Convolutional sparse coding with periodic overlapped group sparsity for rolling element bearing fault diagnosis

To cope with the problem of detecting periodic impulses in rotating machines with certain bearing faults, this paper proposes a novel data-driven dictionary learning and sparse coding algorithm. In our approach, the signal is decomposed into one or several components with each one as a convolution of one atom with a sparse activation vector. This manner of signal decomposition is formulated as a convex problem subject to a constraint that the activation vector should have a structure with periodic group sparsity. The solution to such a problem is an alternative optimizing process, that is, with a given dictionary, a sparse coding problem is solved by a split variable augmented Lagrangian shrinkage algorithm (SALSA), and for a fixed activation vector, the dictionary updating is implemented by solving Lagrange dual problem. The advantages of the proposed model over several other approaches are demonstrated by the experiments on both simulated and real vibration signals. The experimental results indicate that the proposed method can effectively detect and extract the latent weak fault impulses even in the presence of heavy noise