## 5 Conclusions  
The present paper focused on investigating the relationship between the longitudinal level and vertical ballast stiffness, using data mining techniques to analyze the collected data. This understanding is essential for various aspects in railway management including operational efficiency, safety, passenger comfort, and optimal resource allocation. So, this study was initially conducted by calculating ballast stiffness and longitudinal levels, using track recording cars, along a section of the Tehran-Mashhad railway line. The primary data were processed, and the correlation analyses between longitudinal levels and vertical ballast stiffness were conducted using frequency analysis techniques and machine learning algorithms such as linear regression, decision trees, and random forests. The following are the summarized results obtained from investigating the relationship between the longitudinal level and vertical ballast stiffness:  
1. The frequency analysis showed that the power spectrum density of the vertical longitudinal level and ballast stiffness have approximately a 0.67 correlation. These values indicate a rather remarkable relationship between the PSD of these data. Additionally, it revealed a notable correlation in PSD data, particularly in the wavelength of 1-4 rad/m. 2. The correlation analyses, using machine learning methods, demonstrated an appropriate relationship between the rail longitudinal levels and vertical rail deflection. The concluded results revealed that the RMSE of the longitudinal levels and vertical rail deflections data ranged around 0.05 to 0.07. According to the outcomes, the linear regression, random forest, and decision trees achieved better accuracy, respectively. 3. Furthermore, the data mining analyses, used by ML-based algorithms, concluded that the longitudinal level of the rail and vertical ballast stiffness have a considerable relationship. The RMSE values of the linear regression, decision tree, and random forest algorithms were approximately 0.04, 0.045, and 0.05, respectively, indicating that the linear regression method yielded more accurate results. Given that a significant portion of the maintenance costs are attributed to maintaining track stiffness, it becomes imperative to deploy strategies to optimize resource allocation. As recording geometric parameters is faster and more straightforward than assessing track stiffness, it is increasingly interesting to analyze the relationship between track stiffness and track longitudinal levels. In conclusion, this investigation has revealed a significant relationship between the track longitudinal levels, vertical rail deflection, and ballast stiffness of railway tracks. The findings demonstrate that machine learning-based algorithms exhibit a strong capability to mine and analyze this correlation effectively. This insight underscores the potential of advanced analytical techniques in understanding and optimizing railway track maintenance strategies. By leveraging machine learning algorithms, railway operators and maintenance teams can better predict and address issues related to track conditions, ultimately enhancing the safety, efficiency, and longevity of railway infrastructure. Moreover, to improve accuracy, future research can explore more advanced machine learning and deep learning techniques. These research findings establish a fundamental link between ballast stiffness and geometric parameters within the context of infrastructure management. A pragmatic framework for evaluating track health conditions is proposed. By extracting ballast stiffness data from longitudinal measurements, critical insights are gained into the structural integrity of railway superstructures and their associated maintenance requirements. This innovative framework holds significant promise for enhancing decision-making in railway track management planning. **Author Contributions:** Conceptualization, S.M. and H.H. ; methodology, H.H. ; software, H.H and M.K. ; validation, S.M., H.H. and M.K. ; formal analysis, H.H.