阅读说明：本技术 一种基于鸣笛效应下连续通量差的改良交通流分析方法 (Improved traffic flow analysis method based on continuous traffic difference under whistling effect ) 是由 赵敏 黄欣 覃文智 于 2021-08-10 设计创作，主要内容包括：本发明提供一种基于鸣笛效应下连续通量差的改良交通流分析方法,包含以下步骤：S1：在格子流体力学模型的基础上,设计一个带有鸣笛效应下连续通量差的控制函数项,该项函数通过当前连续通量差来判断鸣笛环境下司机是否应该调整速度,使交通流仿真贴近于真实交通流；S2：利用控制理论分析,研究鸣笛效应下连续通量差对交通流的影响。通过考虑了鸣笛效应下连续通量差以使得系统更加符合实际的交通流,可以有效缓解交通拥堵,使交通流更加均匀及稳定,让司机拥有一个更加安全及舒适的行驶体验。(The invention provides an improved traffic flow analysis method based on continuous traffic flow difference under a whistling effect, which comprises the following steps of: s1: on the basis of a lattice hydrodynamics model, a control function item with continuous flux difference under a whistle effect is designed, and the item function judges whether a driver should adjust the speed under the whistle environment or not according to the current continuous flux difference so that the traffic flow simulation is close to the real traffic flow; s2: and (4) analyzing by using a control theory, and researching the influence of the continuous flux difference on the traffic flow under the whistle effect. Continuous flux difference under the whistling effect is considered, so that the system is more consistent with actual traffic flow, traffic jam can be effectively relieved, the traffic flow is more uniform and stable, and a driver has safer and more comfortable driving experience.)

1. An improved traffic flow analysis method based on continuous traffic volume difference under a whistling effect is characterized in that: comprises the following steps:

s1: on the basis of a lattice hydrodynamics model, a control function item with continuous flux difference under a whistle effect is designed, and the item function judges whether a driver should adjust the speed under the whistle environment or not according to the current continuous flux difference so that the traffic flow simulation is close to the real traffic flow;

s2: and (4) analyzing by using a control theory, and researching the influence of the continuous flux difference on the traffic flow under the whistle effect.

2. The improved traffic flow analysis method based on continuous traffic flow difference under whistle effect according to claim 1, characterized in that: the S1 includes the following steps:

step 1.1: determining a differential equation of the lattice fluid mechanics model:

step 1.2: constructing a function term of continuous flux difference under consideration of whistling effect as follows:

where μ is the feedback gain, τ is the reaction time of the whistling effect, q_mFor maximum flux, k is the flux intensity coefficient, b is a constant parameter, and when k is 0, (1+ k) q_j+1-q_jIs the actual flux difference;

step 1.3: defining an optimal velocity function term with maximum velocity and local density as:

wherein v is_maxAt maximum speed, ρ_cIs the local density;

step 1.4: the lattice fluid mechanics model considering the continuous flux difference under the whistling effect is:

3. the improved traffic flow analysis method based on continuous traffic flow difference under whistle effect according to claim 1, characterized in that: the specific steps of the step 2 are as follows:

step 2.1: suppose that the steady-state uniform traffic flow is [ rho ]_n,q_n]^TThe expected density and flux are [ ρ, q ]]^TAnd [ rho ]_n,q_n]^T＝[ρ*,q*]^TAdding small perturbations [ rho ] in the lattice hydrodynamics model⁰,q⁰]And linearizing the lattice fluid mechanics model to obtain:

wherein

Step 2.2: laplace transform is carried out on the two formulas, and high-order terms in the two formulas are ignored, so that:

sP_j+1(s)-ρ_j+1(0)+ρ₀[Q_j+1(s)-Q_j(s)]＝0

wherein P is_j+1(s)＝L(ρ_j+1)，Q_j+1(s)＝L(q_j)，Q_j+1(s)＝L(q_j+1) L (·) is the Laplace transform function, s is the complex frequency;

step 2.3: eliminating the term P by a lattice hydrodynamic model that accounts for the difference in continuous flux under the whistling effect_j+1After(s), the flux equation is obtained as:

wherein the characteristic polynomial is

Step 2.4: let transfer function G(s) beConstruction of Q_j+1(s) and Q_j(s) is as follows:

