Orthogonal matching pursuit algorithm based on a time-varying parameter dictionary and refined secondary selection and its application in rolling bearing fault diagnosis

The performance of the orthogonal matching pursuit (OMP) algorithm in extracting the impacts of bearing faults is crucial for early fault detection in industrial applications. This approach largely depends on the constructed dictionary and the number of iterations. Traditional correlation filtering methods, which are used to determine dictionary parameters, are susceptible to noise, and dictionary atoms with fixed parameters are difficult to adapt to time-varying fault impact characteristics. Additionally, during the sparse decomposition stage, the use of excessive iterations can result in the OMP algorithm reconstructing signals with significant interference components. In this paper, a time-varying parameter and refined secondary selection-based orthogonal matching pursuit (TPRSS-OMP) algorithm are presented. Through time-domain partitioned correlation filtering and K-means clustering, the wavelet parameter interval of the dictionary is determined by utilizing the periodic characteristics of fault impact signals and interval shrinkage methods to construct a wavelet dictionary with time-varying parameters. In the process of calculating the sparse coefficients, the secondary selection-based orthogonal matching pursuit (SS-OMP) algorithm is optimized by directly considering the change in the envelope spectrum kurtosis of the signal reconstructed from the selected atoms. A simulation and three sets of experimental analyses show that the dictionary constructed with the proposed method closely matches the fault characteristics of the signal and can be used to accurately reconstruct the fault impact components of the signal.