As one of the most critical components in rotating machinery, bearings play a vital role in ensuring the stable operation of the equipment. Due to the influence of complex environments, there is uncertainty in the process of bearing fault diagnosis. The Belief Rule Base (BRB) is a modeling method that can effectively handle uncertainty issues. However, in the process of bearing fault diagnosis, with the increase of bearing use time, bearing wear will become more and more serious. When extracting data feature values, different types of fault feature values have similarities, which makes it difficult to distinguish and represent the type of fault in the diagnosis process, resulting in local ignorance. The traditional BRB model cannot solve the local ignorance problem, and with the increase of the number of rules, it will lead to the explosion of rule combinations. To solve the above problems, this paper proposes a Hierarchical Belief Rule Base with power set, Firstly, a Hierarchical Belief Rule Base (HBRB) model is selected to solve the problem of combination rule explosion, and then HBRB is extended to the power set identification framework. Because the power set recognition framework can more effectively represent the ignorant information in the complex system, and solve the local ignorance problem in the bearing fault diagnosis, then, the evidential reasoning algorithm is used to establish the reasoning process of the model. Finally, the parameters of the model are optimized using the projection covariance matrix adaptive evolutionary strategy algorithm. The experimental results show that the proposed method can identify different fault categories with high accuracy, effectively solve the local ignorance problem in bearing faults diagnosis, and has good generalization ability.

In the field of vibration monitoring for rotating machinery, high-precision bearing fault diagnosis faces challenges due to imbalanced measurement data and noise interference from complex environments. To address these issues, this paper proposes a bearing fault diagnosis method based on an ensemble undersampling extended belief rule base (EBRB-EU), aiming to improve the reliability and accuracy of equipment condition assessment. Specifically, to overcome the limitation of using Euclidean distance in EBRB, which fails to effectively capture the differences in the probability distribution of vibration signals, the paper introduces the Kullback-Leibler (KL) divergence to replace the Euclidean distance, providing a more accurate measure of the match between samples and rule antecedent attributes. An ensemble undersampling strategy is then employed to calibrate the training set, reducing the impact of majority class samples on model training. Subsequently, the data is divided into multiple subsets, and a set of parallel sub-EBRB models is constructed. The differential evolution algorithm is used to optimize the parameters of each sub-model, minimizing evaluation bias. Finally, an ensemble voting mechanism is applied to integrate the diagnostic results, enhancing the accuracy of fault state identification. Experimental results demonstrate that the KL divergence-based EBRB-EU model outperforms the Euclidean distance-based EBRB method on multiple datasets, effectively alleviates the data imbalance issue, and exhibits strong resistance to interference.

New energy vehicles (NEVs) are a key technology for achieving the low-carbon transition of the transportation sector. The operational safety and energy efficiency of NEVs are critical for the sustainable development of transportation systems. However, the complex system structure and highly variable operating conditions make health state assessment of NEVs challenging. The belief rule base (BRB) framework combines knowledge-driven and data-driven information to handle uncertainty and has been widely used in health assessment of complex systems. In multi-attribute multi-fault scenarios, BRB models still suffer from combinatorial rule explosion and cognitive bias from a single expert, which lead to increased model complexity and reduced interpretability. To address these issues, this study develops an ensemble BRB method with dual-adaptive feature selection, termed Dual-Adaptive Ensemble BRB (DA-EnBRB). The method employs a dual-adaptive mechanism based on Extreme Gradient Boosting (XGBoost) and mutual information (MI) to dynamically construct compact multi-attribute feature subspaces and to build a BRB expert model in each subspace. A multi-strategy crowned porcupine optimizer (MSCPO) optimizes the parameters of all BRB experts. Class-specific expert weights are then learned and used to fuse sub-model outputs via weighted voting, yielding the final diagnostic result. Experiments on NEV fault diagnosis and NEV energy efficiency assessment demonstrate the effectiveness and generalization capability of DA-EnBRB.

Cross-condition bearing fault diagnosis requires models that remain reliable under load-induced distribution shifts while providing transparent and traceable reasoning. Conventional belief rule bases (BRBs) may repeatedly use correlated vibration evidence during inference, and their Cartesian-product rule construction can rapidly increase rule-base complexity. This study proposes a correlation-decoupled interval belief rule base (CD-IBRB) for cross-condition bearing fault diagnosis. Seven diagnostically relevant time-domain features are selected using XGBoost and transformed into a less-correlated feature space through a Kendall-rank-correlation-guided matrix estimated exclusively from the source training data. Attribute-wise referential points and intervals are then constructed from the transformed training attributes, allowing the rule base to grow additively rather than combinatorially. Initial belief distributions are obtained from interval-level class distributions. The projection covariance matrix adaptation evolution strategy (P-CMA-ES) jointly optimizes the belief degrees, rule reliabilities, and rule weights, while evidential reasoning aggregates the activated interval rules to produce the final diagnostic result. In the primary cross-load bearing experiment, CD-IBRB achieved an accuracy of 0.9702 and a macro-averaged F1 score of 0.9703. It outperformed the strongest BRB variant and data-driven baseline by 7.70 and 6.10 percentage points in accuracy, respectively. Ablation experiments confirmed that removing parameter optimization or attribute decoupling reduced accuracy to 0.9053 and 0.9303, respectively. Additional cross-load and noise-injection experiments further demonstrated the stability of CD-IBRB under load shifts and input disturbances. Across five public multiclass datasets, CD-IBRB achieved a mean accuracy of 0.9004 and consistently outperformed the compared BRB variants. These results demonstrate that CD-IBRB provides a compact, uncertainty-aware, and traceable framework for cross-condition bearing fault diagnosis.