This paper presents the design of a sliding mode surface driven radial basis function neural network compensated proportional-integral-derivative controller (SMS-RBF-PID) to ensure suspension stability of two-degree-of-freedom (2-DOF) suspension systems. An improved radial basis neural network compensator based on sliding mode surface drive was constructed for compensation current output. The compensator learned external disturbances online through the sliding mode surface, and the Adam optimizer was used to update weights in the neural network, to improve the controller’s ability to compensate for external disturbances. The PID output was then combined with the compensation current to form the electromagnet current control law, thus yielding the SMS-RBF-PID controller. Simulation results show that the SMS-RBF compensator effectively overcomes the weak anti-interference performance of traditional PID controllers, and the proposed control algorithm effectively suppresses vibrations in the electromagnet suspension gap under complex disturbances, thereby improving the dynamic performance of the suspension systems.

The dynamic characteristics of a two-degree-of-freedom maglev vehicle with viscoelastic suspension under the action of aerodynamic lift and nonlinear electromagnetic force are studied. The approximate analytical solution of the system is obtained by using the harmonic balance method. The influence of fractional differential coefficient, order, linear stiffness and nonlinear stiffness on the dynamic characteristics of the system is studied and analyzed. The singularity theory is applied to study the static bifurcation of the system. The global bifurcation characteristics of the system are calculated by using the cell mapping algorithm. The analytic necessary conditions for the occurrence of chaos in the system are obtained by using Melnikov theory. The influence of various parameters on the chaotic motion of the system is further analyzed. The dynamic characteristics of the system under specific external excitation amplitude and excitation frequency are studied by using time history diagram, phase plane diagram and Poincare section diagram. The research shows that the peak value of the amplitude-frequency response curve of the system is the highest when there is no fractional order term, and the jump phenomenon will occur at the same time. With the increase of the fractional order term coefficient, the jump phenomenon of the frequency response curve disappears, and the amplitude of the resonance peak decreases. The bifurcation topology shows that the system has chaotic phenomena. As the external excitation frequency increases, the stability of the system in a stable state with a small amplitude increases first and then decreases. As the system speed feedback parameter increases, the stability of the system in a stable state with a large amplitude gradually increases.

Accurate estimation of wheel-rail forces (WRFs) is critical for evaluating vehicle stability and derailment risk. Direct measurement methods using instrumented wheelsets are costly and unsuitable for in-service vehicles due to the necessity of structural modifications to the wheelsets. This study proposes a hybrid framework that combines a physics-informed force-moment equilibrium (FME) model with deep learning-based correction networks for indirect WRFs estimation. The FME model provides initial estimates of wheel axle lateral force (H) and wheel-rail vertical force (Q), validated through multibody dynamics simulations. Error analysis reveals that Q deviations primarily arise from suspension nonlinearity, whereas H errors are largely attributed to the swingarm effect. A convolutional neural network-long short-term memory (CNN-LSTM) network is employed to refine H predictions, achieving Pearson correlation coefficients (PCC) of more than 0.995 and coefficients of determination (R2) of more than 0.990 across various track conditions. In parallel, an LSTM network is applied to correct Q estimates, leading to improvements of 7-58% in PCC and 18-152% in R2 compared with the FME model. Using the corrected H and Q, derailment coefficient Y/Q is accurately evaluated, achieving a PCC of 0.875. The accuracy of the proposed method is validated under realistic operating conditions, where its robust performance across different track types confirms its cross-scenario transferability and demonstrates significant potential for real-time monitoring to enhance the realism of large-scale train safety assessments.

Increasing operating speed, axle load and utilisation intensify contact forces, creepages and excitation frequencies at the wheel-rail interface, making tread and flange degradation a persistent challenge in modern railway operation. Railway wheels are safety-critical load-bearing components, and service performance is governed by coupled evolution of wear, rolling contact fatigue (RCF), out-of-roundness and thermally influenced surface response under vehicle-track coupled dynamics. The review adopts a life-cycle structure covering design and manufacture, in-service degradation with prediction, and condition monitoring with maintenance intervention. For design and manufacture, the discussion covers wheel steel design and heat treatment, profile design and equivalent conicity control, process routes with residual stress management, and durability under regional environments. For in-service operation, wheel-rail system matching, wear and profile evolution modelling and RCF assessment are compared in terms of governing assumptions, required inputs and applicability across operating regimes. For condition-based maintenance, the review links depot inspection, wayside and on-board monitoring and decision rules to intervention options including turning, reprofiling, laser cladding repair and surface strengthening. The review highlights a closed-loop view of wheel life management in which prediction, monitoring and intervention are aligned against route-specific loading spectra, safety margin and whole-life cost.

