Complex systems often experience various faults during operation. These faults can seriously affect system stability. Therefore, building an accurate and efficient fault diagnosis model is highly important. The belief rule base (BRB) is an effective method for fault diagnosis that combines expert knowledge with data-driven approaches. It can effectively handle uncertain information and has been widely applied in this field. However, class imbalance is common in real engineering applications. There are many more normal samples than fault samples, which often reduces the diagnostic accuracy of the model. To address this issue, a hierarchical BRB model based on the One-vs-Rest (OvR) strategy, called OvR-HBRB, is proposed. The model employs the OvR strategy to build a BRB classifier for each fault category to improve diagnostic capability. A learnable belief conversion matrix is designed to transform the outputs of BRB classifiers into multi-class belief distributions required by evidence reasoning (ER) fusion. Model parameters are optimized in stages via the covariance matrix adaptation evolution strategy (CMA-ES) to ensure convergence and diagnostic accuracy. Finally, experiments on the CWRU bearing and gear fault datasets verify the model’s effectiveness. The results show higher diagnostic accuracy under class imbalance conditions.

This research focuses on improving the Harris’ Hawks Optimization algorithm (HHO) by tackling several of its shortcomings, including insufficient population diversity, an imbalance in exploration vs. exploitation, and a lack of thorough exploitation depth. To tackle these shortcomings, it proposes enhancements from three distinct perspectives: an initialization technique for populations grounded in opposition-based learning, a strategy for updating escape energy factors to improve the equilibrium between exploitation and exploration, and a comprehensive exploitation approach that utilizes variable neighborhood search along with mutation operators. The effectiveness of the Improved Harris Hawks Optimization algorithm (IHHO) is assessed by comparing it to five leading algorithms across 23 benchmark test functions. Experimental findings indicate that the IHHO surpasses several contemporary algorithms its problem-solving capabilities. Additionally, this paper introduces a feature selection method leveraging the IHHO algorithm (IHHO-FS) to address challenges such as low efficiency in feature selection and high computational costs (time to find the optimal feature combination and model response time) associated with high-dimensional datasets. Comparative analyses between IHHO-FS and six other advanced feature selection methods are conducted across eight datasets. The results demonstrate that IHHO-FS significantly reduces the computational costs associated with classification models by lowering data dimensionality, while also enhancing the efficiency of feature selection. Furthermore, IHHO-FS shows strong competitiveness relative to numerous algorithms.

Precise fault diagnosis under complex working conditions is critical for ensuring the safety of industrial equipment. The belief rule base (BRB), characterized by its interpretability and capability to handle nonlinear, small-sample data, is inherently suitable for such diagnostic tasks. However, traditional BRB methods are impeded by the combinatorial rule explosion derived from high-dimensional features and the uncertainty introduced by environmental noise. To address structural complexity and environmental uncertainty simultaneously, this paper proposes a deep BRB fault diagnosis method integrated with indicator uncertainty deep BRB uncertainty. First, the extreme gradient boosting algorithm is employed to evaluate feature importance and select key features, constructing a hierarchical deep inference topology. Second, a quantification method based on the average distance of monitoring data is proposed to extract the uncertainty of key indicators, establishing an inference mechanism that fuses this uncertainty. Third, the projected covariance matrix adaptation evolution strategy is utilized to jointly optimize the full parameter set of the model, thereby enhancing generalization performance. Finally, experimental validation is conducted using bearing and gearbox datasets. Results indicate that the proposed method outperforms traditional approaches in terms of comprehensive diagnostic performance, achieving higher fault classification accuracy and stronger robustness, thus validating its superiority in handling interference and uncertain environments.

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.