Analysis of braking data of metro trains

The paper considers the problem of modeling the braking process of trains with the aim of further assessing the quality of braking. It is shown that an approach based on the intellectualization of processing big data characterizing the process of braking of metro trains allows us to refine the development of train control systems in automatic mode and predict the quality and accuracy of stopping. Of particular importance is the emergency braking system for trains, which ensures the safety of passengers and provides emergency braking of the train in the event of an emergency. Mathematical models describing the process of braking an object (subway train) depend on the complexity of the object’s system components. Knowing the distance and braking speed measured by the sensors, it is possible to restore the mathematical model. In the general case, the problem of reconstructing a model is the problem of reconstructing a differential equation from measurement data. This task is incorrect. For practical purposes of assessing the quality of braking, it is enough to assume that such models are described by a system of firstorder ordinary differential equations. Consequently, using the measured data, it is possible to find the statistical characteristics of the braking process and visually evaluate the quality of braking using a set of these statistics and comparing the smoothed phase trajectories of the system (distance-velocity). Thus, inhibition depends on many factors, which is why various inhibitory sequences arise, the assessment of the quality of which represents an actual mathematical problem. It is shown that statistical methods and cluster analysis methods make it possible to extract knowledge about the braking process from measurement data such as the coordinates of metro stations, based on the study of histograms and the application of clustering algorithms to the coordinates of train stops. Characteristic braking trajectories have been identified, and the values of motion kinematics parameters have been obtained. The work uses the Python language, as well as a number of free libraries that satisfy the need for software tools for working with data. Several software methods have been created. Based on the obtained trajectories, it is then possible to determine the braking class. The technology used may be promising in other subject areas. It is shown that the statistical data of the movement of metro trains, the trajectory data obtained from them and visualized representations are big data (Big Data, BD), from which knowledge about the quality of train braking is extracted (Data Mining, DM). The proposed intelligent system for processing such data combines statistical methods of machine learning (ML) and neural networks.