Derivation of an Empirical Model to Estimate the Power Spectral Density of Turbulent Flow Wall Pressure Fluctuations Using Machine Learning Regression Techniques

Abstract

Aircraft cabin noise is a significant contributor to health risks in regular air travellers and crew, being associated with an elevated risk of cardiovascular disease, hearing loss, and sleep deprivation. At cruise conditions, the noise is primarily caused by random pressure fluctuations in the aircraft turbulent boundary layer, and as such the search for an accurate empirical model to predict these fluctuations is an important ongoing research topic. The earliest models by Lowson and Robertson were derived by simplifying and solving the governing Reynolds-averaged Navier-Stokes equations for the fluctuating pressure term, while subsequent models were usually derived via the application of statistical and mathematical techniques to simplify earlier models, or by making appropriate modifications to address apparent shortcomings. However, past research has yet to yield a universally applicable model, with most only being accurate near the Mach and Reynolds numbers they were designed for. However, more recent work by Dominique demonstrated that artificial neural networking, a type of machine learning technique, could potentially produce a model that was accurate under most flight conditions. This thesis extends Dominique's research by creating a new equation via the application of a different machine learning technique (nonlinear least squares regression analysis) and a novel iterative process to develop the model form. The resulting equation was accurate at most Reynolds numbers and low airspeeds (approximately 11 m/s), though more outside data will be needed to fully understand its accuracy and shortcomings. i First, I'd like to express gratitude to my thesis supervisor, Professor Joana Rocha. Thank you for the support, guidance, invaluable advice, and opportunity you have provided me over the last two years. I'd also like to thank my colleagues, Nicholas Thomson and Justin Denne, for their practical advice and support, particularly for helping me overcome the challenges of sifting through and understanding the immense amount of wind tunnel data I worked with. Above all else, I dedicate this thesis to my wonderful parents, Pat and Geoff Huffman, and grandparents, Edward and Doris Baryluk, for their unwavering love and support. Thank you for encouraging me to go on this incredible journey, thank you for believing in me, and thank you for all the help you've provided along the way. I couldn't have done it without you.To all those who helped me, no matter how big or small, thank you. You made it possible to create a thesis I'm proud of.