This paper investigates the growth and treatment of a major type of rail rolling contact fatigue (RCF) known as head checks (HCs). The analysis is based on extensive field data of 212 curved tracks made of R260 steel across the entire Belgian railway network. The HC crack depth was mainly measured by eddy current testing. The growth rates of HCs are analysed in relation to the curve radius, annual traffic load, and rail wear. The key findings are as follows: 1) Tracks with radii between 750 and 1000 m exhibit the highest HC growth rate of about 1.5 mm per 100 million gross tons (MGT) and the largest occurrence probability of about 25 %. 2) A counterintuitive result is that the HC growth per MGT is higher on lines with lower annual traffic loads, consistent with the trend observed in rail wear rates. 3) The artificial wear methods to control RCF, such as preventive grinding, should consider annual traffic load and service time, rather than solely accumulated tonnage, as is the current practice. Based on these findings, a new method is proposed to estimate the magic wear rate for the Belgian railways, which can serve as input for optimising grinding operations to mitigate HCs.

Short pitch corrugation is a typical rail defect that lacks a thorough understanding and adequate root-cause solutions. This paper aims to identify the damage mechanism of short pitch corrugation through a microstructural analysis of a field rail sample. This sample made of R260Mn pearlitic steel was taken from a straight section of the Dutch railway network, and its geometry and surface hardness variation along the corrugation were measured and analyzed. Eleven specimens, including both corrugated and non-corrugated zones, were sectioned from the rail sample and continuously examined using light optical microscopy, scanning electron microscopy and micro-hardness testing. The results indicate that the corrugation damage mechanism can be categorized into three stages: (1) pre-corrugation, characterized by uniform wear and plastic deformation; (2) corrugation initiation, dominated by differential wear; and (3) corrugation growth, involving both differential wear and plastic deformation accumulation. The initiation and growth of corrugation both contribute to an inhomogeneous distribution of plastic deformation layer (PDL) in the rail subsurface, which follows an approximately sinusoidal pattern, matching the corrugation geometry in both wavelength and phase. Consequently, the hardness also varies in phase with the corrugation geometry, with higher hardness values at corrugation peaks. In the non-corrugation zone, the PDL and hardness show relatively small and irregular fluctuations. This study also provides meaningful insights into rail grinding, suggesting that grinding should account for differential PDL thickness to prevent corrugation reoccurrence due to subsurface material inhomogeneity.

Frictional heat is generated at the wheel-rail interface during train operations, particularly under high slip ratios during acceleration and braking. Thermal effects can accelerate wear, induce plastic deformation, and contribute to thermal fatigue. Reliable modelling of wheel-rail contact that considers friction-induced thermal effects is desirable for the accurate prediction of wheel-rail interface deterioration. Several analytical and numerical models have been proposed to simulate thermal or thermomechanical wheel-rail loads but have rarely been validated, especially in high slip ratio scenarios where flash temperatures exceed 200 °C. This study develops and experimentally validates a three-dimensional thermomechanical finite element (FE) wheel-rail contact model for high slip ratio conditions, with contact temperatures reaching 360 °C. The model incorporates key mechanical parameters, including wheel loads, coefficients of friction, and slip ratios. Simulated rail surface temperatures across various slip ratios (5 %, 10 %, and 15 %) are compared with the flash temperatures measured with an onboard infrared thermal camera, showing good agreement with a maximum deviation of 9.9 %. This confirms the reliability of the model for simulating wheel-rail contact under thermal effects.