To improve the operational stability of high-speed maglev trains under complex multi-source excitations, this study aims to clarify the nonlinear dynamic mechanisms induced by controller time delay, slotting disturbance, and suspension-guidance coupling-phenomena that remain insufficiently understood in existing research. A two-degree-of-freedom maglev model is established incorporating suspension-guidance coupling and the fractional viscoelasticity of air springs. A time-delay PD controller is introduced, and the slotting effect is modeled as a harmonic track excitation. The primary resonance response is derived using the multi-scale and harmonic balance methods, and the stability conditions are obtained via Lyapunov's first method and the Routh-Hurwitz criterion. A systematic parametric investigation is conducted to evaluate how time delay, structural nonlinearity, fractional order, and control gains modulate the amplitudefrequency characteristics, stability boundaries, and bifurcation evolution. Time-domain simulations further reveal the transitions among periodic, quasiperiodic, and chaotic responses. The results show that these parameters jointly reshape the resonance peak, shift the instability region, and generate closed frequency islands and multistable behaviors. Time delay is identified as the dominant factor that amplifies nonlinear effects and induces chaotic instability. Increasing the delay leads to frequent alternations between periodic and chaotic states as system parameters vary, highlighting the heightened complexity of the maglev system's dynamics.

Rail transport is becoming more central to integrated mobility systems, yet distributed railway health monitoring still faces a critical power bottleneck. Reliance on external energy supply constrains long-term maintenance-free operation. Harvesting secondary energy generated during train operation, such as vibration, airflow, solar radiation, and heat, offers an alternative. A systematic review is presented to synthesise railway energy harvesting technologies from mechanism to application. Primary conversion routes include piezoelectric, electromagnetic, and triboelectric mechanisms. Auxiliary conversion mechanisms include photovoltaic, thermoelectric, and electrostatic technologies. Vibration harvesters are reclassified by installation domain as onboard, track-mounted, and bridge-mounted, enabling comparative analysis of structural design, output characteristics, durability, and application suitability. Wind, solar, and thermal energy harvesting technologies are integrated to assess multi-source energy supply pathways for intelligent railway monitoring. Evidence indicates that electromagnetic and piezoelectric approaches provide the strongest engineering maturity. Major barriers remain in conversion efficiency under variable excitation, long-term material reliability, and life-cycle economic competitiveness. Future progress should focus on hybrid multi-source architectures, interdisciplinary co-design of materials, devices, and power management, and service condition validation. Experimental datasets for the reviewed devices are provided in Appendix A to support benchmarking across studies.

Heavy-haul railways remain the principal mode of long-distance bulk freight transport because of high carrying capacity, high transport efficiency, and low unit energy consumption. Ongoing development towards longer train formations, higher axle loads, and higher traffic density has intensified the nonlinear dynamic response and multi-system coupling of heavy-haul train systems. Engineering studies on representative Chinese heavy-haul railways, including the Datong–Qinhuangdao and Shuohuang railways, have highlighted practical dynamic problems associated with long-consist and high-axle-load operation under long gradients, sharp-radius curves, and turnout zones. Typical service problems include excessive in-train longitudinal impulse, wheel polygonal wear, abnormal wheel–rail wear and rolling contact fatigue (RCF), and deterioration of wheel–rail interaction in turnout regions. These engineering challenges require an integrated understanding of longitudinal force transmission, wheel–rail interaction, and system-level dynamic response for performance assessment, risk control, and maintenance strategy design. From a review perspective, research progress and development trends are organised into three main branches: in-train longitudinal dynamics, vehicle–track coupled dynamics, and 3D heavy-haul train dynamics. Core theories, modelling methods, and key technologies in each branch are summarised, with emphasis on coupling mechanisms under complex operating conditions and the relationship between dynamic behaviour and service performance. Current studies indicate that the research framework of heavy-haul train system dynamics has become more complete. Modelling methods have developed from simplified formulations to refined and multi-field coupled models, and understanding of coupling mechanisms under complex operating conditions has improved. At the same time, intelligent optimisation and advanced control methods, including virtual coupling or virtual marshalling technologies, show strong potential for engineering application. Future research should focus on improving the refinement level and physical representation of coupled dynamic models, and strengthening consistency among longitudinal, vehicle-track, and 3D dynamic analyses. Meanwhile, it should also accelerate engineering implementation of virtual coupling and intelligent control technologies, and develop real-time monitoring and adaptive control systems supported by big data and Internet of Things (IoT) technologies. The review provides a reference for further theoretical research and technological development in heavy-haul train system dynamics.

