For pantograph-catenary systems, Hardware-in-the-Loop (HiL) testing represents a valuable tool to partly replace expensive and logistically complex in-line tests. However, the regulatory acceptance of such methodologies requires excellent accuracy while keeping real-time performance. This paper proposes a methodology to perform HiL pantograph tests utilising a high-fidelity finite element catenary model that incorporates overlap sections and the simultaneous interaction of a pantograph with two contact wires through a penalty-based formulation. Without loss of generality, the Italian C270 overhead line and the ATR 95 pantograph have been chosen to exemplify the proposed method. To achieve the real-time execution required for HiL environments, the conventional PACDIN software algorithm was modified introducing five simplifying hypotheses. These actions successfully reduced the computational cost while maintaining a high accuracy. System stability and force tracking were ensured using an interaction mass and an LQG controller, mitigating the effect of delays and actuator dynamics. The proposed methodology was validated in a two-stage process: first, by demonstrating good agreement between the real-time algorithm and conventional solvers, then, by comparing HiL results with experimental measurements obtained from an instrumented pantograph during in-line tests. The results show a relative difference in the contact force standard deviation of only 6.2%, falling within the acceptable limits defined by the EN 50318 standard. This work represents a significant milestone in developing robust HiL tools capable of simulating complex overhead contact line discrete features with the accuracy required for high-speed railway applications.
The electrical road system (ERS) truck formation operation is the most common working condition of this new road freight transportation system. Because two neighbouring trucks with unfavourable distance can interrupt the current collection process, the favourable distance must be obtained to prevent it. In this work, the influence of truck formation operation on pantograph-catenary interaction dynamics in ERS is first investigated to determine this favourable distance. Based on the structure of the ERS test line, an ERS pantograph-catenary model with double pantograph is formulated, and the measurement data from the ERS test line are used to validate the present model and provide truck vibration inputs. Through the present model, the influence of double pantograph distance on its dynamic behavior is investigated. It is found that the pantograph distance without truck vibration has little influence on pantograph-catenary interaction, but the truck vibration can heavily influence the same within a certain distance. This influence is dominated by the second frequency peak of the truck vibration, and its change in the panhead can be used to monitor the distance. Based on this, a method is finally given to determine the closest favorable distance between neighboring trucks in ERS.
To support real-time wheel-rail matching monitoring for high-speed trains, this study proposes a unified representation of wheel tread wear over a complete reprofiling cycle. Measured wheel profiles showed dominant hollow wear, mainly in segments BC, CD and DE near the nominal rolling circle. Cubic Non-Uniform Rational B-Spline (NURBS) curves were used to represent worn tread profiles segment by segment. For BC and CD, common control vertices and knot vectors enabled NURBS weight factors to describe profile evolution across mileage stages. For DE, wear was classified as mild, moderate or severe; wear width was represented by intermediate control points and wear depth by NURBS weight factors. Contact-geometry analysis showed good agreement between NURBS-fitted and measured profiles, with normal fitting errors below 0.35, 0.10 and 0.05 mm for BC, CD and DE, respectively. Among the tested regression models, the quadratic polynomial model gave the highest accuracy, with DE wear-depth error below 0.005 mm and wear-area errors for BC, CD, and DE below 0.15 mm2. The method provides a parametric basis for tread evolution characterisation and maintenance decision-making.
In the supercritical speed range, the pantograph-catenary system exhibits clear advantages, including reduced fluctuations in dynamic contact force and limited vertical displacement of the pantograph head, making it highly suitable for train operations above 400 km/h. However, ensuring a stable transition from subcritical conditions (speed ratio < 0.7) to supercritical operation (speed ratio > 1) presents a major challenge, as resonance risks emerge near the critical speed ratio of approximately 1. This study proposes a hybrid-tension catenary configuration strategy to enable supercritical operation. Targeting an operational speed of 500 km/h, the analysis considers acceleration processes and dynamic performance through overlap sections. The results show that increasing the contact-wire tension to approximately 40 kN during acceleration and maintaining the maximum operational speed ratio below 0.8 allow the pantograph-catenary system to reach the supercritical regime. Moreover, optimizing the number of stitch wires and the crossing-point height in overlap sections further improves dynamic performance. The proposed configuration strategy provides a significant step toward achieving supercritical operation and offers essential guidance for the development of next-generation, higher-speed pantograph-catenary systems.
