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.

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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.

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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.

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Reliable estimation of rail useful lifetime can provide valuable information for predictive maintenance in railway systems. However, in most cases, lifetime data is incomplete because not all pieces of rail experience failure by the end of the study horizon, a problem known as censoring. Ignoring or otherwise mistreating the censored cases might lead to false conclusions. Survival approach is particularly designed to handle censored data for analysing the expected duration of time until one event occurs, which is rail failure in this paper. This paper proposes a deep Bayesian survival approach named BNN-Surv to properly handle censored data for rail useful lifetime modelling. The proposed BNN-Surv model applies the deep neural network in the survival approach to capture the non-linear relationship between covariates and rail useful lifetime. To consider and quantify uncertainty in the model, Monte Carlo dropout, regarded as the approximate Bayesian inference, is incorporated into the deep neural network to provide the confidence interval of the estimated lifetime. The proposed approach is implemented on a four-year dataset including track geometry monitoring data, track characteristics data, various types of defect data, and maintenance and replacement (M&R) data collected from a section of railway tracks in Australia. Through extensive evaluation, including Concordance index (C-index) and root mean square error (RMSE) for evaluating model performance, as well as a proposed CW-index for evaluating uncertainty estimations, the effectiveness of the proposed approach is confirmed. The results show that, compared with other commonly used models, the proposed approach can achieve the best concordance index (C-index) of 0.80, and the estimated rail useful lifetimes are closer to real lifetimes. In addition, the proposed approach can provide the confidence interval of the estimated lifetime, with a correct coverage of 81% of the actual lifetime when the confidence interval is 1.38, which is more useful than point estimates in decision-making and maintenance planning of railroad systems.

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The railway industry has the potential to make a strong contribution to the achievement of various sustainable development goals, by an expansion of its role in the transportation system of different countries. To realize this, complex technological and societal challenges are to be addressed, along with the development of suitable state-of-the-art methodologies fully tailored to the particular needs of the wide variety of railway infrastructure types and conditions. Artificial intelligence (AI) methods have been increasingly and successfully applied to solve practical problems in the railway infrastructure domain for over two decades. This paper proposes a review of the development of AI methods in railway infrastructure. First, we present a survey limited to selected journal papers published between 2010 and 2022. Bibliographical statistics are obtained, showing the increasing number of contributions in this field. Then, we select key AI methodologies and discuss their applications in the railway infrastructure. Next, AI methods for key railway components are analyzed. Finally, current challenges and future opportunities are discussed.

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This article proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler–Bernoulli and Timoshenko theories, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler–Bernoulli and Timoshenko partial differential equations (PDEs) are solved using nondimensional equations with the physics-informed loss function. Higher order complex beam PDEs are efficiently solved for forward problems to compute the transverse displacements and cross-sectional rotations with less than 1e−3 % error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space–time domain, even in the case of noisy data. The results suggest that PINNs are a promising strategy for solving problems in engineering structures and machines involving beam systems.@en

The interaction performance of the pantograph-catenary is of great importance as it directly determines the current collection quality and operational safety of trains. The finite element method (FEM) is dominantly used for simulating pantograph-catenary interaction, which is normally computationally heavy. In this work, addressing the tremendous computational cost of FEM models, a surrogate model for fast simulations of pantograph-catenary interaction is proposed using deep learning. A dataset containing 30,000 cases of pantograph-catenary interaction is generated by a validated FEM model. A Long-Short-Term-Memory (LSTM) neural network is proposed to learn the inherent nonlinearity between the input model parameters and the output pantograph-catenary contact force from data. The resulting prediction performance indicates that contact forces predicted by the surrogate model are consistent with those simulated by FEM, while the computational efforts of the surrogate model are negligible compared with FEM. Prediction performances using different network architectures and configurations are compared to determine the optimal setting for a pantograph-catenary system. The LSTM-based surrogate model shows high efficiency for simulating pantograph-catenary interactions and promising practicability in optimising catenary structural parameters for design or upgrade.

