# An Interval Belief Rule Base Method with Attention Enhancement for Bearing Fault Diagnosis Under Variable Operating Conditions

## TL;DR

This paper introduces a new method for diagnosing bearing faults in changing operating conditions using an enhanced rule-based model with attention and optimization.

## Contribution

The novel IBRB-a model integrates expert knowledge with data-driven adaptation and attention mechanisms for improved fault diagnosis under variable conditions.

## Key findings

- The proposed model effectively reduces interval uncertainty through a two-stage fusion strategy based on Evidential Reasoning.
- Experimental results on benchmark datasets confirm the model's effectiveness and generalizability under variable operating conditions.
- The use of P-CMA-ES optimization enhances the model's adaptability and performance in complex industrial systems.

## Abstract

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.