CN115081227A - Optimal speed-based vehicle following model and safety analysis method thereof - Google Patents

Optimal speed-based vehicle following model and safety analysis method thereof Download PDF

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CN115081227A
CN115081227A CN202210762461.7A CN202210762461A CN115081227A CN 115081227 A CN115081227 A CN 115081227A CN 202210762461 A CN202210762461 A CN 202210762461A CN 115081227 A CN115081227 A CN 115081227A
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费蓉
杨璐
黑新宏
李爱民
马梦阳
王战敏
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Xian University of Technology
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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

Optimal speed-based vehicle following model and safety analysis method thereof
Technical Field
The method belongs to the field of microcosmic traffic flow car following, and particularly relates to a car following model based on optimal speed and a safety analysis method thereof.
Background
In recent years, the country continuously increases the investment of funds on the construction of traffic roads, but due to the lack of long-term consideration of urban roads and urban planning, the construction and reconstruction of roads are seriously hindered. In order to relieve road traffic jam, the state has issued various policies for manual control, such as motor vehicle number limit measures, license plate number purchase limit measures and the like, but the problems of traffic jam and the like still cannot be effectively solved. Therefore, alleviating and relieving traffic congestion is a problem that is currently urgently needed to be solved. The traffic flow models may be classified into a macroscopic traffic flow model and a microscopic traffic flow model, wherein the microscopic traffic flow model mainly includes a cellular automaton model and a vehicle-following model. By analyzing the following behavior of the vehicles for limiting lane change and overtaking, the interaction of the vehicles is explored, and a high-precision vehicle following model is established, so that the problems of traffic congestion and the like are favorably alleviated, and the traffic road service level is improved.
With the increasing of available trajectory data, researchers develop a driver behavior model by using a modern machine learning method to form an artificial intelligence model, wherein inexplicability is the biggest defect of the artificial intelligence model, and a traditional model is highly interpretable based on a traffic flow theoretical basis.
Disclosure of Invention
The invention aims to provide a vehicle following model based on optimal speed and a safety analysis method thereof, and solves the problem that the following state and driving safety are not considered in the existing microcosmic traffic flow model.
The invention relates to a vehicle following model based on optimal speed and a safety analysis method thereof, which comprises the following steps:
step 1: constructing an optimal speed model based on vehicle and driver information in a traffic scene;
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;
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.
Further, the specific implementation steps of step 2 are as follows:
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:
Figure BDA0003721426980000021
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: combining constant terms to deviate by n (T + τ + T) can be simplified as:
Figure BDA0003721426980000031
wherein, alpha, beta, mu, lambda, kappa and gamma are constants, and the specific calculation formulas are respectively 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，
Figure BDA0003721426980000032
Figure BDA0003721426980000033
κ＝L+k；
Step 2.3: and obtaining the acceleration limit condition of the following vehicle by using a Newton iteration method.
Further, the specific implementation steps of step 3 are as follows:
step 3.1: assuming stable driving of the fleet, obtaining the steady state position X of the vehicle n 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
Figure BDA0003721426980000034
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
Figure BDA0003721426980000035
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 + tau) is linearized to obtain 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
Figure BDA0003721426980000036
Figure BDA0003721426980000037
Step 3.4: and obtaining the following model stability condition by using a Taylor expansion approximation function as follows:
Figure BDA0003721426980000038
further, the specific implementation steps of step 4 are as follows:
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.
Further, the specific implementation steps of step 5 are as follows:
step 5.1: simulating a motorcade starting process;
step 5.1.1: simulating a real motorcade starting process scene;
step 5.1.2: simulating according to the following strategy provided by the text, and outputting the speed of the following vehicle;
step 5.1.3: simulating according to the following strategy provided by the text, and outputting the following inter-vehicle distance;
step 5.2: simulating a motorcade stopping process;
step 5.2.1: simulating a real motorcade stopping process scene;
step 5.2.2: simulating according to the following strategy provided by the text, and outputting the speed of the following vehicle;
step 5.2.3: simulating according to the following strategy provided by the text, and outputting the following inter-vehicle distance;
step 5.3: simulating the motorcade uniform speed process;
step 5.3.1: simulating a real fleet uniform speed process scene:
