Hyperbolic Hypergraph Neural Networks for Hierarchical Fault Diagnosis in Rotating Machinery

Intelligent fault diagnosis of rotating machinery is essential for ensuring the safety and reliability of industrial systems. While hypergraph neural networks (HGNNs) have recently shown promise for modeling high-order dependencies beyond pairwise graph methods, most existing variants operate in Euclidean space, which is not explicitly aligned with hierarchical fault-response structure (root cause to fault mode to observed response). To address this limitation, we propose Hyperbolic Hypergraph Neural Network (H²GNN), a framework that integrates hyperbolic geometry with hypergraph neural networks for fault diagnosis. Specifically, H²GNN constructs fault-response-aware hyperedges over diagnostic views of vibration signals and performs message passing in the Poincaré ball model, a Riemannian manifold of constant negative curvature commonly used for hierarchical representation learning. We introduce Poincaré hyperedge aggregation via an iterative Fréchet-mean solver, a learnable curvature parameter for adaptive manifold fitting, and a tangent-space classification head. Experiments are conducted on two public benchmarks, namely the Case Western Reserve University (CWRU) bearing dataset and the Machinery Failure Prevention Technology (MFPT) bearing dataset, and report mean accuracies of 99.87% and 99.75%, respectively, outperforming six competing methods, including CNN, GCN, HGNN, dynamic-HGNN, contrastive-HGNN, and spatial-temporal HGNN. Ablation studies indicate that hyperbolic geometry and the adaptive curvature mechanism both contribute to the observed performance gain.