Multiclass classification using logistic-NARX modeling: methods and engineering applications

Abstract

Classification techniques are essential for interpreting complex data across various engineering domains, including signal processing, manufacturing, and environmental monitoring, providing actionable insights and informing critical decision-making processes. System identification and data-driven modeling methodologies offer robust frameworks for analyzing these complex engineering processes. Parametric modeling approaches, notably Nonlinear AutoRegressive models with eXogenous inputs (NARX), are particularly advantageous due to their linear-in-the-parameter form, enabling interpretability and model transparency. Although recent developments have extended NARX methodologies to classification tasks, their application remains predominantly limited to regression and binary classification, leaving multiclass scenarios relatively unexplored. To bridge this gap, this thesis introduces a novel classification algorithm, Logistic-NARX Multinomial, combining logistic regression with NARX modeling principles. This integration facilitates direct interaction among input terms, resulting in sparse, interpretable models where the significance of individual and combined input variables is clearly discernible. Extensive evaluations using benchmark and real-world datasets confirm that Logistic-NARX Multinomial achieves competitive predictive performance compared to traditional classifiers. Additionally, this thesis proposes a practical engineering methodology for railway infrastructure maintenance. Utilizing acceleration data from railway vehicles and multibody simulations, the developed Logistic-NARX Multinomial framework provides interpretable and transparent predictive models capable of effectively assessing track conditions, significantly enhancing geo-referenced decision-making and contributing to improved safety and maintenance practices.