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

Johnny Garcia; Nicolas Salguero; Naveed Iqbal; Brahim Brahmi; Ramy Rashad

cs.ROOct 24, 2026

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

Authors: Johnny Garcia, Nicolas Salguero, Naveed Iqbal, Brahim Brahmi, Ramy Rashad

Organizations: Electrical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia · Electrical Engineering Department and the Interdisciplinary Research Center for Communication Systems and Sensing, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia · Electrical Engineering Department and the Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia · Control and Instrumentation Engineering Department and the Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Abstract

Fault diagnosis during regulated motion requires informative signals even when feedback attenuates tracking deviations. This paper develops an energy-based diagnostic framework that constructs mechanical port-power residuals without a dedicated dynamic observer. Spectral Hamiltonian Algebraic Power Evaluation (SHAPE) combines port-Hamiltonian variables and differential flatness to generate nominal power references from planned motion for fully actuated mechanical systems with collocated actuation. Subtracting these references from commanded effort multiplied by measured flow yields residuals whose final evaluation requires neither recursive observer updates nor measured-state dynamics calculations. Continuous wavelet transform (CWT) scalograms and a shared-encoder convolutional neural network are used to distinguish nominal operation, actuator loss of effectiveness, anomalous friction, and vibration from complete trajectories. Evaluation uses a simulated six degree of freedom Kinova manipulator under model predictive control and fixed plant-model mismatch, with single faults at a specified joint. Across five training seeds and 3000 held-out test runs, SHAPE-CWT achieves a mean accuracy of 84.69 percent, versus 81.67 percent for torque residuals and 97.17 percent for the generalized momentum observer under common CWT processing. The respective sample standard deviations are 0.70, 0.70, and 0.37 percentage points. These results demonstrate useful fault-type discrimination from algebraic power residuals, while severity-excitation profiles and offline velocity perturbations reveal limits to their diagnostic capability.

Figures & tables

Fig. 1: Conceptual architecture and energetic signal flow of the general SHAPE framework. (Top-Right) Algebraic Nominal Reference Generator exploits differential flatness to compute an algebraic nominal port-power baseline directly from planned trajectories. (Top-Left) Closed-Loop Physical System evaluates the commanded-power proxy under feedback control, plant mismatch, disturbances, and physical anomalies. (Bottom) Spectro-Temporal Fault Diagnosis System evaluates the port-power residual vector and maps the resulting 1-D non-stationary residuals into 2-D spectro-temporal signatures for fault diagnosis.

Fig. 2: Simulation implementation and signal flow of the SHAPE framework on the 6-DoF Kinova Gen3 manipulator. (Top-Right) Algebraic Nominal Reference Generator computes the nominal joint state trajectory and baseline joint power profile via inverse dynamics along planned trajectories. (Top-Left) Closed-loop robotic system produces the physical telemetry and commanded joint-power proxy under Flatness-MPC, computed-torque control, model mismatch, and injected faults. (Bottom) Spectro-Temporal Fault Diagnosis System evaluates the per-joint power residual vector, and transforms the 1-D temporal channels via CWT into multi-joint scalogram tensors for CNN classification.

Parameter	Implemented Value
Prediction interval	$T_{p}=0.05~\mathrm{s}$
Maximum horizons	$N_{p,\max}=15$ , $N_{c,\max}=10$
Joint-position bounds	Joints 1, 4, 6: $\pm\pi~\mathrm{rad}$ ; Joints 2, 3, 5: $\pm[2.25,\,2.58,\,2.10]^{\top}~\mathrm{rad}$
Joint-velocity bounds	$\pm 1.3963~\mathrm{rad/s}$ (Joints 1–3); $\pm 1.2217~\mathrm{rad/s}$ (Joints 4–6)
Virtual-acceleration bounds	$\pm 5.2~\mathrm{rad/s^{2}}$ (Joints 1–3); $\pm 10~\mathrm{rad/s^{2}}$ (Joints 4–6)
Nominal-torque bounds	$\pm 39~\mathrm{N\cdot m}$ (Joints 1–3); $\pm 9~\mathrm{N\cdot m}$ (Joints 4–6)

TABLE I: Flatness-MPC and Torque-Mapping Parameters

Configuration	Representation	Input space
M01: SHAPE–CWT	2-D CWT log-power	$\mathbb{R}^{6\times 224\times 448}$
M02: Torque–CWT	2-D CWT log-power	$\mathbb{R}^{6\times 224\times 448}$
M03: GMO–CWT	2-D CWT log-power	$\mathbb{R}^{6\times 224\times 448}$
M04: EO–CWT	2-D CWT log-power	$\mathbb{R}^{1\times 224\times 448}$
M05: SHAPE–Temporal	1-D time sequence	$\mathbb{R}^{6\times 10\,001}$
M06: SHAPE–FFT	1-D amplitude spectrum	$\mathbb{R}^{6\times 1001}$

