The first pipeline builds on a non-linear chirp signal model to accurately track multiple time-varying amplitudes at predefined frequencies, enabling reliable and interpretable monitoring of individual mechanical components. We introduce novel amplitude-tracking methods and demonstrate their robustness through extensive numerical experiments and rigorous statistical validation. The second pipeline adopts a holistic view of vibrational signals and leverages deep learning architectures to capture complex temporal dependencies that are difficult to isolate using amplitude-based tracking alone. Within this framework, we propose ALERT, a novel anomaly detection method for non-stationary time series based on a linear autoregressive latent space. To enable systematic development and evaluation, we introduce a comprehensive experimental testbench, first large-scale dataset of non-stationary vibrational signals with synchronized rotational speed measurements, further enriched with diverse expert-guided degradation scenarios derived from real-world operating conditions. Together, these contributions advance the state of the art toward deployable, real-time anomaly detection systems for long-horizon monitoring in complex industrial environments.