﻿ 排阵式交叉口交通安全分析及鲁棒优化模型
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (7): 984-993.  DOI: 10.11908/j.issn.0253-374x.2019.07.010 0

### 引用本文

ZHENG Zhe, MA Wanjing, ZHAO Jing. Analysis of Traffic Safety and Robust Optimization Model for Tandem Intersection[J]. Journal of Tongji University (Natural Science), 2019, 47(7): 984-993. DOI: 10.11908/j.issn.0253-374x.2019.07.010

### 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. 上海理工大学 管理学院，上海 200093

Analysis of Traffic Safety and Robust Optimization Model for Tandem Intersection
ZHENG Zhe 1, MA Wanjing 1, ZHAO Jing 2
1. Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China;
2. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: Aiming at the traffic design and signal control for the tandem intersection, the traffic conflict technology was used to analyze the traffic safety of the sorting area. The results show that the traffic volume is one of the main factors. On this basis, the robust optimization model of tandem intersection was established by taking the stochastic variation of the traffic volume into consideration. Then, the improved NSGA-Ⅱ algorithm was used to solve the model and the minimum deviation analysis for subjective and objective information(MDASOI) method was used to analyze the optimization results and the robust optimal scheme was obtained. Case analysis and comparison results show that the proposed model can get an optimal timing method by taking into account the interference of import traffic volume stochastic variation. Compared with the traditional Highway Capacity Manual(HCM) and Australian Road Research Board(ARRB) timing method, this model could reduce the average vehicle delay of about 28.80% and 6.29% and the maximum queue length of about 32.43% and 7.41%. Compared with the example scheme, the optimization scheme of this model can reduce traffic conflicts of the left and right by 23.8% and 11.1%, which improves the safety benefit of the whole intersection.
Key words: traffic engineering    traffic conflict    robust optimization    tandem intersections

1 排阵式信号控制方法

 图 1 排阵式交叉口交通组织形式 Fig.1 Traffic organization form of tandem intersection
2 排阵式交叉口交通安全分析 2.1 交通冲突发生机理

(1) 左转车流冲突.设置排序区进口道的方向采用左转保护相位控制，但由于左转及直行车辆在所属相位均可使用排序区全部车道，当左转流量较大或对向直行流量过大且在直行绿灯末期仍持续进入交叉口时，排序区内多车道左转车辆同时运行，内侧左转车辆转弯半径过小，在汇入出口道会与外侧车道左转车辆存在一定冲突，进而与对向直行车辆形成交通冲突.

(2) 直行车流冲突.与左转交通流相似，当主信号直行相位阶段，排序区内直行车流通过交叉口，当直行流量过大时，在主信号直行相位绿灯末期离开排序区的直行车辆可能会与下一相位的车辆发生交通冲突.

(3) 预停车线处分流冲突.由于排序区的特殊设置，排序区内车道功能相同，致使直行车辆或左转车辆在预信号绿灯启亮后，需要从预停车线前的单车多或双车道驶入排序区内的多车道，使得驶入排序区内的车辆要进行车道选择，此时车道选择主要取决于排序区内车道与车辆当前车道的位置关系，故会在预停车线形成分流冲突.

(4) 排序区内合流冲突.排阵式信号交叉口的合流冲突主要发生在3个时段，分别发生于车辆驶入排序区时选择排序区内部车道的合流、主信号绿灯时段排序区内后方车辆争抢通过交叉口与旁侧排队车流的合流以及预信号绿灯末期加速进入排序区的车辆与驶离排序区车流的合流所产生的合流冲突.以上3类合流冲突中，第1类合流冲突是影响较为显著，同时也是排序式信号控制所特有的合流冲突.

