Bayesian cooperative probabilistic Transformer for remaining useful life prediction with uncertainty estimation in industrial equipment

Remaining useful life (RUL) prediction is a key task in prognostics and health management (PHM) of industrial equipment, crucial for enabling reliable predictive maintenance and enhancing equipment reliability. Transformer is widely used for RUL prediction due to its ability to capture remote dynamics and nonlinear responses. However, mainstream Transformers focus on overall prediction accuracy and lack the capability to effectively assess uncertainty of RUL prediction. Furthermore, equal treatment of multi-source information or incorporating additional multi-source information fusion modules during Transformer training can increase prediction uncertainty. To address these challenges, a novel Bayesian cooperative probabilistic Transformer method for machine RUL prediction is proposed, which deeply combines the Bayesian network with the Transformer to comprehensively estimate prediction uncertainty. Prediction uncertainty in Transformer consists of attentional uncertainty, cognitive uncertainty, and aleatoric uncertainty. The core idea is that a negative log-likelihood loss function is first designed to capture attentional uncertainty, while cognitive and aleatoric uncertainties are quantified using Bayesian approach and noise channel. Additionally, an uncertainty-guided multi-source fusion strategy dynamically integrates low and high-uncertainty models for accurate RUL prediction. The performance and advantages of this method are verified by experiments on the C-MAPSS dataset and the nuclear circulating water pump (NCWP) dataset.