Fast Convolutional Sparse Dictionary Learning Based on LocOMP and Its Application to Bearing Fault Detection

Sparse representations based on convolutional sparse dictionary learning (CSDL) provide an excellent framework for extracting fault impulse response caused by bearing faults. In order to achieve fast dictionary learning, most CSDL-based fault diagnosis techniques recommend truncating the original data. However, the choice of truncation length is very difficult. An improper truncation length will lead to the problems of fault pattern rupture and uneven sparsity distribution. By contrast, if the data are not truncated, these problems will not occur. However, this will result in significant memory and computation consumption of CSDL. In order to overcome these problems, a novel CSDL method, a fast CSDL (FCSDL) algorithm, is proposed by combining the local orthogonal matching pursuit (OMP) algorithm with the conjugate gradient least-squares (CGLS) algorithm. The new method can achieve fast dictionary learning without truncating data and occupies very little memory. On this basis, an adaptive bearing fault diagnosis method based on envelope spectrum Kurtosis optimization is further proposed. When the sparsity is unknown, the new method can accurately search for the optimal sparsity and quickly recover the fault impact submerged in noise. The performance of the proposed fault diagnosis method is verified by using simulated signals, open bearing data, and wheelset bearing experimental data. It is compared with the union of a convolutional dictionary learning algorithm (UC-DLA) to highlight the advantages of the proposed method. The test code of reproducible research can be downloaded at https://github.com/aresmiki/FastCSDL .