Federated domain generalization for planetary gearbox fault diagnosis: Frequency band energy matrix-guided fusion with prototype regularization

Federated domain generalization (FDG) addresses privacy-preserving fault diagnosis under cross-client domain shift by learning from source clients for unseen target clients. In planetary gearboxes, varying operating conditions can make the same fault exhibit different fault-related spectral characteristics across clients. Existing FDG methods mainly mitigate these discrepancies through feature learning or federated aggregation, rather than explicitly designing input representations to handle such spectral variations. This makes domain-invariant fault feature learning difficult, while reliable diagnosis also requires same-class compactness across clients and inter-class separability. To address these challenges, this paper proposes Federated Domain Generalization via Frequency Band Energy Matrix (FBEM)-guided Prototype-Regularized Fusion (FedDG-FPRF). The framework operates at two complementary levels. At the input-representation level, FBEM pools neighboring frequency components into compact band-time energy inputs to reduce the influence of local spectral shifts, and gated fusion integrates the resulting features with complementary temporal information from raw waveforms to support domain-invariant fault feature learning across clients. During federated training, PCSA reduces same-class statistical discrepancies in FBEM feature statistics using global style prototypes, while Margin Prototype regularization enhances same-class compactness and inter-class separation in fused embeddings using global class prototypes, jointly promoting feature consistency and discriminability across clients. Experiments under leave-one-domain-out settings show that, compared with five representative FDG methods, FedDG-FPRF improves the average accuracy (Acc) by 4.35–14.00 and 4.54–13.01 percentage points on the laboratory and WT-Planetary gearbox datasets, respectively, with corresponding average F1-score (F1) improvements of 5.31–17.09 and 5.57–15.63 percentage points.