CN115081227A - A vehicle following model based on optimal speed and its safety analysis method - Google Patents

Abstract

The invention discloses a vehicle following model based on optimal speed and a safety analysis method thereof, wherein the method comprises the following steps: constructing an optimal speed model based on vehicle and driver information in a traffic scene; leading in a headway to determine the critical condition of the optimal speed model, and analyzing to obtain the acceleration limited condition of the following model; performing stability analysis on the following model to obtain a stable condition of the following model; comparing the obtained stable following model with other following models, and verifying the fitting accuracy of the model; three typical traffic scenarios were simulated: and verifying the safety of the following model in a motorcade starting process, a motorcade stopping process and a motorcade uniform speed process. The invention solves the problem that the following state and the driving safety are not considered in a microcosmic traffic flow model in the prior art.

Description

A vehicle following model based on optimal speed and its safety analysis method

technical field

The method belongs to the field of vehicle following in micro traffic flow, and specifically relates to a vehicle following model based on an optimal speed and a safety analysis method thereof.

Background technique

In recent years, the state has continuously increased capital investment in the construction of traffic roads. However, due to the lack of long-term consideration of urban roads and urban planning, it has brought many obstacles to the construction and reconstruction of roads. In order to alleviate road traffic congestion, the state has successively issued a variety of policies for artificial control, such as measures to limit the number of motor vehicles, and measures to limit the purchase of license plate numbers. However, problems such as traffic congestion still cannot be effectively solved. Therefore, alleviating and alleviating traffic congestion is an urgent problem that needs to be solved at present. Traffic flow models can be divided into macroscopic traffic flow models and microscopic traffic flow models. The microscopic traffic flow models mainly include cellular automata model and vehicle following model. By analyzing the following behaviors between vehicles to restrict lane changing and overtaking, exploring their interactions, and establishing a high-precision vehicle following model, it will help to alleviate problems such as traffic congestion, thereby improving the level of traffic road services.

With the continuous increase of available trajectory data, researchers use modern machine learning methods to develop driver behavior models, forming artificial intelligence models. Uninterpretability is the biggest disadvantage of artificial intelligence models, while traditional models are based on traffic flow theory. interpretable.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an optimal speed-based vehicle following model and its safety analysis method, which solves the problem that the current microscopic traffic flow model does not take into account the car-following state and driving safety.

An optimal speed-based vehicle following model and its safety analysis method of the present invention, comprising the following steps:

Step 1: Build an optimal speed model based on the vehicle and driver information in the traffic scene;

a _n+1 (t)=α{V[ΔX _n (t)-v _n+1 (t)]}

Among them, t is the time, ΔX _n (t) is the distance between vehicles, α is the driver's sensitivity coefficient; V is the optimal speed function v _n+1 (t) represents the speed of the n+1th vehicle, and a _n+1 represents the th The acceleration of n+1 vehicles;

Step 2: Introduce the critical situation of the headway to determine the optimal speed model, and analyze the acceleration limited conditions of the car-following model;

Step 3: perform stability analysis on the car following model to obtain the stable conditions of the car following model;

Step 4: Compare the obtained stable car-following model with other car-following models to verify the fitting accuracy of the model;

Step 5: Simulate three typical traffic scenarios: the starting process of the fleet, the stopping process of the fleet, and the constant speed process of the fleet, to verify the safety of the car-following model.

Further, the specific implementation steps of the step 2 are:

Step 2.1: Determine the deviation difference between the expected car distance and the actual car gap of the following car after the speed of the leading car changes:

Among them, between time t+τ and time t+τ+T, the car-following car travels at the acceleration of a _n+1 (t+τ), and at time t+τ+T, the deviation difference ε _n ( The value of t+τ+T) is the closest to 0, that is, min|ε _n (t+τ+T)|, only the following acceleration an ₊₁ (t+τ) is an unknown quantity;

Step 2.2: Combining the constant terms, the deviation difference ε _n (t+τ+T) can be simplified as:

κ＝L+k；Among them, α, β, μ, λ, κ, and γ are all constants, and the specific calculation formulas are as follows: α=x _n (t)+x′ _n (t) τ-x _n+1 (t)-x′ _n+1 (t) τ+x′ _n (t) Tx′ _n+1 (t) T,

κ=L+k;

Step 2.3: Use the Newton iteration method to obtain the limited condition of the car-following acceleration.

