Track Modeling Research Articles

Long railway track modelling – A parallel computing approach

This paper presents the development of a dynamics model for long track sections. It is based on an established short track model that utilises the Finite Element Method to describe rails and block models to describe sleepers, ballast and subballast. By implementing a parallel computing method, this innovation enables the construction of a true long track model: by segmenting the long track into shorter segments that are easier to compute. The model facilitates simulations to be run in parallel, thereby permitting simultaneous calculations of various numerical track variables. The model employs a Message Passing Interface framework to seamlessly link the track segments, handling the flow of data among the computing cores designated to each subdivided section. This strategic framework allows the long track model with the capability to simulate tracks of virtually any length, with the only constraints being the available computational resources and time. The claimed contribution about modelling capability is verified using two case studies on a 6km-long track involving different practical and conceptual train operational scenarios: emergency braking and constant braking force with constant train speed. These case studies show the flexibility and scalability of the method and its capability to handle complex track dynamic systems.

Review Kerusakan Keausan Roda Pada Kendaraan Kereta Api

Damage due to wheel wear on railway trains has a significant impact on railway safety and comfort. This review examines various aspects related to wheel wear damage on trains. The primary focus of this review encompasses three critical areas: railway track, wheel-rail interaction, and the trains themselves. The first section discusses the structure and modeling of railway tracks, while the second section explores various types of interactions between wheels and rails as well as related mathematical models. The third section reviews the types of railway vehicles, their mathematical models, and their stability on straight and curved tracks. Furthermore, this review also examines the influence of wheel wear on the dynamic response of the system. It is hoped that this review will provide valuable insights for practitioners and researchers in improving and enhancing the reliability and safety of railway systems.

A framework for dynamic modelling of railway track switches considering the switch blades, actuators and control systems

The main contribution of this paper is the development and demonstration of a novel methodology that can be followed to develop a simulation twin of a railway track switch system to test the functionality in a digital environment. This is important because, globally, railway track switches are used to allow trains to change routes; they are a key part of all railway networks. However, because track switches are single points of failure and safety-critical, their inability to operate correctly can cause significant delays and concomitant costs. In order to better understand the dynamic behaviour of switches during operation, this paper has developed a full simulation twin of a complete track switch system. The approach fuses finite element for the rail bending and motion, with physics-based models of the electromechanical actuator system and the control system. Hence, it provides researchers and engineers the opportunity to explore and understand the design space around the dynamic operation of new switches and switch machines before they are built. This is useful for looking at the modification or monitoring of existing switches, and it becomes even more important when new switch concepts are being considered and evaluated. The simulation is capable of running in real time or faster meaning designs can be iterated and checked interactively. The paper describes the modelling approach, demonstrates the methodology by developing the system model for a novel “REPOINT” switch system, and evaluates the system level performance against the dynamic performance requirements for the switch. In the context of that case study, it is found that the proposed new actuation system as designed can meet (and exceed) the system performance requirements, and that the fault tolerance built into the actuation ensures continued operation after a single actuator failure.

Modeling of heavy charged particle tracks overlap by pair of Al2O3:C, Mg dosimeters

Modeling of heavy charged particle tracks overlap by pair of Al2O3:C, Mg dosimeters

Formulation and Evaluation of the Ballast Shear Interlocking Coefficient based on Analytical, Experimental, and numerical Analyses

The interaction among ballast particles, known as ballast shear interlocking (BSI), significantly influences the dynamic responses of railway track. This research presents a meticulously derived mathematical formulation for calculating BSI stiffness, which is then validated through experimental data obtained from a novel laboratory test procedure. The accuracy of the BSI formulation is demonstrated by its successful prediction of BSI properties in laboratory tests. Additionally, a numerical layered model is introduced to evaluate the sensitivity of the proposed formula to the mechanical and dynamic attributes of the ballasted track. This model highlights the resilience of tracks and emphasizes the critical role of BSI effects in railway track design, offering insights into parameters affecting track behavior. The study comprehensively explores ballast behavior, emphasizing the importance of BSI in track resiliency and advocating for its precise consideration in railway track design, modeling, and maintenance to ensure operational safety and efficiency. The developed methodology not only enhances the modeling of ballasted railway tracks as multi-layer systems but also advances the assessment of shear interlocking effects through laboratory testing.

