrence is x s , when the road density k∈[0,k u' ], that is, the speed of the connected autonomous vehicle CAV is lower than the average speed of the road and it travels at its own speed. Let the trajectory of the connected autonomous vehicle CAV be AB, which can be expressed as: x = x s +v mb (tt s ).

[0056] If the time when the uniform speed connected autonomous driving vehicle CAV leaves the road is t e , and during the driving period of the CAV with a uniform speed, t∈[t s ,t e ], the connected autonomous driving vehicle CAV is always in an effective state, that is, the road density k∈[k d ,k u ]; If the passing rate of the connected autonomous driving vehicle CAV is q r , then for each point on the AB line segment of the CAV motion trajectory, the corresponding cumulative number of vehicles N int For: N int (t) = N s +q r (tt s ) t∈[t s ,t e ],x=x s +v mb (tt s ).

[0057] Line segment AB is used as a solution condition. Under this condition alone, the solution is:

[0058]

[0059] Where D1 , D 2 , D 3 represents the specified area of ​​the plane, Δx is an intermediate variable, representing the relative distance:

[0060]

[0061] S212. Calculate the traffic volume under the influence of connected autonomous driving vehicles (CAV):

[0062] Taking the CAV as the reference system, the traffic on the road near the CAV is in a steady state, that is, in the moving coordinate system. When the CAV maintains a constant speed, the flow and density at any instantaneous cross-sectional position of the road near it remain unchanged, which can be expressed as: Combining the conservation laws, we get:

[0063] Assuming the instantaneous flow rate of any section of the road in the area is q, and the instantaneous density at the section position x is k(x), the average instantaneous speed of the vehicle at the section position is calculated as: The average instantaneous acceleration of the vehicle at the cross-section position is:

[0064] When the road is not congested, that is, the road density is less than the critical density k∈[0,k c ), the average speed, average density and average acceleration at the road section position x in the non-congested state are: v(x)=v f , a(x)=0; when the road is congested, that is, the road density is greater than the critical density k∈[k c ,κ], and substitute into the flow-density function Q, the average speed, average density and average acceleration at the road section position x under the congestion state are calculated, which are expressed as:

[0065]

[0066] Where Δl = l 1 -l 2 represents the number of lane reductions, q 0 =ωκ, which is an intermediate variable.

[0067] In the above method, the upper limit of the vehicle's acceleration is optional and is related to the vehicle speed. The bounded acceleration model A(v) represents the upper limit of the vehicle's acceleration at the current speed. The bounded acceleration model A(v) should satisfy: 1. A(v) ≥ 0, v ∈ [0, v f ],v f is the free flow velocity; 2.A(v)≤a 0 , a 0It is the maximum acceleration of the vehicle during normal driving; 3. A'(v)≤0, which means that the greater the vehicle's driving speed, the smaller the upper limit of acceleration.

[0068] The linear bounded acceleration model is used as an effective approximation of the average acceleration of the vehicle. Based on the moving reference system, the flow-density function Q and the linear bounded acceleration model A(v) in the triangular basic diagram are modified to obtain the flow-density function Q and the linear bounded acceleration model A'(v) based on the moving reference system:

[0069] Q′(k)=Q(k)-v mb ·k

[0070]

[0071] Among them, v mb is the speed of the reference frame, i.e., the speed of the CAV;

[0072] From the above formula, we can see that a is calculated from the cross-section position x, and the function f is defined as: Among them, f(x; q) ≤ 0, and A'(v) ≤ 0, v(x) and a(x) increase monotonically with the independent variable x, then f(x; q) increases monotonically with x, let x = L, substitute into the linear bounded acceleration model A'(v) based on the moving reference system, and simplify to get:

[0073]

[0074] Among them, f(L;q) increases monotonically with q. r is the maximum passing rate of the connected autonomous driving vehicle CAV, satisfying: f(L;q r )=0; The average flow rate of overtaking connected autonomous driving vehicles CAV on the road is obtained under the condition of meeting the bounded acceleration limit.

[0075] The above method, optionally, in S2, based on the influence of connected autonomous driving vehicles CAV at different speeds on the road traffic evolution process, predicting the trajectory of the connected autonomous driving vehicle CAV and calculating the road state evolution, comprises the following steps:

[0076] S221. Single Connected Autonomous Vehicle (CAV) scenario:

[0077] There is a CAV with a constant low speed on the road, and its initial time and space position is (t 0 ,x 0 ), with a velocity of v mb , taking the single connected autonomous driving vehicle CAV as an example, the vehicle trajectory is predicted and the internal boundary conditions are obtained. The specific contents are as follows:

[0078] Step (1): Calculate the current speed of the connected autonomous vehicle CAV at v mb The maximum passing rate q r ;

[0079] Step (2): Calculate the current spatiotemporal position (t mb ,x mb ) under the road cumulative number of vehicles N mb , average road density k mb ; Taking the current position as the starting point, the speed v of the current connected autonomous driving vehicle CAV mb Add a virtual trajectory to the coordinates for the slope and calculate the internal boundary conditions, expressed as: x = x 0 +v mb (tt 0 )t∈[t 0 ,t max ]、N virt-int (x,)t=N mb , where t max It is the maximum time of the road space-time region in the model;

[0080] Step (3): Based on the k calculated in step (1), 0 CAV state classification of connected autonomous driving vehicles, when k∈[0,k d )∪(k u ,k i' ], the networked autonomous driving vehicle CAV is in an invalid state, and the road traffic will not be subject to the networked autonomous driving vehicle CAV. The space-time position of the next iteration cycle of the networked autonomous driving vehicle CAV is (t mb +Δt,x mb +v mb Δt); if k∈(k u' ,κ], at this time, the networked autonomous driving vehicle CAV is in an invalid state and has no effect on road traffic, but the road is congested at this time, and the average vehicle speed will be lower than v mb , at this time the networked autonomous driving vehicle CAV cannot maintain its own speed, calculate the networked autonomous driving vehicle CAV speed v' mb , update the spatiotemporal position of the next iteration cycle of the connected autonomous driving vehicle CAV to (t mb +Δt,x mb +v' mb Δt), and delete all virtual trajectories and their corresponding internal boundary conditions; when k∈[k d ,k u], the CAV is in a valid state, that is, the road traffic is restricted by the CAV, and the internal boundary conditions in the updated solution algorithm are:

[0081]