Further, the specific implementation steps of the step 3 are:

Step 3.1: Assuming that the team runs stably, obtain the steady-state position X _n (t)=(n-1)d _s +v _s t of vehicle n, where the speed of the vehicle is v _s , and the distance between the heads of adjacent vehicles is d _s ;

其中，x_n(t)为车辆n在时刻t的实际位置,z为特征值,ω_j为第j个傅里叶展开参数，具体公式为

Step 3.2: Suppose the lead car is slightly disturbed at time t

Among them, x _n (t) is the actual position of vehicle n at time t, z is the eigenvalue, ω _j is the jth Fourier expansion parameter, and the specific formula is

Step 3.3: Let a _n+1 (t+τ)=g(d _n (t), x′ _n+1 (t), x′ _n (t)), for y″ _n+1 (t+τ) After linearization, y″ _n+1 (t+τ)=g ₁ [y _n (t)-y _n+1 (t)]+g ₂ y′ _n+1 (t)+g ₃ y ′ _n (t), where

Step 3.4: Using Taylor to expand the approximate function, the stability conditions of the car following model are obtained as:

Further, the specific implementation steps of the step 4 are:

Step 4.1: Use the real data set to filter the available car-following pairs;

Step 4.2: Using the screened available car-following pair data, according to the model proposed in this paper, carry out a simulation experiment to obtain the car distance between the car-following car and the leading car at time t+τ;

Step 4.3: Using the screened available car-following pair data, carry out simulation experiments according to other models, and calculate the distance between the car-following car and the leading car at time t+τ;

Step 4.4: Calculate the mean, median, minimum, and maximum of the distance between the vehicles in the model proposed in this paper, other models and the real data set for comparison.

Further, the specific implementation steps of the step 5 are:

Step 5.1: Simulation of the fleet startup process;

Step 5.1.1: Simulate the real fleet start-up process scenario;

Step 5.1.2: Carry out simulation according to the car following strategy proposed in this paper, and output the car following speed;

Step 5.1.3: Carry out simulation according to the car following strategy proposed in this paper, and output the distance between car following cars;

Step 5.2: Simulation of fleet stop process;

Step 5.2.1: Simulate a real fleet stop process scenario;

Step 5.2.2: Carry out simulation according to the car following strategy proposed in this paper, and output the car following speed;

Step 5.2.3: Carry out simulation according to the car following strategy proposed in this paper, and output the distance between car following cars;

Step 5.3: Simulation of the uniform speed process of the fleet;

Step 5.3.1: Simulate the scene of the constant speed process of the real fleet:

Step 5.3.2: Carry out simulation according to the car following strategy proposed in this paper, and output the car following speed;

Step 5.3.3: Carry out simulation according to the car following strategy proposed in this paper, and output the distance between car following cars.

Compared with the prior art, the present invention takes into account the driving safety while considering the car-following state, and based on the optimal speed model, analyzes the situation that the headway is smaller than the minimum headway and is greater than the most comfortable headway, and obtains a critical value. Under the circumstance, the acceleration constraint conditions are guaranteed to ensure the safety of the newly established car-following model. In addition, the stability analysis of the obtained vehicle following model is carried out, and the stability conditions of the vehicle following model are obtained, which provides a basic basis for traffic control and driving strategies, improves the stability of traffic flow, and relieves traffic congestion. The effectiveness and safety of the present invention are verified by simulating three real traffic scenarios—starting, constant speed and stopping processes.

The invention designs a car-following model based on the optimal speed, which ensures that the vehicle is in a car-following state while considering safety, and proves the effectiveness and safety of the car-following model in the driving process by constructing various simulation scenarios .

Description of drawings

Fig. 1 is the flow chart on which a vehicle following model based on optimal speed and its safety analysis method of the present invention are based;

Fig. 2 is a kind of vehicle following model based on optimal speed of the present invention and its safety analysis method fleet start-up process speed simulation prediction diagram;

Fig. 3 is a kind of vehicle-following model based on optimal speed and its safety analysis method of the present invention, which is a simulation prediction diagram of vehicle spacing during the starting process of a fleet;

Fig. 4 is a kind of safety analysis method of the vehicle following model based on the optimal speed of the present invention, the speed simulation prediction diagram of the fleet stop process;

Fig. 5 is a kind of safety analysis method of the vehicle following model based on the optimal speed of the present invention, a simulation prediction diagram of the distance between vehicles during the stopping process of the fleet;

Fig. 6 is a kind of safety analysis method of the vehicle following model based on the optimal speed of the present invention, and the simulation prediction diagram of the speed of the uniform process of the fleet;