Sensitivity of typhoon wind hazard in coastal region to the track modelling and the considered historical best track database

The tropical cyclone (TC) wind hazard is often assessed using the autoregressive type of model and the beta-advection model. In the present study, the beta-advection models are developed using the best track datasets from the China Meteorological Administration (CMA) and the Joint Typhoon Warning Center (JTWC). A comparison of statistics of the TC track parameters along the coastline of mainland China is presented using historical tracks and simulated tracks from the developed models. The comparison is extended by considering an existing autoregressive type of track model. Results show that the number of genesis per year based on the dataset in CMA is about 7% greater than that in JTWC. A comparison of the estimated T-year return period value of the annual maximum TC wind speed, vA-T, is presented using the three different track models. vA-T obtained based on the beta-advection model developed using the dataset from CMA is greater than that by using the dataset from JTWC by about 5%. vA-T estimated using the autoregressive type of model and the beta-advection model indicates that their differences are up to 10% and 12% for T equals 50 and 100 years if the dataset from CMA is considered.

Railway track deflection analysis by using evolutionary algorithms

In contrast to numerical methods, analytical modelling of the railway track is one of the less time-consuming and computationally demanding methods which, in combination with the computing power commonly available today, can form an effective tool for analysing the behaviour of the railway track.This paper deals with the use of iterative methods of evolutionary algorithms, together with analytical modelling, for the purpose of reverse analysis of the measured deflection caused by moving loads acting on the railway track. The theoretical assumptions of the analytical model used, the data collection methodology and the method used for the reverse analysis are presented. The results of the analysis are also presented.

Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

This paper proposes an approach to arranging curvilinear sections of the railroad track, which involves the replacement of two transitional ones and a circular curve with one curvilinear section. Modeling this section implies the construction of a curve in the plan and profile, the joint consideration of which forms the spatial appearance of the curve, which ensures a smooth transition between the rectilinear rails. The need for such transitions is due to the terrain, the need to bypass settlements, and the presence of geological, geographical, and other obstacles that occur when laying railroads. A curvilinear section is modeled in the plan using a curve that is represented in natural parameterization under the law of curvature distribution in the form of a fifth-power polynomial. At the same time, at the start and end points of the section, the curvature and its derivative accept zero values. The outer rail elevation retraction (modeling in the profile) is performed using the curve built, whose sections are also represented in natural parameterization with the dependences of the curvature distribution on the arc length in the form of fourth-power polynomials. At the docking point of the sections, the third order of smoothness is ensured, which implies the equality of values of the functions, their derivatives, the curvature, and a derivative of the curvature from the length of its natural arc. Measures have been proposed to ensure the predefined track gauge retraction. The application of the proposed approach to model a railroad track along the curvilinear section with a variable-radius curve could make it possible to achieve a favorable curvature distribution, a smooth elevation retraction of the outer rail and the track gauge. That would consequently improve the safety of rolling stock running along the curvilinear section of the track, reduce the lateral and vertical efforts that predetermine the wear of rails and wheelsets.