Accurate attitude tracking of six degree of freedom electrohydraulic shaking tables (EHSTs) is restricted by parameter uncertainty, nonlinearity, strong coupling, and external disturbances. Existing sliding mode control schemes are limited by fixed switching gains and the absence of integral compensation, which restrict steady-state accuracy and dynamic adaptability under nonlinear hydraulic effects and multi-axis coupling. An Adaptive Integral Sliding Mode Control (AISMC) scheme is developed to address these factors through two coordinated elements: an integral sliding surface that removes steady state deviation caused by static disturbances such as servo valve dead zones and hydraulic leakage, and an adaptive switching gain that regulates the reaching dynamics online without reliance on conservative bounds; a decay term in the gain update restrains parameter drift and keeps the adaptation bounded. Lyapunov analysis establishes closed loop stability and finite time convergence of the tracking error under bounded uncertainties and excitations. Simulation studies on a six degree of freedom EHST with a broadband random reference (0.1-10 Hz, 10 mm) compare AISMC with Sliding Mode Control (SMC) along X, Y, and Z. Pose tracking shows consistent gains, with the maximum value reduced by about 11.5-11.9 % and the root mean square (RMS) reduced by about 34.9-35.1 %. Pose error decreases from 0.392-0.396 mm to 0.035-0.036 mm in maximum value and from 0.175-0.177 mm to 0.015-0.016 mm in RMS. Acceleration tracking under AISMC approaches the reference in X and Z and improves in Y, while acceleration error decreases by about 83.5 % in X and Y and about 88 % in Z. The results indicate higher control precision, smoother transients with reduced chattering, and robust multi axis coordination suitable for practical vibration testing applications.

Wear and rolling contact fatigue (RCF) severely deteriorate the tribology behaviour and material integrity of railway wheels, posing significant challenges to their health management. Hence, a deeper mechanistic understanding and the development of effective mitigation strategies are urgently required. In this study, a long-term locomotive wheel wear and RCF evolution prediction model were developed that incorporates the fully nonlinear dynamics of heavy-haul locomotive-track coupled system, the non-Hertzian wheel-rail frictional contact behaviour, and iterative updates of the evolving wear and RCF distributions. The numerical investigations indicated that wear and RCF growth of locomotive wheels are primarily caused by the prominent wheel/rail stresses during curving operations, and particularly aggravated at sharp curves. Subsequent numerical and field investigations verified two effective strategies for mitigating locomotive wheel wear and RCF development: (i) optimisation design of wheel profile using an innovative constrained multi-object optimisation (CMOO) method, and (ii) enhancement of the Wheel Slide Protection (WSP) controller. The findings further suggested that these two countermeasures can substantially mitigate locomotive wheel wear and RCF progression by lowering wheelrail tribological interaction and contact stress levels. Overall, this study provides valuable insight into the mechanisms governing wheel wear and RCF evolutions, and supports the enhancement of heavy-haul operational reliability through scientifically informed maintenance practices.

