Federated RUL prediction for bearings under multiple failure modes using connectivity evolution of spectral connected graphs

Reliable degradation trajectories and failure thresholds are essential for accurate bearing remaining useful life (RUL) prediction. However, variations in installation and fault types induce multiple failure modes that severely limit prediction accuracy. This study focuses on developing mode-specific bearing degradation trajectories and failure thresholds using a spectral-feature degradation connected graph. The method aims to automatically determine the degradation starting point, degradation trajectory, and failure threshold without predefined thresholds, enabling reliable RUL prediction under varying failure modes. The degradation features of different failure modes are characterized using envelope-spectrum connected graphs, and a nonlinear hyperplane is adaptively learned from spectral-distribution differences to identify the degradation starting point. On this basis, a degradation connectivity graph is established to describe real-time degradation evolution across multiple failure modes, with the connectivity induced by graph-topology evolution serving as the degradation-trajectory indicator. The failure threshold is then automatically determined when the connected graph splits into disconnected components and its connectivity approaches zero. During federated training, monotonic connectivity decrease and spectral-feature energy increase are imposed as physical-consistency constraints, and a federated degradation scale library is established to provide online bearings with more reliable and flexible RUL estimate values under multiple failure modes. Benchmark dataset validation shows that the proposed method improves RUL prediction accuracy by 26.04% across multiple failure modes, compared with state-of-the-art methods. The NIO real-world dataset further demonstrates an advanced RUL prediction interval ranging from 4.4 to 7.3 days.