Energy-Based Fault Detection and Isolation Framework for Flat Port-Hamiltonian Mechanical Systems

As physical AI increasingly relies on sensing to understand physical systems, reliable condition monitoring of industrial machinery has become more important. Motors are ubiquitous in industrial systems, and increasing system complexity raises the likelihood of simultaneous faults. Accordingly, compound fault diagnosis that identifies multiple fault components and their severities is increasingly required. Because different fault components jointly affect the same vibration signal, their severity classification can be formulated as related tasks, making multi-task learning (MTL) suitable for exploiting shared information. However, conventional shared-trunk architectures force tasks to share a common representation, potentially causing negative transfer because fault components are characterized by different time-frequency regions. To address this issue, this study proposes a Residual Neural Dimension Reductor with Time-Frequency Channel Attention (RNDR-TFCA), an attention-enhanced cross-talk architecture for multi-output compound fault diagnosis. RNDR-TFCA preserves task-specific feature extractors while selectively exchanging information across tasks. Time-frequency attention emphasizes informative intra-task regions, while channel attention enhances useful inter-task information after nonlinear feature fusion. Experiments on a rotor-bearing system with inner-race fault, outer-race fault, misalignment, and unbalance showed that RNDR-TFCA achieved a macro F1 score of 0.898, outperforming single-task, multi-class, shared-trunk, and cross-talk baselines. Ablation experiments confirmed the benefit of jointly applying both attention mechanisms. RNDR-TFCA required 713 K parameters and 170.42 MMACs, only slightly higher than RNDR. Channel-expanded baselines still underperformed RNDR-TFCA, indicating that the gain was not simply attributable to increased model capacity.

This paper transfers three statistical methods from particle physics to multirotor propeller fault detection: the likelihood ratio test (LRT) for binary detection, the CLs modified frequentist method for false alarm rate control, and sequential neural posterior estimation (SNPE) for quantitative fault characterization. Operating on spectral features tied to rotor harmonic physics, the system returns three outputs: binary detection, controlled false alarm rates, and calibrated posteriors over fault severity and motor location. On UAV-FD, a hexarotor dataset of 18 real flights with 5% and 10% blade damage, leave-one-flight-out cross-validation gives AUC 0.862 +/- 0.007 (95% CI: 0.849--0.876), outperforming CUSUM (0.708 +/- 0.010), autoencoder (0.753 +/- 0.009), and LSTM autoencoder (0.551). At 5% false alarm rate the system detects 93% of significant and 81% of subtle blade damage. On PADRE, a quadrotor platform, AUC reaches 0.986 after refitting only the generative models. SNPE gives a full posterior over fault severity (90% credible interval coverage 92--100%, MAE 0.012), so the output includes uncertainty rather than just a point estimate or fault flag. Per-flight sequential detection achieves 100% fault detection with 94% overall accuracy.

This paper presents a port-Hamiltonian formulation of vehicle-manipulator systems (VMS), a broad class of robotic systems including aerial manipulators, underwater manipulators, space robots, and omnidirectional mobile manipulators. Unlike existing Lagrangian formulations that obscure the underlying energetic structure, the proposed port-Hamiltonian formulation explicitly reveals the energy flow and conservation properties of these complex mechanical systems. We derive the port-Hamiltonian dynamics from first principles using Hamiltonian reduction theory. Two complementary formulations are presented: a standard form that directly exposes the energy structure, and an inertially-decoupled form that leverages the principal bundle structure of the VMS configuration space and is particularly suitable for control design and numerical simulation. The coordinate-free geometric approach we follow avoids singularities associated with local parameterizations of the base orientation. We rigorously establish the mathematical equivalence between our port-Hamiltonian formulations and existing reduced Euler-Lagrange and Boltzmann-Hamel equations found in the robotics and geometric mechanics literature.