Q_j(s)＝G(s)Q_j+1(s)

step 2.5: when a + b > 0, provided that mu/tau is positive,Then, the characteristic polynomial d(s) remains in a steady state; when D(s) is in a stable state and the transfer function G(s) satisfies | | G(s) | charging_∞When the traffic flow is less than or equal to 1, the traffic jam phenomenon does not occur in the traffic flow system, namely the traffic flow is in a stable state;

step 2.6: assuming that s is j ω, we get:

step 2.7: suppose thatω∈[0,∞]Then, the sufficiency condition of traffic flow is converted to g (omega) less than or equal to 1, namely:

step 2.8: neglecting ω²After the item, the sufficiency condition of the traffic flow is simplified as follows:

4. the improved traffic flow analysis method based on continuous traffic flow difference under blast effect according to claim 2, characterized in that: the flux intensity coefficient k in S1 has a value range of [ -1,1 ].

Technical Field

The invention relates to the technical field of physical science and engineering, in particular to an improved traffic flow analysis method based on continuous traffic volume difference under a whistling effect.

Background

With the acceleration of the global urbanization process and the rapid development of traffic demands, the traffic situation is increasingly worsened, and the problem of traffic congestion becomes an important problem of modern traffic theory. In order to solve the problem, scholars at home and abroad propose various traffic flow models, such as an automobile following model, a cellular automaton model, a generalized force model, a lattice hydrodynamics model and the like. Automobile following models are widely used to describe individual characteristics of traffic flow using information such as speed, position, acceleration, etc. And the grid fluid mechanics model researches traffic flow characteristics through variation relations among variables such as density, flux and speed.

In recent years, control theory has been widely applied to traffic flow models, and lattice fluid mechanics models have received high attention due to their macroscopic and microscopic properties. Scholars propose lattice fluid mechanics models from the aspects of density difference, flux difference, lattice point position, expected effect and the like to prove the advantages of the models. In 2000, Keiji Konishi et al first studied the traffic jam suppression problem of the car following model using a distributed delay feedback control method. Since then, researchers have proposed many extended automobile following models using control theory. Inspired by the development of an automobile following model control method, the modern control theory of the lattice fluid mechanics model draws great attention. In 2015, gexia et al utilized the flux difference as a feedback signal to suppress traffic congestion. Li yongfu et al propose a new control signal with poor density variation. Cen Bing Ling et al proposed a sub-nearest neighbor interaction control method, and also studied the kink-resistant type of density waves in order to analyze long-term traffic behavior. Peng Guangdong et al combine historical evolution information and feedback control signal to deduce the stability condition of traffic flow, and the numerical simulation result shows that both the feedback control signal and the historical evolution information can alleviate traffic jam, but the feedback control signal plays a more important role in traffic flow than the historical evolution information. Therefore, how to select the feedback control signal and how to select a reasonable parameter value are important for controlling the stability of the traffic flow.

In actual traffic, when a rear vehicle whistles, a front vehicle always adjusts the speed of the current vehicle. In the prior art, most researchers collect useful information of vehicles in front and at the back based on a grid fluid dynamic model, and control a traffic system by using the information as a feedback control signal. Therefore, penguangdong et al fully consider the influence of the difference between the current flux and the maximum flux in the whistle environment on the traffic flow, and simulation results thereof show that the control method of the difference between the maximum flux and the current flux can effectively improve the stability of the traffic flow. In addition, the influence of individual differences on traffic flow under the whistle effect was also studied. In recent years, researchers have conducted theoretical analysis of control over traffic flow stability based on feedback control signals in grid fluid mechanics models and feedback control signals in different environments, and studied feedback signals such as individual differences of drivers and differences between current flux and maximum flux in a whistling environment, but have not considered the influence of continuous flux differences on traffic flow under the whistling effect.

Disclosure of Invention

The invention aims to solve the problem that the influence of continuous flux difference under the whistle effect on traffic flow is not considered in a simulation result in the prior art, and provides an improved traffic flow analysis method based on the continuous flux difference under the whistle effect.

An improved traffic flow analysis method based on continuous traffic volume difference under a whistling effect is characterized in that: comprises the following steps:

s1: on the basis of a lattice hydrodynamics model, a control function item with continuous flux difference under a whistle effect is designed, and the item function judges whether a driver should adjust the speed under the whistle environment or not according to the current continuous flux difference so that the traffic flow simulation is close to the real traffic flow; :

s2: and (4) analyzing by using a control theory, and researching the influence of the continuous flux difference on the traffic flow under the whistle effect.