The road friction coefficient is a key parameter for traffic safety and for advanced driver-assistance systems (ADAS) such as electronic stability control and trajectory planning in autonomous vehicles. Most existing estimation methods rely on dynamic maneuvers, whereas friction estimation during steering at standstill and very low speeds has received limited attention. This paper addresses this gap by introducing two novel friction estimation approaches based on steering torque in standstill and low-speed conditions. The first method employs a Kalman-Bucy filter (KBF) coupled with a simplified brush model, using a single tread element formulation to determine when estimation should be updated or halted. The second method applies an unscented Kalman filter (UKF) to an extended torsional spring model that incorporates a damping term for low-speed maneuvers, while parametric output sensitivity (POS) analysis is used to assess identifiability. Both approaches are compared to an existing method from the literature and are validated in simulation and with experimental data from three vehicles of varying complexity. The results demonstrate accurate and consistent friction estimation during steering at standstill and slow rolling maneuvers, extending the applicability of effect-based methods beyond conventional dynamic driving scenarios.
The rise in wheel rail equivalent conicity after wheel reprofiling leads to an increase in bogie hunting frequency, elastic vibration modes of carbodies are easily excited, which may induce abnormal carbody vibrations. A modal optimisation design framework for high-speed train carbodies is proposed from the perspective of structural design. A specific high-speed train carbody exhibiting abnormal elastic vibration during service is taken as the research object, and the vibration mechanism is first identified based on operational test data. A convolutional neural network (CNN)-based surrogate model is constructed to establish the nonlinear mapping between sectional thickness parameters, carbody mass, and the first-order diamond modal frequency. The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is then employed to carry out high-dimensional size optimisation of the sectional profiles. The optimised carbody is further evaluated through static strength verification, free modal analysis, and rigid-flexible coupled dynamic simulations under equivalent operating conditions. The results show that the proposed optimisation framework achieves significant weight reduction while effectively increasing the first-order diamond modal frequency, thereby suppressing abnormal elastic vibrations and substantially improving passenger comfort. The proposed method provides a practical and effective solution for the lightweight and modal optimisation design of high-speed train carbodies.
To study the propagation of wheel polygonal wear in a case study, a long-term test was performed using a measuring tram to collect continuous data during regular operation. The collected measurement data were localised using a map-matching algorithm. An increase in the signal power of the axle box accelerations was observed continuously over a 5-month measurement period and a mileage of 33,000 km. The concept of virtual measuring stations is introduced to separate excitations from the wheel and rail. The harmonic out-of-roundness is tracked using order decomposition of axle box acceleration, and an exponential growth of the dominant polygons is observed. A self-reinforcing effect of polygonal wear is proven. The quantified growth rate indicates a doubling of the polygon amplitude after approximately 20,000 km. According to the representative distribution of velocity and curve radius, polygonal wheel wear occurs in the frequency range 48-75 Hz. As a root cause, a P2-like mode dominated by axle arch bending is discussed, which falls within the wear frequency range, particularly for embedded tracks. The standard error of regression (SER) and the distribution of the residuals epsilon res(f) are suitable for evaluating the quality of virtual measuring stations.
Autonomous drift control aims to maintain the vehicle states around drift equilibrium conditions, thereby extending the feasible range of vehicle motion control. In this study, an equilibrium compensation framework applicable to vehicle drift control is employed, and a corresponding drift control strategy is proposed under this framework to achieve sustained and stable drift manoeuvres under external disturbances. First, the principles and assumptions of the equilibrium compensation framework are presented, followed by the development of a vehicle dynamics model and an analysis of drift mechanisms and equilibrium states. Based on this foundation, an equilibrium compensation-based model predictive control strategy is designed, along with a controller based on wheel speed dynamics, to enable real-time updates of the reference drift equilibrium and execution of drift manoeuvres. Finally, the effectiveness and feasibility of the proposed control strategy are validated through rapid prototyping experiments. Various test results show that the proposed controller exhibits superior performance in realising continuous and stable drift manoeuvres in comparison with existing advanced control strategies, even under the disturbance.
This paper investigates the spatial alignment of a 1:42 high-speed turnout during diverging operations. A kinematically coupled alignment method is proposed, in which the parameters of the superelevation transition are determined from the corresponding horizontal-alignment parameters. This allows the curvature evolution and superelevation variation to be coordinated within a unified three-dimensional framework. The method combines superelevation, higher-order transition curves, and a transition-transition configuration in which the constant-curvature circular segment is replaced by a transition curve. The existing alignment and four modified configurations are evaluated using a verified vehicle-turnout coupled dynamic model at 160 km/h and the simulated target speed of 200 km/h. The results show that superelevation reduces the sustained lateral wheel-rail force and derailment coefficient during the post-peak decline phase. The transition-transition configurations may produce slightly higher instantaneous peaks at 160 km/h, but limit the growth of dynamic responses as speed increases. At 200 km/h, these configurations reduce the peak lateral wheel-rail force, derailment coefficient, vertical wheel-rail force, wheel-load reduction rate, and car-body lateral acceleration. The seventh-order-seventh-order (7th-7th) configuration provides the most favourable performance. The results indicate that the proposed spatial alignment method has the potential to support diverging operations at 200 km/h.
