Assessing accuracy of k ‐step‐ahead prediction of non‐linear dynamics with uncertainties

Abstract

Prediction of k-step ahead requires an accurate model for a non-linear system. If the non-linearities are simply ignored, there will be the danger of overestimating the output value due to uncertainties. Considering that almost all models have uncertainties, in this study, the accuracy of k-step-ahead prediction is assessed considering the structural, parametric, and algorithmic uncertainties. Then, in order to remove uncertainties from data and achieve an accurate k-step-ahead prediction, interval type-2 fuzzy set is utilised. This study proposes a strategy for modelling symmetric interval type-2 fuzzy sets using their uncertainty degrees and centre of gravities. On the basis of these uncertainty measures, a method is introduced for constructing interval type-2 fuzzy set models using the uncertain interval data. The aim is to provide tools for evaluating a model or a set of models on the basis of predictive accuracy or efficiency for non-linear dynamic applications with uncertainties. Simulation studies demonstrate the effectiveness of the proposed control scheme.