Identifying control performance limits for active noise reduction in nonlinear systems

前馈有源噪声消除系统需要一组与目标位置处的声压级强相关的测量参考信号。相关性的强度可以通过“多重相干”度量来量化，该度量允许确定线性前馈系统的理论控制性能极限。然而，目前还没有一种方法可以用来确定非线性前馈控制系统的潜在性能极限，因此，本项目的目的是发展的方法，可以量化的非线性前馈噪声控制系统的性能极限。为此，目标是：* 开发用于计算非线性系统的维纳级数表示的有效方法;* 研究机器学习算法，用于计算在存在噪声的情况下由给定输入信号引起的输出信号的分量;* 计算“广义相干性”度量来量化它;* 探索混合维纳和机器学习方法在信号的不同方面的使用;* 考虑在特殊情况下的系统，例如短记忆系统，是否可以发展更有效率的算法。这个项目将需要在两个主要领域进行理论和数值发展：维纳级数计算和机器学习。这些方法显示出显着的潜力，使输出信号的因果分量进行估计，从而使控制性能限制被identified.The维纳级数表示的非线性系统是众所周知的，但用于估计的多维内核的方法涉及不切实际的数据量，是非常昂贵的计算。然而，为了识别信号的输出分量，不需要直接计算核本身，而是只需要找到输出的级数展开，其可以以更有效的方式构建。尽管如此，这仍然带来了重大的计算挑战，该项目这一部分的重点是开发允许实际计算维纳展开式中几项的方法。机器学习（ML）回归工具也已被确定为计算因果关系的方法输出的分量。人们认识到，ML代表了一系列非常广泛的方法：这里的重点首先是用于时域预测的卷积神经网络。最初的目标将是应用现有的方法，例如梯度提升算法，以探索其在量化“广义相干性”的背景下的限制，从而非线性前馈系统的性能控制限制。还将探索一种组合方法，使用维纳级数和机器学习输出信号的不同分量。

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.