On Treed Gaussian Processes and piecewise-linear NARX modelling

Abstract

In the scope of nonlinear system identification, traditional parametric models are widely adopted as simplifying approaches to modelling the complexity of nonlinearity. However, many high-order parametric models are disadvantaged due to their inherent demand for model detection and their tendency to overfit in the absence of additional validation processes. Nonparametric models, such as the Gaussian Process (GP), though being naturally exempt from model detection, can involve expensive procedures of model optimisation. This article presents a Linear Kernel Chipman-based Treed Gaussian Processes (LK-CTGP), which is essentially an assembly of simple linear parametric models using a decision tree framework, to model nonlinear systems. The piecewise-linear structure of the LK-CTGP offers a natural geometric solution to modelling nonlinear systems, where no model detection is required. The essence of simplicity from the traditional parametric model is also completely retained within each of the submodels. The effectiveness of the LK-CTGP is illustrated here via a number of case studies from simple synthetic data to experimental data, on which Nonlinear Autoregressive eXogenous (NARX) systems will built from the data for in-depth study.