基于Lennard-Jones势的车辆跟驰动力学特性及模型

doi:10.13229/j.cnki.jdxbgxb20210395

摘要/Abstract

摘要：

为更准确描述道路中前后相邻车辆的跟驰交互行为，利用其与某些微观粒子的热力学表现的相似性，构建车辆跟驰模型。通过系统相似性分析，将车辆类比为狭长管道中的微观粒子，将复杂的车辆跟驰交互行为简化为后车不断寻求与前车保持需求安全距离的动态过程，建立不同情况下的需求安全距离表达式。通过对适用于惰性气体体系热力学分析的Lennard-Jones势函数的数学推导，明确其各变量对势能的影响关系，分析了现有的分子跟驰模型存在的问题。参考Lennard-Jones势函数构建了车辆相互作用势函数，考虑了车道边界产生的道路壁面势的影响，提出了基于Lennard-Jones势的车辆跟驰模型。仿真测试结果表明：对比已有的分子跟驰模型和IDM模型，该模型得出的车辆加速度结果与实际数据的平均绝对误差与均方根误差更低，证明基于Lennard-Jones势的车辆跟驰模型对真实车辆的跟驰行为具有更好的拟合效果。

关键词: 交通工程, 跟驰模型, 分子热力学, Lennard-Jones势, 需求安全距离, 壁面作用势

Abstract:

In order to more accurately describe the car-following interaction behavior of adjacent vehicles on the road， a car-following model is constructed by using its similarity with the thermodynamic performance of some microscopic particles. Through the system similarity analysis, the vehicle is likened to a microscopic particle in a long and narrow pipeline, and the complex vehicle following interaction is simplified into a dynamic process in which the following vehicle constantly seeks to keep a safe distance from the preceding vehicle. The expressions of the safe distance under different conditions are established. Through the mathematical derivation of Lennard-Jones potential function which is suitable for the thermodynamic analysis of inert gas system, the influence of its variables on the potential energy is clarified, and the problems existing in the existing molecular following model are analyzed. The vehicle interaction potential function was constructed by referring to the Lennard-Jones potential function, and the influence of the road wall potential generated by the lane boundary was considered. The vehicle following model based on the Lennard-Jones potential was proposed. The simulation test results show that： Compared with the existing molecular car-following model and IDM model, the mean absolute error and root mean square error of the vehicle acceleration results obtained by this model are lower than the actual data, which proves that the car-following model based on Lennard-Jones potential has a better fitting effect on the real vehicle's car-following behavior

Key words: traffic engineering, car-following model, molecular thermodynamics, Lennard-Jones potential, demand safety distance, wall potential

中图分类号:

U491

曲大义,赵梓旭,贾彦峰,王韬,刘琼辉. 基于Lennard-Jones势的车辆跟驰动力学特性及模型[J]. 吉林大学学报(工学版), 2022, 52(11): 2549-2557.

Da-yi QU,Zi-xu ZHAO,Yan-feng JIA,Tao WANG,Qiong-hui LIU. Car⁃following dynamics characteristics and model based on Lennard⁃Jones potential[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(11): 2549-2557.

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参数	标定值
m	0.7103
n	1.6754
λ₁	29.2322
λ₂	44.4901

运动状态	λ₁	λ₂
常规行驶	1.3401	9.4095
起动加速	0.9548	17.3827
减速停车	66.5029	0.0141

参数	标定值
a/（m·s^-2）	1
b/（m·s^-2）	2
v₀/（m·s^-1）	33.3
s₀/m	10
T/s	1.5

模型	MAE	RMSE
M-MD	1.4867	0.7473
IDM	0.8004	0.5982
GLM	0.3772	0.5240