This paper presents a methodology for detecting and monitoring short pitch corrugation (SPC) under varying measurement conditions using vertical and longitudinal axle box acceleration (ABA) measurements. The main objective of the detection algorithm is to determine the likelihood and approximate severity of SPC presence, providing insights for maintenance planning. The methodology combines a validated three-dimensional finite element (3D-FE) model of the ABA responses at SPC and signal processing techniques to extract meaningful data from the real-world on-board measurements. First, a 3D-FE vehicle-track model is validated and used to quantify the physical relationships in the time–frequency responses of ABA at SPC under different levels of corrugation severity and measurement speeds. Then, a measurement train is instrumented with multiple accelerometers to capture field data on ABA at SPC, which is validated with field inspections and Railprof measurements. Finally, the ABA responses are analyzed based on the number of signals detecting SPC and an assessment of severity based on impact energy due to SPC. The methodology is demonstrated by analyzing the track between Assen and Groningen on the Dutch rail network. Results show that the methodology accurately detects registered SPC locations. Further, a whole track analysis is conducted, from which the methodology proposes new locations and severities of SPC, providing crucial information for rail maintenance planning.

The coefficient of friction (COF), defined as the maximum of the adhesion coefficient for a given contact condition, fluctuates rapidly due to environmental and operational factors. This paper introduces a torque modulation-based method for COF estimation. A simplified analytical model of the Manchester benchmark bogie operating under dry adhesion conditions is used to evaluate this method. The study presents an analytical equation that confirms earlier simulation-based findings showing a phase difference between applied torque modulation and resulting motor angular velocity. This phase relationship is shown to reflect the shape of the adhesion-slip curve. Notably, when the phase difference approaches 90°, the locomotive operates near the point of maximum adhesion, corresponding to the COF. Furthermore, the sensitivity of this approach to key system parameters, including normal load, wheel rolling radius, and modulation frequency, is examined. The findings provide valuable insights into the robustness and applicability of torque modulation-based COF estimation techniques in real-time traction control systems. The estimated COF can be further leveraged for adhesion management, driver advisory systems, and autonomous train operation.

Railway transition zones connecting conventional embankments and rigid struc-tures, such as bridges and tunnels, usually degrade much faster than other railway sections. Efficient health condition monitoring of transition zones is important for preventative track maintenance. In this paper, a methodology for monitoring rail-way transition zones using acceleration measurements on multiple axle boxes (multi-ABA) of a passing train is presented. To showcase its capability, the measurements in the Netherlands, Sweden, and Norway are analyzed and dis-cussed. It is found that different bridges and transition zones exhibit unique char-acteristics including dominant wavelengths and energy distribution. Based on these unique characteristics, the geometry and support conditions at different lo-cations of a transition zone can be evaluated. Higher train speed makes the char-acteristics more pronounced. The results demonstrate that the multi-ABA meas-urement has the potential to evaluate and thus monitor the health conditions of various transition zones.

This paper proposes a novel framework for simulating the dynamics of beams on elastic foundations. Specifically, partial differential equations modeling Euler–Bernoulli and Timoshenko beams on the Winkler foundation are simulated using a causal physics-informed neural network (PINN) coupled with transfer learning. Conventional PINNs encounter challenges in handling large space–time domains, even for problems with closed-form analytical solutions. A causality-respecting PINN loss function is employed to overcome this limitation, effectively capturing the underlying physics. However, it is observed that the causality-respecting PINN lacks generalizability. We propose using solutions to similar problems instead of training from scratch by employing transfer learning while adhering to causality to accelerate convergence and ensure accurate results across diverse scenarios. The primary contribution of this paper lies in introducing a causality-respecting PINN loss function in the context of structural engineering and coupling it with transfer learning to enhance the generalizability of PINNs in simulating the dynamics of beams on elastic foundations. Numerical experiments on the Euler–Bernoulli beam highlight the efficacy of the proposed approach for various initial conditions, including those with noise in the initial data. Furthermore, the potential of the proposed method is demonstrated for the Timoshenko beam in an extended spatial and temporal domain. Several comparisons suggest that the proposed method accurately captures the inherent dynamics, outperforming the state-of-the-art physics-informed methods under standard L²-norm metric and accelerating convergence.