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Timely detection and identification of rail breaks are crucial for safety and reliability of railway networks. This paper proposes a new deep learning-based approach using the daily monitoring data from in-service trains. A time-series generative adversarial network (TimeGAN) is employed to mitigate the problem of data imbalance and preserve the temporal dynamics for generating synthetic rail breaks. A feature-level attention-based bidirectional recurrent neural networks (AM-BRNN) is proposed to enhance feature extraction and capture two-direction dependencies in sequential data for accurate prediction. The proposed approach is implemented on a three-year dataset collected from a section of railroads (up to 350 km) in Australia. A real-life validation is carried out to evaluate the prediction performance of the proposed model, where historical data is used to train the model and future ’unseen’ rail breaks along the whole track section are used for testing. The results show that the model can successfully predict 9 out of 11 rail breaks three months ahead of time with a false prediction of non-break of 8.2%. Predicting rail breaks three months ahead of time will provide railroads enough time for maintenance planning. Given the prediction results, SHAP method is employed to perform cause analysis for individual rail break. The results of cause analysis can assist railroads to plan appropriate maintenance to prevent rail breaks.@en

Aiming to handle the increasing variety and volume of railway infrastructure monitoring data, this paper explores the use of intelligent data fusion methods for automatic anomaly detection of railway catenaries. Three classical data dimensionality reduction methods, namely the principal component analysis (PCA), the autoencoder neural network, and the t-distributed stochastic neighbor embedding (t-SNE) are adopted for the data fusion of catenary monitoring data. Then, anomaly detection can be achieved using new features that are automatically extracted from the original data, which requires no prior knowledge of the data or catenary conditions. A case study using data measured from the Dutch railway is presented to compare the performance of the three methods. Six types of catenary monitoring data, including pantograph-catenary contact force, pantograph-catenary friction force, contact wire thickness, contact wire height and stagger, are used in the presented case study. It is demonstrated that both PCA and autoencoder can detect anomalies from catenary monitoring data, while t-SNE shows little indication of such ability. Further, the autoencoder outperforms PCA in distinguishing anomalies in the case study, likely owing to its superiority in analysing data with nonlinearity. Overall, autoencoder is a promising technique for automating the anomaly detection of railway catenaries. The detection results can provide indicators for failure prediction and maintenance decision making.@en

This paper addresses the problem of determining the distribution of the return current in electric railway traction systems. The dynamics of traction return current are simulated in all three space dimensions by informing the neural networks with the Partial Differential Equations (PDEs) known as telegraph equations. In addition, this work proposes a method of choosing optimal activation functions for training the physics-informed neural network to solve higher-dimensional PDEs. We propose a Monte Carlo based framework to choose the activation function in lower dimensions, mitigating the need for ensemble training in higher dimensions. To further strengthen the applicability of the Monte Carlo based framework, experiments are presented under two loss functions governed by L2 and L∞ norms. The presented method efficiently simulates the traction return current for electric railway systems, even for three-dimensional problems.

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In railway pantograph-catenary systems, the contact surfaces undergo wear in long-term operations, directly affecting interaction performance and potentially deteriorating the current collection quality. The effect of contact wire wear (CWW) on the current collection quality should be evaluated to understand the system's health status in operations. This article presents a stochastic analysis of the pantograph-catenary interaction performance with different levels of CWW based on four years of measurement data. The power spectral density (PSD) estimation is carried out on the measured CWW to obtain their frequency representations. The random time histories of CWW are generated based on the PSDs. A nonlinear finite element model of catenary with a lumped-mass pantograph is built. Using the Monte Carlo method, the stochastic analysis of pantograph-catenary contact force is carried out to investigate the distribution and dispersion of assessment indices with different levels of CWW. The results indicate that the CWW mainly affects the maximum and minimum contact forces instead of the contact force standard deviation. The optimal pantograph-catenary interaction performance is observed certain years after CWW is formed, depending on the traffic density of the railway line, which is at the second year in the presented case study. Then, the performance declines with an increase in service time. Also, higher operating speed causes a more significant dispersion in assessment indices representing a lower current collection quality, particularly at the maximum operating speed (70% of the catenary wave propagation speed).

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The wind deflection of overhead contact lines (OCLs) challenges the stable and safe operation of electrified railways. The steady wind causes the static deflection of the contact line, while the fluctuating wind leads to the OCL buffeting. This paper performs a response spectrum analysis of the wind deflection caused by the combined effects of steady and fluctuating winds. Considering the initial configuration of OCL, an absolute nodal coordinate formulation method is employed to model the OCL. A spatial wind field including the fluctuating wind in three directions is constructed and the aerodynamic forces on the OCL are derived. A nonlinear solution procedure is proposed to include the geometrical nonlinearity and dropper slackness in the evaluation of static wind deflection. The pseudo-excitation method is utilised to evaluate the buffeting response of the OCL with stochastic wind load. The analysis results indicate that the dropper slackness has a significant effect on the vertical static deflection. Under an extreme wind speed of 40 m/s, the contact line is always within the safe working range of pantograph head when only the steady wind load is considered. However, the stochastic wind load causes non-negligible fluctuation of OCL, and the contact line may be outside of the pantograph working range under the same wind speed. Sensitivity analyses on the effects of some key parameters to the OCL buffeting suggest that the increases of damping ratio and the tension class are effective measures to improve the wind-resistance capability of OCL.

