Abstract: The fault signal from the low-speed and heavy-duty machinery contains weak impulse signal and presents sparsity which can represent the feature of initial fault. The redundant dictionary is built according to the dynamic model of mechanical vibration can sparse approximate the impulse signal best. Stage-wise orthogonal matching pursuit is based on the orthogonal matching pursuit and uses the method of frame to decompose signal, which can overcome the matter of overmatching by orthogonal matching pursuit, and can also improve the convergence rate. But this method is complex to compute the presentation of the residual in the sub-library. As the coherent cumulant of two atoms in a set is larger than that not in a set, the shift factor and frequency factor can be confirmed efficiently, then a thin sub-library can be constructed for stage-wise orthogonal matching pursuit. Combining with elimination algorithm to delete the redundant atoms can get a set of atoms which can approximate signal more accurate and sparser.

Key words: initial fault;weak impulse;sparse decomposition;stage-wise orthogonal matching pursuit;coherent cumulant