2.2 评价指标选取及划分

2.3 统计模型 2.3.1 模型建立

 ${y^ * } = \alpha X + \varepsilon$ (1)

 $P\left( {{y_i}} \right) = \left\{ {\begin{array}{*{20}{c}} \begin{array}{l} \mathit{\Pi }\left( {{\chi _1} - \alpha X} \right)\\ \mathit{\Pi }\left( {{\chi _2} - \alpha X} \right) - \mathit{\Pi }\left( {{\chi _1} - \alpha X} \right)\\ 1 - \mathit{\Pi }\left( {{\chi _2} - \alpha X} \right) \end{array}&\begin{array}{l} i = 1\\ i = 2\\ i = 3 \end{array} \end{array}} \right.$ (2)

2.3.2 模型检验

 ${R^2} = \frac{{\sum {{{\left( {{x_i} - \bar X} \right)}^2}} }}{{\sum {\left[ {f\left( {{X_i}} \right) - \bar X} \right]} }}$ (3)

 $\operatorname{Cox} \& \text { Snell }-R^{2}=1-\left[\frac{L_{0}}{L_{v}}\right]^{\frac{2}{K}}$ (4)
 ${\rm{Nagelkerke}} - {R^2} = \frac{{{R^2}}}{{1 - {{\left( {{L_0}} \right)}^{\frac{2}{K}}}}}$ (5)

 ${\chi ^2} = \sum\limits_{i = 1}^k {\frac{{{{\left( {{X_i} - n{p_{{\rm{o}}i}}} \right)}^2}}}{{n{p_{{\rm{o}}i}}}}} \sim {\chi ^2}\left( {k - 1} \right),n \to \infty$ (6)

2.3.3 边际效应

 $\Delta P\left( {{y_i}\left| X \right.} \right) = \alpha \left[ {\varphi \left( {{\chi _{i - 1}} - \alpha X} \right) - \varphi \left( {{\chi _i} - \alpha X} \right)} \right]$ (7)

2.4 数据分析

 图 2 排阵式交叉口交通冲突PET分布 Fig.2 Distribution of the PET for the traffic conflict

3 排阵式交叉口鲁棒优化模型 3.1 假设条件

(1) 排阵式信号交叉口的相位及相序确定;

(2) 各进口道交通流连续到达预停车线;

(3) 分析时段T共分为h个时间间隔，各时间间隔的交通流量随机波动.

3.2 模型建立 3.2.1 目标函数

 $\begin{array}{c}{\min F\left(C, \lambda_{i}\right)=\min \left[f_{1}\left(C, \lambda_{i}\right), f_{2}\left(C, \lambda_{i}\right)\right.} \\ {f_{3}\left(C, \lambda_{i}\right), f_{4}\left(C, \lambda_{i}\right) ]}\end{array}$

 $f_{1}\left(C, \lambda_{i}\right)=\overline{d}_{j}^{t}+\sqrt{\frac{1}{h(h-1)-1} \sum\limits_{t=1}^{h} \sum\limits_{j=1}^{n}\left(d_{j}^{t}-\overline{d}_{j}^{t}\right)^{2}}$ (8)
 $d_{j}^{t}=\frac{C\left(1-\lambda_{i}\right)^{2}}{2\left(1-y_{j}^{t}\right)}+\frac{\overline{N}_{j}^{t} x_{j}^{t}}{q_{j}^{t}}$ (9)
 $\overline{d}_{j}^{t}=\frac{1}{h} \sum\limits_{t=1}^{h} \sum\limits_{j=1}^{n} d_{i}^{t}$ (10)

 ${f_2}\left( {C,{\lambda _i}} \right) = \frac{1}{{\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{s_j}} } {\lambda _i}}}$ (11)

 ${f_3}\left( {C,{\lambda _i}} \right) = \frac{{\sum\limits_{t = 1}^h {\sum\limits_{j = 1}^n p } r_j^tq_j^t}}{{\sum\limits_{t = 1}^h {\sum\limits_{j = 1}^n {q_j^t} } }}$ (12)
 $pr_j^t = \frac{{1 - {\lambda _i}}}{{1 - {\lambda _i}\sum\limits_{j = 1}^n {x_j^t} }}$ (13)