Numerical Modelling of Rail Track on Jointed Rock Formation and Implications of Joint Slip on Track Performance

Numerical Modelling of Rail Track on Jointed Rock Formation and Implications of Joint Slip on Track Performance

Modelling of periodic slab track using time-frequency hybrid Green's function method and its application to vehicle-track dynamic interaction

Periodic slab tracks, as a type of non-ballasted track, are widely used in the high-speed railway and urban subway. Efficient and accurate dynamics modelling of the periodic slab track is a crucial issue for solving the vehicle-track dynamic interaction. In this paper, a time-frequency hybrid Green's function method (GFM) is first developed to model the dynamics of the periodic slab track, in light of the properties of the periodicity, symmetry and attenuation of the Green's functions. By combining with the classical vehicle-rail dynamics model, the simulation of the vehicle-track dynamic interaction is then performed. To improve the computational efficiency, the step-moving window strategy is introduced to characterize the vehicle moving on the infinite length track. The floating slab track, a representation of the periodic slab track, is adopted to reflect the time-spatial distribution of the Green's functions. The truncation errors caused by the presented GFM are analysed by calculating dynamic responses induced by a metro vehicle moving on the floating slab track to determine the truncation parameters. The proposed GFM-based vehicle-track dynamic interaction model is finally validated by comparing with the finite element method (FEM) and the basic dynamic characteristics of the periodic slab track are further investigated. Numerical studies show that the computational accuracy of the GFM-based model is nearly the same with the FEM-based model, but the efficiency can be greatly improved. Moreover, it is concluded that the longitudinal uneven stiffness of the periodic slab track shows a significant influence on the slab displacement and stress, while has a slight influence on the fastener force and slab acceleration.

Curved-ribbon-based track modelling for minimum lap-time optimisation

Three-dimensional road models for vehicular minimum-lap-time manoeuvring are typically based on curvilinear coordinates and generalizations of the Frenet–Serret formulae. These models describe the road as a parametrized ‘ribbon’, which can be described in terms of three curvature variables. In this abstraction the road is assumed laterally flat. While this class of road models is appropriate in many situations, this is not always the case. In this research we extend the laterally-flat ribbon-type road model to include lateral curvature. This accommodates the case in which the road camber can change laterally across the track. Lateral-position-dependent camber is introduced as a generalisation that is required for some race tracks. A race track model with lateral curvature is constructed using high-resolution LiDAR measurement data. These ideas are demonstrated on a NASCAR raceway, which is characterized by large changes in lateral camber angle (approx 10^circ) on some parts of the track. A free-trajectory optimization is employed to solve a minimum-lap-time optimal control problem. The calculations highlight the practically observed importance of lateral camber variations.

Individual Identification of Cheetah (Acinonyx jubatus) Based on Close-Range Remote Sensing: First Steps of a New Monitoring Technique

Wildlife monitoring is an important part of the conservation strategies for certain endangered species. Non-invasive methods are of significant interest because they preserve the studied animal. The study of signs, especially tracks, seems to be a valuable compromise between reliability, simplicity and feasibility. The main objective of this study is to develop and test an algorithm that can identify individual cheetahs based on 3D track modelling using proximal sensing with an off-the-shelf camera. More specifically, we propose a methodological approach allowing the identification of individuals, their sex and their foot position (i.e., left/right and hind/front). In addition, we aim to compare different track recording media: 2D photo and 3D photo models. We sampled 669 tracks from eight semi-captive cheetahs, corresponding to about 20 tracks per foot. We manually placed on each track 25 landmarks: fixed points representing the geometry of an object. We also automatically placed 130 semi-landmarks, landmark allowed to move on the surface, per track on only the 3D models. Geometric morphometrics allowed the measurement of shape variation between tracks, while linear discriminant analysis (LDA) with jack-knife prediction enabled track discrimination using the information from their size and shape. We tested a total of 82 combinations of features in terms of recording medium, landmarks configuration, extracted information and template used. For foot position identification, the best combination correctly identified 98.2% of the tracks. Regarding those results, we also ran an identification algorithm on a dataset containing only one kind of foot position to highlight the differences and mimic an algorithm identifying the foot position first and then an individual factor (here, sex and identity). This led to accuracy of 94.8 and 93.7%, respectively, for sex and individual identification. These tools appear to be effective in discriminating foot position, sex and individual identity from tracks. Future works should focus on automating track segmentation and landmark positioning for ease of use in conservation strategies.

