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摘要: 将三角基本图的交通状态细分为自由流、中断和拥堵；基于非自由流特性，重新划分了U型时空域，以此找到适合的波速范围；重新确定了上游边界累积流量，使得边界函数刻画不过于宽泛；建立了非自由流Newell模型，并提出了使用该模型的判断条件；引入了车辆秩参数，达到在多车道上描述车辆超车现象的目的，并建立了更精确的车辆秩估计模型，从而建立了非自由流Newell扩展模型；提出了针对非自由流下2种情形的车辆轨迹估计算法，根据是否存在超车现象分为先进先出(FIFO)情形与非先进先出(non-FIFO)情形；结合数值模拟和实际交通案例，验证了算法的有效性。研究结果表明：2种情形下的轨迹估计算法都是有效的，当超车现象存在时，non-FIFO情形的估计效果较准确和稳健；在数值模拟研究中，non-FIFO情形的估计误差相对FIFO情形下降13.45%，non-FIFO情形更优；实际交通案例中，2个小汽车数据集在non-FIFO情形的估计误差相对FIFO情形均有所下降，下降幅度分别为2.38%、2.04%，且估计误差均服从高斯混合模型；公交车数据集因不存在超车现象，non-FIFO与FIFO情形的估计误差相等，均为4.90%，且估计误差服从伽马分布。可见，所建立的非自由流Newell模型对于中断多或拥堵状态占比多的交通数据均是有效可行的，且所提出的non-FIFO和FIFO情形的轨迹估计算法效果表现良好。Abstract: The traffic state of the triangular fundamental diagram (TFD) was subdivided into free flow, breakdown, and jam. According to the non-free flow characteristics, the U-shaped spatial-temporal domain was re-divided to find the suitable wave velocity range. The cumulative flow of the upstream boundary was redefined so that the description of the boundary function was not too broad. The Newell's model under non-free flow was established, and the criterion of whether the model can be used was proposed. A parameter of vehicle's rank was introduced to realize the goal of describing multilane overtaking phenomena, and a more accurate estimation model of vehicle's rank was established. Then the Newell's extended model under non-free flow was developed. The vehicle trajectory estimation algorithms were proposed for the two situations of non-free flow, namely first-in-first-out (FIFO) situation and non-first-in-first-out (non-FIFO) situation, which were divided according to whether there was an overtaking phenomenon. The effectiveness of the algorithms was then verified by numerical simulation and real traffic cases. Analysis results show that the trajectory estimation algorithms are effective in both situations. When an overtaking phenomenon occurs, the estimation effect of the non-FIFO situation is more accurate and robust. In the numerical simulation study, the estimation error of the non-FIFO situation decreases by 13.45% compared with that of the FIFO situation, namely that the result of the non-FIFO situation is better. In the real traffic cases, the non-FIFO situation has 2.38% and 2.04% lower estimation errors than the FIFO situation on two car datasets, respectively, and the estimation errors all follow the Gaussian mixture model (GMM). Because there is no overtaking phenomenon in the bus dataset, the estimation errors of the non-FIFO situation and the FIFO situation are equal, which are both 4.90% and follow the Gamma distribution. Therefore, the established Newell's model under the non-free flow is effective and feasible for the traffic data with a large proportion of breakdowns or jams, and the proposed trajectory estimation algorithms of FIFO and non-FIFO situations perform well. 6 tabs, 13 figs, 30 refs.
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图 5 修正系数与平均估计误差关系
Figure 5. Relationship between correction factor and mean estimation error
表 1 模拟数据集参数值
Table 1. Parameter values of simulated dataset
N0/veh W/(km·h-1) K/(veh·km-1) λ M 0 25.27 100 0.6 0.003 2 
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表 2 模拟数据估计误差汇总
Table 2. Summary of simulation data estimation errors
Ef/% σ(Ef) En/% σ(En) $\tilde E$ 21.48 11.988 18.59 8.499 13.45
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表 3 实际交通案例详细信息
Table 3. Details of actual traffic cases
数据集 车辆类型 起点/km 终点/km 车辆数/veh 轨迹点/个 1 小汽车 0.600 2.277 716 178 565 2 小汽车 0.984 2.277 718 147 656 3 公交车 0.874 1.590 35 4 233
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表 4 实际交通案例参数值
Table 4. Parameter values of actual traffic cases
数据集 N0/veh W/(km·h-1) K/(veh·km-1) λ M 1 1 29.16 142.239 1.0 0.000 0 2 1 25.74 185.074 1.3 0.002 5 3 1 22.10 48.931 1.0 0.000 0
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表 5 拟合分布参数值
Table 5. Fitted distribution parameter values
数据集 情形 ω1 μ1 σ12 α ω2 μ2 σ22 β 1 FIFO 0.365 6.692 5.655 0.635 16.032 12.539 non-FIFO 0.382 6.654 5.871 0.618 15.826 10.667 2 FIFO 0.279 4.477 1.573 0.721 13.928 20.061 non-FIFO 0.289 4.368 1.685 0.711 13.788 19.281 3 FIFO 12.889 2.627 non-FIFO
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表 6 实际交通案例估计误差汇总
Table 6. Summary of estimation errors for actual traffic cases
数据集 Ef/% σ(Ef) En/% σ(En) $\tilde E$ 1 12.62 5.504 2 12.32 5.360 2 2.38 2 11.30 5.740 2 11.07 5.721 5 2.04 3 4.90 1.529 0 4.90 1.529 0 0.00
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