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.

As bearings are critical mechanical components, their actual operating conditions exhibit notable dynamic complexity. Multiple factors—including rotational speed fluctuations, sudden load changes, and environmental disturbances—interact in a strongly coupled fashion. This imposes severe challenges on traditional fault diagnosis methods, such as limited interpretability, weak adaptive capacity, and elevated misjudgment rates. Therefore, this paper proposes an Interval Belief Rule Base model integrated with an attention mechanism (IBRB-a) under variable operating conditions. The proposed model combines expert knowledge’s ability to quantify uncertainty with a data-driven adaptation mechanism, thereby addressing the challenge of variable operating conditions in complex industrial systems. First, a novel interval rule construction method is incorporated into the traditional IBRB model, and kernel density estimation (KDE) is employed to select reference values. Second, during the model reasoning process, a two-stage fusion strategy based on Evidential Reasoning (ER) is adopted: progressive information fusion is implemented via the ER analysis algorithm and the ER rule algorithm, which effectively mitigates the interval uncertainty under variable operating conditions. Finally, the constrained projected covariance matrix adaptive evolution strategy (P-CMA-ES) is employed to optimize the model. Furthermore, experimental validation under variable operating conditions is conducted via Case Western Reserve University and Southeast University bearing datasets. The effectiveness and generalizability of the proposed method are validated by the experimental result.

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.

Student exam pass prediction (EPP) is a key task in educational assessment and can help teachers identify students’ learning obstacles in a timely manner and optimize teaching strategies. However, existing EPP models, although capable of providing quantitative analysis, suffer from issues such as complex algorithms, poor interpretability, and unstable accuracy. Moreover, the evaluation process is opaque, making it difficult for teachers to understand the basis for scoring. To address this, this paper proposes an approximate belief rule base (ABRB-a) student examination passing prediction method based on adaptive reference point selection using symmetry. Firstly, a random forest method based on cross-validation is adopted, introducing intelligent preprocessing and adaptive tuning to achieve precise screening of multi-attribute features. Secondly, reference points are automatically generated through hierarchical clustering algorithms, overcoming the limitations of traditional methods that rely on prior expert knowledge. By organically combining IF-THEN rules with evidential reasoning (ER), a traceable decision-making chain is constructed. Finally, a projection covariance matrix adaptive evolution strategy (P-CMA-ES-M) with Mahalanobis distance constraints is introduced, significantly improving the stability and accuracy of parameter optimization. Through experimental analysis, the ABRB-a model demonstrates significant advantages over existing models in terms of accuracy and interpretability.