GWLSTM: A Spatial–Temporal Fusion Graph Wavelet LSTM for Trustworthy Open-Set Fault Diagnosis

Deep-learning (DL)-enabled intelligent fault diagnosis (IFD) has attracted wide attention in prognostics and health management, owing to its powerful data-driven feature-learning capability. However, most existing spatial–temporal fault-diagnosis methods for complex industrial systems characterized by multivariate and strongly coupled sensor data still adopt a two-stage architecture, in which the spatial correlations among sensor channels and the temporal dynamics are modeled separately. This decoupled design limits effective spatial-temporal interaction and degrades robustness undervariable working conditions. Moreover, as this design is typically optimized under closed-set assumptions using softmax-based objectives, it lacks an explicit mechanism to identify previously unseen faults. To overcome these limitations, this study proposes a graph wavelet long–short-term memory (GWLSTM) network that integrates spatial-temporal modeling and open-set recognition within a unified framework. Specifically, a discrete graph wavelet convolution (DGWConv), built upon the discrete graph wavelet transform (DGWT), is embedded into each long–short-term memory network (LSTM) gate to facilitate multiscale spatial-temporal feature extraction. Alearnable soft-shrinkage function is then incorporated to suppress noise-sensitive components and enhance feature robustness. Subsequently, graph wavelet pooling (GWPool) is implemented to aggregate node-level features into compact graph representations, whose graph energies are computed to perform trustworthy open-set fault diagnosis. Extensive experiments under complex working conditions reveal that GWLSTM improves the open-set rejection accuracy by 20%–50%, compared with existing spatial-temporal baselines, while producing only a marginal increase in inference time.