Open Access

ARTICLE

Three-Stage Learning Framework for Compound Fault Diagnosis in Delta 3D Printers via Multi-Output Fusion Ensembles

Lin Fang^1,2, Razi Abdul-Rahman^1,*, Cheng-Fu Yang^3,4,*

1 School of Mechanical Engineering, University Sains Malaysia, Nibong Tebal, Penang, Malaysia
2 School of Urban Construction and Intelligent Manufacturing, Dongguan City University, Dongguan, China
3 Department of Chemical and Materials Engineering, National University of Kaohsiung, Kaohsiung, Taiwan
4 Department of Aeronautical Engineering, Chaoyang University of Technology, Taichung, Taiwan

* Corresponding Authors: Razi Abdul-Rahman. Email: ; Cheng-Fu Yang. Email:

Computer Modeling in Engineering & Sciences 2026, 147(3), 13 https://doi.org/10.32604/cmes.2026.080387

Received 08 February 2026; Accepted 06 May 2026; Issue published 30 June 2026

Abstract

Parallel mechanisms are extensively employed in industrial logistics, food processing, and medical applications. Due to the strong nonlinearity and cross-axis coupling inherent in closed-chain kinematics, fault diagnostic performance is highly sensitive to signal perturbations and class imbalance under noisy measurement conditions. Furthermore, diagnostic models trained under single-fault scenarios often exhibit notable performance degradation when transferred to compound fault conditions as a result of distribution shift. In this study, a Delta 3D printer, as a representative parallel mechanism, is adopted as the experimental platform. An interpretable three-stage diagnostic framework is proposed, in which compound fault diagnosis is reformulated as a multi-output classification problem that simultaneously predicts the health states of the A-, B-, and C-belts. This formulation avoids explicit enumeration of compound fault classes while preserving maintenance-relevant, belt-level diagnostic information. Under a strict leakage-avoidance protocol, a fusion ensemble integrating LightGBM and XGBoost classifiers is employed to enhance robustness and generalization to previously unseen compound fault combinations. On the compound-fault subset of the Delta 3D printer dataset, the proposed method achieves a multi-output Macro-F1 score of 09290, with a 95% bootstrap confidence interval of 0.9198–0.9379. The corresponding belt-wise Macro-F1 scores reach 0.9508, 0.9173, and 0.9189 for the A-, B-, and C-belts, respectively. Moreover, the average inference latency on the compound-fault subset is 0.9305 ms per sample, demonstrating a favorable balance between diagnostic accuracy and computational efficiency for edge-deployment scenarios.

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Keywords

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