﻿ 机非物理隔离路段非机动车行为建模仿真
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (6): 778-786.  DOI: 10.11908/j.issn.0253-374x.2019.06.006 0

### 引用本文

NI Ying, LI Yixin, LI Xuhong, SUN Jian. Modeling and Simulation of the Non-motorized Traffic Flow on Physically Separated Bicycle Roadways[J]. Journal of Tongji University (Natural Science), 2019, 47(6): 778-786. DOI: 10.11908/j.issn.0253-374x.2019.06.006

### 文章历史

1. 同济大学 道路与交通工程教育部重点实验室，上海 201804;
2. 杭州海康威视数字技术股份有限公司，上海 201203

Modeling and Simulation of the Non-motorized Traffic Flow on Physically Separated Bicycle Roadways
NI Ying 1, LI Yixin 1, LI Xuhong 2, SUN Jian 1
1. Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China;
2. Hangzhou Hikvision Digital Technology Co., Ltd., Shanghai 201203, China
Abstract: To accurately depict the characteristics of microscopic motion, and describe two-dimensional movements of non-motorized traffic flow, the comfort-zone theory was put forward for the first time to describe the generation of behavior motivation of cyclists. Besides, based on this new theory, we proposed a three-layered model to describe the movements of non-motorized vehicles from the whole process of behaviors. Comparing with empirical data collected in a physically separated road section in Shanghai and the social force model, the proposed model can reflect the microscopic features better, and the average error of trajectories is only 0.64 m.
Key words: non-motorized traffic flow    comfort-zone theory    two-dimensional simulation    physically separated roadways

1 研究综述

2 模型的建立 2.1 舒适空间理论基本思想

 $\mathit{\Omega} = \varphi (V, P, A, N)$

Lewin认为，个体行为的表现取决于个人与所在环境间的相互作用[29].对非机动车骑行者而言，若当前的舒适空间受到侵犯，骑行压力将随之增大从而感到不适.此时骑行者需要通过调整自身相对位置来追求更加舒适的骑行，超车或跟车等行为随之产生.当然，若周围环境无法满足调整的需求，骑行者则将转而改变自身速度以减轻这种不适感，这便是非机动车采取各种行为的动机来源.因此，舒适空间和行为动机之间存在直接的内在联系，而舒适空间的内涵则具体阐述了行为动机的产生原因，即骑行者行为动机的变化是心理状态受环境影响的外在体现.

 图 1 舒适空间形状 Fig.1 Shape of comfort-zone space

 图 2 舒适空间划分 Fig.2 Division of comfort-zone space
2.2 动机生成-行为决策-动作执行模型

2.2.1 动机层

 ${F_n} = {E_n} \cdot G$ (1)

 ${E_n} = \delta \frac{{\left| {{v_n}} \right|}}{{k \cdot {L_o}}}$ (2)

 $\begin{array}{l} {L_o}(x, y) = \\ {\rm{\;\;}}\frac{{{b^2} \cdot \left[ {a + \sqrt {{a^2} - {b^2}} \cdot \cos (\theta (t) - \gamma (t))} \right]}}{{{b^2} \cdot {{\cos }^2}(\theta (t) - \gamma (t)) + {a^2} \cdot {{\sin }^2}(\theta (t) - \gamma (t))}} \end{array}$ (3)

 $G = \Delta v \cdot M$ (4)

2.2.2 决策层

2.2.3 执行层

(1) 期望速度维持模型

 ${\mathit{\boldsymbol{a}}_{\rm{d}}} = \frac{{{\mathit{\boldsymbol{v}}_{\rm{d}}} - {\mathit{\boldsymbol{v}}_n}}}{\tau }$ (5)

(2) 超车模型

 ${\boldsymbol{a}_{{\rm{k}}z}} = \left\{ {\begin{array}{*{20}{l}} { - 0.12 \cdot \frac{{\Delta \boldsymbol{s}}}{{\Delta t}} + 0.72, {\rm{超越阶段}}}\\ {0.11 \cdot \frac{{\Delta \boldsymbol{s}}}{{\Delta t}} + 1.5, {\rm{其他阶段}}} \end{array}} \right.$ (6)

 ${\mathit{\boldsymbol{a}}_o} = \frac{{{\mathit{\boldsymbol{y}}_{\rm{d}}}}}{2} \cdot \frac{\pi }{{{{\left( {{t_{\rm{o}}}} \right)}^2}}} \cdot \cos \left( {\frac{{{t_{\rm{o}}} - {t^\prime }}}{{{t_{\rm{o}}}}} \cdot \pi } \right)$ (7)

(3) 跟车模型

 ${\mathit{\boldsymbol{a}}_{\rm{f}}}(t) = \alpha {\mathit{\boldsymbol{v}}_n}{(t - \varepsilon )^\beta }\frac{{\Delta \mathit{\boldsymbol{v}}(t - \varepsilon )}}{{\Delta \mathit{\boldsymbol{S}}{{(t - \varepsilon )}^\gamma }}}$ (8)

(4) 减速避让模型

(5) 横向让行模型

 ${\mathit{\boldsymbol{a}}_y} = \frac{{\left| {{\mathit{\boldsymbol{v}}_n}} \right| \cdot \mathit{\boldsymbol{e}} - {\mathit{\boldsymbol{v}}_n}}}{\tau }$ (9)

 ${\mathit{\boldsymbol{F}}_{\rm{b}}} = A \cdot \exp ( - d/B)$ (10)

3 数据采集与模型标定 3.1 数据采集

 图 3 数据采集地点 Fig.3 Study site

3.2 模型参数标定

 图 4 不同车型不同密度下的舒适空间范围 Fig.4 Comfort-zone space range of different kinds of non-motorized vehicles
4 模型仿真及评价

 图 5 仿真逻辑流程 Fig.5 Simulation framework

 $\frac{{{\rm{d}}{v_{mn}}}}{{{\rm{d}}t}} = {f_m} + \sum\limits_{n(n \ne m)} {{f_{mn}}} + \sum\limits_u {{f_{mu}}} + \xi$ (11)

4.1 轨迹特征

 图 6 轨迹匹配程度 Fig.6 Trajectories matching results
4.2 速度分布

 图 7 速度分布 Fig.7 Speed distribution
4.3 空间分布特征

 图 8 车辆间距分布 Fig.8 Interspace distribution
4.4 超车行为特征

 图 9 超车起始时刻纵、横向间距 Fig.9 The distance in longitudinal and lateral directions

5 结语

(1) 首次提出舒适空间理论来表征非机动车行为动机的产生原因.同时，该理论充分考虑了非机动车流的异质性和可压缩性特征，为精细化描述非机动车流特征提供了思路.

(2) 基于舒适空间理论，提出了一种非机动车动机-决策-执行三层框架模型(MDO模型)，来模拟异质非机动车行为从动机的产生，到决策执行的全过程.

(3) 实现了非机动车的二维运动，使模型仿真结果能够更加接近车辆在现实中的运动.

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