Artificial Neural Networks and Guided Gene Expression Programming to Predict Wall Pressure Spectra Beneath Turbulent Boundary Layers

Abstract

This study evaluates the efficacy of two machine learning (ML) techniques, namely artificial neural networks (ANN) and gene expression programming (GEP) that use data-driven modeling to predict wall pressure spectra (WPS) underneath turbulent boundary layers. Different datasets of WPS from experiments and high-fidelity numerical simulations covering a wide range of pressure gradients and Reynolds numbers are considered. For both ML methods, an optimal hyperparameter environment is identified that yields accurate predictions. ANN is observed to be faster and more accurate than GEP with an order of magnitude lower training time and logarithmic mean squared error ($lMSE$), despite a higher memory consumption. Novel training schemes are devised to address the shortcomings of GEP. These include (a) ANN-assisted GEP to reduce the noise in the training data, (b) exploiting the low and high-frequency trends to guide the GEP search, and (c) a stepped training strategy where the chromosomes are first trained on the canonical datasets followed by the datasets with complex features. When compared to the baseline scheme, these training strategies accelerated convergence and resulted in models with superior accuracy ($\approx 30\%$ reduction in the median $lMSE$) and higher reliability ($\approx 75\%$ reduction in the spread of $lMSE$ in the interquartile range). The final GEP models captured the complex trends of WPS across varying flow conditions and pressure gradients, surpassing the accuracy of Goody's model.