 ${f_4}\left( {C,{\lambda _i}} \right) = \max \left( {N_j^t} \right)$ (14)
 $\begin{array}{l} N_j^t = \frac{{C\left( {1 - {\lambda _i}} \right)}}{{3\;600\left[ {1 - \min \left( {x_j^t,1} \right){\lambda _i}} \right]}} + \\ 0.25{c_j}T\left[ {\left( {x_j^t - 1} \right) + \sqrt {{{\left( {x_j^t - 1} \right)}^2} + \frac{{8kx_j^t}}{{{c_j}T}} + \frac{{16kN_j^b}}{{{{\left( {{c_j}T} \right)}^2}}}} } \right] \end{array}$ (15)
 $c_{j}=s_{j} \lambda_{i}$ (16)

3.2.2 约束条件

(1) 周期时长约束.周期时长不宜过短，应确保一个周期内到达预停车线处的车辆可以全部进入排序区内并排空; 同时，周期时长不宜过长，以提高排阵式交叉口通行效率，即

 $C_{\min } \leqslant C \leqslant C_{\max }$ (17)

(2) 有效绿灯时长约束.各相位有效绿灯时间不宜过短，降低通行延误，即

 $C \lambda_{i} \geqslant g_{\text { imin }}$ (18)

(3) 信号控制约束.各相位信号灯时间应满足交叉口通行需求，即

 $\sum\limits_{i=1}^{m}{{{\lambda }_{i}}}+\frac{L}{C}=1,\quad i=1,2,\cdots ,m$ (19)

(4) 饱和度约束.本文模型建立基础为排阵式交叉口处于未饱和或饱和状态，过饱和状态本文模型不予讨论，即

 $\max \left(x_{j}^{t}\right) \leqslant 1$ (20)
3.3 求解算法

3.3.1 最优平均有效函数算法

(1) 确定统计样本总体数量M;

(2) 划分周期时长C的邻域区间[Cδs, C+δs]为M个等距区间;

(3) 建立由数列{1, 2, …, M}随机排列组成的列向量αM×1为随机变换列;

(4) 随机变换列的每一项对应一个总体样本中随机产生的个体样本，选出M个随机样本;

(5) 由排阵式信号交叉口鲁棒优化模型得到平均有效函数，根据选出的随机样本计算每个优化目标fk(Cs)及最优平均有效函数值Fk(C′)：

 $F_{k}\left(C^{\prime}\right)=\frac{1}{M} \sum\limits_{s=1}^{M} f_{k}\left(C_{s}^{\prime}\right), \quad k=\{1,2,3,4\}$

3.3.2 自适应LHS鲁棒度算法

(1) 初始化精确度标量τ，设定单次迭代最小及最大样本数MminMmaxM1=MminMmax=M′+(k－1)ξ.式中，M′为抽样数量; k为解集的鲁棒度; ξ为平衡参数;

(2) 运用LHS抽样法抽取样本并计算相应优化目标属于f(x)的邻域η的百分比p1，令l=2，Ml=Mmax;

(3) 再次运用LHS抽样法抽取样本并计算优化目标属于f(x)的邻域η的百分比pl;

(4) 若|plpl－1|≤τ，则Mk=min(Ml, Ml－1)，pk=pl; 否则l=l+1，$M_{l}=\mu \log \left(\left|\frac{p_{l-1}-p_{l-2}}{\tau}\right|\right)$;

(5) 若k=1时，转至(6);否则，判断pk < P是否成立(P为指定参数)，若成立，则k=k-1，返回对应样本数Mk，否则返回(1);

(6) 令k=k+1，返回(2).