Abstract Wear and rolling contact fatigue (RCF) are regarded as two prominent factors that deteriorate the long-term service performances and aggravate the maintenance costs of metro rails on the small-radius curves; therefore, an effective countermeasure against them is needed. In this work, a long-term rail wear and RCF evolution prediction model based on vehicle–track coupled dynamics and surface material wear and fatigue damage theory is performed, in which an enhanced wheel/rail non-Hertzian contact method is involved. On the other hand, a series of candidate rail profiles are constructed and generated by applying the Gaussian function correction (GFC) method. An improved nondominated sorting genetic algorithm-II (NSGA-II) method is applied for the optimization design of rail profiles, and then we propose two types of rail profiles which take the rail wear or RCF as the optimization objectives. Further, the long-term rail wear and RCF evolution performances subjected to the raw rail profiles and optimally designed ones are compared. The results demonstrate that the optimized rail profiles contribute profitably to alleviate the wheel flange–rail gauge corner frictional contact and, subsequently, can slow down the wear and RCF development of rails on sharp-radius curves. This study can offer a theoretical inspection for wear- and RCF-resistant design of rail grinding profiles.

This paper presents an advanced investigation into vibration control strategies for electro-hydraulic testing systems, with a specific emphasis on sinusoidal swept-frequency techniques. Electro-hydraulic shaking tables (EHSTs) are critical in replicating the dynamic conditions for applications in civil engineering, automotive testing, and seismic assessments. Although widely used, the nonlinear dynamics of EHSTs—characterised by factors such as oil flow friction and dead zones—frequently cause distortion in response signals, particularly during high-frequency vibration testing, thereby limiting system performance. To address these challenges, this study proposes a dual approach. The first method employs offline control through system identification coupled with iterative correction algorithms, while the second uses real-time predictive control based on the system’s frequency response function. A novel composite control strategy is developed, integrating the strengths of both approaches to achieve improved amplitude and phase compensation, thus enhancing both robustness and accuracy in vibration control. The proposed strategy is validated through both simulations and experimental testing on a six-degree-of-freedom electro-hydraulic shaking table, demonstrating significant improvements in phase lag reduction and amplitude tracking, particularly at higher frequencies. This control approach provides an optimised solution for precise vibration control in complex engineering applications.

The brake pipe pressure gradient has a significant impact on the dynamic performance of heavy-haul trains (HHTs). In this study, a pneumatic braking model was developed that considers the influence of the pressure gradient. This model employs a 1D isothermal assumption to simulate the pressure and flow along the brake pipe. Furthermore, a HHT longitudinal-vertical coupling dynamics model was established to evaluate the resulting coupler forces and vibration responses. This model incorporates key components, including locomotives, wagons, and couplers. The simulated brake cylinder pressure was dynamically converted into braking force acting on the wheels. Based on these integrated models, a systematic analysis was conducted to investigate the effects of different pressure gradients on the longitudinal impulse and vibration response characteristics of the HHT. The results show that the pressure gradient leads to a nonlinear reduction in brake pipe pressure along the train length. This reduction significantly lowers the steady-state brake cylinder pressure at the rear wagons and alters the coupler force characteristics during the release process. Moreover, the pressure gradient intensifies the longitudinal and pitch vibrations of the car body and wheelset during the release process, primarily due to the compression stage of the coupler.

Wheel Slide Protection (WSP) controller is a critical component in modern railway trains, which is designed to mitigate wheel sliding behaviours while minimising wheel/rail interface material degradation at braking operations. This study presents a novel vehicle-track coupled dynamics model, incorporating variable friction conditions and a non-Hertzian wheel/rail contact model to more accurately reflect the real-world scenarios. Three types of on-board WSP controllers are integrated into this compositive model: (i) re-adhesion controller, (ii) sliding-mode controller, and (iii) PID-based controller. In addition, a prediction model for long-term wheel tread wear and rolling contact fatigue (RCF) evolutions is introduced utilising real-time calculations of non-Hertzian wheel/rail interactions. The effects of different WSP control algorithms on wheel tread wear and RCF progression are investigated through the extensive numerical simulations. The results indicate that the sliding-mode and PID-based controllers outperform re-adhesion controllers in reducing wheel/rail longitudinal interactions and vibrations, and further contributing to smoother operations. Moreover, it is shown that lower WSP control thresholds significantly reduce wheel tread wear and RCF development in contrast to the higher thresholds which exacerbate these issues. Interestingly, while sliding-mode and PID-based controllers reduce vibrations more effectively, they also result in higher wear and RCF growths when compared to re-adhesion controller, particularly with a high control threshold. The findings provide a theoretical foundation for optimising WSP control systems in railway operations with the goal of enhancing durability, reducing maintenance costs, and improving overall train performances.

