UC Riverside

Condition monitoring in engineering systems requires analytical frameworks that connect physically meaningful signal representations with statistically consistent decision mechanisms. Although spectral analysis, time–frequency methods, and machine learning have each advanced significantly, they are often treated as separate methodological domains. This work presents a unified structural framework that integrates classical spectral techniques, time–frequency representations, and supervised learning within a coherent monitoring architecture. Rather than providing a systematic survey, the study adopts a conceptual perspective to explicitly describe the analytical linkage between signal transformation, feature construction, and statistical inference. The discussion begins with Fourier-based descriptors and power spectral density formulations, and extends to short-time Fourier transform and continuous wavelet transform frameworks, highlighting their resolution characteristics for non-stationary signals. These representations are then connected to feature-space construction and learning-based decision models through an explicit mapping between physical signal properties and statistical inference mechanisms. An illustrative synthetic analysis is included to demonstrate how representation fidelity influences feature-space structure and downstream classification behaviour under transient conditions. These results are intended to provide conceptual insight rather than generalizable performance claims. Applications across multiple engineering domains are discussed to highlight the generality of the proposed framework. Finally, key research challenges, including dynamic operating regimes, data imbalance, interpretability, and computational constraints, are outlined. The proposed framework emphasises the complementary roles of transform-based representation and learning-based inference, providing a structured foundation for scalable and interpretable condition monitoring systems.