Non-linear dynamics identification using Gaussian process prior models within a Bayesian context.

Gaussian process prior models are known to be a powerful non-parametric tool for stochastic data modelling. It employs the methodology of Bayesian inference in using evidence or data to modify or refer some prior belief. Within the Bayesian context, inference can be used for several purposes, such as data analysis, filtering, data mining, signal processing, pattern recognition and statistics. In spite of the growing popularity of stochastic data modelling in several areas, such as machine learning and mathematical physics, it remains generally unexplored within the realm of nonlinear dynamic systems, where parametric methods are much more mature and more widely accepted. This thesis seeks to explore diverse aspects of mathematical modelling of nonlinear dynamic systems using Gaussian process prior models, a simple yet powerful stochastic approach to modelling. The focus of the research is on the application of non-parametric stochastic models to identify nonlinear dynamic systems for engineering applications, especially where data is inevitably corrupted with measurement noise. The development of appropriate Gaussian process prior models, including various choices of classes of covariance functions, is also described in detail. Despite its good predictive nature, Gaussian regression is often limited by several O(N3) operations and O(N2) memory requirements during optimisation and prediction. Several fast and memory efficient methods, including modification of the loglikelihood function and hyperparameter initialisation procedure to speed up computations, are explored. In addition, fast algorithms based on the generalised Schur algorithm are developed to allow Gaussian process to handle large-scale timeseries datasets. Models based on multiple independent Gaussian processes are explored in the thesis. These can be split into two main sections, with common explanatory variable and with different explanatory variables. The two approaches are based on different philosophies and theoretical developments. The benefit of having these models is to allow independent components with unique characteristics to be identified and extracted from the data. The above work is applied to a real physical wind turbine data, consisting of 24,000 points of the wind speed, rotor speed and the blade pitch angle measurement data. A case study is presented to demonstrate the utility of Gaussian regression and encourage further application to the identification of nonlinear dynamic systems. Finally, a novel method using a compound covariance matrix to exploit both the timeseries and state-space aspects of the data is developed. This is referred to as the statespace time-series Gaussian process. The purpose of this approach is to enable Gaussian regression to be applied on nonlinear dynamic state-space datasets with large number of data points, within an engineering context