Directionally weighted and cyclostationary sparsity-assisted wavelet total variation: a unified framework for aero-engine bearing weak fault diagnosis

Weak fault impulses in aero-engine bearings tend to be obscured by significant background noise and multifaceted interference. This makes them difficult to recover using conventional sparse representation techniques. A unified framework termed directionally weighted and cyclostationary sparsity-assisted wavelet total variation (DwCsSaWATV) is proposed to address this issue. A multiscale weighted wavelet total variation model is constructed under the regularisation of a minimax-concave penalty. Convexity analysis provides explicit constraints for regularisation and convexity parameters, enabling adaptive tuning and an efficient sparse iterative solution. To enhance fault discrimination, directional filtering weights sensitive to fault impulses are incorporated into the model. Additionally, an impulse-period estimation and matching strategy are embedded within the sparse iteration to reinforce cyclostationary sparsity, which is achieved by modelling the periodic structure of fault impulses. The resulting DwCsSaWATV framework works under both constant- and variable-speed conditions. Simulation results confirm the method’s robustness and accuracy in impulse estimation. Verification using data from a seeded bearing fault experiment on a simplified aero-engine and ground testing of the Safran engine accessory gearbox demonstrates its effectiveness and superiority in weak fault diagnosis.