Multiscale correntropy matrix representation-based mechanical fault diagnosis under time-varying conditions

Mechanical fault diagnosis under time-varying conditions remains challenging due to speed fluctuations that induce signal nonstationarity. To address this issue, a multiscale correntropy matrix representation method is proposed. First, aligned Fourier decomposition is introduced to decompose multivariate sensor signals into structured multiscale components with consistent frequency alignment across sensors. Then, scale-aligned and scale-varied correntropy matrices are constructed to characterize cross-sensor coupling and within-sensor nonstationarity, respectively, capturing spatial coupling and nonstationary behavior. These matrices are mapped from a Riemannian manifold to Euclidean space via matrix logarithm operations and fused into a compact feature vector for joint signal representation. The effectiveness of the method is evaluated on bearing and gearbox datasets under time-varying and constant speed conditions. The results of comparative and ablation experiments demonstrate that the proposed approach achieves superior performance and practicality compared to existing methods.