An unsupervised multiclass fault diagnosis method and application based on affine-invariant Riemannian metric and spectral clustering

In modern industrial environments, critical components are crucial for the stability and safety of mechanical systems. However, current research on multiclass fault diagnosis using vibration signals has not sufficiently considered the temporal dependencies of data, the coupling between variables, and the scarcity of labeled data. To address these challenges, we propose a novel unsupervised multiclass fault diagnosis method based on the affine-invariant Riemannian metric and spectral clustering (AIRMSC). This method simultaneously accounts for temporal dependencies and variable coupling relationships, effectively resolving the issue of scarce labeled data. Specifically, our method first captures the dynamic states of time-series data through covariance matrices, encapsulating both the temporal dependencies and variable coupling relationships. To enhance the interpretability of the diagnostic results, we utilize the AIRM from Riemannian geometry to evaluate the similarity between matrices and construct complex networks on the manifold of symmetric positive definite matrices. Spectral clustering is then applied to partition these networks, effectively achieving data clustering. The proposed method has been validated using simulated data, the Case Western Reserve University (CWRU) bearing dataset, and actual data from a silicon steel production line. On the CWRU dataset, it achieved a diagnostic accuracy of 98.33%. Compared with existing methods, the proposed AIRMSC proves to be a highly effective unsupervised fault diagnosis approach.