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Register a new userTraffic Queue Length and Pressure Estimation for Road Networks with Geometric Deep Learning Algorithms
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Simon F. G. Ehlers
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Due to urbanization and the increase of individual mobility, in most metropolitan areas around the world congestion and inefficient traffic management occur. Highly necessary intelligent traffic control systems, which are able to reduce congestion, rely on measurements of traffic situations in urban road networks and freeways. Unfortunately, the instrumentation for accurate traffic measurement is expensive and not widely implemented. This thesis addresses this problem, where relatively inexpensive and easy to install loop-detectors are used by a geometric deep learning algorithm, which uses loop-detector data in a spatial context of a road network, to estimate queue length in front of signalized intersections, which can be then used for following traffic control tasks. Therefore, in the first part of this work a conventional estimation method for queue length (which does not use machine learning techniques) based on second-by-second loop-detector data is implemented, which uses detected shockwaves in queues to estimate the length and point of time for the maximum queue. The method is later used as reference but also as additional input information for the geometric deep learning approach. In the second part the geometric deep learning algorithm is developed, which uses spatial correlations in the road network but also temporal correlations in detector data time sequences by new attention mechanisms, to overcome the limitations of conventional methods like excess traffic demand, lane changing and stop-and-go traffic. Therefore, it is necessary to abstract the topology of the road network in a graph. Both approaches are compared regarding their performance, reliability as well as limitations and validated by usage of the traffic simulation software SUMO (Simulation of Urban MObility). Finally, the results are discussed in the conclusions and further investigations are suggested.
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The rapid development of connected vehicle technology and the emergence of ride-hailing services have enabled the collection of a tremendous amount of probe vehicle trajectory data. Due to the large scale, the trajectory data have become a potential substitute for the widely used fixed-location sensors in terms of the performance measures of transportation networks. Specifically, for traffic volume and queue length estimation, most of the trajectory data based methods in the existing literature either require high market penetration of the probe vehicles to identify the shockwave or require the prior information about the queue length distribution and the penetration rate, which may not be feasible in the real world. To overcome the limitations of the existing methods, this paper proposes a series of novel methods based on probability theory. By exploiting the stopping positions of the probe vehicles in the queues, the proposed methods try to establish and solve a single-variable equation for the penetration rate of the probe vehicles. Once the penetration rate is obtained, it can be used to project the total queue length and the total traffic volume. The validation results using both simulation data and real-world data show that the methods would be accurate enough for assistance in performance measures and traffic signal control at intersections, even when the penetration rate of the probe vehicles is very low.
Traffic state estimation (TSE), which reconstructs the traffic variables (e.g., density) on road segments using partially observed data, plays an important role on efficient traffic control and operation that intelligent transportation systems (ITS) need to provide to people. Over decades, TSE approaches bifurcate into two main categories, model-driven approaches and data-driven approaches. However, each of them has limitations: the former highly relies on existing physical traffic flow models, such as Lighthill-Whitham-Richards (LWR) models, which may only capture limited dynamics of real-world traffic, resulting in low-quality estimation, while the latter requires massive data in order to perform accurate and generalizable estimation. To mitigate the limitations, this paper introduces a physics-informed deep learning (PIDL) framework to efficiently conduct high-quality TSE with small amounts of observed data. PIDL contains both model-driven and data-driven components, making possible the integration of the strong points of both approaches while overcoming the shortcomings of either. This paper focuses on highway TSE with observed data from loop detectors, using traffic density as the traffic variables. We demonstrate the use of PIDL to solve (with data from loop detectors) two popular physical traffic flow models, i.e., Greenshields-based LWR and three-parameter-based LWR, and discover the model parameters. We then evaluate the PIDL-based highway TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the advantages of the PIDL-based approach in terms of estimation accuracy and data efficiency over advanced baseline TSE methods.
Selecting an appropriate clustering method as well as an optimal number of clusters in road accident data is at times confusing and difficult. This paper analyzes shortcomings of different existing techniques applied to cluster accident-prone areas and recommends using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Ordering Points To Identify the Clustering Structure (OPTICS) to overcome them. Comparative performance analysis based on real-life data on the recorded cases of road accidents in North Carolina also show more effectiveness and efficiency achieved by these algorithms.
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $mathcal{M}$ using principal bundles with structure group $K$ and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces $mathcal{M}=G/K$, which are instead equivariant with respect to the global symmetry $G$ on $mathcal{M}$. Group equivariant layers can be interpreted as intertwiners between induced representations of $G$, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case $mathcal{M}=S^2=mathrm{SO}(3)/mathrm{SO}(2)$. Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch-Gordan coefficients for $G=mathrm{SO}(3)$, illustrating the power of representation theory for deep learning.
Traffic state estimation (TSE) bifurcates into two main categories, model-driven and data-driven (e.g., machine learning, ML) approaches, while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies introduced hybrid methods, such as physics-informed deep learning (PIDL), which contains both model-driven and data-driven components. This paper contributes an improved paradigm, called physics-informed deep learning with a fundamental diagram learner (PIDL+FDL), which integrates ML terms into the model-driven component to learn a functional form of a fundamental diagram (FD), i.e., a mapping from traffic density to flow or velocity. The proposed PIDL+FDL has the advantages of performing the TSE learning, model parameter discovery, and FD discovery simultaneously. This paper focuses on highway TSE with observed data from loop detectors, using traffic density or velocity as traffic variables. We demonstrate the use of PIDL+FDL to solve popular first-order and second-order traffic flow models and reconstruct the FD relation as well as model parameters that are outside the FD term. We then evaluate the PIDL+FDL-based TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the superiority of the PIDL+FDL in terms of improved estimation accuracy and data efficiency over advanced baseline TSE methods, and additionally, the capacity to properly learn the unknown underlying FD relation.
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