PG-MTCDGNet: A Physics-Grounded Multi-Scale Time-Lagged Dynamic Graph Network for Structured Evidence Reporting in Planetary-Gearbox Fault Diagnosis

Multichannel vibration from a planetary gearbox exhibits operating-condition-dependent interactions across both time scale and lag. Static undirected graphs cannot represent ordered temporal dependence, while repeated graph aggregation can attenuate localized impacts. This paper presents PG-MTCDGNet, a physics-grounded multi-scale time-lagged dynamic graph network for structured evidence reporting in planetary-gearbox fault diagnosis. Phase-synchronous X/Y vibration, transient residuals, Hilbert envelopes, cross-channel coupling, and encoder micro-speed are represented as eight physical nodes. Sparse directed graphs are induced using the angular lags of one, four, and 16 samples from lagged predictive associations and are regularized by label-independent mesh and modulation priors. A time-lagged graph branch is fused with an unsmoothed local-evidence branch, and the complete model is trained with a fold-internal noise-consistency curriculum spanning −6 to 10 dB. The WT dataset comprises 80 continuous raw files and 5120 windows from five health states, two installations, and eight speeds. Under raw-file-isolated, class-installation-speed-balanced five-fold validation, PG-MTCDGNet achieved 99.61% ± 0.33% accuracy, 99.63% ± 0.31% macro-F1, and 0.99999 macro-AUC. Accuracy at 0 dB feature noise was 96.78%. A depth-reduced variant, PG-MTCDGNet-Lite, separates comparable signal descriptors from heterogeneous physical tokens and uses a regularized linear readout. In exploratory installation and speed holdouts, its four-condition file-level accuracy was 88.125%, versus 86.250% for the matched MLP; likewise, macro-F1 was 88.044% versus 84.171%. Removing graph propagation tied its overall accuracy, so this improvement does not establish a unique graph contribution. The 80 recordings were reused during model development, and the results require confirmation on new independent recordings.