Uncertainty-Aware Remaining Useful Life Prediction with Bayesian Deep Learning: A Function-Space Variational Inference Approach

Remaining Useful Life (RUL) prediction is a core component of Prognostics and Health Management (PHM) for industrial equipment, providing a solid foundation for risk-aware maintenance and operational decision-making. However, traditional point estimation methods struggle to cope with the complexity of operational environments and the diversity of degradation mechanisms, leading to limitations in the reliability and practical value of prediction results. Bayesian Neural Networks (BNNs) offer a theoretical basis for uncertainty modeling in RUL prediction, but most existing approaches rely on parameter-space variational approximations, which are constrained by high-dimensional and nonlinear structures and therefore cannot accurately characterize complex posterior distributions. To address these challenges, this paper proposes a Bayesian deep learning method for RUL prediction based on Function-Space Variational Inference (FSVI). By modeling and optimizing the predictive distribution directly in function space, this approach overcomes the limitations of traditional parameter-space inference and significantly enhances the expressiveness and reliability of uncertainty quantification. Experimental results demonstrate that the proposed method outperforms mainstream parameter-space approaches in both predictive accuracy and uncertainty modeling, providing a novel theoretical foundation and technical pathway for trustworthy uncertainty quantification and prediction in equipment health management.