Tensor low-rank and sparse decomposition and its application in bearing fault information separation

Properly separating fault information from noisy measured signals is crucial for effective bearing health sensing. However, conventional fault information separation methods face challenges such as predefined model parameters and poor noise robustness. Additionally, with the advent of Industry Big Data, multichannel monitoring signals present significant challenges for traditional single decomposition approaches. To address these challenges and fully extract potential fault information, this paper introduces a tensor low-rank and sparse decomposition (tensor LRSD) approach for multichannel signal processing. Inspired by matrix LRSD, we construct a tensor LRSD model that adaptively decomposes the signal into a tensor sparse term containing fault information and a low-rank term representing the intrinsic signal pattern. To further enhance the decomposition performance, a maximum correlation-based selection strategy is designed. This strategy evaluates the correlation between each tensor slice and selects appropriate tensor sparse terms for fault information extraction. Simulation analysis and two experimental studies involving typical bearing failures are implemented to verify the capability and superiority of the presented tensor LRSD approach. The consequences demonstrate that the presented method outperforms conventional techniques, showcasing its capability to effectively separate fault information from noisy signals.