A Hierarchical Semantic Knowledge-Distilled Belief Rule Base for Interpretable Fault Diagnosis

Fault diagnosis is essential for the safe and reliable operation of industrial equipment. Deep learning models provide strong fault recognition capabilities, but offer limited transparency, while belief rule bases (BRBs) provide explicit reasoning, but face challenges in representing complex fault relationships and meaningful intermediate states. Existing knowledge distillation methods mainly focus on final outputs and do not explicitly align intermediate semantic states and diagnostic paths. Moreover, conventional classification metrics do not directly evaluate hierarchical reasoning consistency. To address these issues, this paper proposes a hierarchical semantic knowledge-distilled belief rule base (HSD-BRB). Expert-guided semantic modeling assigns explicit meanings to intermediate states, while output-, state-, and path-level knowledge distillation transfers teacher knowledge to the corresponding levels of the BRB. An expert-deviation constraint further preserves the initialized rule knowledge, and a consistency evaluation mechanism quantifies state- and path-level alignment. Experiments on the Southeast University bearing and gearbox datasets achieve mean Accuracies of 95.76% and 96.81% and Macro-F1 scores of 0.9575 and 0.9680, respectively. In the gearbox small-sample setting, the BRB is optimized using 90 labelled samples, while the teacher uses the full 890-sample training partition. The results show improved state- and path-level consistency together with traceable semantic states, rule activations, and final fault beliefs. Overall, HSD-BRB provides an interpretable framework for transferring neural knowledge into hierarchical rule-based fault diagnosis.