Partial Dependence Plots and Data-Driven Surrogates for Aerodynamic Analysis of Airfoil Databases

In this paper, we explore the capabilities of partial dependence functions (PDP) for knowledge discovery in airfoil aerodynamic databases. A surrogate model, essentially a predictive model, can benefit from explainability methods that help users understand latent relationships within the database. Our primary objective is to elucidate the relationship between airfoil geometry-parameterized by the Kulfan Class Shape Transformation (CST)-and aerodynamic coefficients evaluated at a Reynolds number of 100,000. The aerodynamic database was compiled from various airfoils sourced from online databases. First, we used a data-driven polynomial chaos expansion to model the relationship, achieving a highly accurate approximation. Next, we applied PDP and individual conditional expectations (ICE) to investigate the relationships between CST parameters and both the drag coefficients and the lift-to-drag ratio. The results revealed strong interactions and nonlinearity in these relationships, with PDP and ICE effectively visualizing these connections. In summary, we demonstrate that PDP and ICE are valuable methods for deciphering input-output relationships in aerodynamic databases, providing useful insights for aerodynamic designers.