Abstract Shift2Rail is a joint undertaking funded by the EU via its Horizon 2020 program and by main railway stakeholders. Several Shift2Rail projects aim to investigate the application of formal methods to new ERTMS/ETCS railway signalling systems that promise to move European railway forward by guaranteeing high capacity, low cost and improved reliability. We explore the ERTMS/ETCS level 3 full moving block specifications stemming from different Shift2Rail projects using Uppaal and statistical model checking. The results range from novel rigorously formalised requirements to an operational model formally verified against scenarios with multiple trains on a single railway line. From the gained experience, we have distilled future research goals to improve the formal specification and verification of real-time systems, and we discuss some barriers concerning a possible uptake of formal methods and tools in the railway industry. 

/pdf/exploring-the-ertms-etcs-full-moving-block-specification-an-1qypi1j1.pdf

Exploring the ERTMS/ETCS full moving block specification: an experience with formal methods

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. 

Real-time train motion parameter estimation using an Unscented Kalman Filter

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. 

/pdf/a-literature-review-on-train-motion-model-calibration-2an9pbfo.pdf

A Literature Review on Train Motion Model Calibration

Formal Methods and Tools Applied in the Railway Domain

Electromechanical braking technology is an effective way to improve the braking response of mine hoist. Through the analysis of the mine hoist electromechanical mechanical disc brake, a mathematical model including the motor, reducer and thread pair is established. The control process is analyzed in detail, and then the control strategy is obtained. An automatic control system based on linear quadratic regulator and PI controller is proposed. The braking goal of self-adaptive adjustment of braking clearance and on-line adjustment of braking force is realized. Compare the simulation and test results, discuss the performance of the controller. The results of the experiment indicate that the brake gap adjustment time is less than 10 s, stable within 1±0.2 mm, and the steady-state error is less than 2%. The positive pressure of the brake has a linear relationship with the motor voltage, with a slope of 920.4 and an intercept of −1298.88. It can replace the existing hydraulic brakes without the problem of low degree of automation and high pollution, which provides a new way for the control system of electromechanical brake.

Design and test of electromechanical disc brake controller for mine hoist

By analyzing the mechanism of pure air emergency brake for high-speed train, the discrete emergency brake model is established. Aiming at the problem that time-varying hidden parameters cannot be observed directly, the sliding window-based expectation maximization is proposed, and the unobserved time-varying brake parameters are identified. Firstly, the position and size of the sliding window are selected; then, the sliding window-based expectation maximization is used for brake parameter identification; finally, combined with the gradient optimization, the optimal identifications of emergency brake parameters are obtained. The simulation results show that the brake parameters can be identified quickly and accurately by the proposed method. Under uniform noise, the identification errors of friction coefficient and braking ratio are ±0.0068 and ±0.0349, respectively, and the maximum relative errors between the identifications and true values are 2.4807% and 1.3154%, respectively, which can meet the actual requirements of the brake system. The effectiveness and practicability of the proposed model and method are verified.

/pdf/high-speed-train-emergency-brake-modeling-and-online-4lys6t5zwx.pdf

High-Speed Train Emergency Brake Modeling and Online Identification of Time-Varying Parameters

In this paper, the relationship between traction, resistance, braking force, speed and acceleration is discussed A nonlinear parametric state space model is established to describe the dynamic characteristics of running process of high speed train Further, a filtering method based on Gaussian Sum theory and extended Kalman filter is proposed for estimating the states and parameters of nonlinear systems, and is applied to the high speed train model no matter it is affected by Gaussian or non-Gaussian noise Firstly, the probability density function (PDF) of stochastic noise is approximated by a weighted sum of Gaussian PDFs with various means and variances Then Bayesian theory and extended Kalman filter are combined to estimate the running states and model parameters online Lastly, the running process of high speed train is simulated The process is affected by uniformly distributed noise, and the running states and model parameters are estimated online by the proposed method The simulation results show that the change of states and parameters can be effectively tracked, which demonstrates the effectiveness and feasibility of the proposed method

Online parameters identification of high speed train based on Gaussian Sum theory

The invention discloses an industrial system monitoring data recovery method based on on-line PCA. Firstly, the industrial system monitoring data are collected and sorted according to time series. Secondly, based on the on-line PCA method, the dimension reduction model is established to reduce the dimension of the monitoring data collected from the industrial system, that is, to compress the collected data. Finally, a model is established based on the stack noise reduction sparse self-encoder network, and missing data is recovered by using the dimensionally reduced data. The invention can accurately recover the missing data with strong correlation in real time, and has certain understanding of the state of the industrial system.

An on-line PCA-based monitoring data recovery method for industrial system

The invention discloses a train model online parameter identification method based on Gaussian sum filter, comprising the following steps: firstly carrying out force analysis on a train pulling process, and building a nonlinear parameterization state space model of a train; then taking a probability density function of a random noise received by the train as an object, selecting one group of Gaussian probability density functions with different means and variances, and carrying out weighted summation and approximation; and finally combining Bayesian theory and extended Kalman filtering, and obtaining a train state and parameter online estimation result. The method disclosed by the invention solves the problems that modeling of the train pulling process is not accurate, offline parameter identification is difficult to realize real-time control of the train and parameter identification precision is low in the prior art.

Train model online parameter identification method based on Gaussian sum filter

In this paper, the emergency braking of high speed train is studied, and the relationship between the braking force, resistance, speed and deceleration is discussed. According to the Newton's second law of motion, by discretizing the speed and displacement, the emergency braking model of high speed train is established. Further, the unobserved braking parameters of model are identified by the iterative Expectation Maximization (EM) algorithm. Firstly, the conditional expectation of model is designed by E step; then, the conditional expectation is maximized by M step to identify the braking parameters. The simulation results show that, when the initial value is within ± 45% of the true value, the state and braking parameters of train can be estimated quickly and accurately with 1% relative error, which demonstrates the effectiveness and feasibility of the proposed method.

Identification of braking model for high speed train by using expectation maximization

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