3.3.3 改进的NSGA-Ⅱ算法

3.4 决策分析

3.4.1 建立决策矩阵

 ${\theta _{ij}} = \frac{{{y_{ij}} - \min \left( {{y_j}} \right)}}{{\max \left( {{y_j}} \right) - \min \left( {{y_j}} \right)}}$ (21)

 $\theta_{i j}=\frac{\max \left(y_{j}\right)-y_{i j}}{\max \left(y_{j}\right)-\min \left(y_{j}\right)}$ (22)

 $\begin{array}{*{20}{l}} {{\theta _{ij}} = }\\ {\left[ {\begin{array}{*{20}{l}} 1&{{y_{ij}} \in [a,b]}\\ {1 - \frac{{\max \left\{ {a - {y_{ij}},{y_{ij}} - b} \right\}}}{{\max \left\{ {a - \min \left( {{y_j}} \right),\max \left( {{y_j}} \right) - b} \right\}}}}&{{y_{ij}} \notin [a,b]} \end{array}} \right]} \end{array}$ (23)

3.4.2 确定区间指标权重向量

 $\begin{array}{*{20}{c}} {\min g(\bar \nu ) = \sum\limits_{j = 1}^q {{{\left( {\frac{{{{\bar \nu }_j} - {v_{oj}}}}{{{v_{oj}}}}} \right)}^2}} }\\ \text{s}\text{.t}\text{.}\ \ {v_{sj}^a \le {{\bar \nu }_j} \le v_{sj}^b,\sum\limits_{j = 1}^q {{{\bar \nu }_j}} = 1,}\\ {\sum\limits_{j = 1}^q {v_{sj}^a} \le 1,\sum\limits_{j = 1}^q {v_{sj}^b} \ge 1} \end{array}$ (24)
3.4.3 决策方案选取

4 实例分析 4.1 数据采集

 图 3 高峰时段交通流量变化 Fig.3 Variation of traffic flow during peak hours

 图 4 前海路学府路交叉口渠化 Fig.4 Channelization of the intersection in Qianhai Rd. and Xuefu Rd.
 图 5 前海路学府路交叉口信号配时 Fig.5 Signal timing of the intersection in Qianhai Rd. and Xuefu Rd.

4.2 优化目标分析

 图 6 有效优化目标冲突性分析 Fig.6 Analysis of traffic conflict in different effective optimizations

 图 7 各算法优化结果对比 Fig.7 Correlation of results of different algorithms
4.3 配时方案对比

4.4 交通冲突对比

5 结论

(1) 运用交通冲突技术对排阵式交叉口进行交通安全分析，选取PET值为交通冲突评价指标，计算结果显示交通流量和二次冲突为主要影响因素，其中交通流量对交通冲突严重程度影响较为显著;

(2) 在考虑进口道交通流量随机波动性的情况下建立了排阵式交叉口鲁棒优化模型，并将延误指标、通行能力、平均停车率及预停车线前最大排队长度作为优化目标，并应用改进的NSGA-Ⅱ算法进行模型求解，并通过MDASOI法进行决策分析;

(3) 选取实例进行计算分析，分析结果显示排阵式交叉口延误指标和平均停车率间存在明显冲突，道路通行能力和最大排队长度不存在冲突性，平均停车率和最大排队长度存在明显冲突; 与传统NSGA-Ⅱ算法相比，改进算法可明显提高优化解; 与传统决策方法相比，本文模型可有效解决主客观需求问题，得到最优决策方案; 与传统HCM和ARRB相比，本文模型可降低延误指标约28.80%和6.29%，降低最大排队长度约32.43%和7.41%

(4) 通过优化方案与实例方案的交通冲突数据对比显示，优化方案可更多的缓解排阵式信号交叉口的交通冲突，同时与实例方案相比，左转及直行冲突的缓解程度分别提高了23.8%和11.1%，提高了整个交叉口的交通安全效益.但本文相位相序及排阵式组织形式较为固定，在实际应用中交通流量及其他因素的影响有待进一步的研究.

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