This article develops and tests a self-contained railway track monitoring system that fits in existing vehicles without the need for speed and load control. Combining a train-borne laser Doppler vibrometer and axle box accelerometers enables synchronized measurements of train-track response under operational conditions. Utilizing a GPS antenna and video camera, we propose the multisignal processing method to obtain train-track vibrations with train position and speed. Then, we fuse the multiple signals to extract an impact index and a resonance index and further propose an interpretable anomaly detection strategy. We test the system on an operational line at 20-60 km/h under different working conditions and verify the detection results using information from conventional technologies. The impact index peaks near joints and welds, and the resonance index yields a good correlation with the measured track geometry. The developed solution achieves the detection, localization, and quantification of surface and support anomalies in railway tracks.

The Coefficient of Friction (CoF) is an important parameter affecting acceleration and braking behavior of trains, and consequently the inter-train distance and utilization of track. To optimize operation schedules, maximize railway capacity, and realize automatic train operations, reliable measurements of the CoFs experienced by in-service trains are desirable. In this study, a train-borne measurement approach is proposed based on a torque modulation concept. It involves superimposing a small-amplitude sinusoidal signal on the motor torque. Because the wheel-rail friction force acts as variable damping, it causes a phase difference between the angular velocity response of the wheelset and the input modulated torque signal. This phase difference can be used to determine the creep coefficient, i.e., the slope of the creep curve, and then to estimate the CoF in combination with the measured Coefficient of Adhesion (CoA), i.e., the ratio between the wheel-rail friction force and normal load. Simulations of torque modulation with VI-Rail are conducted. Variation of phase difference with the increase of the modulated torque is derived theoretically and compared with numerically obtained results using the VI-Rail multibody dynamics model under different CoF conditions. The good agreement between the results indicates the effectiveness of the proposed measurement concept.

Computer-aided simulations are routinely used to predict a prototype's performance. High-fidelity physics-based simulators might be computationally expensive for design and optimization, spurring the development of cheap deep-learning surrogates. The resulting surrogates often struggle to generalize and predict novel scenarios beyond their training domain. We propose a two-stage methodology addressing the challenge of generalization. It employs physics-based simulators, supplemented with ordinary differential equations integrated into the recurrent architecture, to learn the intrinsic dynamics. The proposed approach captures the inherent causality and generalizes the dynamics irrespective of a data source. The presented numerical experiments encompass five fundamental structural engineering scenarios, including beams on Winkler foundations based on Euler-Bernoulli and Timoshenko theories, beams under moving loads, and catenary-pantograph interactions in railways. The proposed methodology outperforms conventional recurrent methods and remains invariant to data sources, showcasing its efficacy. Numerical experiments highlight its prospects for design optimization, predictive maintenance, and enhancing safety measures.

Polygonal wear is a type of damage commonly observed on the railway wheel tread. It induces wheel-rail impacts and consequent train/track components failure. This study presents a finite element (FE) thermomechanical wheel-rail contact model, which is able to cope with the three possible generation and development mechanisms of polygonal wear: initial defects, thermal effect, and structural dynamics. The polygonal wear-induced impact contact and further development of wear are simulated. The simulated elastic contact solutions are verified against the program CONTACT. Different material properties (elastic, elasto-plastic and elasto-plastic-thermo, i.e. with thermal softening) and initial polygonal profiles are then applied to the FE model to investigate the influence of wheel/rail material and wear amplitude on wheel-rail contact stress and wear development. The simulations indicate that the wheel-rail impact-induced temperature may reach up to 362 ℃ at the contact interface, and the high temperature at the contact area influences wheel-rail contact stress and wear depth.