TABLE II: Diagnostic Input Configurations

Fig. 3: Shared-encoder classifier architectures used for the six diagnostic configurations. (a) Component-wise encoding, fixed-order late fusion, and four-class classification flow. (b) Two-dimensional encoder used for the CWT configurations. (c) One-dimensional encoder used for the temporal and Fourier configurations. Encoder parameters are shared across the active branches within each independently trained classifier.

Protocol	Scope and Evaluation Design
E0	Primary test benchmark ( $3000$ runs, $750$ parents); M01–M06.
E1	Primary fault runs stratified by physical anomaly severity; M01–M06; descriptive.
E2-A	Observational $4\times 6$ amplitude–frequency grid on the $750$ Primary vibration runs; M01–M06; descriptive.
E2-B	Controlled $300$ -run frequency sweep at fixed vibration amplitude; M01–M04; frequency-resolved recall intervals.
E3	Primary test stratified by post-fault dynamic excitation quartiles; M01–M06; descriptive.
E4	Ten offline sensor-perturbation conditions applied to Primary test trajectories; M01–M04; descriptive.

TABLE III: Diagnostic Evaluation Protocols

(a) Overall classification and binary detection
Metric	SHAPE	Torque	GMO	EO
Accuracy	$84.69$ $\pm 0.70$	$81.67$ $\pm 0.70$	$97.17$ $\pm 0.37$	$84.62$ $\pm 1.70$
Macro- $F_{1}$	$0.8453$ $\pm 0.0071$	$0.8166$ $\pm 0.0061$	$0.9716$ $\pm 0.0038$	$0.8433$ $\pm 0.0179$
Sensitivity	$88.05$ $\pm 1.65$	$83.77$ $\pm 1.92$	$96.95$ $\pm 0.35$	$90.54$ $\pm 1.22$
MDR	$11.95$ $\pm 1.65$	$16.23$ $\pm 1.92$	$3.05$ $\pm 0.35$	$9.46$ $\pm 1.22$
FAR	$6.21$ $\pm 1.71$	$5.33$ $\pm 1.98$	$0.19$ $\pm 0.07$	$2.24$ $\pm 0.56$

TABLE IV: Clean Primary Test Results Under CWT, Reported as Five-Seed Mean

\pm

Sample Standard Deviation. Metrics Are Percentages Except Dimensionless Macro-

F_{1}

. FAR and MDR Denote False-Alarm and Missed-Detection Rates

Fig. 4: LoE and Friction diagnosis by SHAPE, Torque, and EO under CWT on Primary test. Cells show five-seed mean percentages: (a) correct fault-type identification; (b) true faulty runs assigned to any fault class. B1–B4 follow the fault-specific severity intervals in Section IV , from lowest to highest. Q1–Q4 are training-defined strata of post-fault measured Joint-2 velocity RMS. All panels share a 0%–100% scale.

Fig. 5: LoE and Friction diagnosis by the CWT, Temporal, and FFT SHAPE pipelines on Primary test. Cells show five-seed mean percentages: (a) correct fault-type identification; (b) true faulty runs assigned to any fault class. B1–B4 follow the fault-specific severity intervals in Section IV , from lowest to highest. Q1–Q4 are training-defined strata of post-fault measured Joint-2 velocity RMS. All panels share a 0%–100% scale.

Requirement	SHAPE	Torque	GMO	EO
Measured position input	No	No	Yes	Yes
Measured velocity input	Yes	No	Yes	Yes
Dynamics evaluated at measured state	No	No	Yes	Yes
Observer states	0	0	6	1
Residual channels	6	6	6	1

TABLE V: Six-Joint Residual-Evaluation Requirements. Inputs Concern the Final Residual Mapping, Not Controller Sensing; All Methods Use Command Torques. Reference Generation Is Excluded, and State Counts Denote Recursive Observer Variables

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Motor compound fault diagnosis using an attention-based cross-talk architecture

Wonjun Yi, Wonho Jung, Junho Kim, Rismaya Kumar Mishra+1

Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea

Fault Diagnosis Industrial Fault Diagnosis Multi-Task Learning Bearing Fault Diagnosis

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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.

Abstract

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