FIG. 7 is a simulation prediction diagram of the vehicle spacing during a constant speed process of a fleet of vehicles in a safety analysis method based on an optimal speed vehicle following model of the present invention.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

Referring to accompanying drawing 1, the vehicle following model and its safety analysis method based on the optimal speed of the present invention comprise the following steps:

Step 1: Build an optimal speed model based on the vehicle and driver information in the traffic scene;

a _n+1 (t)=α{V[ΔX _n (t)-v _n+1 (t)]}

Among them, t is the time, ΔX _n (t) is the distance between vehicles, α is the driver's sensitivity coefficient; V is the optimal speed function v _n+1 (t) represents the speed of the n+1th vehicle, and a _n+1 represents the th The acceleration of n+1 vehicles;

Step 2: Introduce the critical situation of the headway to determine the optimal speed model, and analyze the acceleration limited conditions of the car-following model;

Step 3: perform stability analysis on the car following model to obtain the stable conditions of the car following model;

Step 4: Compare the obtained stable car-following model with other car-following models to verify the fitting accuracy of the model;

Step 5: Simulate three typical traffic scenarios: the starting process of the fleet, the stopping process of the fleet, and the constant speed process of the fleet, to verify the safety of the car-following model.

In step 2, the headway time is introduced to determine the critical situation of the optimal speed model, and the specific steps of obtaining the acceleration limited condition of the car following model are as follows;

Step 2.1: Determine the deviation difference between the expected car distance and the actual car gap of the following car after the speed of the leading car changes:

Among them, between time t+τ and time t+τ+T, the car-following car travels at the acceleration of a _n+1 (t+τ), and at time t+τ+T, the deviation difference ε _n ( The value of t+τ+T) is the closest to 0, that is, min|ε _n (t+τ+T)|, only the following acceleration an ₊₁ (t+τ) is an unknown quantity;

Step 2.2: Combining the constant terms, the deviation difference ε _n (t+τ+T) can be simplified as:

κ＝L+k；Among them, α, β, μ, λ, κ, and γ are all constants, and the specific calculation formulas are as follows: α=x _n (t)+x′ _n (t) τ-x _n+1 (t)-x′ _n+1 (t) τ+x′ _n (t) Tx′ _n+1 (t) T,

κ=L+k;

Step 2.3: Use the Newton iteration method to obtain the limited condition of the car-following acceleration. In this embodiment, the headway is set to be less than 1.55 seconds as the minimum and safe headway, and greater than 2.6 seconds is the maximum headway. When the headway is less than At 1.55 seconds, the car-following car must decelerate, and the limited conditions for its acceleration are:

When the head-to-head distance is greater than 2.6 seconds, the car-follower must accelerate, and the limited conditions for its acceleration are:

In step 3, the stability analysis of the car-following model is performed to obtain the stable conditions of the car-following model. The specific steps are:

Step 3.1: Assuming that the team runs stably, obtain the steady-state position X _n (t)=(n-1)d _s +v _s t of vehicle n, where the speed of the vehicle is v _s , and the distance between the heads of adjacent vehicles is d _s ;

其中，x_n(t)为车辆n在时刻t的实际位置,z为特征值,ω_j为第j个傅里叶展开参数，具体公式为

Step 3.2: Suppose the lead car is slightly disturbed at time t

Among them, x _n (t) is the actual position of vehicle n at time t, z is the eigenvalue, ω _j is the jth Fourier expansion parameter, and the specific formula is

Step 3.3: Let a _n+1 (t+τ)=g(d _n (t), x′ _n+1 (t), x′ _n (t)), for y″ _n+1 (t+τ) After linearization, y″ _n+1 (t+τ)=g ₁ [y _n (t)-y _n+1 (t)]+g ₂ y′ _n+1 (t)+g ₃ y ′ _n (t), where

Step 3.4: Using Taylor to expand the approximate function, the stability conditions of the car following model are obtained as:

In step 4, the obtained stable car-following model is compared with other car-following models to verify the fitting accuracy of the model, and the specific steps are as follows;

Step 4.1: Use the real data set to filter the available car-following pairs;

Step 4.2: Using the screened available car-following pair data, according to the model proposed in this paper, carry out a simulation experiment to obtain the car distance between the car-following car and the leading car at time t+τ;

Step 4.3: Using the screened available car-following pair data, carry out simulation experiments according to other models, and calculate the distance between the car-following car and the leading car at time t+τ;

Step 4.4: Calculate the mean, median, minimum, and maximum of the distance between the vehicles in the model proposed in this paper, other models and the real data set for comparison.

