Morphological component analysis under non-convex smoothing penalty framework for gearbox fault diagnosis

The sparse representation methodology has been identified to be a promising tool for gearbox fault diagnosis. The core is how to precisely reconstruct the fault signal from noisy monitoring signals. The non-convex penalty has the ability to induce sparsity more efficiently than convex penalty. However, the introduction of non-convex penalty usually influences the convexity of the model, resulting in the unstable or sub-optimal solution. In this paper, we propose the non-convex smoothing penalty framework (NSPF) and combine it with morphological component analysis (MCA) for gearbox fault diagnosis. The proposed NSPF is a unify penalty construction framework, which contains many classical penalty while a new set of non-convex smoothing penalty functions can be generated. These non-convex penalty can guarantee the convexity of the objective function while enhancing the sparsity, thus the global optimal solution can be acquired. The simulation and engineering experiments validate that the NSPF enjoys more reconstruction precision compared to the existing penalties.