[0082] At the same time, the time and space position of the next iteration cycle of the connected autonomous driving vehicle CAV is updated as (t mb +Δt,x mb +v mb Δt);

[0083] Step (4): Determine whether the connected autonomous driving vehicle CAV has left the road section, that is, determine whether the space-time position of the vehicle at the next moment exceeds the solution area. If it does not exceed the solution area, return to step (2); otherwise, end the calculation and obtain the updated internal boundary conditions;

[0084] S222. Multiple connected autonomous vehicles (CAVs):

[0085] There are n uniform and low-speed connected autonomous driving vehicles CAV on the road, and the CAV number set is P = {1, 2, ..., n}. Let the initial spatiotemporal position of the connected autonomous driving vehicle CAV be Its own speed is The following steps are used to calculate the vehicle trajectory and its internal boundary conditions in the multi-connected autonomous driving vehicle CAV scenario:

[0086] Step (1): Calculate the speed of the connected autonomous vehicle CAV i The maximum pass rate under

[0087] Step (2): sort the connected autonomous driving vehicles CAVs in set P from downstream to upstream according to their positions on the road, to obtain set M;

[0088] Step (3): Traverse the elements in the set M, and then calculate the trajectory of CAVi within each iteration period Δt according to the steps in the above single-network autonomous driving vehicle CAV algorithm, update the vehicle position and solve the internal boundary conditions N in the algorithm. int (x, t); then determine whether the i-th connected autonomous driving vehicle CAV has left the solution area. If it has left the solution area, delete the vehicle number from the connected autonomous driving vehicle CAV set P;

[0089] Step (4): After deleting the vehicle number, reorder the connected autonomous driving vehicles CAV in the set from downstream to upstream according to their positions on the road, and update the set M;

[0090] Step (5): When the connected autonomous driving vehicle CAV set P is not empty, return to step (3), otherwise end the calculation; and obtain the solution algorithm after updating the internal boundary conditions.

[0091] It can be seen from the above technical solutions that, compared with the prior art, the method for deducing continuous traffic flow state under the influence of intelligent networked vehicles of the present invention has the following beneficial effects:

[0092] (1) Accurately calculate vehicle passing rate: fully consider factors such as the lane-changing behavior, acceleration behavior, and the speed of the mobile bottleneck vehicle, and accurately calculate the vehicle passing rate;

[0093] (2) Considering the impact of intelligent connected vehicles: Given the initial conditions of the road, the road state evolution results under the influence of one or more CAVs are calculated efficiently and accurately;

[0094] (3) High solution efficiency: It can accurately solve the road status at a certain time and space location or a certain time and space area, and the results can be used for traffic management and control. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0096] Figure 1 A flow chart of a method for deducing a continuous traffic flow state under the influence of an intelligent networked vehicle disclosed in the present invention;

[0097] Figure 2 A schematic diagram of the vehicle conservation area disclosed in the present invention;

[0098] Figure 3 Solving the model under the piecewise linear boundary conditions disclosed in the present invention;

[0099] Figure 4 It is a basic diagram of the networked autonomous driving vehicle disclosed in the present invention;

[0100] Figure 5 It is a schematic diagram of the internal boundary conditions disclosed in the present invention;

[0101] Figure 6 The road state evolution diagram without CAV influence disclosed in the present invention;

[0102] Figure 7 This is a diagram of the road state evolution under the influence of a single CAV disclosed in the present invention.

[0103] Figure 8 This is a road state evolution diagram under the influence of multiple CAVs disclosed in the present invention.

[0104] Fig. 9 The road state evolution diagram for calculating the passing rate based on the maximum traffic capacity disclosed in the present invention;

[0105] Fig.10 10(a) is a numerical calculation result, and 10(b) is a simulation result.

[0106] Fig.11 11(a) is a comparison of the road state evolution results of the mixed flow scenario disclosed in the present invention, wherein 11(b) is the simulation result, 11(c) is the model result of this study, and 11(c) is the maximum peer capability model result. DETAILED DESCRIPTION

[0107] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0108] In this application, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0109] The present invention can be used in many general or special computing device environments or configurations, such as personal computers, server computers, handheld or portable devices, tablet devices, multi-processor devices, distributed computing environments including any of the above devices or devices, etc.

[0110] Reference Figure 1 As shown, the present invention discloses a method for deducing a continuous traffic flow state under the influence of an intelligent networked vehicle, comprising the following steps:

[0111] S1. Without considering CAV, a road state evolution model is established based on the first-order macro traffic flow model, and the established road state evolution model is solved to obtain the basic framework of the mixed traffic flow state evolution model of HV and CAV;

[0112] S2. Based on the mobile bottleneck theory, networked autonomous driving vehicles (CAVs) of different speeds are modeled, and their impact on the road traffic evolution process is calculated. Combined with the basic framework of the HV and networked autonomous driving vehicle (CAV) mixed traffic flow state evolution model in S1, a state evolution model that considers the joint effects of road bottlenecks and networked autonomous driving vehicles (CAVs) is established.

[0113] Furthermore, the basic framework of the mixed traffic flow state evolution model of HV and connected autonomous driving vehicle CAV in S1 is determined based on the conservation rate, LWR model and Hamilton-Jacobi equation, including the following steps:

[0114] S111. Calculation of conservation rate:

[0115] Establish as attached Figure 2 In the scene, x 1 to x 2 In the area, the road section has no entrance or exit, and the vehicle travels normally for Δt time and Δt = t 2 -t 1 , let N 1 , N 2 They are respectively passing through the section x in the time Δt 1 , x 2 The number of vehicles, q 1 ,q 2 is the cross section x 1 , x 2 The average flow rate is Area [x 1 ,x 2 ]The number of vehicle changes in Δt time is ΔN = N 2 -N 1 =ΔqΔt;

[0116] Assume that the region [x 1 ,x 2 ] in the section of t 1 , t 2 The average vehicle density at each time is k 1 , k 2 , since there is no entrance or exit on the road section, let Δx = x 2 -x 1 , then the area [x 1 ,x 2The cumulative number of vehicle changes ΔN within Δt is expressed as: ΔN = k 1 Δx-k 2 Δx=-ΔkΔx; we get ΔkΔx+ΔqΔt=0, and further we get: If we set Δt→0, Δx→0, we get the following conservation equation, also called conservation rate: Where k(t,x) and q(t,x) represent the instantaneous density and instantaneous flow respectively;

[0117] S112. Determine the state evolution model using the LWR model and Hamilton-Jacobi equation:

