Identifying control performance limits for active noise reduction in nonlinear systems

Feedforward active noise cancellation systems require a set of measured reference signals that are strongly correlated with the sound pressure level at a target location. The strength of the correlation can be quantified by a "multiple coherence" metric that allows the theoretical control performance limit of linear feedforward systems to be determined. However, at present there is no method available to identify the potential performance limit of nonlinear feedforward control systems.

Therefore the aim of this project is to develop methods that can quantify the performance limits of nonlinear feedforward noise control systems. Towards this, the aims are to:

* develop efficient methods for computing the Wiener Series representation of nonlinear systems;
* investigate Machine Learning algorithms for computing the component of output signals caused by a given input signal, in the presence of noise;
* compute a "generalised coherence" metric to quantify this;
* explore the use of hybrid Wiener and Machine Learning approaches for difference aspects of the signals;
* consider whether special cases of systems allow algorithms of greater efficiency to be developed, e.g. short-memory systems.

This project will require theoretical and numerical development in two main areas: Wiener Series computation and Machine Learning. These approaches show significant potential for enabling the causal component of output signals to be estimated, and hence allowing control performance limits to be identified.

The Wiener Series representation of nonlinear systems is well known, but methods for estimating the multi-dimensional kernels involve impractical volumes of data and are extremely computationally expensive. However, in order to identify the output component of the signals, it is not necessary to directly compute the kernels themselves, rather only the series expansion of the output needs to be found which can be framed in a more efficient way. Nevertheless, this still presents significant computational challenges, and the focus of this part of the project is to develop methods that allow practical calculation of several terms in the Wiener expansion.

Machine Learning (ML) regression tools have also been identified as a method for computing the causal component of an output. It is recognised that ML represents an extremely wide array of methods: here the focus will initially be on convolutional neural networks for time-domain prediction. Initially the aim will be to apply existing methods, e.g. gradient boosting algorithms, to explore their limits within the context of quantifying the "generalised coherence" and hence the performance control limits of nonlinear feedforward systems.

A combined approach will also be explored, using both Wiener Series and Machine Learning for different components of the output signals.