Data-Driven Symbolic Regression for the Modelling of Correlation Functions of Wall Pressure Fluctuations Under Turbulent Boundary Layers

The turbulent boundary layer (TBL) is an important source of noise and vibrations in transport engineering. In fact, the wall-pressure fluctuations (WPFs) associated with the turbulence can significantly excite a structure which, in turn, radiates acoustic power, generating discomfort to passengers, pilots, and disturbing the surrounding environment. A good description of these fluctuations is required to accurately predict the propagation of noise and the induced vibrations. Mathematical models of TBL excitation take the form of statistical space-time correlation functions and their corresponding wavevector-frequency spectra. Many models are present in literature, and all of them are semi- or fully empirical, in which derivation can be considered somewhat ad hoc, even though rooted in the physics of the phenomenon. The direct consequences are that these models describe quite well the dataset on which they are based, but seldom provide a satisfactory agreement over the complete range of available data. Their prediction capability is limited to particular frequency and wavenumber ranges, and usually require the calibration of several coefficients to match amplitudes and transition frequencies between the several frequency regimes observed during the experiments. The idea underpinning this work is to exploit the increasing number of experimental data, along with the exponential improvement of data-driven techniques, to give new lifeblood to the derivation of WPFs models. In particular, the potentialities of symbolic regression through Gene Expression Programming (GEP) are investigated to derive new empirical models that are not based on already existing ones but are estimated by training the algorithm on experimental data.