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.

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.

In the analysis of complex engineering systems, managing uncertainty and optimizing information processing structures are critical for reliable state prediction. The Belief Rule Base (BRB) provides a powerful machine learning approach for integrating expert knowledge with uncertain information. However, mitigating the combinatorial complexity of BRBs through conventional structure simplification often causes unintended information loss, introducing systematic prediction biases that undermine reliability. To address the trade-off between system complexity and modeling accuracy, this study proposes an adaptive belief rule base framework integrating sensitivity analysis with posterior consistency calibration (BRB-ARR). First, an information-driven rule screening mechanism is developed to dynamically determine the pruning threshold based on optimized Mean Square Error (MSE) fluctuations. This method effectively filters redundant rules while avoiding the cognitive biases associated with fixed empirical values. Second, a low-dimensional optimization process is employed to readjust the parameter vector, significantly enhancing computational efficiency. Finally, a posterior calibration module is introduced to compensate for the systematic biases caused by dimensionality reduction, strictly preserving the interpretability of the core inference architecture. To validate the effectiveness of the proposed framework, experimental evaluations are conducted on petroleum pipeline networks and liquid propellant launch vehicles. In the petroleum pipeline scenario, the rule base scale is reduced by over 60 percent from 56 to approximately 20 rules, while the parameter dimensionality decreases from 338 to 122. Compared to the conventional model, the mean squared error is reduced from 0.5291 to 0.3619. Furthermore, in the liquid propellant launch vehicle case, the model achieves a prediction accuracy of 98.57 percent with a mean squared error of 0.00029 while reducing the rule scale from 441 to 109. These results demonstrate that the BRB-ARR model effectively balances structural compactness with high precision prediction, offering a novel approach to uncertainty modeling in intelligent systems.