In high-speed rail operations, contact wire irregularity in a catenary is a common disturbance to the pantograph-catenary interaction performance, which directly affects the quality of current collection. To describe the pointwise stochastics of contact wire irregularity, the power spectral density (PSD) function for contact wire irregularity is proposed, and its effect on the pantograph-catenary interaction is investigated. First, a preprocessing procedure is proposed to eliminate the redundant information in the measured irregularities based on the ensemble empirical mode decomposition (EEMD). Then, the upper envelope of the irregularity, which contains all the information regarding the dropper positions on the contact wire, is extracted. A form of the PSD function is suggested for contact wire irregularities. A methodology is proposed to include the effect of random irregularities in the assessment of the interaction performance of a pantograph-catenary. A developed target configuration under dead load (TCUD) method is employed to calculate the initial configuration of the catenary, in which the dropper points on the contact wire are placed on their exact positions. Finally, the effect of the random contact wire irregularities on the contact force is investigated through 500 numerical simulations at each operating speed. The present results indicate that random irregularities have a direct impact on the pantograph-catenary contact, including an increment in the dispersion of the contact force statistics. The stochastic analysis shows that over 70% of the results with irregularities are worse than the ideal result without irregularities.

The wind-induced vibration of the high-speed catenary and the dynamic behaviour of the pantograph–catenary under stochastic wind field are firstly analysed. The catenary model is established based on nonlinear cable and truss elements, which can fully describe the nonlinearity of each wire and the initial configuration. The model of the aerodynamic forces acting on the messenger/contact wire is deduced by considering the effect of the vertical and horizontal fluctuating winds. The vertical and horizontal fluctuating winds are simulated by employing the Davenport and Panofsky spectrums, respectively. The aerodynamic coefficients of the contact/messenger wire are calculated through computational fluid dynamics. The wind-induced vibration response of catenary is analysed with different wind speeds and angles. Its frequency-domain characteristics are discussed using Auto Regression model. Finally, a pantograph model is introduced and the contact force of the pantograph–catenary under stochastic wind is studied. The results show that both the wind speed and the attack angle exert a significant effect on the wind-induced vibration. The existence of the groove on the contact wire cross-section leads to a significant change of the aerodynamic coefficient, which affects largely the aerodynamic forces applied on the catenary wires, as well as the vibration response. The vibration frequency with high spectral power mainly concentrates on the predominant frequency of the fluctuating wind and the natural frequency of catenary. The increase in the wind speed results in a significant deterioration of the current collection. The numerical example shows that a relatively stable current collection can be ensured when the wind flows at the relatively horizontal direction.

In this survey paper, we comprehensively examine the ongoing research concerning the interaction between pantographs and catenaries, a vital aspect in ensuring uninterrupted electricity supply to trains. Future perspectives for future studies to ensure satisfactory performance at 400 km/h and above are preliminarily explored. Initially, this paper provides an overview of the current design and assessment system. A systematic survey on the numerical modelling of pantograph-catenary interaction is conducted. The applicability of current assessment quantities to speeds of 400 km/h and above is preliminarily investigated with a numerical model. The potential of optimising parameters for improving interaction performance is also explored at this speed level. The paper further reviews and preliminarily analyses the effects of common disturbances, such as geometric deviation and aerodynamics, on the pantograph-catenary interaction performance at 400 km/h and above. To prolong the expectancy life of the system, the paper also reviews contact wire wear prediction models and discusses their potential application at 400 km/h and above. Overall, this paper offers insights into the current state of research on pantograph-catenary interaction for high-speed railways and proposes future directions for improving the system to ensure optimal performance at speeds of 400 km/h and above.

In electric railways, the interaction performance of the pantograph–catenary systems (PCS) is crucial for maintaining a stable current supply. Establishing high-fidelity numerical models based on the finite-element method (FEM) is a common practice, but it also has substantial computational complexity. The Koopman operator, a promising candidate for data-driven modeling, provides a global linear representation of nonlinear dynamic systems. In this article, we develop a novel generalized Koopman neural operator (GKNO) implemented by an autoencoder and an improved Transformer for modeling complex nonlinear dynamic systems with large-scale degrees of freedom. It consists of an observable function, an evolution function, and an invertible observable function. First, the encoder, as the embedding model, maps the state variables of the original system into observable space with linear dynamics. Then, an improved Transformer model is proposed to learn the evolution function in the embedding space based on an autoregressive task. Finally, the decoder reconstructs the state variables of the original system from the embedding space. Experimental results on the PCS model demonstrate that GKNO can capture the intrinsic evolution patterns to represent high-dimensional and nonlinear PCS dynamics, significantly reducing computational complexity and solution time. Comparative experiments show that GKNO achieved considerable solution accuracy with negligible consumption of computing resources, providing a promising potential for parameter optimization and pantograph hardware-in-the-loop (HIL) test rigs.

Due to the intrinsic nonlinear characteristics and complex structure of the high-speed catenary system, a modelling method is proposed based on the analytical expressions of nonlinear cable and truss elements. The calculation procedure for solving the initial equilibrium state is proposed based on the Newton–Raphson iteration method. The deformed configuration of the catenary system as well as the initial length of each wire can be calculated. Its accuracy and validity of computing the initial equilibrium state are verified by comparison with the separate model method, absolute nodal coordinate formulation and other methods in the previous literatures. Then, the proposed model is combined with a lumped pantograph model and a dynamic simulation procedure is proposed. The accuracy is guaranteed by the multiple iterative calculations in each time step. The dynamic performance of the proposed model is validated by comparison with EN 50318, the results of the finite element method software and SIEMENS simulation report, respectively. At last, the influence of the catenary design parameters (such as the reserved sag and pre-tension) on the dynamic performance is preliminarily analysed by using the proposed model.