The paper defines a computational framework for the derivation of digital twins of multibody (MB) simulations. The framework integrates longitudinal train dynamics (LTD) and MB codes. The digital twins are based on kernel regressions and classifications, and they can predict the running safety of freight trains during emergency air brake operations. The digital twins include two types of models, namely scalar regressions for the evaluation of the running safety indexes and a binary classifier for the detection of unsafe running conditions. The inputs for the digital twins can be easily obtained from common LTD codes. With 400 training samples, the scalar regression models have an average R2 score around 0.8, while a basic binary classifier can correctly label 90% of data. A weighted classifier can minimise misclassification of unsafe conditions, but this comes at the cost of worsened classification of safe behaviour. Overall, good accuracy can be achieved with the advantage of a small dataset. Once trained, the evaluation of the digital twins is 6 orders of magnitude faster than launching multibody simulations. The combination of good prediction capabilities and outstanding computational times can thrust the use of kernel regressions as surrogates of MB simulations.
A rollover index should be utilised to detect rollover of an articulated heavy vehicle and provide early warning to drivers. Usually, the rollover index is calculated based on the roll plane model of sprung mass. However, obtaining the model parameters of the sprung mass in real time, such as the centre of gravity and roll centre, which change with different loads, is a challenging task. Based on the roll plane model of the unsprung mass, a method is developed for calculating the rollover index of a multi-axle semi-trailer in this paper. The lateral-load transfer ratio for each axle of a multi-axle semi-trailer is calculated using the axle roll rate measured by a gyro sensor, suspension deflection measured by two displacement sensors and suspension torques identified by an adaptive sliding mode observer. The rollover indices calculated using the roll plane models of sprung and unsprung masses are compared and analysed. The results show that the rollover index calculated using the roll plane model of the unsprung mass has high accuracy and is less affected by suspension roll stiffness, centre of gravity height and roll centre height. The proposed calculation method is easy to implement in rollover warning and control systems.
A high-precision method was developed for evaluating flange-climb derailment risk in railway vehicles during low-speed operation on sharp curves by utilising data obtained from a single instrumented wheelset and advanced state-estimation techniques. The limitations of conventional derailment quotient-based safety evaluations often result in excessive conservatism. Thus, a multidimensional evaluation framework based on the wheel/rail lateral contact position and normalised transverse creepage was established. state-space expression of the wheel/rail contact model and the Unscented Kalman Filter were employed to simultaneously estimate critical contact conditions (angle of attack, friction coefficient, and contact position) from measurement inputs for a single instrumented wheelset. The proposed method was validated through extensive running tests on a purpose-built experimental track. The strong agreement between the estimated variables and directly observed wheel/rail behaviour supports the reliability and accuracy of the new approach. Compared to standard evaluation criteria, the method significantly reduces false-positive safety warnings, appropriately reclassifying nearly half of the cases previously classified as dangerous. This enables railway operators to optimize safety margins and maintenance planning without unnecessary cost escalation. The findings demonstrate that integrated measurement and estimation frameworks can substantially improve running-safety evaluations. Prospects for future research include examining the applicability of the framework to other speed ranges and vehicle conditions, and its adaptation to severe running conditions.
This paper presents an analytical solution for the optimal suspension parameters for ride comfort and road holding, using a single-axle Half-Car Model (HCM) that incorporates an anti-roll bar (ARB). While existing studies rely on numerical optimisation, a generalised analytical formulation that explicitly reveals the influence of ARBs on suspension performance and provides insight for the design process has not yet been presented. Building on the Quarter-Car Model (QCM), we define corresponding performance indicators for the HCM and use covariance analysis to derive their closed-form expressions under uncorrelated road excitations. The findings reveal that including an ARB significantly affects the optimal suspension parameters, requiring higher damping to maximise comfort and reduced suspension stiffness to maximise road holding. Moreover, while ARBs are traditionally valued for enhancing cornering stability, their inclusion degrades both comfort and road holding performance during straight-line steady-state conditions motion, highlighting an inherent trade-off when including ARBs. Finally, and via numerical optimisation, we show that a linear combination of the independent optimums provides a useful approximation for combined optimisation of comfort and road holding. Overall, this work extends suspension optimisation from the QCM to the HCM, offering analytical insight into how ARBs affect comfort and road holding.
Suspension optimisation involves finding a balance between several competing application-specific objectives. Traditionally, these are ride comfort, grip and workspace usage. This balance is further complicated when aerodynamic considerations enter the puzzle, and the overarching objective is to win a race. A method is presented that uses optimal control to find the suspension setup that minimises laptime. To achieve this, a multibody vehicle model and 3D track representation of Sonoma Raceway are employed. Results from this work are presented for two characteristically differing corners that then motivate a final full track run. This optimised suspension is then compared with a baseline setup derived from a linear stochastic minimisation strategy.
