The breakpoints of fundamental diagrams (FDs) are an important foundation for estimating capacity, identifying traffic conditions, and determining the phase regime of multi-regime FDs. Unfortunately, to our best knowledge, there has been little research on determining breakpoints in a scientific way. This paper applies a Gaussian mixture model (GMM) to describe multi-component traffic conditions, and introduces the GMMs of traffic flow parameters (speed and occupancy). In order to avoid the possible singularities or degeneracies of typical maximum likelihood (ML) estimation, maximum a posteriori (MAP) estimation is introduced for the parameter estimation. The minimum cumulative probability method is then proposed for the determination of critical parameters at breakpoints. Nine datasets collected from the Caltrans Performance Measurement System (PeMS) are used for the estimation and validation of the proposed methods. The results show that the proposed methods can effectively divide up traffic conditions and determine breakpoints. Meanwhile, the effects of mixture weight and vehicle type on breakpoints are investigated and the proposed methods show stable performance in the determination of breakpoints under different conditions. The estimated critical occupancies and speeds are also applied for capacity estimation and calibration of the triangular FD model and three-regime speed-occupancy relationship.

中文翻译：

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确定基本图的断点

基本图 (FD) 的断点是估计容量、识别交通状况和确定多状态 FD 的相位状态的重要基础。不幸的是，据我们所知，很少有关于以科学方式确定断点的研究。本文应用高斯混合模型（GMM）来描述多分量交通状况，并介绍了交通流参数（速度和占用率）的 GMM。为了避免典型最大似然（ML）估计可能出现的奇异性或退化性，在参数估计中引入了最大后验（MAP）估计。然后提出最小累积概率方法来确定断点处的关键参数。从 Caltrans 绩效测量系统 (PeMS) 收集的九个数据集用于估计和验证所提出的方法。结果表明，所提出的方法可以有效地划分交通状况并确定断点。同时，研究了混合气重量和车辆类型对断点的影响，并且所提出的方法在不同条件下确定断点时表现出稳定的性能。估计的临界占有率和速度也适用于三角 FD 模型和三态速度-占有率关系的容量估计和校准。研究了混合物重量和车辆类型对断点的影响，并且所提出的方法在不同条件下确定断点时表现出稳定的性能。估计的临界占有率和速度也适用于三角 FD 模型和三态速度-占有率关系的容量估计和校准。研究了混合物重量和车辆类型对断点的影响，并且所提出的方法在不同条件下确定断点时表现出稳定的性能。估计的临界占有率和速度也适用于三角 FD 模型和三态速度 - 占有率关系的容量估计和校准。