step 5.3.2: simulating according to the following strategy provided by the text, and outputting the speed of the following vehicle;
step 5.3.3: the following inter-vehicle distance is output according to the following strategy simulation provided by the text.
Compared with the prior art, the invention considers the following state and the driving safety, analyzes the conditions that the headway is smaller than the minimum headway and larger than the most comfortable headway based on the optimal speed model, obtains the acceleration monthly constraint condition under the critical condition and ensures the safety of the newly established following model. And the stability analysis is carried out on the obtained car following model to obtain the stability condition of the following model, so that the basic basis is provided for traffic control and driving strategies, the stability of traffic flow is improved, and traffic jam is relieved. The effectiveness and safety of the invention are verified by simulating three real traffic scenes, namely the starting, uniform speed and stopping processes.
The invention designs a following model based on optimal speed, which guarantees that a vehicle is in a following state while considering safety, and proves the effectiveness and safety of the following model in the driving process through a plurality of constructed simulation scenes.
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FIG. 1 is a flow chart of a vehicle-following model based on optimal velocity and a safety analysis method thereof according to the present invention;
FIG. 2 is a speed simulation prediction diagram of a vehicle following model based on optimal speed and a security analysis method thereof in a fleet starting process according to the present invention;
FIG. 3 is a vehicle distance simulation prediction diagram of a vehicle following model based on optimal speed and a security analysis method thereof in a vehicle fleet starting process;
FIG. 4 is a speed simulation prediction diagram of a fleet stopping process of a safety analysis method of a vehicle following model based on optimal speed according to the present invention;
FIG. 5 is a diagram of a simulated prediction of vehicle distance during a vehicle fleet stopping process according to a safety analysis method of a vehicle following model based on an optimal speed of the present invention;
FIG. 6 is a speed simulation prediction diagram of a uniform speed process of a fleet of a vehicle safety analysis method based on an optimal speed of the invention;
FIG. 7 is a diagram of a vehicle distance simulation prediction in a uniform velocity process of a vehicle fleet based on a safety analysis method of a vehicle following model with an optimal velocity according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples.
Referring to fig. 1, the vehicle following model based on the optimal speed and the safety analysis method thereof of the present invention include the following steps:
step 1: constructing an optimal speed model based on vehicle and driver information in a traffic scene;
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;
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.
Step 2, introducing the headway time to determine the critical condition of the optimal speed model, and analyzing to obtain the acceleration limited condition of the following model;
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:
Figure BDA0003721426980000061
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 |. epsilon 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:
Figure BDA0003721426980000071
wherein, alpha, beta, mu, lambda, kappa and gamma are constants, and the specific calculation formulas are respectively 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，
Figure BDA0003721426980000072
Figure BDA0003721426980000073
κ＝L+k；
Step 2.3: utilize newton's iterative method to obtain the restricted condition of car acceleration of following to be followed, set for in this embodiment that the locomotive headway is less than 1.55 seconds and is minimum safe headway, is greater than 2.6 seconds and is the biggest headway, and when the headway is less than 1.55 seconds, the car that follows must slow down, and the restricted condition of its acceleration is:
Figure BDA0003721426980000074
when the headway is more than 2.6 seconds, the following vehicle must accelerate, and the limited conditions of the acceleration are as follows:
Figure BDA0003721426980000075
and 3, carrying out stability analysis on the following model to obtain the stable conditions of the following model, and specifically comprising the following steps:
step 3.1: assuming stable driving of the fleet, obtaining the steady state position X of the vehicle n 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
Figure BDA0003721426980000076
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
Figure BDA0003721426980000077
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) 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
Figure BDA0003721426980000078
Figure BDA0003721426980000081
Step 3.4: and (3) obtaining the following model stability condition by using a Taylor expansion approximation function:
Figure BDA0003721426980000082
in step 4, performing a comparison experiment on the obtained stable following model and other following models to verify the fitting precision of the model, wherein the specific steps are as follows;
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 the real data set, and comparing.
Three typical traffic scenarios are simulated in step 5: and verifying the safety of the following model in a motorcade starting process, a motorcade stopping process and a motorcade uniform speed process.