Wheel-rail high-frequency interaction is closely related to the formation of railway short-wave defects. Finite element (FE) method has been widely used to simulate wheel-rail dynamic systems, but its validity in modelling high-frequency interaction has not been fully demonstrated in three dimensions (3D). This work aims at comprehensively validating the 3D FE modelling of wheel-rail high-frequency interaction using a downscale V-Track test rig. First, the FE model of the V-Track is developed that comprehensively includes the 3D track elasticity. The simulated track dynamic behaviours are validated against hammer tests, and the major vibration modes are analyzed employing modal analysis. Afterwards, the simulate wheel-rail dynamic responses are comprehensively compared with measurement results up to 10 kHz. Their characteristic frequencies are identified and correlated to the eigenmodes of the vehicle-track system. The results indicate that the proposed 3D FE model is capable of comprehensively and accurately simulating the 3D track dynamics and wheel-rail dynamic interaction of the V-Track up to 10 kHz. Rail vibrations dominate the wheel-rail dynamic contact within 10 kHz, while the wheel vibrations play an increasingly important role at higher frequencies and become decisive near the wheel eigenmode frequencies. The V-Track overall achieves dynamic similarity to the real vehicle-track system.

A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data.

Inefficient management of rail surface defects can increase maintenance costs, safety hazards, service disruptions, and catastrophic failures like rail breaks. To achieve adequate management, having effective technology capable of timely detecting and frequently monitoring rail defects is of utmost importance. The aim is early detection of defects to maintain safety levels and prevent the re-appearance due to residual damages.

Various measurement technologies, such as visual inspections, geometry profile measurements, and other measurement techniques, have been used for the detection of rail defects. While these methods provide insights, they often lack the capability for early-stage defect detection. Thus, most of these technologies are suitable for reactive maintenance since they detect defects when they reach a certain severity level. Axle box acceleration (ABA) technology provides a solution capable of frequent monitoring, mounted on trains in operation without dedicated measurement vehicles (see figure 71-1). Its basic principle is to use a train as a moving load that excites the infrastructure and to detect defects by evaluating the time-frequency characteristics of the dynamic response measured by accelerometers installed on axle boxes of the train. ABA systems have shown promise in detecting defects in the early stages. However, its widespread application and need for robustness require further validation and development. This work presents the results of detecting and monitoring rail surface defects using ABA technology.

This work presents the results of a measurement campaign to demonstrate the effectiveness of the axle box acceleration (ABA) technology for detecting rail defects. The measurements were conducted along the Iron Ore line between Sweden and Norway for the IN2TRACK3 project. This line is mostly single-track with passenger-freight mixed traffic and heavy axle load. Historical data and track information data were not considered in this study. By analyzing data acquired from the accelerometers in vertical and longitudinal directions, rail defects were detected in near real-time using big-data analytics. For our validated sections, 100% of rail defects (including squats) were detected using time-frequency analysis and an outlier detection approach. The methodology also allows for identifying priority locations, e.g., defective welds, joints, transition zones, etc., and its use for prescriptive maintenance recommendations is being explored in the framework of the IAM4RAIL project.

Short pitch corrugation has been a problem for railways worldwide over one century. In this paper, a parametric investigation of fastenings is conducted to understand the corrugation formation mechanism and gain insights into corrugation mitigation. A three-dimensional finite element vehicle–track dynamic interaction model is employed, which considers the coupling between the structural dynamics and the contact mechanics, while the damage mechanism is assumed to be differential wear. Various fastening models with different configurations, boundary conditions, and parameters of stiffness and damping are built up and analysed. These models may represent different service stages of fastenings in the field. Besides, the effect of train speeds on corrugation features is studied. The results indicate: (1) Fastening parameters and modelling play an important role in corrugation formation. (2) The fastening longitudinal constraint to the rail is the major factor that determines the corrugation formation. The fastening vertical and lateral constraints influence corrugation features in terms of spatial distribution and wavelength components. (3) The strengthening of fastening constraints in the longitudinal dimension helps to mitigate corrugation. Meanwhile, the inner fastening constraint in the lateral direction is necessary for corrugation alleviation. (4) The increase in fastening longitudinal stiffness and damping can reduce the vibration amplitudes of longitudinal compression modes and thus reduce the track corrugation propensity. The simulation in this work can well explain the field corrugation in terms of the occurrence possibility and major wavelength components. It can also explain the field data with respect to the small variation between the corrugation wavelength and train speed, which is caused by frequency selection and jump between rail longitudinal compression modes.

