Underdetermined Blind Source Separation Based on Source Number Estimation and Improved Sparse Component Analysis

The signal acquisition process is limited by the installation position and number of sensors in particular types of equipment. Moreover, the observed signals are often compounded by all sources. In order to solve these problems, an underdetermined blind source separation (UBSS) approach with source number estimation and improved sparse component analysis (SCA) is studied. Firstly, the angular probability distribution of scatter as one of measures is obtained in time-frequency (TF) domain based on the sparsity of observations. Meanwhile, the energy sum of each frequency bin as another measure is calculated to eliminate the influence of poor sparsity or non-sparsity. Source number estimation can be obtained by selecting a small peak value between the above two measures. Then, the frequency bins corresponding to these peaks of the energy sum are clustered into two categories, whose first row in cluster center matrix is regarded as the corresponding column of estimated mixing matrix. Finally, the combinatorial algorithm of L1-norm is used to realize the estimation of source signals. Simulation results demonstrate that the proposed method can effectively separate the simulated vibration signals and is more accurate than traditional clustering and hyperplane space methods. Additionally, the natural frequency and damping ratio of modal response can be accurately identified in the test of measured cantilever beam hammering.