Sparsity-based signal extraction using dual Q-factors for gearbox fault detection

Early detection of faults developed in gearboxes is of great importance to prevent catastrophic accidents. In this paper, a sparsity-based feature extraction method using the tunable Q-factor wavelet transform with dual Q-factors is proposed for gearbox fault detection. Specifically, the proposed method addresses the problem of simultaneously extracting periodic transients and high-resonance component from noisy data for the gearboxes fault detection purpose. Firstly, a sparse optimization problem is formulated to jointly estimate the useful components from the noisy observation. In order to promote wavelet sparsity, non-convex regularizations are employed in the cost function of the optimization problem. Then, a fast converging, computationally efficient iterative algorithm which termed SpaEdualQA (the sparsity-based signal extraction algorithm using dual Q-factors) is developed to solve the formulated optimization problem. The derivation of the proposed fast algorithm combines the split augmented Lagrangian shrinkage algorithm (SALSA) with majorization–minimization (MM). Finally, the effectiveness of the proposed SpaEdualQA is validated by analyzing numerical signals and real data collected from engineering fields. The results demonstrated that the proposed SpaEdualQA can effectively extract periodic transients and high-resonance component from noisy vibration signals.