[0118] The LWR model is applicable to situations where the road state changes with time and location but is always in a state of equilibrium, that is, it satisfies the conservation rate scenario. In the LWR model, it is assumed that the basic traffic graph exists, that is: q = Q(k), where Q represents the function of flow and density, and substituting it into the conservation rate formula yields:

[0119] Let N(t,x) represent the cumulative number of vehicles passing through position x at time t. By default, the function numbers the vehicles in ascending order according to their appearance. When the vehicle numbered n passes through the road position x at time t, then N(t,x)=n, and N(t,x)>0, which increases monotonically for the time variable t. According to the flow definition, the instantaneous flow and instantaneous density of the road section at a certain time are obtained as follows:

[0120]

[0121] Assuming that N(t,x) is second-order differentiable, we get the Hamilton-Jacobi equation:

[0122]

[0123] Among them, the flow-density function Q is the Hamiltonian operator of the equation. Solving the equation can obtain the road state parameters at any spatiotemporal position of the road, and then realize the analysis of the spatiotemporal evolution of the road state at the macro level.

[0124] Furthermore, the road state evolution model established in S1 using the boundary condition, the Hopf-Lax formula and the triangle basic diagram in the absence of a connected autonomous driving vehicle CAV mainly includes the following steps:

[0125] S121. Consider the solution conditions:

[0126] Generally, it is difficult to directly solve the partial differential equation. Instead, a special solution that satisfies certain conditions is sought. These conditions are called the fixed solution conditions. In the state evolution problem discussed in the present invention, the road should meet certain conditions. For example, the initial density value of the road, this condition is called the initial condition.

[0127] Consider the following problem of solving the Hamilton-Jacobi equation:

[0128]

[0129] in, Represents the road space-time region boundary: g(r,y) represents the solution condition, which consists of three parts: Road upstream input flow function and the maximum downstream output flow function of the road

[0130]

[0131] S122. Use the Hopf-Lax formula to solve the Hamilton-Jacobi equation:

[0132] First, we introduce the Legendre transform: for a smooth convex function Q: and any definition: Q * (p) is the Legendre transformation induced by the function Q; the Hopf-Lax formula means that for the well-defined problem of the Hamilton-Jacobi equation, the Hamilton operator Q that satisfies the convex function condition is used to define the function L and the solution u(t,x) of the equation, which can be expressed as:

[0133]

[0134] Among them, g(r,y) represents the solution condition, r, y represent the initial time and initial position;

[0135] From a physical perspective, u(t,x) can be intuitively interpreted as the value of the cumulative number of vehicles at a given time t and position x in the road space-time area is equal to the minimum value obtained from all possible initial points (r,y). This reflects the connection between the Hamilton-Jacobi equation and the convex function. In this way, the problem of solving partial differential equations can be transformed into an optimization problem, thereby simplifying the calculation.

[0136] S123. Model solution based on triangle basic graph:

[0137] The flow-density function Q in the triangular basic graph is defined as follows, where v f is the free flow speed and the characteristic wave speed in non-congested conditions, k c is the critical density, κ is the blocking density, -ω is the characteristic wave speed during congestion; let C = k c v f , Substituting Q(k) into the previous equation and performing Legendre transformation on it, we can obtain L(u), where u∈[ω,v f ],C=k c v f Substituting L(u) into the Hopf-Lax formula, we get the final result N(t,x):

[0138]

[0139] S124. Solve the general well-defined problem by solving the algorithm:

[0140] As attached Figure 3 ,The general well-defined problem is solved by the solution algorithm. In order to facilitate modeling and solving, the initial road density is set as a piecewise linear function to approximate the actual situation.

[0141] Let the initial road density be a piecewise linear function, divide the road into multiple small sections, and the density of each section at the initial moment is a linear function, expressed as: Similarly, the flow input at the starting point of the road at the future moment is expressed as a piecewise linear function, which is expressed as: Where i and j are the segment numbers of position and time respectively, k(t 0 ,x) represents the road at the initial time t 0 , the density at position x, q(t,x 0 ) and q(t,x n ) represent the starting point x of the road 0 At time t, the flow input and the road end point x n The maximum passable flow at time t; the corresponding cumulative vehicle number function is calculated and used as the initial condition and boundary condition, expressed as:

[0142]

[0143] in, are all piecewise linear functions, i and j are the segment numbers of position and time respectively. It represents the cumulative number of vehicles at the road section position x at the initial time, with the subscript t 0 represents the initial time, is the initial condition, Represents the initial position x of the road segment 0The cumulative number of vehicles at the location is denoted by the subscript t 0 represents the initial moment, is the boundary condition, Indicates the end position x of the road segment 0 The cumulative number of vehicles at the location is denoted by the subscript t 0 represents the initial time, is the boundary condition, and the function Together they form the solution condition of the equation, corresponding to the previous N(r,y);

[0144] S125. Substitute the flow-density function Q in the basic triangular traffic diagram and calculate the solutions under its individual action respectively; the solution results can be divided into four types:

[0145] (1) Consider only the initial conditions When in effect:

[0146] Let x∈[x i ,x i+1 ) When 0≤k i ≤k c , and get N i (t,x), where D 1 , D 2 Represents a specified area on a plane. The density k is obtained according to the definition i (t,x).

[0147]

[0148] (2) Consider only the initial conditions When in effect:

[0149] Let x∈[x i ,x i+1 ) When k c ≤k i When ≤κ:

[0150]

[0151] (3) Consider only boundary conditions When in effect:

[0152] Let t∈[t j ,t j+1 ) is the road upstream flow input: Assume that in the flow-density function, The two solutions of f ,k b , where k f ≤k b ,available:

[0153]

[0154] 4) Consider only boundary conditions When in effect:

[0155] Let t∈[t j ,t j+1 ) is the maximum output of the road end flow rate. Assume that in the flow-density function, The two solutions of f ,k b , where k f ≤k b ,available:

[0156]

[0157]

[0158] S126. According to the Hopf-Lax formula, for any point (t, x) in the solution region, the solution under the complete solution condition is as follows, where N i represents the i-th initial / boundary condition, i min Indicates the number corresponding to the minimum value.

