A blind source separation method for time-delayed mixtures in underdetermined case and its application in modal identification

Abstract

A novel blind source separation (BSS) method for time-delayed mixtures in underdetermined case is studied in this paper. The proposed method not only addresses the problem of source separation with limited sensors but also avoids the influence of propagation delay. Firstly, the sparse domain is converted by utilizing the spectrum of observed signals to perform modulus operation in time-frequency (TF) domain, which appears several clustering lines in the scatter plot. Secondly, based on the linear clustering features of observed signals in the sparse domain, the angular probability distribution of preprocessing scatter is calculated to estimate the source number. Thirdly, the frequency bin corresponding to the peak of distance between scatter and original point is selected to construct the binary TF mask according to the estimated source number, and then the spectrum of recovered source is obtained via mask. Finally, the estimated sources considering padding line are calculated to eliminate the boundary effect in time domain. Experimental results demonstrate that the proposed method can effectively recover the simulated vibration sources with time-delayed mixtures in underdetermined case. In addition, two experimental validations manifest that compared with state-of-the-art algorithms, the proposed method improves signal separation performance and identifies the natural frequency of monomodal response successfully.