Preferably, the S1 includes the following steps:

step 1.1: determining a differential equation of the lattice fluid mechanics model:

step 1.2: constructing a function term of continuous flux difference under consideration of whistling effect as follows:

where μ is the feedback gain, τ is the reaction time of the whistling effect, q_mFor maximum flux, k is the flux intensity coefficient, b is a constant parameter, and when k is 0, (1+ k) q_j+1-q_jIs the actual flux difference;

step 1.3: defining an optimal velocity function term with maximum velocity and local density as:

wherein v is_maxAt maximum speed, ρ_cIs the local density;

step 1.4: the lattice fluid mechanics model considering the continuous flux difference under the whistling effect is:

preferably, the specific steps of step 2 are:

step 2.1: suppose that the steady-state uniform traffic flow is [ rho ]_n,q_n]^TThe desired density and flux are [ rho ]^*,q^*]^TAnd [ rho ]_n,q_n]^T＝[ρ^*,q^*]^TIn the latticeAdding small perturbation [ rho ] into sub-fluid mechanics model⁰,q⁰]And linearizing the lattice fluid mechanics model to obtain:

wherein

Step 2.2: laplace transform is carried out on the two formulas, and high-order terms in the two formulas are ignored, so that:

wherein P is_j+1(s)＝L(ρ_j+1)，Q_j+1(s)＝L(q_j)，Q_j+1(s)＝L(q_j+1) L (·) is the Laplace transform function, s is the complex frequency;

step 2.3: eliminating the term P by a lattice hydrodynamic model that accounts for the difference in continuous flux under the whistling effect_j+1After(s), the flux equation is obtained as:

wherein the characteristic polynomial is

Step 2.4: let transfer function G(s) beConstruction of Q_j+1(s) and Q_j(s) is as follows:

Q_j(s)＝G(s)Q_j+1(s)

step 2.5: when a + b > 0, provided that mu/tau is positive,The characteristic polynomial d(s) remains in a steady state. When D(s) is in a stable state and the transfer function G(s) satisfies | | G(s) | charging_∞When the traffic flow is less than or equal to 1, the traffic jam phenomenon does not occur in the traffic flow system, namely the traffic flow is in a stable state.

Step 2.6: assuming that s is j ω, we get:

step 2.7: suppose thatThe sufficiency of traffic flow conditions are converted to g (ω) ≦ 1, i.e.:

step 2.8: neglecting ω²After the item, the sufficiency condition of the traffic flow is simplified as follows:

preferably, the flux intensity coefficient k in S1 is in the range of [ -1,1 ].

The improved traffic flow analysis method based on the continuous flux difference under the whistle effect considers the continuous flux difference under the whistle effect so that the system is more consistent with the actual traffic flow, and finds that the increase of the ratio of the feedback gain to the reaction time of the whistle effect or the reduction of the intensity coefficient of the flux can obviously promote the stability of the traffic flow in the process of simulating the traffic flow by using numerical simulation.

Drawings

FIG. 1 is a flow chart of an improved traffic flow analysis method based on continuous traffic flow difference under whistling effect according to the present invention;

FIG. 2 is a Baud chart of the response time ratio of feedback gain and whistling effect and different values of flux intensity coefficient for the improved traffic flow analysis method based on continuous flux difference under whistling effect provided by the invention;

FIG. 3 is a graph of density-time variation of 2, 25, 55, 80 grid points in a grid hydrodynamic model of Takashi Nagatani within 1-200s under different values of the ratio of feedback gain to reaction time of the whistle effect in constant parameters according to the improved traffic flow analysis method based on continuous flux difference under the whistle effect provided by the invention;

FIG. 4 is a graph of density-time variation of the 2 nd, 25 th, 55 th and 80 th lattice points in the penguang lattice fluid mechanics model in 1-200s under different values of the ratio of the feedback gain to the reaction time of the whistle effect in constant parameters according to the improved traffic flow analysis method based on the continuous flux difference under the whistle effect provided by the invention;

fig. 5 is a graph of density-time variation of 2 nd, 25 th, 55 th and 80 th grid points in a grid fluid mechanics model in 1-200s under different values of flux intensity coefficient in the ratio of feedback gain to reaction time of whistling effect according to the improved traffic flow analysis method based on continuous flux difference under whistling effect in one embodiment of the invention;

FIG. 6 is a graph of density-time variation of the 2 nd, 25 th, 55 th and 80 th lattice points in the grid fluid mechanics model in Peng light over 10000-;

fig. 7 is a graph of density-time variation of 2 nd, 25 th, 55 th and 80 th grid points in 10000-.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments.