[0159]

[0160] Furthermore, S2 models CAVs of different speeds based on the mobility bottleneck theory and calculates their impact on the road traffic evolution process, including the following steps:

[0161] S211 establishes internal boundary conditions:

[0162] For CAV, internal boundary conditions can be established to calculate the evolution of road conditions under the action of CAV at low speed. Figure 4 , based on the basic triangular diagram, consider the velocity v mb The uniform speed connected autonomous driving vehicle CAV, let q r is the passing rate of CAV, that is, the average flow rate of CAVs passing low-speed CAVs per unit time on a multi-lane road. Points A and C are a straight line q = q r +kv mb The intersection points with the basic graph have corresponding densities k d , k u , k d <k u , point D is the straight line q=kv mb The intersection with the basic graph has a corresponding density of k u'The road flow q can be expressed as: q = min {Q(k), q r +kv mb}.

[0163] At a constant speed CAV v mb Under the action of , the basic road traffic diagram becomes a quadrilateral OACE. d ,k u ], the maximum road flow is q = q r +kv mb , indicating that the road traffic is restricted by the low-speed CAV, and the CAV is defined as being in an “effective state”. If the length of the CAV is ignored, then k d ,k u are the flow rates downstream and upstream of the connected autonomous vehicle CAV, respectively. d )∪(k u ,κ], the road traffic will not be subject to the CAV, and the CAV is defined as being in an “invalid state”. In addition, when k∈(k u' ,κ], the average speed of road vehicles will be lower than v mb , the connected autonomous vehicle CAV is affected by the traffic on the road and cannot maintain its own speed v mb , at this time, the speed v' of the connected autonomous driving vehicle CAV mb It can be found through the flow-density function in the original basic graph:

[0164]

[0165] When the speed of the CAV and the passing rate of the CAV are known, the flow-density relationship in the basic graph of the road is expressed as q = min{Q(k),q r +kv mb}express;

[0166] See also Figure 5 As shown in Figure 2, there is a CAV with a constant speed in the multi-lane road, and its appearance time on the road is t. s , the position of occurrence is x s , when the road density k∈[0,k u' ], that is, the speed of the connected autonomous vehicle CAV is lower than the average speed of the road and it travels at its own speed. Let the trajectory of the connected autonomous vehicle CAV be AB, which can be expressed as: x = x s +v mb (tt s ). If the time when the uniform speed connected autonomous driving vehicle CAV leaves the road is te , and during the driving period of the CAV with a uniform speed, t∈[t s ,t e ], the connected autonomous driving vehicle CAV is always in an effective state, that is, the road density k∈[k d ,k u ]; If the passing rate of the connected autonomous driving vehicle CAV is q r , then for each point on the AB line segment of the CAV motion trajectory, the corresponding cumulative number of vehicles N int For: N int (t) = N s +q r (tt s )t∈[t s ,t e ],x=x s +v mb (tt s );

[0167] Line segment AB is used as a solution condition, that is, an internal boundary condition. Under the action of this internal boundary condition alone, the solution is:

[0168]

[0169] Where D 1 , D 2 , D 3 represents the specified area of ​​the plane, Δx is an intermediate variable, representing the relative distance:

[0170]

[0171] The above formula can be used to calculate the cumulative number of vehicles and road density at any point (t, x) in the road space-time area under all fixed solution conditions, and the calculation complexity is only related to the number of fixed solution conditions.

[0172] S212. Calculate the traffic volume under the influence of connected autonomous driving vehicles (CAV):

[0173] When solving the internal boundary conditions and using the Hopf-Lax formula, the key parameter is the CAV pass rate q r , which represents the average flow of CAV vehicles that overtake low-speed CAV vehicles per unit time on a multi-lane road. The present invention will model and solve the CAV passing rate from a meso-level, and apply it in a framework based on the Hopf-Lax formula.

[0174] Consider a three-lane scenario with a CAV with a uniform speed of v mbWhen a conventional vehicle overtakes the vehicle in front by overtaking, it will change lanes in advance behind the vehicle, thereby generating a lane reduction area. Here, it is assumed that the length of this area is L. For the convenience of modeling and calculation, a one-dimensional moving coordinate system is established along the direction of vehicle travel on the road, and the moving speed of the coordinate system is v mb , that is, it remains relatively stationary with the CAV. Assuming that the lane change in the lane reduction area is linear, the number of road lanes l in the lane reduction area x∈[0,L] can be expressed as follows, where l 1 and l 2 Respectively represent the number of lanes before and after lane reduction.

[0175]

[0176] Taking the CAV as the reference system, the traffic on the road near the CAV is in a steady state, that is, in the moving coordinate system. When the CAV maintains a constant speed, the flow and density at any instantaneous cross-sectional position of the road near it remain unchanged, which can be expressed as: Combining the conservation laws, we get: Its physical meaning is that under steady-state conditions, the instantaneous flow rate of any section of the road is the same. Here, it is represented as the area near the vehicle. The fewer the number of road lanes, the greater the instantaneous density of road vehicles. That is, the road traffic is simplified into a certain fluid for modeling and calculation.

[0177] Assuming the instantaneous flow rate of any section of the road in the area is q, and the instantaneous density at the section position x is k(x), the average instantaneous speed of the vehicle at the section position is calculated as: The average instantaneous acceleration of the vehicle at the cross-section position is:

[0178] When the road is not congested, that is, the road density is less than the critical density k∈[0,k c ), the average speed, average density and average acceleration at the road section position x in the non-congested state are: v(x)=v f , a(x)=0; when the road is congested, that is, the road density is greater than the critical density k∈[k c ,κ], and substitute into the flow-density function Q, the average speed, average density and average acceleration at the road section position x under the congestion state are calculated, which are expressed as:

[0179]

[0180] Where Δl = l 1 -l 2 represents the number of lane reductions, q 0 =ωκ, which is an intermediate variable.

[0181] Assuming the vehicle acceleration is a, the bounded acceleration model can be expressed as A(v): a≤A(v). The bounded acceleration model A(v) should satisfy: 1.A(v)≥0,v∈[0,v f ],v f is the free flow velocity; 2.A(v)≤a 0 , a 0 It is the maximum acceleration of the vehicle during normal driving, which is a constant; 3. A'(v)≤0, which means that the greater the vehicle's driving speed, the smaller the upper limit of the vehicle's acceleration should be.

