Generalized Koopman Neural Operator for Data-driven Modelling of Electric Railway Pantograph-catenary Systems

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 is a common practice but with substantial computational complexity. Koopman Operator, a promising candidate for data-driven modelling, provides a global linear representation of nonlinear dynamic systems. In this paper, we develop a novel Generalized Koopman Neural Operator (GKNO) implemented by an Autoencoder and an improved Transformer for modelling complex nonlinear dynamic systems with large-scale degrees of freedom. It consists of an observable function, an evolution function, and an invertible observable function. Firstly, 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.