Kriging-based multi-objective optimization on high-speed train aerodynamics using sequential infill criterion with gradient information

For models with large numerical simulation costs, such as high-speed trains, using as few samples as possible to construct a high-precision surrogate model during aerodynamic multi-objective optimization is critical to improving optimization efficiency. This study proposes a sequential infill criterion (SIC) appropriate for the Kriging surrogate model to address this issue. Three multi-objective functions are employed to test the feasibility of constructing a surrogate model based on SIC, and the SIC surrogate model then performs multi-objective aerodynamic optimizations on the high-speed train. The findings indicate that the expected improvement infill criterion (EIC) in the first stage can enhance the global prediction accuracy of the SIC. An infill criterion based on EIC that fuses gradient information (PGEIC) in the second stage is proposed to seek samples in the Pareto front. The PGEIC surrogate model achieves the lowest generational distance and prediction error. The performance of EIC for global search, EIC for Pareto front search, and infill criterion for Pareto front search using only gradient information is poor. The final PGEIC-SIC surrogate model of train aerodynamics has less than 1% prediction error for the three optimization objectives. The optimal solution reduces the aerodynamic drag force of the head car and the aerodynamic drag and lift force of the tail car by 4.15%, 3.21%, and 3.56%, respectively, compared with the original model. Furthermore, sensitivity analysis of key parameters revealed that the nose height v(1), cab window height v(3), and lower contour line have a greater impact on aerodynamic forces. Moreover, the nose and cab window heights of the optimal model have been reduced, and the lower contour line is concave. Correspondingly, the streamlined shape appears more rounded and slender.