Yuanyuan Qu

The accurate assessment of lithium-ion battery State of Health (SOH) is fundamental to the safe and reliable operation of battery management systems. The Belief Rule Base (BRB) integrates quantitative monitoring data and qualitative expert knowledge, thereby supporting SOH assessment. However, existing BRB models produce point-value outputs. The uncertainty of the assessment results cannot be quantified, nor can the belief level of the assessment be characterized. Moreover, information loss is caused by traditional evidential reasoning (ER) when interval belief degrees are processed. Interval reliability is not adequately addressed in existing optimization methods, as interval quality is not incorporated into the objective function. To address these problems, an interval SOH assessment method based on the Interval Belief Rule Base with Interval Evidential Reasoning (IBRB-IER) is proposed. Rule belief degrees are extended from point values to interval forms, enabling uncertainty quantification. Interval information is preserved throughout the fusion process by adopting interval evidential reasoning algorithms. A multi-objective composite fitness function is designed. Global parameter optimization is achieved through the projected covariance matrix adaptation evolution strategy (P-CMA-ES). SOH estimation intervals are finally produced as outputs. The effectiveness of the proposed method in SOH interval assessment is validated through experiments on the NASA dataset.

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.