Supervision, data analysis and communication algorithms monitor trains, exploiting most of their available computational power. On-board eco-driving algorithms such as Driver Advisory Systems (DAS) are no exception, as the computational power available limits their complexity and features. This was the case of Roltijd, the in-house developed DAS based on coasting advice of NS, the main Dutch passenger railway undertaking. This platform calculated the coasting curves at every second by integrating the equations of motion numerically, assuming that the track is flat. However, generating more complex driving advice required replacing this coasting curve calculation by a more computationally-efficient algorithm. In this article we propose a new coasting advice algorithm based on the analytical solutions of the train motion model, assuming that gradients and speed limits are piecewise constant functions of the train location. We analyse the qualitative properties of these solutions using bifurcation theory, showing that bifurcations arise depending on the value of the gradient and the applied tractive effort. We validate the proposed algorithm, finding that our algorithm is accurate and can be 15 times faster than the previous method. This allowed NS to implement our algorithm on their trains, contributing daily to the sustainable mobility of 1.3 million passengers.

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A large variety of supervision, data analysis and communication algorithms monitor trains, exploiting most of their available computational power. On-board eco-driving algorithms such as Driver Advisory Systems are no exception, as the computational power available can limit their complexity and features. This was the case of Roltijd, the in-house developed Driver Advisory System based on coasting advice of Nederlandse Spoorwegen (NS), the main Dutch passenger railway undertaking. This platform cal-culated the coasting curves at every second by integrating the equations of motion numerically, assuming that the track is fl at. However, the plans of NS regarding gener-ating more complex driving advice require replacing this coasting curve calculation by a more computationally-effi cient algorithm. In this article we propose a new coasting advice algorithm based on the analytical solutions of the train motion model’s diff er-ential equations that assumes the gradients and speed limits as piecewise constant functions of the train location. We analyze the qualitative properties of these solutions using the theory of dynamical systems, showing that bifurcations arise depending on the value of the gradient and the applied tractive eff ort. We validate the proposed algorithm by comparing its performance and accuracy against the previous method and a train trajectory optimizer based on a pseudospectral method, fi nding that our algorithm is accurate and can be 15 times faster than the previous method. This allows NS to implement the proposed method on the trains running in the Dutch railway network, contributing daily to the sustainable mobility of 1.3 million passengers.@en

Automatic Train Operation (ATO) is a technology to support or automate train driving for increasing service punctuality, energy efficiency and rail infrastructure capacity. Conflict-free train path planning is crucial to the effective deployment of ATO, which allows ATO-equipped trains to operate according to schedule with different train driving strategies. As different train driving strategies lead to various passing times, current planning practice is inadequate to avoid route conflicts as it only sets target arrival or passing times at stops or major junctions. Therefore, conflict-free train path planning needs the definition of a Train Path Envelope (TPE) that contains time targets or windows defined at discrete locations called timing points to tolerate schedule deviations due to different driving styles. The number and location of the timing points, as well as the associated time targets or windows, is a decision problem. This paper proposes a framework to design a robust set of timing points and their associated time windows in a TPE to enable operational conflict-free train path planning against the driving strategies utilised. This framework relies on a Train Path Slot model which extends the definition of TPE from time windows at a discrete set of locations to an integrated blocking time stairway pattern continuously defined across all locations over a train route. The Train Path Slot model considers three relevant train driving strategies, i.e., energy-efficient driving with or without coasting as well as minimum-time driving considering slight delays. A Linear Programming model is formulated to compute the conflict-free Train Path Slots as constraints for train operation. To meet the optimised Train Path Slots, we analyse several possible sets of timing points in a TPE that are only located at stops or signal positions along the train routes. Those timing point sets are then compared in terms of total Train Path Slot overlap time, capacity, energy efficiency and driving performance indicators. Our research supports infrastructure managers in resolving the imminent problem of timing point determination and TPE computation to reach their capacity goals. At the same time, it allows sufficient driving flexibility for railway undertakings.@en