Current metaheuristic algorithms are typically confined to inspiration from singular perspectives, isolated biological behaviours, or individual phenomena, resulting in inherent limitations that have motivated this study. Diverging from conventional approaches, this paper explores complex biological systems from an ecosystem perspective and conducts comprehensive system modelling, analysis, and algorithmic innovation. Specifically, a novel metaheuristic optimization algorithm inspired by the self-regulating and restorative phenomena observed in sequoia forest ecosystems called the Sequoia Optimization Algorithm (SequoiaOA) is proposed. The sequoia ecosystem exhibits distinctive characteristics including collective growth, resource sharing and networking, adaptability and resilience, reproduction and diversity, and elite retention. Building upon these phenomena, this work presents the first formulation of SequoiaOA, developing its mathematical model and engineering applications through algorithmic modelling and validation from the perspective of ecosystem complexity, self-regulation, and resilience in macro systems. Comparative experiments employing CEC2017 and CEC2022 benchmark functions demonstrate the algorithm's effectiveness through benchmarking against six established metaheuristic algorithms. SequoiaOA achieved superior performance in over 40 % of test functions, outperforming competitors in terms of mean values and variance of objective function measures. Furthermore, its efficacy in addressing real-world multi-constrained engineering challenges was validated through eight engineering design problems. Additional modelling and application experiments in UAV path planning underscore its practical applicability to trajectory optimization tasks. The in-depth discussions reveal that SequoiaOA possesses significant potential for future enhancements and demonstrates broad suitability for diverse optimization problems. The implementation code is available in the Appendix.

To enhance the robustness of SD oscillator system, an electromagnet with state feedback control is introduced above the oscillator, considering the nonlinear characteristics of the electromagnetic force. Initially, the system's steady-state amplitude-frequency response, phase-frequency response, and backbone curve are determined using the averaging method. These results are compared with the traditional SD oscillator, analyzing the influence of state feedback parameter on vibration isolation effectiveness and acceleration transmissibility. Subsequently, differences in bifurcation diagrams between the conventional SD oscillator and the electromagnetic SD oscillator are examined, focusing on how parameters affect the system's dynamic bifurcation characteristics. Finally, employing the cell mapping method, the global bifurcation characteristics are analyzed, investigating how parameters influence the number of attractors and the area of their attraction domains. The research indicates that the system exhibits rich nonlinear characteristics, and that appropriate selection of state feedback parameters can effectively suppress chaos and bifurcations induced by external excitation, thereby enhancing the system's stability and vibration isolation performance.

Carbon fiber reinforced polymer (CFRP) laminated composites are gradually adopted in next-generation high-speed train bogie frames due to their superior mechanical properties. However, the failure behavior of CFRP structures under service conditions remains insufficiently understood. To address this, a progressive fatigue damage method based on element-level analysis is employed and integrated into a novel rigid-flexible coupled high-speed train model incorporating CFRP laminated bogie frames. In particular, the model established here enables real-time updates of material stiffness, strength, and governing equations in the degradation progresses based on the finite element method (FEM) and the floating frame of reference, making it particularly well-suited for analyzing the failure behavior of CFRP laminated bogie frame under service conditions. Numerical results indicate that under the excitation of track irregularity, there are three main failure modes of the bogie frame during high-speed train operation (running 100 kilometers on a straight track with a constant speed 300 km/h), i.e., matrix tensile failure (FM3), matrix compression failure (FM4), and tensile delamination (FM5). Specifically, FM3 occurs when the E12 is reduced by approximately 46%-48%, FM4 is triggered with a 21%-23% reduction in E12, and FM5 is associated with a reduction of interlaminar tensile strength (S3t) by about 85%-87%. These findings may offer practical design guidance. Among others, symmetric +/- 45 degrees ply orientations should be incorporated in shear-critical regions, such as the curved areas of the side beam, to enhance shear stiffness and delay matrix-dominated failure. Additionally, localized reinforcements, such as applying interlayer resin near the suspension areas, can help mitigate delamination risk. The numerical strategy provides a robust foundation for fatigue prediction, optimization, and the development of damage-tolerant designs for CFRP bogie frames in high-speed rail applications.

