Double-dictionary signal decomposition method based on split augmented Lagrangian shrinkage algorithm and its application in gearbox hybrid faults diagnosis

Gearbox with hybrid distributed and localized faults usually generates coupled modulation vibration signal. It is hard to decompose the coupled signal for precise diagnosis. To solve this problem, a novel signal decomposition method is proposed on the basis of double-dictionary and split augmented Lagrangian shrinkage algorithm (SALSA). The dictionary possessing high similarity to fault features consists of steady modulation sub-dictionary and impact modulation sub-dictionary. The SALSA is improved by adding a hard threshold de-noising to obtain optimal sparse coefficients of steady modulation and impact modulation components. Key parameters including Lagrange multipliers (λs, λp), penalty factor μ of SALSA and hard threshold ε are studied to determine their optimal value ranges. Kinds of simulation signals show the effectiveness of the proposed method, and experimental tests on fixed-shaft gearbox and planetary gearbox further verify the reliability. Comparative analyses with methods respectively based on matching pursuit and tunable Q-factor wavelet transform indicate that the proposed method is superior to the other two methods in calculation efficiency and anti-noise performance, especially when these two kinds of modulation components are completely coupled in some resonance bands.