Step 5.1: simulating a motorcade starting process;
step 5.1.1: the real motorcade starting process scene is simulated, and in the embodiment, the motorcade starting process is set as follows: the motorcade starting process mainly simulates the crossroad, and when the traffic signal lamps are green, the motorcade starts the process of driving through the crossroad. Assuming that a fleet of 5 cars each 10ft long waits for green lights at the intersection, all vehicles in the fleet are at rest and the inter-vehicle distance between each two cars is 20 ft. When the time t is equal to 0, the traffic light is changed from red light to green light, and the guided vehicle is guided at 8ft/s 2 The following vehicles in the motorcade are started one by one;
step 5.1.2: simulating according to the following strategy provided by the text, and outputting the speed of the following vehicle, wherein the specific result is shown in the attached figure 2;
step 5.1.3: simulating according to the following strategy provided by the text, and outputting the following inter-vehicle distance, wherein the specific result is shown in the attached figure 3;
step 5.2: simulating a motorcade stopping process;
step 5.2.1: the real motorcade stopping process scene is simulated, in the embodiment, the motorcade stopping process is set as follows: first, a fleet of 5 cars, each 10ft/s long, was driven at a constant speed of 20ft/s with a 60ft/s inter-vehicle distance between the cars. At this time, the guide vehicle is set to 13ft/s 2 The following vehicles are subjected to deceleration parking one by one along with the guide vehicle, and whether the motorcade has collision is checked;
step 5.2.2: simulating according to the following strategy provided by the text, and outputting the following speed, wherein the specific result is shown in figure 4;
step 5.2.3: simulating according to the following strategy provided by the text, and outputting the following inter-vehicle distance, wherein the specific result is shown in the attached figure 5;
step 5.3: simulating the motorcade uniform speed process;
step 5.3.1: the real motorcade uniform velocity process scene is simulated, in the embodiment, the motorcade uniform velocity process is set as follows: firstly, leading vehicles of a fleet consisting of 5 vehicles run at a constant speed of 20ft/s, 4 following vehicles run at a speed of 30ft/s, and the distance between the two vehicles is 60 ft;
step 5.3.2: simulating according to the following strategy provided by the text, and outputting the following speed, wherein the specific result is shown in figure 6;
step 5.3.3: the following strategy proposed herein was simulated to output the following inter-vehicle distance, the results of which are shown in fig. 7.
Computer program code for carrying out the execution flow of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + +, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. 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 latter scenario, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
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, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block 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 will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The units described in the embodiments of the present disclosure may be implemented by software or hardware. Where the name of a unit does not in some cases constitute a limitation of the unit itself, for example, the first retrieving unit may also be described as a "unit for retrieving at least two internet protocol addresses".
The foregoing description is only exemplary of the preferred embodiments of the disclosure and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the disclosure herein is not limited to the particular combination of features described above, but also encompasses other embodiments in which any combination of the features described above or their equivalents does not depart from the spirit of the disclosure. For example, the above features and (but not limited to) the features disclosed in this disclosure having similar functions are replaced with each other to form the technical solution.

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
Figure FDA0003721426970000021
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:
Figure FDA0003721426970000022
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:
Figure FDA0003721426970000023
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，
Figure FDA0003721426970000024
Figure FDA0003721426970000031
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
Figure FDA0003721426970000032
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
Figure FDA0003721426970000033
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
Figure FDA0003721426970000034
Figure FDA0003721426970000035
Step 3.4: and obtaining the following model stability condition by using a Taylor expansion approximation function as follows:
Figure FDA0003721426970000036
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.
CN202210762461.7A 2022-06-29 2022-06-29 Optimal speed-based vehicle following model and safety analysis method thereof Pending CN115081227A (en)

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* Cited by examiner, † Cited by third party
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CN116469245A (en) * 2023-04-04 2023-07-21 北京工业大学 Network-connected hybrid driving formation integrated test system and method for multiple traffic simulation fusion

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