Distributed Remaining Useful Life Prediction for Multi-Site Systems via Personalized Probabilistic Federated Learning

The limited availability of complete run-to-failure trajectories at individual sites severely constrains the reliability of prognostics, thereby motivating cross-site collaboration. Nevertheless, stringent privacy regulations preclude the sharing of raw operational data, calling for distributed learning frameworks that leverage statistical summaries while preserving data locality. In this context, most existing distributed methods for remaining useful life prediction rely solely on aggregating point estimates and adopt a shared global model across sites, which hinders uncertainty quantification and fails to capture local degradation heterogeneity. To address these challenges, we propose a probabilistic personalized federated framework. The framework is formulated as a hierarchical Bayesian learning scheme, in which site-specific posteriors are inferred into a global consensus posterior that is recursively propagated back as an informative prior for local refinement. This posterior–prior coupling facilitates coherent uncertainty quantification while balancing cross-site knowledge transfer and site-specific adaptation. We further introduce a divergence-based personalization mechanism that regulates the interaction between local information and shared global knowledge. The degree of global knowledge transfer is dynamically governed by the Hellinger distance between local and global posteriors, enabling data-adaptive personalization and improving predictive robustness under heterogeneous operating conditions. We establish theoretical risk bounds at both local and server levels. Extensive numerical experiments demonstrate improved predictive accuracy, scalability, and robustness, and a real-world case study across multiple wind farms further validates its effectiveness for privacy-preserving multi-site prognostics and maintenance decision support.