Spectral sparse random feature decomposition and its application in rotating machinery composite fault diagnosis

Abstract Sparse random mode decomposition (SRMD) is a new signal decomposition method that integrates sparse random feature models with clustering methods. The method firstly represents the input signal as a series of sparse random feature points in time-frequency space, then employs clustering algorithms to cluster these sparse feature points into different modes, and finally decomposes the signal into a series of modes. Due to its excellent signal decomposition capability, SRMD has been applied in various fields, including mechanical fault diagnosis, biological signal processing, and image processing. However, the performance of SRMD is constrained by its own hyperparameters, and the results are strongly influenced by the clustering method. To overcome these shortcomings, the spectral sparse random feature decomposition (SSRFD) is proposed. In the process of representing a signal as sparse random features, we design the fault characteristic frequency amplitude energy ratio (FCFAER) index and employ the zebra optimization algorithm (ZOA) to select two key parameters: window length and relative error coefficient. Thus, an optimal sparse spectrum representation of the signal is obtained to alleviate the effects of SRMD hyperparameters; in the process of mode separation, the sparse random feature correlation spectrum (SRFCS) is proposed, which indicates the frequency ranges of the sparse random feature points corresponding to different modes within the sparse spectrum of the signal. Lastly, the automatic division of SRFCS is realized through parameterless scale space division, so that the sparse random features can be reasonably classified and clustered into modes respectively, and the separation of different modes in the signal can be realized without using the clustering method. Finally, the viability and usefulness of the proposed method are proved through composite fault data from the rolling bearings and the RV reducer gears in rotating machinery. The results show that the method has good composite fault characteristics separation and extraction capability.