Performance Limits of Active Noise Control for Nonlinear Systems: A Machine Learning Perspective

Active noise control (ANC) uses microphones and actuators to minimise unwanted noise and improve sound quality and comfort. This thesis investigates the performance limits of ANC systems in nonlinear dynamical systems, with a particular emphasis on automotive and headphone applications. Both feedback and feedforward ANC systems are considered, and their limitations are analysed from a machine learning perspective. In feedback ANC, instabilities can develop within the feedback loop due to changes in the plant, which result in undesirable artefacts, such as `squeal'. To address this, a deep learning model is proposed to detect and pre-empt instabilities in real time, demonstrating high effectiveness in preventing instability-related artefacts. Secondly, a model capable of tracking the peak height in the sensitivity transfer function is developed. This peak is indicative of the stability margins of the system, and could be used to enable smoother control and improve performance. The developed model accurately estimates the peak height in the majority of cases, although its performance degrades under certain conditions. In feedforward ANC, both the nonlinear dynamics of the transmission pathway and additional noise restrict the efficacy of linear control strategies, particularly in automotive contexts. These factors lead to practical and theoretical limits on performance. To investigate the practical performance limits, convolutional neural networks (CNNs) are assessed for their ability to learn the behaviour of nonlinear dynamical systems. Their performance varies significantly across different systems, making it difficult to predict their behaviour under varying excitation conditions or when applied to new systems. The Wiener series is then used as a framework to understand the variability of CNN performance. A novel Gaussian Process Generalised Wiener Series (GPGWS) method is introduced that is able to calculate the third-order Wiener kernel for nonlinear systems with practical memory lengths. The GPGWS is used to quantify system complexity via higher-order kernel estimation, offering new insights into CNN learnability. One perspective is that CNNs learn a Wiener-like representation of the system, offering insight into their generalisation capabilities and clarifying which aspects of the system have, and have not, been captured. In addition, the Wiener series offers insight into power scaling laws, which are also observed across multiple machine learning domains. These scaling laws are used to illustrate a potential method for identifying the \textit{practical} performance limits of ANC by estimating the improvements in CNN performance that could be achieved by increasing the quantity of training data. In order to identify the \textit{theoretical} performance limits, the nonlinear coherence metric is estimated using a novel reverse modelling framework, capable of separating noise from modelling error. This enables the estimation of theoretical ANC performance limits in practical settings. Collectively, these contributions form a framework for identifying the practical and theoretical limits of ANC applied to nonlinear dynamical systems.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Massingham, Joseph

Advisor dc:contributor.advisor

• Butlin, Tore

• machine learning
• nonlinear dynamical systems
• nonlinear vibrations
• wiener series
• volterra series
• convolutional neural networks

Licence

• https://www.repository.cam.ac.uk/bitstreams/57829738-60c5-423c-85c8-da0b0dea14f4/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.122799

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/391807