1. Introduction
An improved and more astute comprehension of railway track conditions stands as a paramount concern within the industry, impacting operations, safety, passenger comfort, resource utilization, and beyond. Notably, a significant share of operational and maintenance costs, up to 60%, is attributed to ballast layer upkeep, necessitating the implementation of optimized strategies and resource allocation [
1,
2,
3]. On the other hand, the most important factor ensuring the safe operation of rail vehicles lies in track geometry, which helps the efficiency and performance of railway tracks [
4,
5]. Investigating the correlation between the geometrical conditions of the track and the performance and quality of the components of ballasted tracks can lead us to a reasonable understanding of the condition of railway tracks. Railway managers pay particular attention to the geometrical conditions of tracks, recognizing the challenge inherent in assessing their operational status [
6,
7].
In modern railway maintenance practices such as track recording cars, mechanized machines play a pivotal role in recording, monitoring, and inspecting track geometrical conditions. While moving at the specified speed on the track, they can capture various parameters such as geometrical irregularities and track stiffness. Geometric parameters of railway tracks including longitudinal levels (LLs), horizontal alignments (ALs), track gauge (GAU), cross-level (XLV), and twist (TWI) play a crucial role in ensuring the safe operation of rail vehicles and improving the efficiency and performance of railway tracks. On the other hand, one of the other main factors that plays a key role in the maintenance of railway tracks is ballast stiffness. Even though track stiffness measurement is not commonly used in the inspection of railway tracks, there are a large amount of railway track specifications that are directly or indirectly related to track stiffness, which helps managers and railway engineers make maintenance decisions by discovering knowledge from these data [
8,
9,
10]. So, the interpretation of track stiffness can help decision-makers and senior managers determine a strategy and plan for the maintenance and repair of railway tracks. In recent years, significant strides have been made in the development of continuous track measurement methods [
11,
12,
13,
14,
15,
16,
17,
18].
Track stiffness plays a crucial role in influencing the dynamic behavior of railway tracks and their interaction with wheels. In addition, the geometric quality of tracks is directly correlated with track maintenance, and both are directly related to track stiffness. A high stiffness of the track enhances its load-carrying capacity and reduces the displacement of the track. On the other hand, high track stiffness leads to an increase in dynamic forces, especially in the contact area between the wheel and the rail, leading to increased damage to track components, including sleepers and the ballast [
19]. Changes in track stiffness along the route lead to changes in track/wheel interaction forces, resulting in varying settlements and geometric deterioration along the track. Numerous studies have been conducted on track stiffness in recent years, illuminating its pivotal role in railway infrastructure [
20,
21,
22,
23].
Generally, limited research has been performed to investigate the mutual effects of track stiffness, which represents the characteristics of the track substructure and track geometry, indicative of the track superstructure. Shi et al. conducted a critical review of studies and their future trends regarding track stiffness irregularity (TSI) and presented a new concept of critical values of track stiffness irregularity for the integrated management of track geometry [
24]. Pozavak et al. delved into determining the optimal track stiffness concerning its effect on track geometric quality, considering it dependent on the individual stiffness of all superstructure and substructure elements, as well as their mutual compatibility [
25]. In the Canadian railway network, Roghani et al. compared a dataset of track geometric failures which were related to track roughness and stiffness. This comparison, besides confirming the relationship between track stiffness and track failures, led to providing allowable values of roughness and stiffness, along with a risk diagram for the maintenance and repair of the railway track [
26]. Berggren presented a novel method aimed at extracting new insights from collected data, sourced from geometric quality, dynamic stiffness, and ground-penetrating radar [
27,
28]. Nielsen et al. evaluated data collected by a track recording car from 1999 to 2016, focusing on investigating the geometric deterioration of the track within wavelengths of 1 to 25 m. They examined the correlation between changes in track stiffness and geometric irregularities to understand their impact on track maintenance and repair [
29,
30]. Grossoni et al. investigated the role of track vertical stiffness variations on the long-term track deterioration behavior through a series of computational experiments, leading to the presentation of a process to generate vertical stiffness representative of real-world track conditions [
31].
