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

Aug 5, 2026

Upload by Miles

Aircraft cabin noise contributes to health risks for frequent travelers and crew, including cardiovascular disease, hearing loss, and sleep deprivation. During cruise, noise is driven mainly by random pressure fluctuations in the turbulent boundary layer, motivating the need for an empirical predictive model. Earlier formulations simplified Reynolds-averaged Navier–Stokes pressure terms, while later approaches refined assumptions or applied statistical methods. This thesis extends prior neural-network work by deriving a new model using nonlinear least squares regression and an iterative process, achieving strong accuracy across most Reynolds numbers and low airspeeds (~11 m/s), with limitations requiring additional data for full assessment.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages147

Reading Time6 h 10 min

AccessFree to download

Introduction

State of the Art

Sound Emission from Aircraft Turbulent Boundary Layers

Machine Learning

Numerical Methods

Current Models

Statistical Techniques

Methodology

Data Importing and Processing

Model Creation and Implementation in R

Assessing Model Accuracy

Results

Candidate Models

Final Model

Model Validation

Discussion

Conclusion and Future Work

Appendix A: PSD Plots of Wind Tunnel Experiments

Appendix B: Fitted Coefficients, AIC, and BIC Values

Derivation of an Empirical Model to Estimate the Power Spectral Density of Turbulent Flow Wall Pressure Fluctuations Using Machine Learning Regression Techniques by Zachary Huffman A thesis presented to the Faculty of Graduate and Postdoctoral Affairs in partial fulfilment of the requirements for the degree of Master of Applied Science in Aerospace Engineering Ottawa-Carleton Institute for Mechanical and Aerospace Engineering Department of Mechanical and Aerospace Engineering Carleton University Ottawa, ON, Canada 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. Acknowledgements First, I’d like to express gratitude to my thesis supervisor, Professor Joana Rocha. Thankyou 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. Thankyou 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. Contents Abstract i Acknowledgements ii List of Figures viii List of Tables ix Acronyms x Nomenclature xiii 1 Introduction 1 2 State of the Art 5 2.1 Sound Emission from Aircraft Turbulent Boundary Layers .......... 5 2.2 Machine Learning ................................. 12 3 Numerical Methods 17 3.1 Current Models .................................. 17 3.1.1 Description and Derivation of Existing Models ............. 17 3.1.2 Accuracy and Shortcomings of Existing Models ............ 24 3.2 Statistical Techniques ............................... 26 3.2.1 Stages of Deriving Empirical Models .................. 26 3.2.2 Exploratory Data Analysis ........................ 27 3.2.3 Dimensional Analysis ........................... 37 3.2.4 Model Development ............................ 38 3.2.5 Model Eval

FAQs

What problem does the thesis address?

The thesis targets accurate prediction of power spectral density (PSD) of turbulent-flow wall pressure fluctuations, which drive dominant aircraft cabin noise during cruise conditions.

How does the thesis build its empirical model?

It derives a new model using nonlinear least squares regression and an iterative process to determine the model form, extending earlier machine-learning-based research.

How accurate is the resulting equation and under what conditions?

The resulting equation is accurate at most Reynolds numbers and at low airspeeds of approximately 11 m/s.

Why is additional data still needed?

The thesis notes that more outside data is required to fully understand the model’s accuracy limits and shortcomings beyond the tested conditions.

Aug 5, 2026

Upload by Miles