Complex dynamic system identification and probabilistic prediction using NARMAX and machine learning methods

System identification serves as a cornerstone in the formation of mathematical models for dynamical systems from the interpretation of observed data. Not only does this play a pivotal role in expounding complex relationships, but it also optimizes system performance, essential for architecting reliably robust controllers and fostering accurate predictions across multiple scientific and engineering realms. Nevertheless, model uncertainty in system identification poses consequential effects on the dependability of these models and the decision-making mechanisms within intricate systems. Addressing model uncertainty is fundamental for bolstering the resilience of the identified models. However, contemporary research often falls short, demonstrating a general lack of systematic approaches towards the efficacious evaluation and quantification of uncertainties. Moreover, there lies an inadequacy in research efforts to delve into sophisticated methodologies and emergent tools with the capability of efficiently navigating model uncertainty. This consequently overlooks potential avenues for the optimization of system identification and prediction in the face of inherent ambiguities and complexities inherent within dynamic systems. This thesis undertakes an examination of model uncertainty within NARMAX, an essential but commonly neglected component within system identification and modelling. The study accentuates the tangible influence model uncertainty wields upon decision-making within complex dynamic systems. The research introduces a polynomial based NARMAX model, leveraging the FROLS algorithm in conjunction with set theory for the quintessential quantification of uncertainty. Additionally, this thesis gives rise to several innovative methodologies, such as the DeepNARMAX network. This network maintains the interpretability and accuracy inherent to NARMAX while proficiently managing high dynamic scenarios. The network’s efficacy is put to the test in real-world applications, such as weather and power forecasting models. Further innovations presented within this thesis include the SW-NARMAX model that pertains to seasonal weather forecasting and the MAB-NARMAX model capable of the efficient detection of model structures using a mask matrix.