Inferring empirical wall pressure spectral models with Gene Expression Programming

This paper presents a new data-driven approach for the establishment of empirical models describing turbulent boundary layer wall-pressure spectra. Unlike other models presented in literature, the new models are not derived by extending previously existing ones, but are directly built from a given dataset through symbolic regression using a machine learning algorithm known as Gene Expression Programming. Two modifications of the GEP algorithm presented in literature are proposed in this work to cope with some issues that are specific to the modelling of wall pressure spectra: a new power terminal and a local optimization loop. The validity of the new approach is first demonstrated using as input a dataset synthesized following the Chase-Howe and Goody models. The method is then applied to experimental data for a flat plate boundary layer. The results indicate that the wall pressure model obtained with the proposed approach remains consistent with previous formulations for zero pressure gradient, while showing a better match with the data and suggesting new ways to predict the influence of moderate pressure gradient