An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information

Wang, Kun; Wang, Tao; Zhou, Zhijie; Ming, Zhichao; Lian, Zheng; Wang, Kejun

doi:10.3390/e28060674

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Open AccessArticle

An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information

by

Kun Wang

¹

,

Tao Wang

^1,*,

Zhijie Zhou

²

,

Zhichao Ming

³,

Zheng Lian

³ and

Kejun Wang

³

¹

College of Combat Support, PLA Rocket Force University of Engineering, Xi’an 710025, China

²

College of Computer Science and Information Engineering, Harbin Normal University, Harbin 150025, China

³

College of Missile Engineering, PLA Rocket Force University of Engineering, Xi’an 710025, China

^*

Author to whom correspondence should be addressed.

Entropy 2026, 28(6), 674; https://doi.org/10.3390/e28060674 (registering DOI)

Submission received: 7 April 2026 / Revised: 2 June 2026 / Accepted: 5 June 2026 / Published: 11 June 2026

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Abstract

To address the challenges of linguistic fuzziness, cognitive variability across fault modes, and the risk of model distortion during optimization, this paper proposes an interpretable belief rule-based fault diagnosis method for complex equipment considering linguistic fuzzy information. First, to address the difficulty experts face in providing precise probability values, an interval grey number table is constructed. By converting linguistic fuzzy information into interval grey representations, the approach quantifies the uncertainty inherent in expert judgments while fully preserving the boundary information of the underlying knowledge. Second, recognizing that expert familiarity varies across different fault modes, a certainty degree fusion method is introduced. This method utilizes fusion weights to mitigate the interference of low-confidence evidence during rule generation. Finally, an interpretable parameter optimization method featuring dynamic knowledge anchoring is designed to constrain model parameters within the reasonable bounds defined by expert knowledge. Validation on an electromechanical actuator demonstrates that the proposed method not only achieves superior diagnostic performance but also ensures model usability and interpretability in practical engineering applications.

Keywords: fault diagnosis; belief rule base; linguistic fuzzy information; interpretability

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MDPI and ACS Style

Wang, K.; Wang, T.; Zhou, Z.; Ming, Z.; Lian, Z.; Wang, K. An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information. Entropy 2026, 28, 674. https://doi.org/10.3390/e28060674

AMA Style

Wang K, Wang T, Zhou Z, Ming Z, Lian Z, Wang K. An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information. Entropy. 2026; 28(6):674. https://doi.org/10.3390/e28060674

Chicago/Turabian Style

Wang, Kun, Tao Wang, Zhijie Zhou, Zhichao Ming, Zheng Lian, and Kejun Wang. 2026. "An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information" Entropy 28, no. 6: 674. https://doi.org/10.3390/e28060674

APA Style

Wang, K., Wang, T., Zhou, Z., Ming, Z., Lian, Z., & Wang, K. (2026). An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information. Entropy, 28(6), 674. https://doi.org/10.3390/e28060674

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An Interpretable Belief Rule-Based Fault Diagnosis Method for Complex Equipment Considering Linguistic Fuzzy Information

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