Sparsity-aware tight frame learning for rotary machine fault diagnosis

It is a challenging problem to find sufficiently sparse approximation dictionaries tailed to machine vibration signals with different failure modes. Therefore, this paper describes and analyzes a novel tight frame learning scheme for machine fault diagnosis. The objective cost is evolved by integrating the tight frame constraint into the popular dictionary learning model. The resulting tight frame design strategy thus could be formulated as a nonconvex optimization problem which can be solved by alternatively implementing hard thresholding operation and singular value decomposition. Then, fault information is sparsely represented over the learned dictionary and could be effectively detected through sparse pursuit techniques. Compared with the state of the art analytic wavelet tight frame, the proposed algorithm has two main advantages: firstly, the tight frame filters are directly learned from the noisy signals and thus the sparse intrinsic structures of feature information could be profoundly captured. Secondly, sparse level of representation coefficients is promoted largely and the process of extracting fault feature information is highly adaptive. Moreover, the performance of the proposed framework is evaluated through numerical experiments and its superiority with respect to the analytic wavelet tight frame is further demonstrated through performing the diagnosis of an engineering gearbox.