Influence of track foundation on the performance of ballast and concrete slab tracks under cyclic loading: Physical modelling and numerical model calibration

Ballast and slab railway track structures are constructed from different materials, thus requiring different maintenance strategies. Therefore, this paper compares the settlement performance of both structures using laboratory experiments, and calibrates numerical models based upon the results. Firstly, a comparison of the short and long-term behaviour of ballasted and slab tracks under cyclic loading is performed at full-scale. Both tracks have the same track foundation but a different track superstructure, and are subject to 3 million cycles of loading. The results are used to develop and calibrate the short-term response of a 3D finite element model of both track structures. They are also used to calibrate an empirical permanent deformation model for the track foundation, where the number of load cycles and stresses are the main inputs. A strong agreement is found between the numerical and experimental results. This justifies the track modelling approach in predicting the long-term behaviour of track structures where the subgrade is influential.

A Stochastic Tropical Cyclone Model for the Northwestern Pacific Ocean with Improved Track and Intensity Representations

Tropical cyclones (TCs) present a considerable threat to people and engineering facilities in coastal and offshore regions. Accurate estimation of long-return-period ocean environmental parameters such as wind and waves are limited by sparse historical observations. Thus, stochastic tropical cyclone models (STCMs) are widely used to generate large amounts of artificial synthetic TCs, which can reduce the uncertainty in TC hazard risk assessments. To this end, we developed a new STCM with improved modeling for the TC track and intensity. A linear superposition moving model (LSMM) is proposed for track modeling, in which the translation speeds and directions are expressed as the linear superposition of two parts, representing the temporal development of TCs and the environmental influences, respectively, using a weighting factor. In addition, a three-point intensity model (TPIM) is proposed, in which a third point in addition to the starting and ending points, i.e., the “strongest point” with the lowest central pressure in a TC track, is determined first. Then TC strengthening and decaying is simulated by random sampling. The sensitivity and robustness of this model are analyzed in this study. By comparing with historical data and common models without applying the LSMM and TPIM, it was found that the proposed STCM significantly improves the modeling of TC tracks and the temporal development of TC intensities.

Three-dimensional numerical modelling of railway track with varying air voids content bituminous subballast

The use of bituminous subballast (BS) in railways has gained importance due to structural and geometrical enhancing properties of these infrastructures. Oftentimes, during renovations the paving quality control of bituminous mixtures is compromised due to reduced time span. To verify the effects of significant air voids content variation on the mechanical response of railway tracks, this paper performed a 3-D numerical modelling of a Brazilian railway renovated with BS. First, the BS was characterised in laboratory for model inputs. Then, 3-D numerical models were developed assuming two constitutive behaviour for the BS: linear elastic and linear viscoelastic. An all granular track was also simulated for comparisons. Numerical results were compared with actual instrumented test section. As expected, displacements on foot-of-rail and stresses on the subgrade were reduced when using BS. Moreover, the different air voids content of the bituminous mixture evaluated herein caused low variation in the overall track response.

Multiple object tracking using feature fusion in hierarchical LSTMs

Multiple object tracking sets the foundation for many intelligent video applications. The authors present a novel tracking solution using the ability of recurrent neural networks to effectively model complex temporal dynamics between objects irrespective of appearances, pose, occlusions, and illumination. For online tracking, a real-time and accurate association of objects with active tracks poses the major algorithmic challenge. Additionally, re-entry of objects should also be correctly resolved. They follow tracking-by-detection methodology using hierarchical long short term memory (LSTM) network structure for modelling the motion dynamics between objects by learning the fusion of appearance and motion cues. Existing works capture object's perspective for tracking within the detected bounding boxes. They also incorporate object instance segments for track modelling by applying the maskRCNN detector. They present a novel motion coding scheme that anchors the LSTM structure to effectively model the motion and relative position between objects in a single representation scheme. The proposed motion representation and deep features representing objects appearances are fused in an embedded space learned by the hierarchical LSTM structure for predicting the object to track association. The authors present experimental validation of the proposed approach on multiple object tracking challenge datasets and demonstrate that their solution naturally deals with major tracking challenges under all uncertainties.

