An Effective Two-Stage Clustering Method for Mixing Matrix Estimation in Instantaneous Underdetermined Blind Source Separation and Its Application in Fault Diagnosis

The underdetermined blind source separation (UBSS) has been considered to be a novel signal processing technique, which can separate the fault source signals from their mixtures. The mixing matrix estimation is a major step in the UBSS, this paper focuses on boosting the accuracy level of the estimated mixing matrix in the underdetermined case. Since the traditional clustering algorithms may not capture the signal characteristics well and secure a satisfactory estimation of the mixing matrix, an effective two-stage clustering algorithm is proposed to estimate the mixing matrix through a combination of hierarchical clustering and K-means. More specifically, first, the sum of frequency points energy in the time-frequency (TF) domain is calculated to estimate the number of source signals before clustering, and the initial clustering centers are obtained with a hierarchical clustering algorithm. Second, after eliminating outliers deviating from the initial clustering centers with the cosine distance, the new clustering centers are obtained by recalculating the mean value of each sub-cluster. Finally, the new clustering centers are set as the initial clustering centers of the K-means algorithm to estimate the mixing matrix. Extensive simulations and experiments show that the proposed method can effectively separate the source signals and ensure an estimate of the mixing matrix that is substantially more accurate than the K-means algorithm alone.