Novel Multivariate Nonlinear Signal Processing Methods for Modelling and Prediction

许多自然现象是由复杂的机制产生的，我们不知道它们的产生机制。然而，我们可以观察到一些我们可以用来代表这一现象的测量方法。例如，我们可以测量风速和风向，但风的行为受到大气一般循环的影响，以及一些局部因素，如气压、湿度、温度和地形。这些关系很难理解，描述这些数据的数学模型非常复杂，而且往往不够准确。然而，这些观察为我们提供了一些重要的信息，而对它们现在和未来行为的了解在人类事务中发挥着重要作用。例如，有关未来风速值的知识可以帮助避免列车脱轨和风力发电场的效率。该项目将展示了解和成功使用潜在的非线性动力学和信号形态特征，结合先进的非线性建模和预测，是否有助于可靠地同时估计多变量信号的分量。我们在具有良好定义的代数运算的多维数学框架中进行这项研究。这也将有助于缓解同时预测非平稳、非线性和非高斯信号(如风)的理论和实践限制，以及提高算法在不确定和噪声下工作的效率。我们可以避免每1000 GWh风能生产排放1千吨二氧化碳的事实支持了这一高级非线性多变量建模研究的商业和环境影响。

Many natural phenomena are generated by complex mechanisms for which we do not know their generating mechanisms. We can however observe a few measurements which are available to us and which represent that phenomenon. For instance, we can measure wind speed and direction, but the behaviour of wind is influenced by general circulations of the atmosphere, together with some local factors, such as air pressure, humidity, temperature and landscape. These relationships are very difficult to understand, and the mathematical models to describe those data are very complex and often not sufficiently accurate. These observations, however, provide us with some imporant information, and the knowledge an understanding of their present and future behavior plays major role in human affairs. For instance, the knowledge about the future values of wind speed can help avoid train derailment and efficiency of wind farms.This project will show whether the understanding and successful use of the underlying nonlinear dynamics and signal modality characterisation, combined with advanced nonlinear modelling and forecasting will contribute to a reliable simultaneous estimation of the components of multivariate signals. We perform this research in the multidimensional mathematical framework with well defined algebraic operations. This will also help to mitigate theoretical and practical limitations in forecasting simultaneously nonstationary, nonlinear and non-Gaussian signals, such as wind, together with the improved efficiency of algorithms working under uncertainty and noise.The fact that we can avoid the emission of 1 kTon of CO2 per every 1000 GWh of wind energy production supports the commercial and environmental impact of this advanced nonlinear multivariate modelling research.