The initial fault identification based on improved OMP algorithm

As the low-speed and heavy-duty machinery presents serious nonlinear dynamic characteristic when working, it is difficult to extract the fault feature, but the vibration signal is approved to be sparse and only contains several weak impulses which can represent the initial fault feature of the machinery. So the redundant dictionary is introduced to approximate the vibration signal, the algorithm such as Matching Pursuit(MP), Orthogonal Matching Pursuit(OMP), Basis Pursuit(BP) and Method of Frames(MOF) can present the fault signal efficiently, and the related approving algorithm can also improve the convergence rate, but the large calculation and long operation time is a common difficulty. An improved algorithm is introduced in this thesis, the redundant dictionary is separated through envelopment analysis and with convolution can confirm the optimal scaling factor and shift factor. Then transform the pursuit algorithm to Fast Fourier Transform Algorithm(FFT) to confirm the optimal frequency factor and phase factor. As the use of FFT and dictionary division, this algorithm can improve the operation efficiency obviously.