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

Yaakoub Berrouche

TL;DR

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, is presented.

Abstract

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.

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

TL;DR

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, is presented.

Abstract

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.
Paper Structure (28 sections, 1 theorem, 5 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 28 sections, 1 theorem, 5 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Notation
  4. Problem formulation and datasets
  5. HUMS 2023 benchmark (experimental)
  6. Controlled simulated dataset
  7. Proposed method: LDME
  8. Dual-path denoising
  9. Multi-scale enhancement and fractional-domain operator
  10. A compact property statement
  11. Condition indicators and anomaly fusion
  12. Theoretical Foundations of the Physics-Informed Operators
  13. Experimental protocol and evaluation
  14. Experimental Validation by using the Case Western Reserve University (CWRU) Bearing Dataset benchmark
  15. Data sources
  16. ...and 13 more sections

Key Result

Proposition 3.1

If the fault-induced mode $d(t)$ is composed of localized impulsive events with harmonic modulation in a narrow band and the background modes $m_i(t)$ are smooth and spectrally separated, then the output of $\mathcal{L}_{LDME}$ concentrates a larger fraction of the total energy into the fault mode $

Figures (10)

  • Figure 1: Schematic of HUMS-Equipped Helicopters and the Key Flight Parameters Monitored for Usage and Structural Health Assessment.
  • Figure 2: An illustration of the planetary gear with the faulted planet gear matania2024anomaly.
  • Figure 3: An example of how the fault spreads during the experiment matania2024anomaly.
  • Figure 4: LDME processing pipeline (denoising, enhancement, decision fusion).
  • Figure 5: Illustration of the three bearing fault conditions considered in this study: (a) inner race fault, (b) rolling element (ball) fault, and (c) outer race fault.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Proposition 3.1: Energy concentration, informal
  • proof
  • Remark 1