In step 5, three typical traffic scenarios are simulated: the starting process of the fleet, the stopping process of the fleet, and the constant speed process of the fleet to verify the safety of the car-following model.

Step 5.1: Simulation of the fleet startup process;

Step 5.1.1: Simulate a real fleet starting process scenario. In this embodiment, the fleet starting process is set as follows: the fleet starting process mainly simulates an intersection, and when the traffic light is green, the fleet starts driving through the intersection. Suppose there is a convoy of 5 cars each 10ft in length waiting for the green light at an intersection, all vehicles in the convoy are stationary, and the distance between the two cars is 20ft. At time t=0, the traffic light changes from red to green, the leading car starts at an acceleration of 8ft/s ² , and the following cars in the convoy will start following one by one;

Step 5.1.2: Carry out the simulation according to the car following strategy proposed in this paper, and output the car following speed. The specific results are shown in Figure 2;

Step 5.1.3: Carry out simulation according to the car following strategy proposed in this paper, and output the distance between car following cars. The specific results are shown in Figure 3;

Step 5.2: Simulation of fleet stop process;

Step 5.2.1: Simulate a real fleet stop process scenario. In this embodiment, the fleet stop process is set as follows: First, a fleet of 5 cars with a length of 10ft/s is formed, and all cars are driven at 20ft/s. The speed is constant and the distance between the two vehicles is 60ft/s. At this time, set the guide car to perform emergency braking at an acceleration of 13ft/s ² , check whether the following vehicles decelerate and stop one by one with the guide car, and whether there is a collision in the fleet;

Step 5.2.2: Carry out the simulation according to the car following strategy proposed in this paper, and output the car following speed. The specific results are shown in Figure 4;

Step 5.2.3: Carry out simulation according to the car following strategy proposed in this paper, and output the distance between car following cars. The specific results are shown in Figure 5;

Step 5.3: Simulation of the uniform speed process of the fleet;

Step 5.3.1: Simulate the scene of the constant speed process of a real convoy. In this embodiment, the uniform speed process of the convoy is set as follows: First, in a convoy composed of 5 vehicles, the leading cars all drive at a constant speed of 20ft/s, and the 4 cars follow Driving at a speed of 30ft/s with a distance of 60ft between the two vehicles;

Step 5.3.2: Carry out the simulation according to the car following strategy proposed in this paper, and output the car following speed. The specific results are shown in Figure 6;

Step 5.3.3: Carry out simulation according to the car following strategy proposed in this paper, and output the distance between car following cars. The specific results are shown in Figure 7.

Computer program code for carrying out the execution flows of the present disclosure may be written in one or more programming languages, including object-oriented programming languages—such as Java, Smalltalk, C++, and conventional procedural programming language - such as "C" language or similar programming language. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any kind of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (eg, using an Internet service provider through Internet connection).

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code that contains one or more logical functions for implementing the specified functions executable instructions. It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It is also noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented in dedicated hardware-based systems that perform the specified functions or operations , or can be implemented in a combination of dedicated hardware and computer instructions.

The units involved in the embodiments of the present disclosure may be implemented in a software manner, and may also be implemented in a hardware manner. Wherein, the name of the unit does not constitute a limitation of the unit itself under certain circumstances, for example, the first obtaining unit may also be described as "a unit that obtains at least two Internet Protocol addresses".

The above description is merely a preferred embodiment of the present disclosure and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the disclosure involved in the present disclosure is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, and should also cover, without departing from the above-mentioned disclosed concept, the technical solutions formed by the above-mentioned technical features or Other technical solutions formed by any combination of its equivalent features. For example, a technical solution is formed by replacing the above features with the technical features disclosed in the present disclosure (but not limited to) with similar functions.

Claims (6)

1. A vehicle following model based on optimal speed and a safety analysis method thereof are characterized by comprising the following steps:

step 1: constructing an optimal speed model based on vehicle and driver information in a traffic scene;

step 2: leading in a headway to determine the critical condition of the optimal speed model, and analyzing to obtain the acceleration limited condition of the following model;

and step 3: performing stability analysis on the following model to obtain a stable condition of the following model;

and 4, step 4: comparing the obtained stable following model with other following models, and verifying the fitting accuracy of the model;

and 5: three typical traffic scenarios were simulated: and verifying the safety of the following model in a motorcade starting process, a motorcade stopping process and a motorcade uniform speed process.