Development of a Mathematical Model for a Railway Track Using a Gray-Box Modelling Technique

Mathematical model of a system provides the relationship between the input and the output variables. There are different methods of modelling a system, viz. utilising system dynamics, black box modelling and gray-box modelling. In literature, there are many works that describe modelling of a railway track using the system dynamics of a track or interaction between track and train wheel. In standard black-box modelling, most of the time standard test signals such as impulse and step are used to model a system. In this paper, a simple method is described that uses “system subjected to a pulse input” to model a system. This approach is very helpful especially in modelling of a railway track as the track may be subjected to an impulse, step or any signal (i.e. pulse of variable length) in between depending on the speed of the train.

Measurement, analysis, and model updating based on the modal parameters of high-speed railway ballastless track

Abstract The occurrence of high-speed railway wheel-rail defects is closely related to the vibration characteristics of the track structures, which can be affected by service conditions. Theoretical models are the main measures to study this problem. However, due to the modeling simplification and initial parameters used in current track modeling methods, it is difficult to accurately simulate the vibration characteristics of in-serving track structures. To supplement this shortcoming, by conducting a series of research works, including: (1) a modal test on a ballastless track; (2) the sensitivity analysis of the modal parameters of the ballastless track; (3) designing and carrying out of three model updating schemes based on the measured modal parameters, this paper obtained a model that is highly consistent with the vibration characteristics of the actual track structure. The research work can provide a reliable reference for modal testing, vibration analysis and model updating of ballastless track structures.

Theoretical modelling of a vehicle-slab track coupled dynamics system considering longitudinal vibrations and interface interactions

Traction or braking operations are usually applied to the motor cars or locomotives for acceleration and deceleration, especially in perilous mountain high-speed railways that have complex and large gradient sections. Under such a circumstance, the wheel-rail longitudinal interactions may become more intense, which could induce longitudinal impact on the track structure. In this paper, some new concepts are introduced to account for this rarely concerned issue. Two typical interface interactions for a slab track system are fully considered, involving the longitudinal resistance between the rail and rail pad based on the Dahl friction model, and the longitudinal cohesive force between the prefabricated slab and CA (cement asphalt) mortar layer based on the bilinear cohesive zone model. By introducing system longitudinal vibrations and implementing the interface interactions into the classical vehicle-track system, a novel vehicle-slab track vertical-longitudinal coupled dynamics model is established, and investigated under the combined excitation of rail irregularities and polygonal wheel wear in traction conditions. Results indicate that the developed model is capable of capturing the longitudinal interactions between the track structures and enables considering initiation or evolution of the damage at the interface between the track slab and CA mortar subjected to complex train dynamic loads.

Simulating Charge Deposition by Cosmic Rays Inside Astronomical Imaging Detectors

In the context of space astronomy missions, accurate and fast modeling of spurious images generated by solar and galactic cosmic rays (GCRs) in imaging detectors is critical in order to assess and mitigate their detrimental effects. Currently, it is only possible to accurately reproduce the CR images including energy loss straggling, with the use of complex Monte Carlo particle transport codes. However, these codes are difficult to use and cannot be easily included in instrument simulation pipelines. Presented here is CosmiX, a novel, open-source, and Python-based CR model, overcoming the above-mentioned limitations, yet still capable of accurately reproducing the CR images, paving the way for semianalytical Monte Carlo modeling of the CR tracks. These are demonstrated by using CosmiX to reproduce irradiation test data of a PLATO charge-coupled device (CCD) and in-orbit CR data of Gaia CCD detectors.