Periodic overlapping group elastic net for fault diagnosis

It is a challenging problem to extract the periodic impulses from vibrational signals for fault diagnosis of rotating machines under strong background noise. Thus, in this paper, we propose a novel algorithm called periodic overlapping group elastic net to detect periodic impulses effectively. The novel penalty called overlapping group elastic net(OGEN) combines elastic net and overlapping group sparsity to promote sparsity within and across each group, and it can also be a generalization of many existed famous penalties like the lasso, group lasso, sparse group lasso, etc. Then, OGEN is extended to periodic overlapping group elastic net(POGEN) via constructing a periodic binary sequence to effectively model the periodic information. Moreover, an optimization algorithm based on majorization minimization is derived to minimize the objective function. Finally, the performance of the proposed algorithm is evaluated by numerical simulation through comparison with periodic overlapping group sparsity (POGS) and overlapping group sparsity (OGS), and effectiveness of the algorithm further demonstrates through carrying out the diagnosis of a motor rolling bearing.