Automatic Train Operation (ATO) is a technology to support or automate train driving for increasing service punctuality, energy efficiency and rail infrastructure capacity. Conflict-free train path planning is crucial to the effective deployment of ATO, which allows ATO-equipped trains to operate according to schedule with different train driving strategies. As different train driving strategies lead to various passing times, current planning practice is inadequate to avoid route conflicts as it only sets target arrival or passing times at stops or major junctions. Therefore, conflict-free train path planning needs the definition of a Train Path Envelope (TPE) that contains time targets or windows defined at discrete locations called timing points to tolerate schedule deviations due to different driving styles. The number and location of the timing points, as well as the associated time targets or windows, is a decision problem. This paper proposes a framework to design a robust set of timing points and their associated time windows in a TPE to enable operational conflict-free train path planning against the driving strategies utilised. This framework relies on a Train Path Slot model which extends the definition of TPE from time windows at a discrete set of locations to an integrated blocking time stairway pattern continuously defined across all locations over a train route. The Train Path Slot model considers three relevant train driving strategies, i.e., energy-efficient driving with or without coasting as well as minimum-time driving considering slight delays. A Linear Programming model is formulated to compute the conflict-free Train Path Slots as constraints for train operation. To meet the optimised Train Path Slots, we analyse several possible sets of timing points in a TPE that are only located at stops or signal positions along the train routes. Those timing point sets are then compared in terms of total Train Path Slot overlap time, capacity, energy efficiency and driving performance indicators. Our research supports infrastructure managers in resolving the imminent problem of timing point determination and TPE computation to reach their capacity goals. At the same time, it allows sufficient driving flexibility for railway undertakings.@en

The dynamics of a moving train are usually described by means of a motion model based on Newton's second law. This model uses as input track geometry data and train characteristics like mass, the parameters that model the running resistance, the maximum tractive effort and power, and the brake rates to be applied. It can reproduce and predict train dynamics accurately if the mentioned train characteristics are carefully calibrated. The model constitutes the core element of a broad variety of railway applications, from timetabling tools to Driver Advisory Systems and Automatic Train Operation. Among the existing train motion model calibration techniques, those that use operational data are of particular interest, as they benefit from on- board recorded data, capturing the train dynamics during operation. In this literature review article we provide an overview of the train motion model calibration techniques that have been published in the scientific literature between January 2000 and December 2021 and either use operational data or can be minimally adapted to use it. To this end, we present a critical overview of the existing train motion model calibration approaches, distinguishing online calibration that analyzes data on- the-go and offline calibration that analyzes historical data batchwise. We propose a research agenda and highlight some potential goals to be tackled in the near future: from devising accurate online calibrators for eco-driving applications to quantitizing the physical sources of parameter variation. Last, we discuss practical recommendations for practitioners and scholars inferred from the current state of the art.

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An accurate train motion model is a key component of a wide spectrum of railway applications, from timetabling algorithms to Automatic Train Operation systems. Therefore, model calibration has become crucial in the railway industry, although this topic has not received the attention and recognition in academia that its practical relevance deserves. Several data-driven techniques have been devised to calibrate train dynamics models, although an overview that describes the current state of the art in the field and highlights the following steps to be researched is still missing in the literature. Thus, this article has four main goals. First, giving a brief insight into the broad variety of techniques used for train motion model calibration, focusing on those techniques that use on-board measurements and are applicable in railway operation. Second, highlighting the main research steps to be tackled, considering the current main challenges in railway research. Third, outlining practical recommendations to practitioners who need to calibrate their algorithms and applications. And fourth, contributing to giving train motion model calibration its due recognition.@en

Train movement dynamics are usually modelled by means of Newton's second law. The resulting dynamic equation can be very precise if the parameters that it depends on are determined accurately. However, these parameters may vary in time and show wide variations, making the calibration task nontrivial and jeopardizing the performance of a broad variety of applications in the railway industry: from timetable planning and railway traffic simulation to Driver Advisory Systems and Automatic Train Operation. In this article, the online train motion model calibration problem is addressed with a special focus on energy-efficient on-board applications. To this end, location and speed measurements are assumed to be available for a train running under normal operation conditions. A well-known real-time parameter estimation algorithm, the Unscented Kalman Filter, is combined with a driving regime calculator and a post-processing module in order to obtain bounds and statistics of parameters such as the maximum applied tractive effort and power, the applied brake rates, the cruise speed and the length of the final coasting and braking. The proposed framework is tested in a case study with real data from trains operating on the Eindhoven-’s-Hertogenbosch corridor in the Netherlands. Results obtained show that UKF is able to track the speed and location measurements and to estimate the parameters that model the running resistance in the dynamic equation. The proposed driving regime and the post-processing modules can determine the current regime accurately and give a deeper insight into the variations of the driving style, respectively.

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In the paper the observed parameter variations of a single train into the trajectory optimization problem is incorporated. The computed trajectories should be energyefficient and robust with respect to the realized parameter configuration. A new approach for modelling the Train Trajectory Optimization problem under parametric uncertainty in terms of a minimax optimal control problem with a finite set of observed parameter configurations presented.@en