Physics-Guided Tiny-Mamba Transformer for Reliability-Aware Early Fault Warning

Reliability-centered prognostics for rotating machinery requires early warning signals that remain accurate under nonstationary operating conditions, domain shifts across speed/load/sensors, and severe class imbalance, while keeping the false-alarm rate small and predictable. We propose the Physics-Guided Tiny-Mamba Transformer (PG-TMT), a compact tri-branch encoder tailored for online condition monitoring. A depthwise-separable convolutional stem captures micro-transients, a Tiny-Mamba state-space branch models near-linear long-range dynamics, and a lightweight local Transformer encodes cross-channel resonances. We derive an analytic temporal-to-spectral mapping that ties the model's attention spectrum to classical bearing fault-order bands, yielding a band-alignment score that quantifies physical plausibility and provides physics-grounded explanations. To ensure decision reliability, healthy-score exceedances are modeled with extreme-value theory (EVT), which yields an on-threshold achieving a target false-alarm intensity (events/hour); a dual-threshold hysteresis with a minimum hold time further suppresses chatter. Under a leakage-free streaming protocol with right-censoring of missed detections on CWRU, Paderborn, XJTU-SY, and an industrial pilot, PG-TMT attains higher precision-recall AUC (primary under imbalance), competitive or better ROC AUC, and shorter mean time-to-detect at matched false-alarm intensity, together with strong cross-domain transfer. By coupling physics-aligned representations with EVT-calibrated decision rules, PG-TMT delivers calibrated, interpretable, and deployment-ready early warnings for reliability-centric prognostics and health management.