Relational spectral descriptors for multi-sensor vibration-based motor fault diagnosis

Multi-sensor vibration monitoring is important for industrial electric motors operating within coupled drivetrains (e.g., motor–pump assemblies) because faults affect not only local vibration energy but also transmission relationships between measurement locations. However, many existing approaches either rely on isolated handcrafted features or use deep models that treat sensor channels as independent stacked inputs, without explicitly modeling inter-sensor coupling. To address this limitation, we introduce a relational spectral descriptor that represents each vibration window using compact node-level statistics together with pairwise descriptors derived from multi-band magnitude-squared coherence and cross-spectral phase. Speed-aware frequency bands and coherence-based gating are incorporated to preserve diagnostically meaningful coupling while suppressing weak interactions. The resulting representation can be used by both vectorized and structured downstream learners, allowing the contribution of the descriptor itself to be separated from that of the downstream learning architecture. We evaluate the proposed descriptor under a strict grouped record-level anti-leakage protocol on the public 4TU motor–pump dataset and the public Machinery Fault Database (MAFAULDA), with the strong handcrafted ITSF+WPT baseline reported directly under the same main protocol rather than only in an auxiliary setting. Under in-distribution evaluation, FLAT_MLP_REL reaches 99.14% mean test macro-F1 on 4TU (mean of three random seeds), with MAIN_GNN reaching 99.10%, outperforming ITSF+WPT at 92.95%; on MAFAULDA, the same descriptor design transfers without modification and reaches 99.58% mean test macro-F1. Under a harder 4TU cross-folder protocol, the flat relational descriptor achieves 72.35% macro-F1, outperforming a raw-signal 1D-CNN baseline evaluated under the same protocol. A preliminary descriptor-level anti-noise evaluation and a cross-severity generalization study on MAFAULDA further illustrate the operating envelope of the proposed representation. Together, these results indicate that explicit spectral coupling provides a compact, interpretable, and practically useful representation for multi-sensor industrial fault diagnosis.