Sparse representation based on parametric impulsive dictionary design for bearing fault diagnosis

In the early stage of bearing failure, the transient features are not obvious. It is a big challenge to extract the weak transient features under strong background noise. The sparse representation provides an effective and novel path to describe mechanical vibration signals. By the aid of this model, the transients induced by the local fault can be extracted more accurately from the vibration signals. However, the choice of representation dictionaries has a great impact on the results. A satisfactory dictionary should fulfill the following two conditions. Firstly, the atoms in the dictionary must match with the features to be extracted; secondly, the atoms themselves have low coherence with each other to ensure the approximation accuracy by the sparse coding algorithms. Unluckily the existing dictionaries used for fault feature extraction do not fulfill the requirements. The parametric dictionaries like the Gabor dictionary do not fully match with the fault features. The learned dictionaries cannot guarantee the incoherence requirement, besides, the atoms in the learned dictionary may not contain the damped oscillation transient features under the high noise intensity. In order to address above problems, a parametric impulsive dictionary is designed for bearing fault feature extraction in this paper. The parameters of the Laplace wavelets, which are highly matched with the local bearing fault features, are discretized by the modified alternating projection method. The obtained dictionary with a low mutual-coherence is close to being an equiangular tight frame (ETF) which guarantees the accurate recovery of the representation coefficients. Furthermore, the correlation iteration stopping criteria is introduced in the orthogonal matching pursuit (OMP) algorithm. Compared with the classical residual energy stopping criteria, it performs better on feature extraction. The superiority of the proposed method is verified by the numerical simulations. Moreover, a motor bearing experiment and the signal analysis of a real wind turbine generator are carried out to further validate the effectiveness of the method. (C) 2019 Elsevier Ltd. All rights reserved.