车车通信环境下考虑交通拥堵状态的碰撞时间混合分布建模研究

赖子良; 王江锋; 李晔; 刘兴华

doi:10.3963/j.jssn.1674-4861.2022.02.007

车车通信环境下考虑交通拥堵状态的碰撞时间混合分布建模研究

doi: 10.3963/j.jssn.1674-4861.2022.02.007

赖子良^{1, 2,},
王江锋^3, ,,
李晔^{1, 2},
刘兴华^{1, 2}

1.
同济大学道路与交通工程教育部重点实验室上海 201804
2.
同济大学交通运输工程学院上海 201804
3.
北京交通大学综合交通运输大数据应用技术交通运输行业重点实验室北京 100044

基金项目:

国家自然科学基金项目 61973028

国家自然科学基金项目 71961137006

“车联网”教育部-中国移动联合实验室开放基金项目 ICV-KF2019-01

详细信息

作者简介:
赖子良（1998—），硕士研究生. 研究方向: 交通设计、规划与管理. E-mail: 1194786267@qq.com

通讯作者:
王江锋（1976—），博士，教授. 研究方向: 智能交通、车路协同. E-mail: wangjiangfeng@bjtu.edu.cn

中图分类号: U491.2
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出版历程
- 收稿日期: 2021-08-31
- 网络出版日期: 2022-05-18

A Time-to-collision Hybrid Distribution Model Considering Congestion Under a Vehicle-to-vehicle Communication Environment

LAI Ziliang^{1, 2
,},
WANG Jiangfeng^{3
, ,},
LI Ye^{1, 2},
LIU Xinghua^{1, 2}

1.
The Key Laboratory of Road and Traffic Engineering of Ministry of Education, Tongji University, Shanghai 201804, China
2.
College of Transportation Engineering, Tongji University, Shanghai 201804, China
3.
Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China

摘要

摘要: 碰撞时间（TTC）是评价车车碰撞风险的有效指标，然而该指标分布规律受到交通状态影响。为研究车车（V2V）通信环境下不同交通状态的TTC分布规律，通过构建基于LTE-V技术的车车通信环境，开展实车实验获取4种典型城市道路中的驾驶数据。考虑加速度和航向角建立动态冲突辨识模型，计算车辆以任意角度接近时的TTC值；针对TTC值的结果出现多峰值现象，将交通流分为“拥堵、缓行、畅通”这3种状态，构建了考虑交通流状态的高斯混合模型以描述不同交通状态下的TTC分布规律，并采用最大期望（EM）算法进行参数求解。将所建高斯混合模型与负指数分布、对数正态分布、负指数/对数正态混合分布这3种传统的TTC分布模型进行对比，采用校正决定系数R²评价模型的拟合优度，并通过K-S检验验证模型的有效性。在此基础上，将所建高斯混合模型应用于非车车通信条件下不同交通状态的TTC分布拟合描述，进一步验证模型的适用性。结果表明：车车通信环境下“拥堵、缓行、畅通”这3种交通状态下的高斯分布均值逐渐增大，所处交通场景的碰撞风险依次降低；考虑交通状态的TTC高斯混合模型拟合优度为0.950 5，相较于其他TTC混合分布模型，拟合优度提升了0.057 5。
- 智能交通 /
- 碰撞时间 /
- 高斯混合模型 /
- 交通状态 /
- 车车通信 /
- EM算法
Abstract: Time-to-collision(TTC)is an effective variable to evaluate the risk of vehicle collision, however it is highly correlated with traffic states. In order to study the TTC distributionat different traffic states under a vehicle-to-vehicle(V2V)communication environment, a test environment based on the long-term evolution-vehicle (LTE-V) technology is developed, and a field experiment is carried out to collect driving behavior data on four typical urban roads. A dynamic conflict identification model considering acceleration and heading angle of tested vehicles is developed to estimate the TTC when the vehicle approached at any angle. Since there are several peaks with- in the distribution of the TTC data, traffic flows are divided into the following three states: congested, slow, and free-flow. A Gaussian mixture model(GMM) considering traffic congestion state is developed to describe the TTC distribution under different traffic states, and an expectation-maximization (EM) algorithm is used to estimate the parameters of the GMM. Three traditional distribution models of TTC including negative exponential, lognormal, and negative exponential / lognormal mixed are compared with the GMM. The goodness of fit of the model is evaluated by adjusted R², and the effectiveness of the model is verified by a K-S test. Then, the GMM is applied to the description of TTC distribution fitting under the condition of non V2V communication to further verify the applicability of the model. The results show that, the mean of Gaussian distribution for three traffic states of"congested, slow, and free-flow"gradually increases in the V2V communication environment, and the collision risk of each traffic scene decreases in turn. Moreover, the goodness of fit of the GMM is 0.950 5, which is 0.057 5 higher than the other mixed distribution models.
- intelligent transportation /
- time-to-collision /
- Gaussian mixture model /
- traffic state /
- vehicle-to-vehicle communication /
- expectation-maximization algorithm

HTML全文

图 1 车辆圆半径示意图

Figure 1. Description of vehicle circle radius

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图 2 车辆碰撞时相对位置关系图

Figure 2. Relative position in case of vehicle collision

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图 3 EM算法主要流程

Figure 3. The main flow of EM algorithm

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图 4 外场实验道路

Figure 4. The field experimental road

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图 5 车车通信环境下4种等级道路的TTC分布拟合结果

Figure 5. TTC distributions fitting results of four grades of urban roads in V2V communication

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图 6 不同环境下GMM拟合结果

Figure 6. GMM fitting results in different environments

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表 1 实验组 & 对照组 & 背景车辆组的模型输入数据

