﻿ 平纵组合线形几何特征对车速变化的影响
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (5): 620-625, 666.  DOI: 10.11908/j.issn.0253-374x.2018.05.008 0

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WANG Xuesong, WANG Xiaomeng, YANG Xiaohan. Effect of Combined Horizontal and Vertical Curve on Speed Change[J]. Journal of Tongji University (Natural Science), 2018, 46(5): 620-625, 666. DOI: 10.11908/j.issn.0253-374x.2018.05.008.

文章历史

1. 同济大学 道路与交通工程教育部重点试验室，上海 201804;
2. 同济大学 数学科学学院，上海 200092

Effect of Combined Horizontal and Vertical Curve on Speed Change
WANG Xuesong1, WANG Xiaomeng2, YANG Xiaohan2
1. Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China;
2. School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Abstract: The Tongji University Driving Simulator was used to conduct experiment and collect speed data. Speed change was divided into three intervals: substantial speed decrease, steady speed (minimal change) and substantial speed increase. Multinomial Logistic models were used to investigate the relationships between geometric design characteristics of combined curves and adjacent segments and speed changes. The results show that: for combined curves, it is more difficult to maintain speed as the lengths of combined curves and the mean grades of combined curves increase; the probability to increase speed is higher when combined curves are down-slopes; the probability to maintain speed is higher when combined curves turn left; it is more difficult to maintain speed as the grade changes between the preceding segments and the combined curves increase; the probability to decrease speed is higher when the curvatures of the following segments increase.
Key words: combined horizontal and vertical curve    adjacent segment    speed change    quantitative relationship    driving simulator

Gibreel等[11]利用雷达测速仪实地采集组合线形路段的车速，发现平曲线凹曲线的实际运行速度比传统模型预测结果高，而平曲线凸曲线则相反，说明组合线形对车速的影响比单一线形复杂.Wang等[12]对组合线形与横向加速度定量关系的研究结果表明，平曲线上坡、下坡的曲率与横向加速度正相关，坡度与横向加速度负相关, 平曲线凸曲线的长度、曲率与横向加速度正相关, 平曲线凹曲线的曲率与横向加速度正相关.大部分的研究只考虑了组合线形半径、坡长、坡度等几何设计要素，缺乏对相邻路段的研究.相邻路段几何特征可能会影响驾驶员在组合线形上的驾驶行为，如驾驶员在平曲线上坡行驶，下游路段为下坡将会影响视距，进而使其减速，车速发生变化.

1 组合线形及相邻路段几何特征提取

 图 1 组合线形几何特征 Fig.1 Geometric characteristics of combined curves

 图 2 组合线形与相邻路段示意图 Fig.2 Diagram of combined curves and adjacent segments

2 实验与数据采集 2.1 同济大学驾驶模拟器

 图 3 同济大学驾驶模拟器 Fig.3 Tongji University Driving Simulator

2.2 三维虚拟驾驶场景

(1) 道路逻辑层

(2) 三维环境建模

(3) 模型数据库优化

 图 4 永吉高速公路三维虚拟驾驶场景构建过程 Fig.4 Three-dimensional scene construction process of Yongji Freeway
3 实验与数据采集 3.1 实验人员

3.2 实验流程

(1) 实验准备.向驾驶员介绍实验内容及注意事项.完成个人信息、驾驶经验等基本信息采集.

(2) 模拟试驾.驾驶员进入驾驶舱，调节座椅，并熟悉舱内环境，之后进行约10 min的直行、转弯、超车及刹车等训练，熟悉模拟器操作.

(3) 正式实验.驾驶场景光线充足，路面条件干燥良好.为了减少交通环境对车速的影响，驾驶场景中不设置其他干扰车辆.由于道路双侧的几何线形不同，驾驶员需要完成双侧驾驶.

(4) 填写《眩晕不适调查问卷》.问卷通过“0为无不适、1为轻微不适、2为中等程度不适、3为严重不适”评价驾驶员有无眩晕不适症状.结果显示，30位驾驶员均无不适.

(5) 填写《驾驶模拟器场景反馈评价问卷》.问卷通过“真实、一般、不真实”3个等级评价驾驶模拟场景的真实度，如道路标志标线真实性、护栏树木真实性等，超过87%的驾驶员认为实验场景真实可靠.

3.3 数据采集

 $\Delta v = {v_2} - {v_1}$

 图 5 车速差分布 Fig.5 Distribution of speed difference

4 多项Logistic回归模型

 $\begin{array}{l} {\rm{log}}\left( {\frac{{P\left( {y = 1} \right)}}{{P\left( {y = M} \right)}}} \right) = {\alpha _1} + \sum\limits_{k = 1}^K {{\beta _{1k}}{x_k}} \\ {\rm{log}}\left( {\frac{{P\left( {y = 2} \right)}}{{P\left( {y = M} \right)}}} \right) = {\alpha _2} + \sum\limits_{k = 1}^K {{\beta _{2k}}{x_k}} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \vdots \\ {\rm{log}}\left( {\frac{{P\left( {y = m} \right)}}{{P\left( {y = M} \right)}}} \right) = {\alpha _m} + \sum\limits_{k = 1}^K {{\beta _{mk}}{x_k}} \end{array}$

 ${\rm{log}}\left( {\frac{{P\left( {y = 1} \right)}}{{P\left( {y = 2} \right)}}} \right) = {\alpha _1} + \sum\limits_{k = 1}^K {{\beta _{1k}}{x_k}}$

 ${\rm{log}}\left( {\frac{{P\left( {y = 3} \right)}}{{P\left( {y = 2} \right)}}} \right) = {\alpha _3} + \sum\limits_{k = 3}^K {{\beta _{3k}}{x_k}}$

AIC是衡量统计模型拟合优良性的指标，值越低，说明模型拟合越好.AIC的计算公式为

 ${\rm{AIC}} = ( - 2{\rm{ln}}L) + 2\left( {q + s} \right)$ (1)

5 组合线形几何特征与车速变化关系分析

5.1 组合线形的车速变化模型

5.2 组合线形加相邻路段的车速变化模型

6 结语

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