Unraveling Mixtures: A Novel Underdetermined Blind Source Separation Approach via Sparse Component Analysis

Underdetermined blind source separation (UBSS) is a critical technique in the field of intelligent mechanical operation and maintenance that allows for the disentanglement of source signals from their mixtures without the need for prior knowledge or extensive sensor information. The accuracy of source signal recovery depends on the estimation of the mixing matrix. To promote sparsity in source signals, we employed methods such as sparse representation and sparse component analysis. Traditional approaches, such as the Short-Time Fourier Transform (STFT), often suffer from limited time-frequency resolution, motivating the adoption of the Synchronous Extraction Transformation (SET) algorithm, which closely approximates the ideal time-frequency transform. SET significantly enhances the sparsity of the signals, thus facilitating the separation of the mixed signals. In the context of sparse component analysis, we introduce an improved density peaks clustering (DPC) method that successfully resolves source number estimation issues and robustly eliminates outliers. This improvement leads to a more accurate mixing matrix estimation. To determine the cluster centers, we employed K-means clustering, further refining our source separation process. In summary, our study presents an innovative approach that combines the Synchronous Extraction Transformation (SET) with ‘an improved density peaks clustering (DPC)’ method and K-means for mixing matrix estimation. Source signal recovery was achieved using the shortest-path algorithm. Extensive simulations and experiments validate the effectiveness of the method, outperforming the traditional techniques. When applied to rolling bearing fault diagnosis, the proposed approach effectively separates complex signals and accurately identifies the fault characteristic frequencies.