This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and aim to predict the deflection of beams and the magnitude of the loads. The mathematical representation of the moving load considered involves a Dirac delta function, to capture the effect of the load moving across the structure. Approximating the Dirac delta function with PINNs is challenging because of its instantaneous change of output at a single point, causing difficulty in the convergence of the loss function. We propose to approximate the Dirac delta function with a Gaussian function. The incorporated Gaussian function physical equations are used in the physics-informed neural architecture to simulate beam deflections and to predict the magnitude of the load. Numerical results show that PIML is an effective method for simulating the forward and inverse problems for the considered model of a moving load.

The conventional vertical track quality index (TQI) based on the standard deviation of longitudinal levels yields standardized railway track condition assessment. Nevertheless, its capability to identify problems is limited, particularly in the ballast and substructure layers when abrupt changes affect train-track interaction. Previous research shows that dynamic responses from moving trains via axle box acceleration (ABA) measurements can quantify abrupt changes in the vertical dynamic responses. Thus, this paper proposes a framework to design an enhanced vertical TQI, called EnVTQI, by integrating track longitudinal levels and dynamic responses from ABA measurements. First, measured ABA signals are processed to mitigate the influence of variation in measurement speed. Then, substructure and ballast-related features are extracted, including scale average wavelet power (SAWP) in the ranges 0.04 m^-1 to 0.33 m^-1 (substructure) and 1.25 m^-1 to 2.50 m^-1 (ballast). This enables identifying track conditions at different track layers. Finally, EnVTQI is determined by weight averaging between the conventional vertical TQI and the ABA features from moving trains. The performance of EnVTQI is evaluated based on 48 segments of a 200-m track on a Dutch railway line. The results indicate that EnVTQI helps to distinguish track segments that cause poor train-track interaction, which the conventional TQI does not indicate. EnVTQI can supplement the conventional TQI, improving the effectiveness of track maintenance decision-making.

Vibrations resulting from dynamic vehicle-track interactions (VTI) offer valuable insights into track conditions. This paper presents an approach for track condition monitoring by detecting and quantifying multiple track degradations using a digital twin of the VTI system. Unlike existing techniques that focus on a specific degradation type at a single track component, our proposed method provides a generic and integrated framework. By combining a physics-based VTI model with a data-driven model, we dynamically update the digital twin’s state based on measured axle-box accelerations (ABA). We introduce a local ABA feature extracted from its spectrogram and demonstrate its effectiveness in distinguishing various degradations at different track positions. The implementation and capability of the proposed approach were demonstrated in a case study conducted on a transition zone of a railway bridge. The simultaneous track stiffness variations in the railpad/fastening and ballast layers were successfully detected, confirming the effectiveness of our approach. The case study also showcases the generality, interpretability, efficiency, and robustness of the proposed approach in identifying concurrent degradation. Our proposed framework opens new possibilities for cost-effective continuous track monitoring for railway infrastructure management.

This paper presents a big data-based analysis of the rail wear of the whole Belgian railway network measured in 2012 and 2019. Wear rates are reported, discussed, and quantitatively formulated as functions of critical factors in terms of curve radius, annual tonnage (rail age), high rail in curves, an average from both rails in straight tracks at rail top (vertical wear) and gauge corner (45° wear) and for steel grade R200 and R260. The influence of preventive grinding is also analysed. The wear rates are derived in an aggregated manner for the whole network. The wear rates do not show significant change with changes in rolling stock over the years, implying that the wear rates could also hold for other networks. It is found that R200 shows, on average, a 34% higher wear rate than R260. Also, the wear rate per tonnage is lower for high-loaded tracks. Thus, time is a relevant factor in explaining the wear evolution of low-loaded tracks; for instance, the effect of corrosion may have an important role. The paper provides statistically significant information that can be used for wear modelling, understanding and treating rolling contact fatigue based on the wear rate and developing tailored rail maintenance strategies.