[0182] The linear bounded acceleration model is used as an effective approximation of the average acceleration of the vehicle. Based on the moving reference system, the flow-density function Q and the linear bounded acceleration model A(v) in the triangular basic diagram are modified to obtain the flow-density function Q and the linear bounded acceleration model A'(v) based on the moving reference system:

[0183] Q′(k)=Q(k)-v mb ·k

[0184]

[0185] Among them, v mb is the velocity of the reference frame, i.e., the velocity of the uniform CAV;

[0186] From the above formula, we can see that a is calculated from the cross-section position x, and the function f is defined as: Among them, f(x; q) ≤ 0, and A'(v) ≤ 0, v(x) and a(x) monotonically increase with the independent variable x, then f(x; q) monotonically increases with x, let x = L, substitute the linear bounded acceleration model A'(v) based on the moving reference system, and simplify it to get:

[0187]

[0188] Among them, f(L;q) increases monotonically with q. If q is defined r is the maximum passing rate of the connected autonomous driving vehicle CAV, then q r Satisfies: f(L;q r )=0; By solving the problem, we can get the average flow rate of overtaking connected autonomous driving vehicles CAV on the road under the condition of meeting the bounded acceleration limit.

[0189] Furthermore, in S2, based on the influence of CAVs of different speeds on the road traffic evolution process, the trajectory of CAVs is predicted and the road state evolution is calculated, including the following steps:

[0190] S221. Single Connected Autonomous Vehicle (CAV) scenario:

[0191] There is a CAV with a constant low speed on the road, and its initial time and space position is (t 0 ,x 0 ), with a velocity of v mb , taking the single connected autonomous driving vehicle CAV as an example, the vehicle trajectory is predicted and the internal boundary conditions are obtained. The specific contents are as follows:

[0192] Step (1): Calculate the current speed of the connected autonomous vehicle CAV at v mb The maximum passing rate q r ;

[0193] Step (2): Calculate the current spatiotemporal position (t mb ,x mb ) under the road cumulative number of vehicles N mb , average road density k mb ; Taking the current position as the starting point, the speed v of the current connected autonomous driving vehicle CAV mb Add a virtual trajectory to the coordinates for the slope and calculate the internal boundary conditions, expressed as: x = x 0 +v mb (tt 0 )t∈[t 0 ,t max ]、N virt-int (x,)t=N mb , where t max It is the maximum time of the road space-time region in the model;

[0194] Step (3): Based on the k calculated in step (1), 0 CAV state classification of connected autonomous driving vehicles, when k∈[0,k d )∪(k u ,k i' ], the networked autonomous driving vehicle CAV is in an invalid state, and the road traffic will not be subject to the networked autonomous driving vehicle CAV. The space-time position of the next iteration cycle of the networked autonomous driving vehicle CAV is (t mb +Δt,x mb +v mb Δt); if k∈(k u' ,κ], at this time, the networked autonomous driving vehicle CAV is in an invalid state and has no effect on road traffic, but the road is congested at this time, and the average vehicle speed will be lower than v mb , at this time the networked autonomous driving vehicle CAV cannot maintain its own speed, calculate the networked autonomous driving vehicle CAV speed v'mb , update the spatiotemporal position of the next iteration cycle of the connected autonomous driving vehicle CAV to (t mb +Δt,x mb +v' mb Δt), and delete all virtual trajectories and their corresponding internal boundary conditions; when k∈[k d ,k u ], the CAV is in a valid state, that is, the road traffic is restricted by the CAV, and the internal boundary conditions in the updated solution algorithm are:

[0195]

[0196] At the same time, the time and space position of the next iteration cycle of CAV is updated as (t mb +Δt,x mb +v mb Δt);

[0197] Step (4): Determine whether the connected autonomous driving vehicle CAV has left the road section, that is, determine whether the space-time position of the vehicle at the next moment exceeds the solution area. If it does not exceed the solution area, return to step (2); otherwise, end the calculation and obtain the updated internal boundary conditions.

[0198] S222. Multiple connected autonomous vehicles (CAVs):

[0199] There are n number of CAVs with uniform and low speed on the road, and the CAV serial number set is P = {1, 2, ..., n}. Let the initial spatiotemporal position of the CAV be Its own speed is The following steps are used to calculate the vehicle trajectory and its internal boundary conditions in the multi-connected autonomous driving vehicle CAV scenario:

[0200] Step (1): Calculate the speed of the connected autonomous vehicle CAVi The maximum pass rate under

[0201] Step (2): sort the connected autonomous driving vehicles CAVs in set P from downstream to upstream according to their positions on the road, to obtain set M;

[0202] Step (3): Traverse the elements in the set M, and then calculate the trajectory of CAVi within each iteration period Δt according to the steps in the above single-network autonomous driving vehicle CAV algorithm, update the vehicle position and solve the internal boundary conditions N in the algorithm. int(x, t); then determine whether the i-th connected autonomous driving vehicle CAV has left the solution area. If it has left the solution area, delete the vehicle number from the connected autonomous driving vehicle CAV set P;

[0203] Step (4): After deleting the vehicle number, reorder the connected autonomous driving vehicles CAV in the set from downstream to upstream according to their positions on the road, and update the set M;

[0204] Step (5): When the connected autonomous driving vehicle CAV set P is not empty, return to step (3), otherwise end the calculation; and obtain the solution algorithm after updating the internal boundary conditions.

[0205] In a specific embodiment, Figure 1 As shown, the present invention provides a method for deducing a continuous traffic flow state under the influence of an intelligent networked vehicle, comprising the following steps:

[0206] (1) Establish a numerical simulation scenario to implement and visualize the theoretical analysis and solution algorithm of the present invention. First, set the basic road scenario as a three-lane highway straight road, the road length is 3 km, and the simulation time is 600 s. The road traffic obeys the triangular basic diagram, and the specific basic diagram parameters are set as: free flow speed v f =28m / s, critical density k c =15, blocking density κ = 67. Initial road density In the range of 0-500m, set it to 5, in the range of 500-1000m, set it to 50, and in the range of 500-3000m, set it to 15. Future traffic input for the road In the 0-250s range, set to 1300, in the 250-300s range, set to 1500, and in the 350-600s range, set to 1000. Maximum output of future traffic on the road In the range of 0-100s, it is set to 1500, in the range of 150-200s, it is set to 1000, in the range of 200-300s, it is set to 1300, and in the range of 300-600s, it is set to 1500. The density unit is veh / (km·lane) and the flow unit is veh / (h·lane).

[0207] (2) Calculate the initial road density Road traffic input and maximum output of road traffic The road state evolution results under the conditions, such as Figure 6 As shown in the figure, by calculating the maximum flow rate of the road The setting can well simulate the congestion phenomenon in the downstream of the road. At the same time, the state evolution model proposed by the invention has a very clear description of the traffic wave caused by congestion in the road.

