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 浙江大学学报(工学版)  2017, Vol. 51 Issue (10): 2005-2011  DOI:10.3785/j.issn.1008-973X.2017.10.015 0

### 引用本文 [复制中英文]

dx.doi.org/10.3785/j.issn.1008-973X.2017.10.015
[复制中文]
JI Xue-bin, WANG Hui, SONG Chun-yue. Traffic flow modeling and safety analysis in hydropower construction based on cellular automata[J]. Journal of Zhejiang University(Engineering Science), 2017, 51(10): 2005-2011.
dx.doi.org/10.3785/j.issn.1008-973X.2017.10.015
[复制英文]

### 通信联系人

orcid.org/0000-0001-8695-5649.
Email: hwang@iipc.zju.edu.cn

### 文章历史

Traffic flow modeling and safety analysis in hydropower construction based on cellular automata
JI Xue-bin , WANG Hui , SONG Chun-yue
College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China
Abstract: A traffic flow model in hydropower construction was proposed based on cellular automata (CA). The model considered the difference of slope, drivers' psychological quality and dump trucks' performance. The function of randomization probability and the function of lane-changing probability were defined. Traffic accident rules were introduced in order to analyze the relationship between traffic accident and headway distance. The probability of occurrence of traffic accident was analyzed under different headway distance with low speed and median speed. The traffic flow model was verified by comparing simulation result with real data. The safety distance obtained from simulation with low speed and median speed was similar to that in corresponding norm, and the error was acceptable.
Key words: cellular automata (CA)    slope    traffic accident    safety distance

1 模型描述

 图 1 车辆状态示意图 Fig. 1 Schematic of vehicles' states
1.1 跟驰规则

 图 2 车辆上坡时的受力分析 Fig. 2 Vehicle's stress analysis on uphill road

 ${T_1} - {F_1} - G\sin \theta = ma,$ (1)
 $a = \frac{{{T_1} - {F_1}}}{m} - g\sin \theta .$ (2)

 ${F_2} + G\sin \theta - {T_2} = mb,$ (3)
 $b = \frac{{{F_2} - {T_2}}}{m} + g\sin \theta .$ (4)

 $a = {a_{\rm{m}}} + C.$ (5)

 $C = \left\{ {\begin{array}{*{20}{c}} { - {a_{\rm{m}}},以概率\;{p_{\rm{a}}};}\\ {0,其他.} \end{array}} \right.$ (6)

 ${p_{\rm{a}}} = g\sin \theta /{a_{\rm{m}}}.$ (7)

 $b = {b_{\rm{m}}} + D.$ (8)

 $D = \left\{ {\begin{array}{*{20}{c}} {{b_{\rm{m}}},以概率\;{p_{\rm{b}}};}\\ {0,其他.} \end{array}} \right.$ (9)

 ${p_{\rm{b}}} = g\sin \theta /{b_{\rm{m}}}.$ (10)

 ${p_{\rm{a}}} = g\eta /{a_{\rm{m}}},$ (11)
 ${p_{\rm{b}}} = g\eta /{b_{\rm{m}}}.$ (12)

CA模型中的随机慢化主要是描述由于实际行驶中各种不确定因素的存在, 导致驾驶员产生随机减速的行为.在实际中, 随机慢化不仅与车辆的速度有关, 还与驾驶员的心理素质有关, 定义随机慢化概率为一个与车辆速度和驾驶员心理素质相关的函数,

 ${p_{\rm{s}}}\left( {{k_1},v} \right) = {k_1}\exp \left( { - v/{\gamma _1}} \right).$ (13)

1) 确定随机慢化概率：

 $p = {p_{\rm{s}}}\left( {{k_1},v} \right).$ (14)

2) 加速：

 ${v_i} = \left( {t + \frac{1}{3}} \right) = \min \left\{ {{v_i}\left( t \right) + a,{v_{\max }}} \right\}.$ (15)

3) 减速：

 ${v_i}\left( {t + \frac{2}{3}} \right) = \min \left\{ {{v_i}\left( {t + \frac{1}{3}} \right),{\rm{ga}}{{\rm{p}}_i}\left( t \right)} \right\}.$ (16)

4) 随机慢化：

 ${v_i}\left( {t + 1} \right) = \left\{ \begin{array}{l} \max \left\{ {{v_i}\left( {t + \frac{2}{3}} \right) - b,0} \right\},以概率\;p;\\ {v_i}\left( {t + \frac{2}{3}} \right),\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;其他. \end{array} \right.$ (17)

5) 位置更新：

 ${X_i}\left( {t + 1} \right) = {X_i}\left( t \right) + {v_i}\left( {t + 1} \right).$ (18)
1.2 换道规则

1) 换道动机：

 ${\rm{ga}}{{\rm{p}}_i}\left( t \right) < \min \left\{ {{v_i}\left( t \right) + {a_{\rm{m}}},{v_{\max }}} \right\},$ (19)
 ${\rm{ga}}{{\rm{p}}_{i,{\rm{f}}}}\left( t \right) > {\rm{ga}}{{\rm{p}}_i}\left( t \right).$ (20)

2) 安全条件：

 ${\rm{ga}}{{\rm{p}}_{i,{\rm{b}}}}\left( t \right) > {d_{{\rm{safe}}}}.$ (21)

 ${p_{\rm{c}}}\left( {{k_1},{k_2},\eta } \right) = {k_1}{k_2}\exp \left( { - \eta /{\gamma _2}} \right).$ (22)

1.3 交通事故

 ${\rm{ga}}{{\rm{p}}_i}\left( t \right) \le {v_{\max }},$ (23)
 ${v_{i + 1}}\left( t \right) > 0,$ (24)
 ${v_{i + 1}}\left( {t + 1} \right) = 0.$ (25)

2 案例仿真研究

2.1 模型参数定义与设置

 $\rho = \frac{N}{{2L}} = \frac{{{N_{\rm{f}}} + {N_{\rm{e}}}}}{{2L}}.$ (26)

 $V = \frac{1}{{T - {t_0} + 1}}\sum\limits_{t = {t_0}}^T {\left( {\frac{1}{N}\sum\limits_{i = 1}^N {{v_i}\left( t \right)} } \right)} .$ (27)

 $J = \rho V.$ (28)

 ${P_{{\rm{ac}}}} = \frac{{{N_{{\rm{ac}}}}}}{N}.$ (29)

2.2 交通流模型仿真及验证

 图 3 元胞自动机模型仿真结果与实际数据的流量-密度对比图(η=3%, μ1=0.8) Fig. 3 Comparison diagram between simulation of cellular automata model and real data with η=3% and μ1=0.8

2.3 事故率与安全距离

 图 4 不同最大速度下事故率与密度的关系图(η=3%, μ1=0.8) Fig. 4 Probability of Pac as function of density under various vmax with η=3% and μ1=0.8

 图 5 Nac(d)的频率分布直方图 Fig. 5 Probability density histogram of Nac(d)

 $f\left( x \right) = \frac{1}{{\sqrt {2{\rm{\pi }}} \sigma }}\exp \left[ { - \frac{{{{\left( {x - \mu } \right)}^2}}}{{2{\sigma ^2}}}} \right]; - \infty < x < + \infty .$ (30)

 ${\rm{Loss}} = \frac{1}{{2k}}\sum\limits_{j = 1}^k {{{\left[ {P\left( {{d_j}} \right) - f\left( {{d_j}} \right)} \right]}^2}} .$ (31)

 $\mathop {\min }\limits_{\mu ,\sigma } {\rm{Loss}}.$ (32)

 图 6 损失函数迭代曲线 Fig. 6 Iteration curve of loss function

3 结语