Referring to fig. 1 to 7, an improved traffic flow analysis method based on continuous flux difference under whistling effect first determines differential equation of lattice fluid mechanics model:

adding function terms of continuous flux difference under whistling effectThe lattice hydromechanical model is then:

mu is feedback gain, tau is reaction time of whistling effect, q_mFor maximum flux, k is the flux intensity coefficient, b is a constant parameter, and when k is 0, (1+ k) q_j+1-q_jIs the actual flux difference, v_maxAt maximum speed, ρ_cFor local density, optimumThe velocity function term is defined as:

in one embodiment, the flux intensity coefficient k has a value of-1, and in another embodiment, the flux intensity coefficient k has a value of 1. In other embodiments, the flux intensity coefficient k takes any value of [ -1,1 ].

Suppose that the steady-state uniform traffic flow is [ rho ]_n,q_n]^TThe desired density and flux are [ rho ]^*,q^*]^TAnd [ rho ]_n,q_n]^T＝[ρ^*,q^*]^TAdding small perturbations [ rho ] in the lattice hydrodynamics model⁰,q⁰]And linearizing the lattice fluid mechanics model to obtain:

wherein

Laplace transform is performed on the two equations, and high-order terms are ignored, so that:

P_j+1(s)＝L(ρ_j+1)，Q_j+1(s)＝L(q_j)，Q_j+1(s)＝L(q_j+1) L (·) is the Laplace transform function, s is the complex frequency;

eliminating term P by applying the lattice fluid mechanics model of the present invention_j+1After(s), the flux equation is obtained as:

a characteristic polynomial of

Let transfer function G(s) beConstruction of Q_j+1(s) and Q_j(s) is as follows:

Q_j(s)＝G(s)Q_j+1(s)

when a + b > 0, provided that mu/tau is positive,When D(s) is in steady state and transfer function G(s) satisfies | | G(s) |_∞When the traffic flow is less than or equal to 1, the traffic jam phenomenon does not occur in the traffic flow system, namely the traffic flow is in a stable state.

Assuming that s is j ω, we get:

suppose thatThen the sufficiency condition that the traffic flow tends to steady state is converted to g (omega) 1 or less, namely:

neglecting ω²After the item, the sufficiency condition that the traffic flow tends to be steady is simplified as follows:

in order to verify the effect of the invention, MATLAB is applied to carry out numerical simulation verification.

Fig. 2 is a bode diagram of the present invention under different values of the ratio μ/τ of the feedback gain to the reaction time of the whistling effect, the constant parameter b, and the flux intensity coefficient k, and the stability of the traffic flow depends on the peak value of the bode curve. As shown in fig. 2, fig. 2(a) shows baud curves when b is 0, μ/τ is 0.2,0.4, and 0.6, and fig. 2(b) to (d) show baud curves when b is 0.5, μ/τ is 0.2,0.4, and 0.6, k is 0.4,0, and-0.4, respectively. It can be seen that, as the ratio μ/τ of the feedback gain to the reaction time of the whistle effect increases, the peak value of the corresponding baud curve decreases, and as the intensity coefficient k of the flux decreases, the peak value of the corresponding baud curve also decreases, which indicates that controlling the continuous flux difference can significantly promote the stability of the traffic flow.

Fig. 3 is a graph showing the density-time change of the 2 nd, 25 th, 55 th and 80 th lattice points in the lattice fluid mechanics model of Takashi Nagatani within 1 to 200s when the constant parameter b is 0 and the ratio μ/τ of the feedback gain to the reaction time of the whistle effect is 0. As shown in fig. 3, the kink type of the density wave oscillates sharply at all lattice points, which causes instability in traffic flow.

Fig. 4 is a graph showing density-time changes of 2 nd, 25 th, 55 th, and 80 th lattice points in a fluid mechanics model of a penlight lattice in 1 to 200s, when a constant parameter b is 0, according to the present invention, the ratio μ/τ of the feedback gain to the reaction time of the whistling effect is different. As shown in fig. 4, fig. 4(a) to (c) are density-time curves of the 2 nd, 25 th, 55 th, and 80 th lattice points at b ═ 0 and μ/. tau ═ 0.2,0.4, and 0.6, respectively. It can be seen that as the ratio μ/τ of the feedback gain to the response time of the whistle effect increases, the oscillation of the density wave tends to be gentle, which indicates that only the whistle effect is considered to alleviate the traffic jam to some extent, but the density fluctuation of the traffic flow attenuates slowly.