[0208] (3) Add one or more controlled connected autonomous vehicles CAV to the above scenario, and perform calculations according to the algorithm of the single connected autonomous vehicle CAV and multiple connected autonomous vehicles CAV in the present invention. The results are as follows: Figure 7 and Figure 8 As shown in the figure, the model accurately depicts the state evolution process of the entire road. By comparison, it can be seen that the model can effectively describe the road state evolution process under the superposition of different connected autonomous driving vehicles (CAVs).

[0209] (4) The maximum road capacity is used to calculate the pass rate for comparison. Under this condition, the road state evolution diagram under the influence of multi-networked autonomous driving vehicles CAV is as follows: Fig. 9 As shown in the figure, the model proposed in the present invention can effectively describe the impact of low-speed connected autonomous driving vehicles (CAVs) on the downstream arrival pattern of the road.

[0210] (5) The proposed state evolution model was simulated and verified based on SUMO simulation. The simulation scenario is a three-lane highway straight road, and the effective area of ​​the simulation road is 20 km long. The networked autonomous driving vehicle CAV enters the road network at the same time as the manually driven vehicle. In the first group of simulation experiments, a temporary bottleneck is set. The bottleneck appears for 1000 seconds, and the purpose is to wait for the road network simulation warm-up to end. The duration of the temporary bottleneck is 600 seconds, and the total average flow input of the simulated road network is 3000veh / h. The basic road map parameters are the same as the numerical simulation. The simulation time of the road is set to 3600 seconds.

[0211] (6) The road state evolution results and simulation results calculated based on the model proposed by the present invention are as follows: Fig.10 As shown. Fig.10 As can be seen in the numerical calculation results of road state evolution ( Fig.10 (a)) and simulation results ( Fig.10 (b)) is basically consistent, and the model proposed by the present invention effectively describes the impact area caused by temporary bottlenecks. Through calculation, the numerical calculation result of the simulated road is 40veh / (km·lane), and the accuracy rate is 82%.

[0212] (7) Based on the previous set of simulation experiments, the CAV in the random control area slowed down to 40 km / h within 1000s to 1500s, and returned to normal after 1500s. The road state evolution results calculated based on the model proposed by the present invention, the road state evolution results using the maximum road capacity to calculate the pass rate, and the simulation results are as follows: Fig.11As shown, Fig.11 (a) is the simulation result, Fig.11 (b) is the model result of this study. Fig.11 (c) is the result of the maximum peer capacity model. It can be seen that the numerical simulation results of the road state evolution based on the model proposed by the present invention are basically consistent with the simulation results, and the impact of the networked autonomous driving vehicle CAV on the road is effectively analyzed. The numerical calculation result of the simulated road is 37veh / (km·lane), with an accuracy of 84%.

[0213] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can refer to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can refer to the partial description of the method embodiment. The system and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without creative work.

[0214] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for deducing continuous traffic flow state under the influence of intelligent networked vehicles, characterized in that: The following steps are involved: S1. Without considering the CAV, a road state evolution model is established based on the first-order macro traffic flow model, and the established road state evolution model is solved to obtain the basic framework of the mixed traffic flow state evolution model of human-driven vehicles HV and CAV; S2. Based on the mobile bottleneck theory, networked autonomous driving vehicles (CAV) of different speeds are modeled, and their impact on the road traffic evolution process is calculated. Combined with the basic framework of the mixed traffic flow state evolution model of manually driven vehicles HV and networked autonomous driving vehicles CAV in S1, a state evolution model considering the joint effects of road bottlenecks and networked autonomous driving vehicles CAV is established.

2. According to claim 1, a method for deducing continuous traffic flow state under the influence of intelligent networked vehicles is characterized in that: The basic framework of the mixed traffic flow state evolution model of manually driven vehicles HV and connected autonomous vehicles CAV in S1 is determined based on the conservation rate, LWR model and Hamilton-Jacobi equation, including the following steps: S111. Calculation of conservation rate: In the area from x1 to x2 of the basic section of the expressway, the road section has no entrance or exit, and vehicles travel normally for Δt time and Δt = t2-t1. Let N1 and N2 be the number of vehicles passing through sections x1 and x2 within Δt time, and q1 and q2 be the average flow through sections x1 and x2 within Δt time, then The number of vehicles changing in the area [x1, x2] within the time Δt is ΔN = N2-N1 = ΔqΔt, where ΔN greater than 0 means that the number of vehicles leaving the road section is greater than the number of vehicles entering the road section; Assume that the average vehicle density of the road section in the area [x1, x2] at time t1 and time t2 is k1 and k2 respectively. Since the road section has no entrance or exit, let Δx = x2-x1. Then the cumulative number of vehicle changes ΔN in the area [x1, x2] within the time Δt is expressed as: ΔN = k1Δx-k2Δx = -ΔkΔx; we get ΔkΔx+ΔqΔt = 0, and further get: If we set Δt→0, Δx→0, we get the following conservation equation, also called conservation rate: Where k(t,x) and q(t,x) represent the instantaneous density and instantaneous flow of the road at position x at time t, respectively; S112. Determine the state evolution model using the LWR model and Hamilton-Jacobi equation: In the LWR model, it is assumed that the basic traffic map exists, that is, q = Q (k), where Q represents the function of flow and density in the basic traffic map. Substituting the above formula into the conservation rate formula, we get: Let N(t,x) represent the cumulative number of vehicles passing through position x at time t. By default, the function numbers the vehicles in ascending order according to their appearance. When the vehicle numbered n passes through the road position x at time t, then M(t,x)=n, and N(t,x)>0, which increases monotonically for the time variable t. According to the flow definition, the instantaneous flow of the road section at a certain time is obtained as: Similarly, the instantaneous density of the road section at a certain time is: Assuming that N(t,x) is second-order differentiable, we get the Hamilton-Jacobi equation: Among them, the flow-density function Q is the Hamiltonian operator of the equation. By solving the equation, the road state parameters at any spatiotemporal position of the road can be obtained, and then the spatiotemporal evolution of the road state can be analyzed at the macro level.

