# An interpretable vibration-enhanced BRB model for rolling bearing fault diagnosis

## TL;DR

This paper introduces a new interpretable model for diagnosing faults in rolling bearings using vibration data and improved rule-based reasoning.

## Contribution

The novel Vibration-Enhanced BRB model improves interpretability and performance for small-sample fault diagnosis in rolling bearings.

## Key findings

- VE-BRB effectively maps continuous vibration signals to rule matching space using energy matrix representation.
- The model demonstrates robustness and interpretability validated on real-world bearing datasets.
- P-CMA-ES optimization enhances the model's performance under various operational conditions.

## Abstract

The operational condition of rolling bearings is essential to the reliability of industrial machinery, making fault diagnosis a critical research topic. Although deep learning has gained widespread attention in this domain, its black-box character and reliance on a large number of training samples limit its practical applicability. In contrast, knowledge-driven intelligent diagnostic models have gained increasing interest due to their superior interpretability and robustness under small-sample conditions. The Belief Rule Base (BRB) model is a representative example of such interpretable methods. However, the conventional BRB models struggle to process continuous signals, limiting their effectiveness in real-world bearing fault diagnosis. This study proposes a novel Vibration-Enhanced Belief Rule Base (VE-BRB) model designed to address this limitation. First, the window feature extraction method is used to preprocess the continuous vibration signal. Bearing fault features are extracted from low-frequency and high-frequency to construct an energy matrix representation. Thereby, the original continuous vibration signal can be effectively mapped to the rule matching space. Second, the model is reasoned through an evidential reasoning (ER) algorithm. This guarantees the interpretability of the model. Finally, the projection covariance matrix adaptation evolution strategy (P-CMA-ES) is employed as the optimization process. To validate the effectiveness of the proposed method, the test was performed using bearing datasets from Case Western Reserve University and Huazhong University of Science and Technology under various conditions.