基于方差异质性随机参数模型的汇合行为分析

doi:10.13229/j.cnki.jdxbgxb.20220614

摘要/Abstract

摘要：

为研究高速公路交织区入口匝道车辆汇入主线的换道行为，基于方差异质性随机参数模型构建了车辆汇入换道模型，先从NGSIM数据集中提取7个在统计上显著且对换道行为有影响的解释变量，然后将其引入方差异质性随机参数模型探索潜在异质性，计算各变量平均边际效应量化对换道行为的影响，最后提出了“个体样本精度”指标对模型进行比较。研究结果表明：汇入车辆与目标车道领车的车头间距、目标车道领车宽度、辅助车道领车速度对换道行为产生了显著的影响，且汇入车辆在辅助车道上的纵向位置显著影响汇入车辆与目标车道领车的车头间距，方差异质性随机参数模型比未考虑方差异质性的随机参数模型和二元Logit模型具有更高的拟合优度和模型精度，能够更好地解释车辆汇入行为中的潜在异质性。本文的研究成果可应用于自动驾驶辅助系统和交通流仿真软件中，对阐明车道变换行为的机理有一定的参考价值。

关键词: 交通运输安全工程, 方差异质性随机参数模型, 汇合行为, 高速公路, 交织区

Abstract:

In order to study the merging behavior of vehicles in the interweaving area of a freeway， a random parameter model with heterogeneity in variances was used to build a vehicle lane-changing model. Seven explanatory variables that had a significant effect on lane-changing behavior statistically， extracted from NGSIM dataset， was introduced to random parameter model with heterogeneity in variances. The potential heterogeneity was explored by the model. The average margin effects were calculated to quantify the effects of explanatory variables on lane-changing behavior， and individual sample accuracy was established to compare the model accuracy. The results of the study indicate that the space headway between the merging vehicle and the putative leading vehicle， the width of the putative leading vehicle and the speed of the leading vehicle in the auxiliary lane have significant effects on lane-changing behavior， and the longitudinal position of the merging vehicle affects significantly the space headway between the merging vehicle and the putative leading vehicle. Compared with random parameter model that don't consider the variance heterogeneity and binary logit model， random parameter model with heterogeneity in variances has the highest goodness of fit and model accuracy， and can better explain the unobserved heterogeneity during the lane-changing. The results of this paper can be applied to the autonomous driving assistance system and traffic flow simulation software and can shed light on the mechanism of lane-changing behavior.

Key words: transportation safety engineering, random parameter model with heterogeneity in variance, merging behavior, freeway, interweaving area

中图分类号:

U491.2

邬岚,赵乐,李根. 基于方差异质性随机参数模型的汇合行为分析[J]. 吉林大学学报(工学版), 2024, 54(4): 883-889.

Lan WU,Le ZHAO,Gen LI. Analysis of merging behavior based on random parameter model with heterogeneity in variances[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(4): 883-889.

图/表 9

图1

表 1

候选解释变量描述"

变量名称	变量解释
$V$ /（m·s^-1）	M车车速
$V 1$ /（m·s^-1）	PL车车速
$V 2$ /（m·s^-1）	PF车车速
$V 3$ /（m·s^-1）	L车在辅助车道上的速度
$Δ V 1$ /（m·s^-1）	M车和PL车速度差
$Δ V 2$ /（m·s^-1）	M车和PF车速度差
$Δ V 3$ /（m·s^-1）	M车和L车速度差
$Δ D$ /m	PL车与PF车纵向距离差
$Δ D 1$ /m	M车与L车车头间距
$Δ D 2$ /m	M车与PL车头间距
$Δ X 1$ /m	M车与PL车横向距离差
$Δ X 2$ /m	M车与PF车横向距离差
$L 1$ /m	PL车长度
$L 2$ /m	PF车长度
$W 1$ /m	PL车宽度
$W 2$ /m	PF车宽度
$Y$ /m	M车辅助车道上纵向位置

表 1

表2

随机参数分布形式比较"

分布形式	威布尔分布	正态分布	对数正态分布
含随机参数的变量	$Δ D 2$ ， $V 3$	$Δ D 2$ ， $V 3$ ， $W 1$	$Δ D 2$
AIC	592.4	586.2	591.7
McFadden Pseudo R²	0.551	0.558	0.550
对数似然函数值	-286.21	-282.11	-286.87

表2

表3

表4

模型参数估计结果"

解释变量	二元Logit模型		随机参数模型		方差异质性随机参数模型
解释变量	系数	P值	系数	P值	系数		P值
$Δ V 1$	-0.602	0.00	-0.923	0.00	-1.033	0.00
$Δ X 2$	-1.063	0.00	-1.564	0.00	-1.672	0.00
$V 3$	-0.094	0.00	-0.108（0.080）	0.00 （0.03）	-0.125 （0.089）	0.01（0.07）
$Δ D 1$	0.016	0.00	0.021	0.00	0.021	0.03
$Y$	0.011	0.00	0.025	0.00	0.020	0.02
$Δ D 2$	0.127	0.00	0.220（0.076）	0.000 （0.00）	0.274（0.200）	0.00（0.00）
方差 $Δ D 2 : Y$	/		/		-0.018	0.01
$W 1$	-1.112	0.00	-1.590（0.562）	0.01 （0.06）	-1.964（0.631）	0.01（0.10）
常数项	5.569	0.00	7.605	0.00	8.803	0.00

表4

表5

方差异质性随机参数模型各变量边际效应"

变量	边际效应/%	变量	边际效应/%
$Δ V 1$	-21.5	$Y$	6.14
$Δ X 2$	-32.18	$Δ D 2$	22.4
$V 3$ $/ Δ D 1$	-7.05/4.3	$W 1$	-21

表5

图2

图3

图4

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	二元Logit 模型	随机参数模型	方差异质性随机参数模型
AIC	599.9	586.2	569.5
BIC	638.5	639.29	627.35
McFadden Pseudo R²	0.530	0.558	0.572
对数似然函数值	-291.93	-282.11	-272.73
样本精度	86.41%	87.28%	87.39%
个体样本精度	71.58%	73.99%	75.07%