Semi-empirical modeling of wall-pressure spectra in pressure-gradient boundary layers using gene expression programming

Accurate, fast, and robust prediction of wall-pressure spectra (WPS) in pressure-gradient boundary layers remains challenging due to strong non-equilibrium effects. In this work, gene expression programming (GEP) is employed as an interpretable, data-driven framework to address these limitations of classical semi-empirical models, including the Goody model and its extensions, whose validity is restricted under pressure-gradient conditions. Targeted improvements to GEP are introduced by incorporating a Goody-type-model-based optimization strategy together with a multi-model hybrid scheme, which significantly enhances convergence behavior and model robustness. As a result, a predictive model with improved accuracy and robustness is obtained, and validation results show that the proposed model consistently outperforms existing conventional models and a generic deep neural network on the test dataset. Shapley value analysis further suggests that the local pressure gradient and its accumulated history effects play a dominant role in determining the WPS.