## 4 Conclusions  
The present research focuses on two methods of measuring the zigzag length in railway transportation. The first method, also referred to as the laboratory method, is based on video recordings acquired during the data acquisition process. The data were post-processed in the laboratory using a precise measurement method. Since this method is highly precise, it has the disadvantage of being able to take measurements after a time interval, implying that it is not a real-time measurement. This method is currently employed for the national railway transportation system. The second method, also referred to as the real-time method, proposes a real-time measure of zigzag length based on the tracking of a specific track image. The measurement was carried out utilizing various dimensions of the track images and the average filters applied. In order to determine performance, the results obtained with this method were compared to those obtained with the first method. This comparison showed strong correlations between the results in the majority of the examined zones, but it also identified two categories of zones where this method is not advised. In these zones, the first method can be used to correct the results. Finally, the possibility of modeling and predicting the zigzag length using hybrid deep neural networks was investigated. The data used in this investigation were the results of the first method. The application of an artificial neural network (ANN) for predicting stagger length significantly influences important operational components of the pantograph-catenary system (PCS), thus affecting its reliability. The forecasted stagger values enable predictive maintenance by indicating when displacement approaches the operational limits, which could result in pantograph wear, wire damage, or the failure of the PCS. The forecasting model enables the operators to predict deviations under different circumstances (e.g., changes in wind or speed) and adapt parameters such as contact force accordingly. Figure 26: The correlation between measured values, tested predictions, and one-step-ahead predictions, along with the update sequence of data for zigzag length values: (a) samples representation, (b) scatter plot. If the stagger exceeds the acceptable limits, the train's operating speed could be adjusted dynamically to prevent excessive damage to the contact points. This real-time data may be helpful in adjusting the pantograph's pressure on the contact wire and optimizing the force applied under different atmospheric conditions to ensure consistent power transfer and minimize the risk of problems. The ANN allows the connection between monitoring and proactive management, resulting in a reduction in unexpected downtime and an increase in component duration, enhancing overall system reliability. Potential future advances could include integrating the system with the Internet of Things (IoT) technology, which would allow for remote monitoring and control. This would enable real-time messages to be sent to maintenance staff and train operators, allowing for more rapid problem solving. The system's huge data collection can be used to perform advanced predictive analysis and in tasks involving machine learning. Forecasting models can be used to predict potential problems, as well as optimize maintenance schedules. Real-time measurement of the zigzag distance permits the prediction of abnormal values that exceed the range that is allowed. This can be accomplished by using methods based on machine learning and could be quite useful in preventing damage. Conceptualization, C.P., G.M. and M.P. ; methodology, C.P. and G.M. ; software, M.P., G.M. and C.P. ; validation, M.P. and C.P. ; investigation, G.M. ; resources, C.P. ; writing--original draft preparation, G.M. and M.P. ; writing--review and editing, M.P. and C.P. ; visualization, G.M. ; supervision, C.P. All authors have read and agreed to the published version of the manuscript.