Fig. 5 is a graph showing the change in density with time of the 2 nd, 25 th, 55 th, and 80 th lattice points in the lattice fluid dynamic model of the present invention within 1 to 200s for different values of the intensity coefficient k of the flux when μ/τ is 0.2 in the present invention. As shown in fig. 5, fig. 5(a) to (c) show density-time curves of 2 nd, 25 th, 55 th, and 80 th grid points at μ/τ of 0.2 and k of 0.4,0, -0.4, respectively. It can be seen that as the intensity coefficient k of the flux decreases, the fluctuation of the density wave is more gradual than that of fig. 4, which indicates that the stability of the traffic system can be significantly improved by considering the continuous flux difference under the blast effect.

Fig. 6 is a graph showing density-time changes of 2 nd, 25 th, 55 th and 80 th lattice points in 10000-. As shown in fig. 6, fig. 6(a) to (c) are density-time curves of the 2 nd, 25 th, 55 th, and 80 th lattice points at b ═ 0 and μ/. tau ═ 0.2,0.4, and 0.6, respectively. It can be seen that the oscillation amplitude of the density wave gradually decreases as the ratio μ/τ of the feedback gain to the reaction time of the whistle effect increases, in accordance with the results in fig. 4. Further, the oscillation amplitude of the density wave enters a steady state when μ/τ is 0.6.

Fig. 7 is a graph of density-time variation of 2 nd, 25 th, 55 th, 80 th lattice points in 10000-. As shown in fig. 7, fig. 7(a) - (c) show the density-time curves for μ/τ of 0.2 and k of 0.4,0, -0.4, respectively. It can be seen that when k is 0.4, the flux effect of the leading vehicle increases, causing the leading vehicle to accelerate to exacerbate traffic congestion; when k is-0.4, the flux effect of the front vehicle is weakened, so that the front vehicle is decelerated to avoid the rear-end collision phenomenon. Further, when k is-0.4, the oscillation amplitude of the density wave enters a steady state. This indicates that the intensity coefficient of the flux has an important influence on the stability of the traffic flow, and the stability of the traffic flow is significantly enhanced as the intensity coefficient k of the flux is decreased.

From the numerical simulation results, when the continuous flux difference under the whistle effect in the traffic system is considered, the stability of the traffic flow is gradually enhanced along with the increase of the ratio mu/tau of the feedback gain to the reaction time of the whistle effect or the reduction of the intensity coefficient k of the flux.

Comparing fig. 3, fig. 4 and fig. 5, the density waves of all lattice points in the lattice fluid mechanics model of Takashi Nagatani in fig. 3 oscillate vigorously, resulting in unevenness of traffic flow; the fluctuation of the density wave of the corresponding grid point in the peng contained grid fluid mechanics model in fig. 4 is gradually smooth, but a long time may be needed to enable the traffic flow to reach the expected density and flux, and the fluctuation of the density wave of the corresponding grid point in the grid fluid mechanics model in the invention in fig. 5 is more smooth, which shows that the continuous flux difference term in the invention can obviously improve the stability of the traffic system.

Comparing fig. 6 and 7, the fluctuation of the density wave of the corresponding grid points in the peng-contained grid fluid mechanics model in fig. 6 is gradually smooth as in fig. 4, but it may also take a long time to make the traffic flow reach the desired density and flux; however, the fluctuation amplitude of the density wave corresponding to the lattice point in the lattice fluid dynamic model of the present invention in fig. 7(a) - (b) is significantly smaller than that in fig. 6(a), which indicates that the continuous flux difference term in the present invention can significantly improve the stability of the traffic flow.

It should be noted that various standard components used in the present invention are commercially available, non-standard components are specially customized, and the connection manner adopted in the present invention, such as bolting, welding, etc., is also a very common means in the mechanical field, and the inventor does not need to describe herein any further.

The above description is only an example of the present invention, and is not intended to limit the present invention, and it is obvious to those skilled in the art that various modifications and variations can be made in the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.