The Derivation of an Empirical Model to Estimate the Power Spectral Density of Turbulent Boundary Layer Wall Pressure in Aircraft Using Machine Learning Regression Techniques

Abstract

Aircraft cabin noise poses a health risk for regular passengers and crew, being connected to a heightened risk of cardiovascular disease, hearing loss, and sleep deprivation. At cruise conditions, its most significant cause is random pressure fluctuations in the turbulent boundary layer of aircraft, and as such the derivation of an accurate model to predict the power spectral density of these fluctuations remains an important ongoing research topic. Early models (such as those by Lowson and Robertson) were derived by simplifying the governing equations, the Reynolds-averaged Navier Stokes equations, and solving for fluctuating pressure. Most subsequent equations were derived either by applying statistical and mathematical techniques to simplify the Robertson and Lowson models or by making modifications to address apparent shortcomings. Overall, these models have had varying success—most are accurate near the Mach and Reynolds numbers they were designed for, but less accurate under other conditions. In response to this shortcoming, Dominique demonstrated that a novel technique (machine learning, specifically artificial neural networking) could produce a model that is accurate under most flight conditions. This paper extends this research further by applying a different machine learning technique (nonlinear least squares regression analysis) and dimensional analysis to produce a new model. The resulting equation proved accurate under its design conditions of low airspeed (approximately 11 m/s) and low turbulent Reynolds number (approximately 850,000). However, a larger dataset with more diverse flight conditions would be required to make the model more generally applicable.