Table 1. Input data of experimental group, control group, and background group

输入数据	数据含义	单位
∆x	前车与后车的横向相对距离	m
∆y	前车与后车的纵向相对距离	m
V_x1/V_x2	前车/后车的横向速度	m/s
V_y1/V_y2	前车/后车的纵向速度	m/s
a_x1/a_x2	前车/后车的横向加速度	m/s2
a_y1/a_y2	前车/后车的纵向加速度	m/s2
α₁/α₂	前车/后车航向角	（°）
w₁/ w₂	前车/后车角速度	（°）/s

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表 2 车车通信环境各等级道路TTC的数据量分布

Table 2. The number of TTC values of each grade road in V2V communication

道路等级	t_TTC/s的数据量
道路等级	(0, 50 s]	(50, 100 s]	(100, 150 s]	(150, 200 s]	(200, 250 s]	(250, 300 s]	(300, 400 s]	(400, 500 s]	(500, 600 s]	(600, 700 s]
快速路	4 045	28	5	3	2	0	2	1	2	1
主干路	3 117	16	6	6	3	2	2	1	0	0
次干路	1 345	23	10	3	4	3	5	0	0	1
支路	1 641	12	15	1	0	1	3	2	0	0

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表 3 车车通信环境各等级道路TTC计算结果

Table 3. TTC calculation results of each grade road in V2V communication

道路等级	原始数据量	有效t_TTC	最小值/s	概率密度峰值/s	均值/s	标准差/s
快速路	8 756	4 045	1.625	8.879	12.774	8.104
主干路	5 462	3 117	1.537	8.514	12.192	7.655
次干路	3 849	1 345	1.156	8.468	11.791	10.225
支路	4 327	1 641	1.228	8.285	11.455	8.683

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表 4 实验组 & 对照组 & 背景车辆组TTC计算结果

Table 4. TTC calculation results of experimental group, control group, and background group

分组情况	原始数据量	有效t_TTC	最小值/s	概率密度峰值/s	均值/s	标准差/s
实验组	20 927	9 906	1.156	8.012	11.402	8.102
对照组	20 668	9 938	1.735	7.362	13.235	8.948
背景车辆组	1 020	413	1.071	7.528	14.352	11.654

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表 5 车车通信环境各等级道路TTC拟合参数结果

Table 5. TTC fitting parameters of different levels' roads in V2V communication

模型	参数	快速路	主干路	次干路	支路
负指数分布	λ	0.077 8	0.081 0	0.083 7	0.078 9
负指数分布	adj.R²	0.346 0	0.283 9	0.325 4	0.240 5
	μ	2.213 0	2.167 4	2.041 2	2.121 0
对数正态分布	σ	0.544 6	0.513 2	0.616 2	0.567 6
	adj.R²	0.850 9	0.833 2	0.827 0	0.824 8
	w	0.182 0	0.314 2	0.468 4	0.218 0
负指数/对数	λ'	0.047 5	0.061 7	0.055 9	0.038 2
正态	μ'	2.170 5	2.102 3	1.895 1	2.051 9
混合分布	σ'	0.480 5	0.394 9	0.332 8	0.482 1
	adj.R²	0.887 2	0.900 3	0.889 1	0.893 0
	w₁	0.512 2	0.535 1	0.583 8	0.603 3
	w₂	0.306 6	0.350 9	0.292 0	0.280 6
	w₃	0.181 2	0.114 0	0.124 2	0.116 1
	μ₁	8.240 2	7.974 3	7.113 3	6.982 0
高斯混合分布	μ₂	14.194 6	15.690 6	15.124 8	13.977 5
高斯混合分布	μ₃	24.755 6	26.953 9	23.369 8	29.704 6
	σ₁	4.434 9	6.036 6	5.403 2	5.339 0
	σ₂	10.401 1	17.762 2	23.810 9	21.992 4
	σ₃	89.776 0	77.872 4	68.359 6	115.072 5
	adj.R²	0.937 2	0.935 9	0.917 0	0.950 5

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表 6 种模型K-S检验结果

Table 6. K-S test results of the four models

道路等级	样本量	p-value
道路等级	样本量	负指数分布	对数正态分布	负指数/ 对数正态混合分布	高斯混合分布
快速路	4 045	7.584×10^-3/不通过	0.086 4/通过	0.108 3/通过	0.162 1/通过
主干路	3 117	6.305×10^-3/不通过	0.109 7/通过	0.135 8/通过	0.173 9/通过
次干路	1 345	9.016×10^-5/不通过	0.125 6/通过	0.136 5/通过	0.328 5/通过
支路	1 641	4.792×10^-4/不通过	0.073 1/通过	0.096 5/通过	0.142 8/通过

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表 7 实验组 & 对照组 & 背景车辆组GMM参数及K-S检验结果

Table 7. Results of GMM fitting parameters and K-S test of experimental group, control group, and background group

参数	实验组	对照组	背景车辆组
w₁	0.580 7	0.413 7	0.459 0
w₂	0.275 8	0.407 3	0.333 0
w₃	0.143 5	0.179 0	0.208 0
μ₁	7.084 5	7.567 1	7.715 8
μ₂	12.814 8	13.057 8	15.624 8
μ₃	26.154 8	27.429 2	34.234 2
σ₁	5.724 9	5.274 7	7.582 5
σ₂	17.806 8	17.106 7	29.910 1
σ₃	103.178 8	112.246 3	121.185 6
样本量	9 906	9 938	413
adj.R²	0.923 7	0.940 3	0.759 4
p-value	0.215 7	0.346 0	0.073 1
检验结果	通过	通过	通过

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