Over the past few decades, numerous researchers have directed their attention towards condition monitoring and track maintenance [
32,
33,
34,
35]. One of the appropriative approaches that can be employed to achieve this aim is data mining, which is used in railway engineering in various subjects, as mentioned by Villarejo et al. [
36], Bergquist and Söderholm [
37], Famurewa et al. [
38], Sauni et al. [
39], and Thaduri et al. [
40]. In the data mining approach, machine learning (ML) techniques are generally used to find data correlation. Several ML techniques (both supervised and unsupervised methods) are utilized to survey the maintenance of railway tracks. Sresakoolchai et al. tried to improve the efficiency of maintenance activities, especially railway component defects and track geometry, utilizing deep reinforcement learning integrated with digital twin techniques [
41]. Gerum et al. used random forest (RF) and recurrent neural network (RNN) techniques to predict railway track maintenance work and found that the accuracy of the RNN and RF were about 80% and 77%, respectively [
42]. In another study, Consilvio et al. used an unsupervised machine learning algorithm (K-means clustering) and a supervised learning method (support vector machine) to manage the railway earthwork and track circuit maintenance [
43]. Falamarzi et al. used Pearson correlation analysis to predict the track gauge and realized that the prediction accuracy of the support vector machine (SVM) is higher in curved sections, while the artificial neural network (ANN) has better accuracy in straight sections [
44]. Lee et al. predicted the track geometry degradation by the ANN and SVR techniques [
45]. Martey et al. employed several unsupervised algorithms and supervised ML techniques (including cluster analysis, multiple linear regression, decision tree regression, random forest regression, and support vector regression) to analyze the influence of geocell installation on track geometry quality [
46]. In order to predict the railway track geometry parameters, Sresakoolchai et al. developed deep ML models using 3D recurrent neural network-based techniques [
47]. Popov et al. studied the potential of two unsupervised ML techniques (including autoencoder and K-means clustering) to localize track defects based on geometry measurements [
48]. Mehrali et al. studied the use of data mining techniques in surveying railway track geometry parameters and track stiffness [
49]. However, to the best of the authors’ knowledge, the literature pertaining to the relationship between track stiffness and geometrical parameters has remained notably scarce. Therefore, there is a pressing need for further research and studies to formulate a coherent and systematic approach towards clarifying the connection between track stiffness and geometrical parameters.
In general, an innovative approach to the effective management of railway maintenance activities involves establishing a relationship between different track properties. This perspective allows engineers to rapidly assess track health conditions without extensive record-keeping. Based on the literature review conducted above, there is limited knowledge regarding the correlation between the geometric parameters and structural characteristics of railway tracks. Among the track properties, ballast stiffness and track geometry are two significant parameters that play a crucial role in maintenance, yet a comprehensive correlation study between them has not been conducted. Therefore, the current study aims to survey the relationship between vertical track stiffness and track geometry, with a specific focus on two crucial representatives: vertical ballast stiffness and the longitudinal level. To achieve this, track geometric data and vertical track deflection measurements were collected along the Tehran–Mashhad railway line in Iran. Various correlation analyses were then conducted using both frequency-based methods and machine learning techniques. First, the relationship between vertical rail deflection and longitudinal level was examined by calculating the power spectrum density (PSD) of the collected data. This analysis aims to investigate the correlation between the data obtained from the track recording car and stiffness recording car. By analyzing the PSD, this study seeks to identify patterns and relationships that can provide insights into the impact of vertical rail deflection on track longitudinal levels and ballast stiffness, contributing to improved track maintenance and performance evaluation. Next, this study evaluated and compared the effectiveness of frequency analysis with three machine learning algorithms—linear regression, decision tree, and random forest—in analyzing the relationship between vertical track stiffness and track geometry. These correlation analyses provide insights into how variations in ballast stiffness impact the vertical longitudinal level of the track, contributing to a deeper understanding of track performance and maintenance needs.
The insights mentioned above can reveal the potential of advanced analytical techniques in understanding and optimizing railway track maintenance strategies. By leveraging machine learning algorithms, railway maintenance teams can more accurately predict and address issues related to track conditions. The remainder of this paper is organized as follows:
Section 2 presents the data acquisition process, detailing the methods and equipment used to gather the necessary data for track longitudinal level and vertical track deflection measurements along the Tehran–Mashhad railway line.
Section 3 discusses the algorithms employed in correlation mining analyses, including both frequency-based techniques and machine learning algorithms such as linear regression, decision tree, and random forest algorithms.
Section 4 provides a comprehensive analysis and discussion of the results, highlighting key findings and their implications. Finally,
Section 5 concludes this paper, summarizing the main contributions and suggesting potential areas for future research.
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:
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.
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.
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.