Mechanical-Electrical Compound Faults

• Mechanical-electrical compound faults are simultaneous interacting failures in electromechanical systems that merge mechanical wear (e.g., cracks, bearing wear) with electrical anomalies (e.g., insulation breakdown).
• Modeling these faults uses finite element analysis and phase-field frameworks to capture crack-induced resistance increases and dynamic coupling under various operating conditions.
• Advanced diagnostic techniques, including sensor fusion and deep learning, enable accurate fault classification and severity estimation to improve predictive maintenance.

Mechanical-Electrical Compound Faults represent a class of system degradations that arise from concurrent failures in both mechanical and electrical domains within electromechanical devices, structures, and transmission systems. Interaction effects between mechanical defects (such as cracks, bearing wear, rotor unbalance) and electrical anomalies (such as insulation breakdown, short circuits, voltage unbalance) can lead to complex fault propagation, nonlinear response signatures, and mutually reinforcing degradation mechanisms. Compound faults require specialized modeling, simulation, and diagnostic techniques capable of isolating, characterizing, and quantifying the interdependence between mechanical and electrical phenomena across a range of operating conditions.

1. Fundamental Principles and Definitions

Mechanical-electrical compound faults are defined as simultaneous, interacting failure modes in which mechanical damage (e.g., material fracture, wear, misalignment) coexists and influences electrical properties (e.g., resistance, conductivity, current symmetry) in a coupled system. In metallic thin films subjected to mechanical loading, for example, crack formation leads to electrical resistance growth governed by the crack topology; in rotating machinery, bearing faults may induce both vibrational and current signal anomalies.

Core phenomena include:

• Topological crack-induced electrical degradation:
  • For films, the normalized resistance $R$ grows with fourth power of crack length ($\ell$) and second power of areal crack density ($D$), as $R/R_0 = 1 + \pi D \ell^2 + \pi^2 D^2 \ell^4$ (Glushko et al., 2019).
• Dynamic coupling in transmission lines:
  • Damage variable $\varphi$ simultaneously reduces mechanical stiffness and electrical conductivity $\sigma_E = (1-\varphi)^2 \sigma_{E,T}$, leading to positive feedback under thermal stress and environmental loading (KC et al., 2024).
• Rotor and stator compound interactions in machines:
  • Hybrid diagnostic models rely on multiple sensor modalities capturing both mechanical (vibration, shaft dynamics) and electrical (phases, currents, voltages) signals (Chen et al., 5 Jan 2026).

2. Modeling and Simulation Methodologies

Modeling compound faults requires capturing the multiphysics coupling and stochastic behavior of interacting mechanical and electrical subsystems.

2.1 Finite Element and Topological Models

• Crack–resistance mapping:
  • Quasi-3D finite element models represent a polymer-supported conductor as a rectangular sheet with randomly oriented through-thickness cracks. The explicit formula $R(\ell, D)$ provides scale-free predictions of electrical degradation driven by crack topology. The dimensionless "Cracking Factor" CF = $D\ell^2$ serves as a universal damage metric (Glushko et al., 2019).

2.2 Thermo-Electro-Mechanical Phase-Field Frameworks

• Power transmission lines:
  • Governing equations span mechanical momentum balance, phase-field damage evolution, heat conduction (inc. Joule heating and environmental effects), and quasi-static Maxwell equations for current continuity. The framework solves coupled PDEs for displacement $u(x,t)$, temperature $\theta(x,t)$, damage variable $\varphi(x,t)$, and voltage $V(x,t)$, integrating feedback loops between mechanical aging, temperature rise, and electrical conductivity (KC et al., 2024).

2.3 Hybrid System Simulation

• All-electric APU systems:
  • Joint system modeling integrates a variable-step continuous-time starter/generator (SG) with a fixed-step DLL-based gas generator (GG). The SG is simulated in MATLAB/Simulink (using stiff solvers and multi-loop TTSC fault insertion), while the GG, discretized in state-space, receives SG shaft power as input. Real-time data exchange captures compound fault propagation via mechanical-electrical coupling (Mao et al., 12 Jun 2025).

3. Diagnostic Feature Extraction and Classification

Compound fault diagnosis leverages multimodal sensor fusion and frequency-domain features:

• Signal acquisition:
  • Synchronized triaxial vibration, three-phase current, torque, and key-phase signals collected under variable speed/torque profiles provide comprehensive behavior mapping (Chen et al., 5 Jan 2026).
• Feature engineering:
  • Time-domain: RMS, kurtosis, crest factor;
  • Frequency-domain: spectral energy, harmonic content, sideband amplitude ratios;
  • Time-frequency: STFT, wavelet scalograms;
  • Envelope detection isolates mechanical impulses related to bearing faults.
• Compound fault representation:
  • Multi-label classification frameworks assign independent binary/fault-severity outputs per fault type, reflecting physically distinct origins and avoiding combinatorial class explosion (Yi et al., 15 Apr 2025, Rico et al., 9 Apr 2025).