3. The method for deducing continuous traffic flow state under the influence of intelligent networked vehicles according to claim 2, characterized in that: The road state evolution model established in S1 without a connected autonomous driving vehicle CAV using the boundary condition, the Hopf-Lax formula and the triangle basic diagram mainly includes the following steps: S121. Consider the solution conditions: A coordinate system is established, where the horizontal axis represents time, the vertical axis represents distance, and the origin of the coordinate system represents the time t=0 and the starting point of the road x0; consider the following solution problem of the Hamilton-Jacobi equation: in, Represents the road space-time region boundary: g(r,y) represents the solution condition, which consists of three parts: the initial density function of the road Road upstream input flow function and the maximum downstream output flow function of the road The formula is as follows: S122. Use the Hopf-Lax formula to solve the Hamilton-Jacobi equation: First, we introduce the Legendre transform: for smooth convex functions and any definition: Q * (p) is the Legendre transformation induced by the function Q; the Hopf-Lax formula means that for the well-defined problem of the Hamilton-Jacobi equation, the Hamilton operator Q that satisfies the convex function condition is used to define the function L and the solution u(t,x) of the equation, which can be expressed as: Among them, g(r,y) represents the solution condition, r and y represent the initial time and initial position respectively; S123. Model solution based on triangle basic graph: The flow-density function Q in the triangular basic diagram is defined as: Among them, v f is the free flow speed and the characteristic wave speed in non-congested conditions, k c is the critical density, κ is the blocking density, -ω is the characteristic wave speed during congestion; let c = k c v f , Substitute Q(k) into the previous formula and perform Legendre transformation to obtain: Among them, u∈[ω,v f ],C=k c v f ; The physical meaning of the Legendre transformed function L(u) here is: when there is an observed vehicle traveling at speed u on the road, the maximum flow rate that exceeds the vehicle is L(u); Substituting L(u) into the Hopf-Lax formula, the final result is: S124. Solve the general well-defined problem by solving the algorithm: Let the initial road density be a piecewise linear function, divide the road into multiple small sections, and the density of each section at the initial moment is a linear function, expressed as: Similarly, the flow input at the starting point of the road at the future moment is expressed as a piecewise linear function, which is expressed as: Where i and j are the segment numbers of position and time, respectively, k(t0,x) represents the density of the road at the initial time t0 and position x, q(t,x0) and q(t,x n ) represent the flow input at the starting point x0 at time t and the flow input at the end point x n The maximum passable flow at time t; the corresponding cumulative vehicle number function is calculated and used as the initial condition and boundary condition, expressed as: in, are all piecewise linear functions, i and j are the segment numbers of position and time respectively. represents the cumulative number of vehicles at the road section position x at the initial time, and the subscript t0 represents the initial time, which is the initial condition. represents the cumulative number of vehicles at the initial position x0 of the road section, and the subscript t0 represents the initial time, which is the boundary condition. represents the cumulative number of vehicles at the end position x0 of the road section, and the subscript t0 represents the initial time, which is the boundary condition, and the function Together they form the solution condition of the equation, corresponding to the previous N(r,y); S125. Substitute the flow-density function Q in the basic triangular traffic diagram and calculate the solutions under its individual action respectively; the solution results can be divided into four types: (1) Consider only the initial conditions When in effect: Let x∈[x i ,x i+1 ) When 0≤k i ≤k c ,get According to the definition, the density is: Where D1 and D2 represent the plane specified area: (2) Consider only the initial conditions When in effect: Let x∈[x i ,x i+1 ) When k c ≤k i When ≤κ, we get: According to the definition, the density is: Where D1 and D2 represent the plane specified area: (3) Consider only boundary conditions When in effect: Let t∈[t j ,t j+1 ) is the road upstream flow input: Assume that in the flow-density function, The two solutions of k f ,k b , where k f ≤k b ,available: According to the definition, the density is: Where D1 and D2 represent the plane specified area: 4) Consider only boundary conditions When in effect: Let t∈[t j ,t j+1 ) is the maximum output of the road end flow rate. Assume that in the flow-density function, The two solutions of k f ,k b , where k f ≤k b ,available: According to the definition, the density is: Where D1 and D2 represent the plane specified area: S126. According to the Hopf-Lax formula, for any point (t, x) in the solution region, the solution under the complete solution condition is: Where N i represents the i-th initial or boundary condition, i min Indicates the solution condition number corresponding to the minimum value.

4. The method for deducing continuous traffic flow state under the influence of intelligent networked vehicles according to claim 3 is characterized in that: In S2, the connected autonomous driving vehicles (CAVs) with different speeds are modeled based on the mobility bottleneck theory to calculate their impact on the road traffic evolution process, including the following steps: S211 establishes internal boundary conditions: When the speed of the CAV and the passing rate of the CAV are known, the flow-density relationship in the basic graph of the road is expressed as q = min{Q(k),q r +kv mb }express; There is a CAV with a constant speed on the multi-lane road. Its appearance time on the road is t s , the position of occurrence is x s , when the road density k∈[0,k u' ], that is, the speed of the connected autonomous vehicle CAV is lower than the average speed of the road and it travels at its own speed. Let the trajectory of the connected autonomous vehicle CAV be AB, which can be expressed as: x = x s +v mb (tt s ); If the time when the uniform speed connected autonomous driving vehicle CAV leaves the road is t e , and during the driving period of the uniformly connected autonomous driving vehicle CAV t∈[t s ,t e ], the connected autonomous driving vehicle CAV is always in an effective state, that is, the road density k∈[k d ,k u ]; If the passing rate of the connected autonomous vehicle CAV is q r , then for each point on the AB line segment of the CAV motion trajectory, the corresponding cumulative number of vehicles N int For: N int (t) = N s +q r (tt s ) t∈[t s ,t e ],x=x s +v mb (tt s ); Line segment AB is used as a solution condition, that is, an internal boundary condition. Under the action of this internal boundary condition alone, the solution is: According to the definition, the corresponding density can be obtained as: Where D1, D2, and D3 represent the specified area of ​​the plane, and Δx is an intermediate variable, indicating the relative distance: S212. Calculate the traffic volume under the influence of connected autonomous driving vehicles (CAV): Taking the CAV as the reference system, the traffic on the road near the CAV is in a steady state, that is, in the moving coordinate system. When the CAV maintains a constant speed, the flow and density at any instantaneous cross-sectional position of the road near it remain unchanged, which can be expressed as: Combining the conservation laws, we get: Assuming the instantaneous flow rate of any section of the road in the area is q, and the instantaneous density at the section position x is k(x), the average instantaneous speed of the vehicle at the section position is calculated as: According to the definition of acceleration, the average instantaneous acceleration of the vehicle at the cross-section position is calculated as: When the road is in a non-congested state, that is, the road density is less than the critical density k∈[0,k c ), the average speed, average density and average acceleration at the road section position x in the non-congested state are: v(x)=v f , a(x)=0; When the road is in a congested state, that is, the road density is greater than the critical density k∈[k c ,κ], and substitute into the flow-density function Q, the average speed, average density and average acceleration at the road section position x under the congestion state are calculated, which are expressed as: Among them, Δl=l1-l2 represents the number of lane reductions, and q0=ωκ is an intermediate variable.

