BaS-former: a trustworthy model of machinery fault diagnosis for quantifying aleatoric uncertainty under noise discrepancy

Trustworthy machinery fault diagnosis aims to enhance the reliability and transparency of model decisions; however, its theoretical and applied research remains in the nascent stages. In real-world industrial settings, the acquisition of fault samples is exceptionally challenging because machinery often operates under normal conditions for extended periods. Furthermore, the collected signals are commonly contaminated by strong and varying background noise. This leads to significant shifts in the signal’s feature distribution, complicating the quantification of aleatoric uncertainty of the diagnostic results. To address these challenges, this paper proposes a novel trustworthy machinery fault diagnosis model, BaS-former. First, we construct a Bayesian window self-attention mechanism by reparameterizing the conventional self-attention as a random variable that follows a variational distribution. By updating this distribution, our model effectively leverages an infinite ensemble of Transformers, thereby enhancing its generalisation and robustness. In addition, we design an aleatoric uncertainty quantification scheme to represent the credibility of the model’s diagnostic results under varying noise conditions. Experimental datasets for bearing and gearbox were employed to validate the proposed method. The results demonstrate that our method not only achieves high diagnostic accuracy but can also characterise the relationship between varying noise intensity and aleatoric uncertainty, significantly outperforming several baseline and state-of-the-art models.