Blind source separation of multi mixed vibration signal based on parallel factor analysis

Considering the problem of blind source separation without known number of sources for complicated mechanical system, this paper proposes a novel blind source separation (BSS) algorithm based on parallel factor analysis (PARAFAC). In the proposed method, the centralized sensor data are firstly divided into non-overlapping range blocks of fixed size, and single time-delay covariance matrices of each data block are calculated and stacked in a third-order tensor, i.e. parallel factor model; then the core consistency diagnostic is used to estimate the best components number of parallel factor model, thus the vibration source number can be obtained. Finally the mixing matrix is precisely estimated by parallel factor decomposition, and the source signals can be obtained. The unique identifiability of PARAFAC model must be satisfied under loose constraints, so the blind source separation can be solved by the proposed method. The simulation results prove that the proposed method can accurately estimate the mixing matrix from the multi-source mixture of non-stationary signal. Finally the proposed algorithm is used for the multi-source mechanical vibration test, and further verifies the efficiency of the proposed method.