Abstract In the field of industrial automation and intelligent manufacturing, accurate assessment of the health status of electromechanical equipment is crucial for preventing failures, improving productivity, and reducing maintenance costs. However, due to the complexity of the equipment operating environment and the uncertainty of the observed data, the existing belief rule base (BRB)-based assessment methods face the problems of exponential growth of the rule size (combinatorial rule explosion) and impaired model interpretability. To this end, this paper proposes an explainable BRB with interval structure (EBRB-I) method. The method improves belief rules by introducing interval structure and constructs a health status assessment model to alleviate the combinatorial rule explosion problem. Meanwhile, a data similarity-based interval division method is applied to optimize rule partitioning and improve model accuracy. In addition, interpretability constraints are added in the parameter optimization process to preserve the interpretability of the optimized model. In order to test the effectiveness of the model, experiments were carried out using the measured data of the EQ6BT diesel engine. Experimental results demonstrate that the EBRB-I model consistently achieves an accuracy exceeding $97$% across multiple iterations and outperforms various comparison methods. Meanwhile, its rule base size is reduced by more than $33$% compared to the traditional BRB model, significantly improving evaluation efficiency. Furthermore, interpretability analysis indicates that the EBRB-I model’s belief distribution aligns more closely with expert knowledge, verifying its interpretability.

Abstract Intrusion detection in industrial control systems is of great significance to maintain the normal operation of infrastructure. However, the current common intrusion detection models cannot effectively use the semi-quantitative information consisting of expert knowledge and quantitative data, and most of them lack interpretability. Belief Rule Base (BRB), as a hybrid system, can effectively utilize both expert knowledge and historical data. Therefore, this paper proposes a new intrusion detection model for industrial control systems based on a variable interval structure BRB (VI-BRB). Firstly, the interval structure is introduced into BRB. By changing the conjunctive into disjunction, the method of rule generation is changed, and the problem of combinational explosion is effectively solved. Secondly, in view of the difficulty of determining the model interval, a variable interval structure is proposed. By changing fixed intervals into variable intervals, the optimal model structure can be found to improve model performance. Thirdly, an improved enhanced whale optimization algorithm (E-WOA) is proposed to handle the complex constraints in the optimization process of BRB while maintaining the interpretability of the model as much as possible. Finally, by conducting experiments on a natural gas pipeline dataset, VI-BRB achieved an accuracy of 97.3%. The experimental results indicate that VI-BRB can maintain high interpretability while obtaining high accuracy.

Medical assisted decision-making plays a key role in providing accurate and reliable medical advice. But in medical decision-making, various uncertainties are often accompanied. The belief rule base (BRB) has a strong nonlinear modeling capability and can handle uncertainties well. However, BRB suffers from combinatorial explosion and tends to influence explainability during the optimization process. Therefore, an interval belief rule base with explainability (IBRB-e) is explored in this paper. Firstly, pre-processing using extreme gradient boosting (XGBoost) is performed to filter out features with lower importance. Secondly, based on the filtered features, explainability criterion is defined. Thirdly, evidence reasoning (ER) rule is chosen as an inference tool, while projection covariance matrix adaptive evolutionary strategy (P-CMA-ES) algorithm with explainability constraints is chosen as an optimization algorithm. Lastly, the validation of the model is performed through a breast cancer case. The experimental results show that IBRB-e has good explainability while maintaining high accuracy.

Optimal maintenance decision for a sensor network aims to intelligently determine the optimal repair time. The accuracy of the optimal maintenance decision method directly affects the reliability and safety of the sensor network. This paper develops a new optimal maintenance decision method based on belief rule base considering attribute correlation (BRB-c), which is designed to address three challenges: the lack of observation data, complex system mechanisms, and characteristic correlation. This method consists of two sections: the health state assessment model and the health state prediction model. Firstly, the former is accomplished through a BRB-c-based health assessment model that considers characteristic correlation. Subsequently, based on the current health state, a Wiener process is used to predict the health state of the sensor network. After predicting the health state, experts are then required to establish the minimum threshold, which in turn determines the optimal maintenance time. To demonstrate the proposed method is effective, a case study for the wireless sensor network (WSN) of oil storage tank was conducted. The experimental data were collected from an actual storage tank sensor network in Hainan Province, China. The experimental results validate the accuracy of the developed optimal maintenance decision model, confirming its capability to efficiently predict the optimal maintenance time.

As the generalization of fuzzy systems, the belief rule base (BRB) expert system is transparent and interpretable. However, the interpretability of BRB has almost been ignored recently and leads to the decrease of model credibility. The main reason is the lack of unified guidelines for establishing an interpretable BRB expert system. In this article, the interpretability characteristics of BRB are summarized systematically, which can be used as the guideline of BRB establishment. Four interpretability criteria are proposed to ensure the interpretability of BRB in the optimization. A modified optimization algorithm with the interpretability constraints transformed from the interpretability criteria is further developed. As such, an interpretable BRB can be established. A case study for health state evaluation of the aerospace relay is conducted to verify the effectiveness of the proposed method.