2. The optimal velocity-based vehicle-following model and the safety analysis method thereof according to claim 1, wherein:

the optimal speed model in the step 1 is as follows:

a _n+1 (t)＝α{V[ΔX _n (t)-v _n+1 (t)]}

wherein t is time, Δ X _n (t) is the inter-vehicle distance, and alpha is the driver sensitivity coefficient; v is an optimized velocity function V _n+1 (t) represents the speed of the (n + 1) th vehicle, a _n+1 Represents the acceleration of the (n + 1) th vehicle;

wherein, the vehicle distance is delta X _n (t) the calculation method is as follows:

ΔX _n (t)＝x _n (t)-x _n+1 (t)

in the formula, x _n (t) and x _n+1 (t) indicates the leading distance and the following position at time t, respectively.

3. The optimal velocity-based vehicle-following model and the safety analysis method thereof according to claim 2, wherein:

calculating the expected distance D between the following vehicles in the step 2 _n+1 Distance DeltaX from actual vehicle _n (t) difference in deviation ε between _n (t) in which

ΔX _n (t)＝x _n (t)-x _n+1 (t)，ε _n (t)＝ΔX _n (t)-D _n (t) in the formula, x' _n (t)、x′ _n+1 (t) represents the inter-vehicle distance, x 'of the leading vehicle and the following vehicle at the time t' _n (t)、x′ _n+1 (t) represents the speed of the leading vehicle and the following vehicle at the time t, tau represents the reaction time, L represents the vehicle length distance of the leading vehicle, k represents the buffer distance between the two vehicles after parking, a _n (t)、a _n+1 (t) represents the maximum deceleration of the leading vehicle and the following vehicle, respectively.

4. The optimal-velocity-based vehicle-following model and the safety analysis method thereof according to claim 3, wherein the acceleration-limited condition in step 2 is:

step 2.1: determining deviation between the expected inter-vehicle distance of the following vehicles and the actual inter-vehicle distance after the speed of the guiding vehicle is changed:

wherein, between the time T + tau and the time T + tau + T, the following vehicle is driven by a _n+1 (T + T) acceleration, and a deviation epsilon of the following vehicle at the time of T + T _n The value of (T + τ + T) is closest to 0, i.e., min ε _n (T + tau + T) |, where the formula is only the acceleration a of the following vehicle _n+1 (t + τ) is an unknown quantity;

step 2.2: incorporating constant terms, deviation epsilon _n (T + τ + T) can be simplified as:

wherein, alpha, beta, mu, lambda, kappa and gamma are constants, and the specific calculation formulas are as follows:

α＝x _n (t)+x′ _n (t)·τ-x _n+1 (t)-x′ _n+1 (t)·τ+x′ _n (t)·T-x′ _n+1 (t)·T，

κ＝L+k；

step 2.3: and obtaining the acceleration limit condition of the following vehicle by using a Newton iteration method.

5. The optimal-velocity-based vehicle-following model and the safety analysis method thereof according to claim 4, wherein the step 3 is implemented by the following steps:

step 3.1: assuming stable driving of the fleet, a steady state position X of the vehicle n is obtained _n (t)＝(n-1)d _s +v _s t, wherein the speed of the vehicle is v _s The distance between the heads of adjacent vehicles is d _s ；

Step 3.2: suppose that the lead vehicle is weakly interfered at time t

Wherein x is _n (t) is the actual position of the vehicle n at time t, z is a characteristic value, ω _j For the jth Fourier expansion parameter, the specific formula is

Step 3.3: let a _n+1 (t+τ)＝g(d _n (t),x′ _n+1 (t),x′ _a (t)), for y ″) _a+1 (t + τ) was linearized to give y ″) _n+1 (t+τ)＝g ₁ [y _n (t)-y _n+1 (t)]+g ₂ y′ _n+1 (t)+g ₃ y′ _n (t) in which

Step 3.4: and obtaining the following model stability condition by using a Taylor expansion approximation function as follows:

6. the optimal-velocity-based vehicle-following model and the safety analysis method thereof according to claim 5, wherein the step 4 is implemented by the following steps:

step 4.1: screening available following pairs by using the real data set;

step 4.2: carrying out a simulation experiment according to the model provided by the text by using the screened available following pair data to obtain the vehicle distance between the following vehicle and the guiding vehicle at the moment of t + tau;

step 4.3: carrying out simulation experiments by utilizing the screened available following pair data according to other models, and calculating to obtain the distance between the following vehicle and the guiding vehicle at the moment of t + tau;

step 4.4: and calculating the mean value, the median, the minimum value and the maximum value of the distance between vehicles in the model, other models and real data set, and comparing.

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