Fractional Filtering and Anomaly-Guided Diagnostics: The Local Damage Mode Extractor (LDME) for Early Gear Fault Detection

Early and reliable detection of gear faults in complex drivetrain systems is critical for aviation safety and operational availability. We present the Local Damage Mode Extractor (LDME), a structured, physics-informed signal processing framework that combines dual-path denoising, multiscale decomposition, fractional-domain enhancement, and statistically principled anomaly scoring to produce interpretable condition indicators without supervision. LDME is organized in three layers: (i) dual-path denoising (DWT with adaptive Savitzky-Golay smoothing) to suppress broadband noise while preserving transient fault structure; (ii) multi-scale damage enhancement using a Teager-Kaiser pre-amplifier followed by a Hadamard-Caputo fractional operator that accentuates non-sinusoidal, low-frequency fault signatures; and (iii) decision fusion, where harmonics-aware Fourier indicators are combined and scored by an unsupervised anomaly detector. Evaluation using the Case Western Reserve University (CWRU) bearing dataset, the HUMS 2023 planetary gearbox benchmark, and a controlled simulated dataset shows that LDME consistently distinguishes nominal, early-crack, and propagated-crack stages under various operating conditions. LDME identifies the primary detection event earlier (198 cycles) than HT-TSA (284 cycles) and advances maintenance recommendation time from 383 to 365 cycles. We discuss its relation to prior art, limitations, and future theoretical directions. All code and experimental configurations are documented for reproducibility.