4. Data-Driven and Deep Learning Approaches

Recent advances target scalable, robust classification under realistic compound fault scenarios:

• FFT-enhanced 1D-CNN:
  • Frequency-domain input tensors from multiple sensor channels facilitate the fusion of mechanical and electrical signatures. Multi-head binary classifiers yield high accuracy (93.93% for compound faults on PHM Beijing dataset), outperforming raw-signal approaches (Rico et al., 9 Apr 2025).
• Multi-Output Classification (MOC) with Frequency Layer Normalization (FLN):
  • MOC networks process STFT spectrograms, outputting severity estimates for each fault type via task-specific heads. FLN normalizes features along the frequency axis, preserving harmonic signatures central to mechanical/electrical discrimination. Adaptation losses (MK-MMD, EM) enable transfer learning across domains with minimal labeled data, enhancing macro F1 across variable operating conditions (Yi et al., 15 Apr 2025).

Approach	Input Features	Fault Output Format
FFT-1DCNN (Rico et al., 9 Apr 2025)	DFT amplitudes from 21 sensors	Binary indicators (17 faults)
MOC+FLN (Yi et al., 15 Apr 2025)	STFT spectrograms from multi-channel time series	Severity (per fault type)
SVM/CNN/LSTM (Chen et al., 5 Jan 2026)	Hybrid time/frequency features	Multi-label, multi-class

5. Experimental Validation and Benchmark Datasets

Controlled datasets underpin model validation, sensitivity analysis, and benchmarking:

• Motor fault multi-mode dataset:
  • 282 runs under 24 conditions (single/compound faults) with annotated severity levels, supporting cross-validation strategies across speed and load variability (Chen et al., 5 Jan 2026).
• Flexible electronics resistance–crack law:
  • Film samples (Ag on PEN/PET) loaded to 20% strain, with in-situ resistance measurement and SEM-imaged crack morphology matching analytical predictions (Glushko et al., 2019).
• Transmission line scenarios:
  • Deterministic and fuzzy PCM-driven studies quantify the probability of failure under Texas-wind, California-wildfire, Alaska-icing, with sensitivity dominated by fracture energy, fatigue, and base current (KC et al., 2024).
• APU joint sim benchmark:
  • APS5000 data validates multi-rate simulation against reference third-party models and measured transients for both steady-state and fault-induced responses, ensuring fidelity of electromechanical coupling (Mao et al., 12 Jun 2025).

6. Design Guidelines and Advanced Interpretation

Interpretation of compound fault phenomena informs design and online monitoring:

• Scale-independent safe-cracking design:
  • Flexible electronics may tolerate high crack density if crack lengths are tightly controlled, enabling reliable device operation via CF-limited process monitoring (Glushko et al., 2019).
• Transmission system risk quantification:
  • Positive feedback between damage, conductivity, and heating amplifies compound fault risk; environmental extremes must be modeled as probabilistic events influencing long-term reliability (KC et al., 2024).
• Diagnostic pipeline best-practices:
  • Combined feature vectors (vibration + current), normalization by baseline at each operating point, order-tracking for speed-variant harmonics, and hybrid convolutional/temporal models are optimal for real-world deployment (Chen et al., 5 Jan 2026).
• Compound fault FDI:
  • Adaptive thresholds, joint observers (e.g., EKF with expanded state space), multi-rate fault detection isolating mechanical and electrical sources, and system-level dynamic simulation are pivotal in high-integrity applications (Mao et al., 12 Jun 2025).

7. Perspectives and Open Challenges

• Compound fault phenomena require further investigation under unsteady, non-stationary operating conditions and partially labeled environments (Yi et al., 15 Apr 2025).
• Scalable, interpretable multi-label classifiers capable of transferable feature learning (across rpm/torque domains) remain an active area of research.
• Quantitative understanding of cross-domain feedback loops and failure probabilities in large-scale infrastructures will benefit from continued advancement in stochastic multiphysics modeling (KC et al., 2024).
• Benchmark datasets with annotated ground-truth for compound fault scenarios, especially in complex machines and transmission systems, are critical for comparative evaluation and methodological progress (Chen et al., 5 Jan 2026).

Mechanical-electrical compound faults thus constitute a key frontier in reliability engineering, health monitoring, and data-driven diagnosis, with an active research agenda integrating multiphysics simulation, advanced signal processing, and domain-adaptive machine learning.