SPARSE FEATURE SELECTION AND REGIME IDENTIFICATION FOR ADVANCED PROGNOSTIC METHODS FOR COMPLEX SYSTEMS

Abstract

This dissertation introduces two novel methods—Sparse Multivariate Functional Fusion Predictors (SMFFP) and Data-Driven Regime Clustering with Spectral Approximation (DRC-SA)—to enhance interpretable prognostic modeling for complex systems, particularly aircraft engines and Switch-Mode Power Supplies (SMPS). While traditional black-box approaches, such as deep learning, often achieve high predictive accuracy, their lack of interpretability limits their utility in safety-critical applications. In contrast, SMFFP and DRC-SA provide a transparent, data-driven framework capable of capturing system degradation patterns with both precision and clarity. The SMFFP method integrates sparse multivariate functional predictions with Koopman operator theory to create interpretable models. By mapping nonlinear system dynamics into a linear framework, Koopman theory enables the identification of key observables that characterize system behavior. Additionally, sparse feature selection techniques within SMFFP further enhance model clarity by isolating the most critical predictors while maintaining competitive predictive performance, even in data-constrained environments. Complementing SMFFP, the DRC-SA method identifies operational regimes critical for accurate degradation predictions. Using spectral clustering with the Nyström approximation, DRC-SA effectively clusters spatio-temporal patterns under both normal and anomalous conditions. Rather than treating an operational regime as purely normal or anomalous, DRC-SA captures regime-specific variability, allowing it to classify regimes that may exhibit both normal and anomalous health conditions as either distinct sub-regimes or variations of a single regime, depending on the persistence and structural differences of the anomalies. This facilitates detailed classification of operational regimes, ensuring that predictive insights align with real-world operational changes and enabling the early detection of system degradation. Together, SMFFP and DRC-SA provide a robust and interpretable framework for Prognostics and Health Management (PHM) in complex systems. These methods address the critical need for predictive maintenance solutions that prioritize transparency and reliability in safety-critical applications.