Unlike traditional meta-heuristic algorithms that typically draw inspiration from a single biological or collective behaviour, this paper introduces a novel meta-heuristic approach from a holistic natural perspective. Drawing on the principles of biological evolution, collective behaviours within populations, and the self-regulation mechanisms of ecosystems, the proposed algorithm is termed Nature-Inspired Adaptive Differential Evolution (NIADE). By integrating multiple strategies and global optimisation concepts, NIADE effectively addresses complex problems characterised by numerous interacting variables, thus overcoming the limitations inherent in existing algorithms that depend primarily on single strategies or local optimisation methods. This integration provides innovative pathways for solving complex optimisation challenges. The algorithm's performance is evaluated using benchmark functions from CEC2017 and CEC2022 and compared with seven prominent algorithms. Statistical analysis via Wilcoxon rank-sum tests and Friedman test statistics confirms the superiority of NIADE. Furthermore, the effectiveness of NIADE in solving multi-constrained real-world engineering problems is validated through the CEC2020 Real-World Constrained Problems set. Additionally, its applicability to unmanned aerial vehicle (UAV) path planning is demonstrated through modelling and practical experiments, presenting a promising new solution in this domain. Finally, the paper discusses potential improvements and future research directions for the NIADE algorithm. The algorithm's source code is available in the Appendix D.

Nonlinear frequency division multiplexing (NFDM) offers a possible solution to the fiber nonlinearity-induced signal distortion in the optical fiber networks. However, the application of NFDM is challenged during the information retrieval after perturbed propagation. The paper proposes a novel, to the best of our knowledge, nonlinear frequency domain neural network (NN)-based equalizer that exploits the phase relationship between modulated information on different eigenvalues. Similar parameters are utilized in a time-domain NN to address the overall complexity issue of the receiver. Such configurations enhance performance and reduce the computational complexity. In the dual-polarization NFDM (DP-NFDM) transmitting systems, the proposed NN-based equalizers successfully maintain a low bit error rate (BER) after up to 2800 km transmission, demonstrating an effective approach to address the perturbation issue in NFDM. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI)training, and similar technologies, are reserved.

Eigen mode and eigen value evaluation is crucial in optical waveguide design and is quite time consuming. It is known that the perturbation method can compute the modes efficiently for an index perturbed structure based on the known eigen modes and thereby avoids the time consuming eigen value decomposition process. However, the perturbation method can only be applied to the waveguide structures with small index variations, and hence it poses a significant constraint to the applicability of the method to the optical waveguide inverse design problem, which might have large index variations. In this paper, an adiabatic perturbation theory is proposed to tackle this problem. The eigen modes and the propagation constants of the optical waveguides are evaluated gradually by adding the index variation with respect to the previous step. While keeping the index variation to a small value within a step, the optical waveguide structure achieves a significant index change in total and thereby enables the application of the perturbation theory to the optical waveguide inverse design problem.

A physics-based vehicle–track coupled dynamic model embedding a hydraulic electromechanical regenerative damper (HERD) is developed to quantify electrical power recovery and wear depth in high-speed service. The HERD subsystem resolves compressible hydraulics, hydraulic rectification, line losses, a hydraulic motor with a permanent-magnet generator, an accumulator, and a controllable; co-simulation links SIMPACK with MATLAB/Simulink. Wheel–rail contact is computed with Hertz theory and FASTSIM, and wear depth is advanced with the Archard law using a pressure–velocity coefficient map. Both HERD power regeneration and wear depth predictions have been validated against independent measurements of regenerated power and wear degradation in previous studies. Parametric studies over speed, curve radius, mileage and braking show that increasing speed raises input and output power while recovery efficiency remains 49–50%, with instantaneous electrical peaks up to 425 W and weak sensitivity to curvature and mileage. Under braking from 350 to 150 km/h, force transients are bounded and do not change the lateral wear pattern. Installing HERD lowers peak wear in the wheel tread region; combining HERD with flexible wheelsets further reduces wear depth and slows down degradation relative to rigid wheelsets and matches measured wear more closely. The HERD electrical load provides a physically grounded tuning parameter that sets hydraulic back pressure and effective damping, which improves model accuracy and supports calibration and updating of digital twins for maintenance planning.