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Brace sleeve (BS) fasteners, i.e., nut and bolt, are small components but play essential roles in fixing BS and cantilever in railway catenary system. They are commonly inspected by onboard cameras using computer vision to ensure the safety of railway operation. However, most BS fasteners cannot be directly localized because they are too small in the inspection images. Instead, the BS is first localized for detecting the BS fastener. This leads to a new problem that the localized BS boxes may not contain the complete BS fasteners due to low localization accuracy, making it infeasible to further diagnose the fastener conditions. To tackle this problem, this article proposes a novel pipeline for BS fastener looseness diagnosis. First, the competitive deep learning model Faster RCNN ResNet101 is used to coarsely localize BSs. Second, an action-driven reinforcement learning agent is adopted to refine the coarse-localized boxes through a dynamic position searching process. Then, BS fasteners are extracted from the refined localized BS image by the deep segmentation model YOLACT++, which is fast and interpretable. Finally, a looseness diagnosis criterion based on segmented information are proposed. We evaluate the performance of submodels independently and the overall performance of the whole model on a real-life catenary image dataset collected from a high-speed line in China. The test results show that the proposed method is effective for BS looseness detection in railway catenary.

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Brace Sleeve (BS) plays an essential role in connecting and fixing cantilevers of railway catenary systems. It needs to be monitored to ensure the safety of railway operations. In the literature, image processing techniques that can localize BSs from inspection images are proposed. However, the boxes produced by existing methods can contain incomplete and/or irrelevant information of the localized BS. This reduces the accuracy of BS condition diagnosis in further analyses. To address this issue, this paper proposes the use of an action-driven reinforcement learning method that adopts the coarse-localized box provided by existing methods, and finds the movements needed for the box to approach to the true BS position automatically and accurately. In contrast to the existing methods that predict one position of the box containing a BS, the proposed action-driven method sees the localization problem as a dynamic position searching process. The localization of BS is achieved by following a sequence of actions, which in this paper are position-moving (up, down, left or right), scale-changing (scale up or scale down) and shape-changing (fatter or taller). The policy of selecting dynamic actions is obtained by reinforcement learning. In the experiment, the proposed method is tested with real-life images taken from a high-speed line in China. The results show that our method can effectively improve the localization accuracy for 81.8% of the analyzed images. We also analyze cases where the method did not improve the localization and suggest further research lines.@en

The growing variety of data from condition monitoring of high-speed railways offer unprecedented opportunities to improve railway infrastructure maintenance. For condition monitoring of railway catenaries, this paper proposes a data-driven approach that uses a Bayesian network (BN) to integrate the inspection data from catenaries into a key performance indicator (KPI). The BN topology is structured based on the physical relationships among data types, including train speed, dynamic stagger and height of the contact wire, pantograph head acceleration, and pantograph-catenary contact force. The tailored performance indicators are individually defined and extracted from the five types of data as the BN input. As the output of the BN, the KPI is defined as the overall condition level of the catenary considering all defects that can be reflected by the data types. Finally, using historical inspection data and maintenance records from a section of the Beijing-Guangzhou high-speed line in China, the BN parameters are estimated to establish a probabilistic relationship between the input and output. An approach that applies the estimated BN to catenary condition monitoring is proposed. Testing of the BN-based approach using new inspection data shows that the output KPI can adequately represent the catenary condition, leading to a nearly 66.2% reduction in the false alarm rate of defect detection compared with current practice. It is also tested that when the input data quality is not ideal, the approach can still work acceptably on noisy data with a signal-to-noise ratio greater than 3 dB or with one type of data missing.

