Low-Rank and Sparsity Co-Induced Tensor Singular Space Decomposition Model for Variable-Speed Rolling Bearings Fault Feature Extraction

To address the challenge of extracting bearing fault features under variable-speed conditions with strong background noise interference, this paper proposes a novel fault feature extraction method based on a low-rank and sparsity co-induced induced tensor singular space decomposition model for rolling bearings. Firstly, short-time Fourier transform (STFT) is employed to construct a highorder time-frequency tensor from multichannel time-varying vibration signals, revealing the low-rank and sparsity of fault characteristics within the tensor singular space. Secondly, guided by the low-rank and sparsity co-induced mechanism, a tensor singular space decomposition model is developed. This model incorporates adaptive threshold function to enforce low-rank constraints and integrates norm 112 regularization to enhance element-wise sparsity, thereby effectively extracting fault components. Furthermore, a multichannel global energy-weighted fusion evaluation strategy is proposed to integrate time-frequency feature distributions across channels, significantly improving the robustness of weak fault feature extraction under high-noise conditions. The effectiveness and superiority of the proposed method are systematically investigated through both simulated and experimental case studies. Results demonstrate that the method effectively eliminates background noise interference in measurements while enhancing fault feature resolution, thereby offering a new paradigm for bearing fault diagnosis under variable-speed conditions.