A branched Fourier neural operator for efficient calculation of vehicle-track spatially coupled dynamics

In railway transportation, the evaluation of track irregularities is an indispensable requirement to ensure the safety and comfort of railway vehicles. A promising approach is to directly use vehicle dynamic responses to assess the impact of track irregularities. However, the computational cost of obtaining the dynamic response of the vehicle body using dynamics simulation methods is large. To this end, this study proposes a physics-informed neural operator framework for vehicle-track spatially coupled dynamics (PINO-VTSCD) calculation, which can effectively acquire the vehicle dynamic response. The backbone structure of PINO-VTSCD is established by the branched Fourier neural operator, which features one branch for outputting car body responses and the other branch for estimating the responses of bogie frames, wheelsets, and rails. The relative L2 loss (rLSE) of PINO-VTSCD under the optimal hyperparameter combination is 4.96%, which is 57% lower than the convolutional neural network-gated recurrent unit model. Evaluation cases from large-scale simulations and real-world track irregularities show that the proposed framework can achieve fast solution in scenarios such as different wavelength-depth combinations and different wavelength ranges. Compared with the traditional vehicle-track coupled model, the speedup of the PINO-VTSCD model is 32x. The improved computational efficiency of the proposed model can support many railway engineering tasks that require repetitive calculations.