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The catenary insulator maintains electrical insulation between catenary and ground. Its defects may happen due to the long-term impact from vehicle and environment. At present, the research of defect detection for catenary insulator faces several challenges. 1) Localization accuracy is low, which causes the localized object to be incomplete or/and merge with unnecessary background. 2) Horizontal localization brings inevitable unnecessary information because horizontal box cannot fit well with the shape of insulator. 3) Supervised learning models for defects recognition are unreliable as the available defect samples are insufficient to train models well. To address these issues, this article proposes a novel two-stage defect detection method. In the localization stage, a novel localization network called TOL-Framework is constructed to reduce the background and realize tighter oriented localization. Compared with general basic framework Faster R-CNN, the TOL-Framework cascades a regression module inside basic framework and adds an external postprocess network, which is adversarially trained by standard insulators to refine the localization. These two novel steps greatly improve the oriented localization accuracy. In the defect detection stage, an adversarial reconstruction model that is trained only using normal samples is proposed to evaluate the defect states. A comparison with other methods is conducted using a dataset collected from a 60km section of the Changsha-Zhuzhou railway line in China. The results show the proposed method has the highest localization accuracy, and is effective for insulator defect detection.@en

The condition monitoring of railway infrastructures is collecting big data for intelligent asset management. Making the most of the big data is a critical challenge facing the railway industry. This study focuses on one of the main railway infrastructures, namely the catenary (overhead line) system that transmits power to trains. To facilitate the effective usage of catenary condition monitoring data, this study proposes an unsupervised anomaly detection approach as a pre-processing measure. The approach trains autoencoders to reduce the dimensionality of multisensor data and generate discriminative features between healthy and anomalous data. By testing the reconstruction errors using the trained autoencoders, anomalous data that indicate potential defects of catenary can be identified without prior information and human intervention. A case study on a section of high-speed railway catenary in China shows that the approach can automatically distinguish between healthy and anomalous data. The output anomalous data can save a considerable amount of computation time and manpower in further interpretations aiming to pinpoint defects.@en

Real-time railway traffic management is important for the daily operations of railway systems. It predicts and resolves operational conflicts caused by events like excessive passenger boardings/alightings. Traditional optimization methods for this problem are restricted by the size of the problem instances. Therefore, this paper proposes a reinforcement learning-based timetable rescheduling method. Our method learns how to reschedule a timetable off-line and then can be applied online to make an optimal dispatching decision immediately by sensing the current state of the railway environment. Experiments show that the rescheduling solution obtained by the proposed reinforcement learning method is affected by the state representation of the railway environment. The proposed method was tested to a part of the Dutch railways considering scenarios with single initial train delays and multiple initial train delays. In both cases, our method found high-quality rescheduling solutions within limited training episodes.@en

The condition-based maintenance of high-speed railway catenary is an important task to ensure the continuous availability of train power supply. To improve the condition monitoring of catenary, this paper presents a novel scheme to detect catenary local irregularities using pantograph head acceleration measurements. First, a series of experimental inspections is carried out in a section of the Beijing-Guangzhou high-speed line in China. The time intervals between the inspections are shortened from the traditional six months to about 40 days, which enables monitoring the short-term degradation of local irregularities. Then, based on the wavelet packet entropy, an approach is proposed to detect local irregularities with different scales in length. Criteria for identifying and verifying the local irregularities are established based on the gradient and repeatability of entropy from multiple measurements. Results from the experimental inspections show that different scales of local irregularities can be detected by the proposed scheme. By using frequent inspections, local irregularities can be effectively verified after about seven inspections. The spatial distribution of local irregularities is found to be closely related to the catenary structure. These findings provide valuable information to deploy the scheme for a railway network.@en

When two electric multiple units are non-electrically connected together for improving the transport capacity in high-speed railways, double pantographs frequently operate simultaneously to decrease the current capacity on a single pantograph collector. In this case, the contact force between the trailing pantograph and the catenary severely fluctuates due to the wave propagation along the catenary triggered by the leading pantograph. Therefore, this paper proposes two estimator-based H∞ control strategies for active double-pantograph to decrease the contact force fluctuation considering the actuator time delay. To obtain the pantograph states, a robust recursive state estimation method is presented, which can effectively deal with randomly missing measurements. In addition, to overcome parametric uncertainties and non-differentiable actuator time delay, two robust multi-objective H∞ controllers involving linear matrix inequalities are introduced according to whether the time delay can be predetermined or not. The effectiveness and robustness of the control strategies are investigated through implementing a nonlinear double-pantograph-catenary system model. Simulation results show that, for both the leading pantograph and the trailing pantograph, the proposed control strategies can decrease the contact force fluctuation with high efficiency even though the actuator time delay exists.@en