An extended interval structure automated belief rule-based bearing fault diagnosis method for complex engineering systems

Abstract Reliable bearing fault diagnosis requires models that remain accurate under changing operating conditions while providing transparent diagnostic reasoning. Conventional belief rule base (BRB) methods are interpretable but suffer from rule-combination explosion, reliance on expert-defined rule bases, and inflexible inference procedures. This study proposes an extended interval structure automated belief rule base model (EIBRB-Auto). Eight physically meaningful vibration features are first selected using XGBoost. An adaptive interval merging-based rule extraction algorithm (AIM-RE) then constructs eight-dimensional hyperrectangular rules directly from training data under four purity and separability constraints. This process compresses 1,376 training samples into 156 interpretable rules without Cartesian rule combinations. During diagnosis, samples matching the extracted rules are classified directly, whereas unmatched samples are processed using evidential reasoning (ER). The attribute weights, rule weights, and consequent belief degrees are subsequently optimized using P-CMA-ES. In a cross-load bearing experiment using 20 N data for training and 40 N data for testing, EIBRB-Auto achieved an accuracy of 97.82% and directly classified 72.02% of the test samples. Compared with ER-only inference, the hybrid mechanism reduced total inference time by 54.50% and achieved a 2.20-fold speedup without reducing diagnostic accuracy. EIBRB-Auto also outperformed the compared BRB variants and conventional classifiers in the bearing experiment and achieved the highest accuracy on three of four public benchmark datasets. These results demonstrate that EIBRB-Auto provides an effective balance among diagnostic performance, reasoning efficiency, and rule-level interpretability.