5. The method for deducing continuous traffic flow state under the influence of intelligent networked vehicles according to claim 4, characterized in that: The upper limit of the vehicle's acceleration is related to the vehicle speed. The bounded acceleration model A(v) represents the upper limit of the vehicle's acceleration at the current speed. The bounded acceleration model A(v) should satisfy: 1.A(v)≥0,v∈[0,v f ],v f is the free flow speed; 2. A(v)≤a0, a0 is the maximum acceleration of the vehicle during normal driving, which is a constant value; 3. A'(v)≤0, which means that the higher the vehicle's speed, the smaller the upper limit of the vehicle's acceleration should be; The linear bounded acceleration model is used as an effective approximation of the average acceleration of the vehicle. Based on the moving reference system, the flow-density function Q and the linear bounded acceleration model A(v) in the triangular basic diagram are modified to obtain the flow-density function Q and the linear bounded acceleration model A'(v) based on the moving reference system: Q′(k)=Q(k)-v mb ·k Among them, v mb is the speed of the reference frame, i.e., the speed of the CAV; From the above formula, we can know that the average acceleration a of the road vehicle is calculated from the cross-sectional position x, and the function f is defined as: f(x; q)≤0, and A'(v)≤0, v(x) and a(x) increase monotonically with the independent variable x, then f(x; q) increases monotonically with x, let x=L, substitute into the linear bounded acceleration model A'(v) based on the moving reference system, and simplify to obtain: Among them, f(L;q) increases monotonically with q. If q is defined r is the maximum passing rate of CAV, then q r Satisfies: f(L;q r )=0; By solving it, we can get the average flow rate of overtaking CAV on the road under the condition of meeting the bounded acceleration limit.

6. The method for deducing continuous traffic flow state under the influence of intelligent networked vehicles according to claim 5, characterized in that: In S2, based on the impact of CAVs of different speeds on the road traffic evolution process, the trajectory of CAVs is predicted, and the road state evolution calculation is performed according to the trajectory prediction results, including the following steps: S221. Single Connected Autonomous Vehicle (CAV) scenario: There is a CAV with a constant low speed on the road. Its initial time and space position is (t0, x0) and its speed is v mb , taking the single connected autonomous driving vehicle CAV as an example, the vehicle trajectory is predicted and the internal boundary conditions are obtained. The specific contents are as follows: Step (1): Calculate the current speed of the connected autonomous vehicle CAV at v mb The maximum passing rate q r ; Step (2): Calculate the current spatiotemporal position (t mb ,x mb ) under the road cumulative number of vehicles N mb , average road density k mb ; Taking the current position as the starting point, the speed v of the current connected autonomous driving vehicle CAV mb Add a virtual trajectory to the coordinates for the slope and calculate the internal boundary conditions, expressed as: x = x0 + v mb (t-t0)t∈[t0,t max ]、N virt-int (x,t)=N mb , where t max It is the maximum time of the road space-time region in the model; Step (3): Categorize the CAV state of the connected autonomous driving vehicle according to k0 calculated in step (1). d )∪(k u ,k u' ], the networked autonomous driving vehicle CAV is in an invalid state, and the road traffic will not be subject to the networked autonomous driving vehicle CAV. The space-time position of the next iteration cycle of the networked autonomous driving vehicle CAV is (t mb +Δt,x mb +v mb Δt); if k∈(k u' ,κ], at this time, the networked autonomous driving vehicle CAV is in an invalid state and has no effect on road traffic, but the road is congested at this time, and the average vehicle speed will be lower than v mb , at this time the networked autonomous driving vehicle CAV cannot maintain its own speed, calculate the networked autonomous driving vehicle CAV speed v' mb , update the spatiotemporal position of the next iteration cycle of the connected autonomous driving vehicle CAV to (t mb +Δt,x mb +v' mb Δt), and delete all virtual trajectories and their corresponding internal boundary conditions; when k∈[k d ,k u ], the CAV is in a valid state, that is, the road traffic is restricted by the CAV, and the internal boundary conditions in the updated solution algorithm are: At the same time, the time and space position of the next iteration cycle of the connected autonomous driving vehicle CAV is updated as (t mb +Δt,x mb +v mb Δt); Step (4): Determine whether the connected autonomous driving vehicle CAV has left the road section, that is, determine whether the space-time position of the vehicle at the next moment exceeds the solution area. If it does not exceed the solution area, return to step (2); otherwise, end the calculation and obtain the updated internal boundary conditions; S222. Multiple connected autonomous vehicles (CAVs): There are n number of CAVs with uniform and low speed on the road, and the CAV serial number set is P = {1, 2, ..., n}. Let the initial spatiotemporal position of the CAV be Its own speed is The following steps are used to calculate the vehicle trajectory and its internal boundary conditions in the multi-connected autonomous driving vehicle CAV scenario: Step (1): Calculate the speed of the connected autonomous vehicle CAVi The maximum pass rate under Step (2): sort the connected autonomous driving vehicles CAVs in set P from downstream to upstream according to their positions on the road, to obtain set M; Step (3): Traverse the elements in the set M, and then calculate the trajectory of CAVi within each iteration period Δt according to the steps in the above single-network autonomous driving vehicle CAV algorithm, update the vehicle position and solve the internal boundary conditions N in the algorithm. int (x, t); then determine whether the i-th connected autonomous driving vehicle CAV has left the solution area. If it has left the solution area, delete the vehicle number from the connected autonomous driving vehicle CAV set P; Step (4): After deleting the vehicle number, reorder the connected autonomous driving vehicles CAV in the set from downstream to upstream according to their positions on the road, and update the set M; Step (5): When the connected autonomous driving vehicle CAV set P is not empty, return to step (3), otherwise end the calculation; and obtain the solution algorithm after updating the internal boundary conditions.

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