Aerodynamic shape optimization on high-speed trains using multi-fidelity surrogate model combined with transit strategy

Journal article, 2026

Engineering problems such as the aerodynamics optimization of high-speed trains (HSTs) that require large-scale numerical simulations necessitate the utilization of multi-fidelity surrogate models to address the inherent conflict between accuracy and computational expense. This research presented a multi-fidelity Kriging surrogate modeling method combined with the transit strategy (TMFK), which leverages both low-fidelity and high-fidelity samples to generate the medium-fidelity surrogate model as a transit model. This model is subsequently refined using high-fidelity samples. The efficacy and precision of the TMFK model are evaluated through the single-objective and multi-objective test functions, followed by its application in the optimization of the HST aerodynamic performances. The results indicate that the TMFK surrogate model constructed with the transit model achieves higher accuracy compared to multi-fidelity surrogate models built solely using scaling functions. Moreover, a transit model with higher accuracy is particularly advantageous for establishing high-precision TMFK models. The prediction errors of the aerodynamic drag force of the head car (DH), tail car (DT), and the lift force of the tail car (LT) of the optimal model for the TMFK model are 0.10%, 0.87%, and 0.40%, respectively. In the optimal model, the surface pressure on the tail car nose exhibits an increase compared to that of the original model, accompanied by a reduction in the scale of vortices and slipstream velocity in the wake. Consequently, reductions of 1.73%, 7.04%, and 18.76% are observed in DH, DT, and LT, respectively. Furthermore, the height of the nose tip, gear region, and the profile of the lower contour line have significant impacts on optimization objectives, particularly on the DT and LT. Notably, the influence of design variables on the DH is relatively minor compared to the effects on the DT and LT.