4th-Order Polynomial Analysis of Dimensionless Aerodynamic Drag for a Minibus

Abstract

This investigation assesses polynomial regression model development in the context of computationally efficient surrogates for parametric modelling of minibus aerodynamic drag coefficient . Three alternative regression models (Models A, B, C), based on sets of three dimensionless terms ( ), were compared using a dataset of 114 CFD simulations with the windows closed. Although Model C, a 4th-order, 3-input model, showed the best in-sample fit (R2 = 0.8024, RMSE = 0.0199), 10-fold cross-validation revealed it to be the most over fit. Model B, a 4th-order, 2-input model, consistently achieved the lowest mean CV-RMSE (0.0280), establishing it as the most stable regression model. Statistical analysis indicates that the aerodynamic profile is predominantly multivariable, with strong three-variable interactions ; the effects of higher-order speed terms are negligible. Residual vs. fitted plots and the normal Q-Q plot show that the polynomial models successfully capture the global response trend, while local fit could be improved through refinements or more flexible machine-learning surrogates to better quantify the extreme nonlinear dynamics at the edges of the parameter space.