Explainable artificial intelligence (XAI) is crucial in education for making educational technologies more transparent and trustworthy. In the domain of student performance prediction, both the results and the processes need to be recognized by experts, making the requirement for explainability very high. The belief rule base (BRB) is a hybrid-driven method for modeling complex systems that integrates expert knowledge with transparent reasoning processes, thus providing good explainability. However, class imbalances in student grades often lead models to ignore minority samples, resulting in inaccurate assessments. Additionally, BRB models face the challenge of losing explainability during the optimization process. Therefore, an explainable student performance prediction method based on dual-level progressive classification BRB (DLBRB-i) has been proposed. Principal component regression (PCR) is used to select key features, and models are constructed based on selected metrics. The BRB’s first layer classifies data broadly, while the second layer refines these classifications for accuracy. By incorporating explainability constraints into the population-based covariance matrix adaptation evolution strategy (P-CMA-ES) optimization process, the explainability of the model is ensured effectively. Finally, empirical analysis using real datasets validates the diagnostic accuracy and explainability of the DLBRB-i model.

The stable operation of aerospace equipment is important for space safety, and the fault diagnosis of aerospace equipment is of practical significance. A fault diagnosis system needs to establish clear causal relationships and provide interpretable determination results. Fuzzy fault tree analysis (FFTA) is a flexible and powerful fault diagnosis method, which can deeply understand causes and fault mechanisms. The interval belief rule base (IBRB) can describe uncertainty. In this paper, an interpretable fault diagnosis model (FFDI) for aerospace equipment based on FFTA and the IBRB is presented for the first time. Firstly, the initial FFDI is constructed with the assistance of FFTA. Second, a model inference is implemented based on an evidential reasoning (ER) parsing algorithm. Then, a projection covariance matrix adaptive evolutionary strategy algorithm with an interpretability constraints (IP-CMA-ES) optimization algorithm is used for optimization. Finally, the effectiveness of the FFDI is verified by a flywheel dataset. This method ensures the completeness of the rule base and the interpretability of the model, avoids the problem of exploding certain combinations of rules, and is suitable for the fault diagnosis of aerospace equipment.

Student performance prediction (SPP) is a pivotal task in educational analytics, enabling proactive interventions and optimized resource allocation by educators. Traditional SPP models are often hindered by their complexity and lack of interpretability. This study introduces a novel SPP framework, the Belief Rule Base with automated construction (Auto–BRB), designed to address these issues. Firstly, reference values are derived through data mining techniques. The model employs an IF–THEN rule-based system integrated with evidential reasoning to ensure both transparency and interpretability. Secondly, parameter optimization is achieved using the Projected Covariance Matrix Adaptive Evolution Strategy (P–CMA–ES), significantly enhancing model accuracy. Moreover, the Akaike Information Criterion (AIC) is then applied to fine-tune the balance between model accuracy and complexity. Finally, case studies on SPP have shown that the Auto–BRB model has an advantage over traditional models in terms of accuracy, while maintaining good interpretability. Therefore, Auto–BRB has excellent application effects in educational data analysis.

The failure of variable speed heat pump (HVSP) is a key factor affecting the energy consumption and operational efficiency of HVAC systems (heating, ventilation, and air conditioning). However, the existing fault diagnosis techniques still have deficiencies in the diagnosis of HVSP failures, making it difficult to achieve a balance between the accuracy and interpretability of the model. The belief rule base (BRB) is an effective diagnostic algorithm that can provide clear decision logic. However, the HVSP fault diagnosis model based on BRB still needs to maintain its interpretability. Therefore, this paper proposes a new interpretable approximate BRB (ABRB-i) HVSP fault diagnosis method. In the ABRB-i model, through the analysis of HVSP failures, a structured and optimized interpretability is constructed. Furthermore, a new interpretable assessment criterion is defined as the objective function to optimize the trade-off between model interpretability and accuracy. At the same time, the improved projected covariance matrix adaptive evolution strategy (P-CMA-ES) is used to maintain the interpretability of the model optimization process. Through experimental analysis, it is concluded that compared with traditional fault diagnosis methods, this method has outstanding effects in achieving model accuracy and interpretability.

In response to the challenges posed by multifactorial nonlinear relationships and uncertainties, and to address the limitations of the existing Belief Rule Base (BRB) in nonlinear fitting, uncertainty representation, and parameter optimization, this paper presents an improved reliable modeling method using a nonlinear belief rule base (R-NBRB). First, the linear inference mechanism is replaced by a smooth nonlinear S-function. This replacement better adapts to nonlinear dynamics in complex industrial systems. Second, attribute reliability is quantified through a reliability assessment method. Data, reliability, and expert knowledge are integrated using the Evidential Reasoning (ER) algorithm. Uncertainty is expressed in the form of belief degrees. Finally, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm is applied to optimize the inference parameters. Decision bias caused by insufficient expert knowledge is thereby reduced. Experiments were conducted on a task involving the detection of a petroleum pipeline leak. The mean squared error (MSE) of the R-NBRB model is only 0.2569. This represents a 28.24% reduction compared with the BRB model. The proposed method’s effectiveness and adaptability in complex industrial situations are confirmed.