Blind source separation of convolutive mixtures towards modal identification

Abstract

Blind source separation (BSS) based signal processing techniques have shown significant promise for ambient modal identification of structural and mechanical systems. Many of these methods operate on the assumption that the underlying sources are mixed instantaneously, known as the instantaneous mixing model. If the data contains time synchronization (TS) errors, such as offsets and drifts commonly associated with wireless sensor networks, the equations of motion cannot be reduced to the instantaneous form in the time domain, and must be treated as convolutive mixtures. While other avenues such as time-synchronization protocols exist in the literature to address TS issues, an alternate algorithmic solution within the modal identification framework is presented here. In the proposed method, the convolutive mixtures of measurements are first transformed into instantaneous mixtures in the frequency domain, and then the complex BSS method is employed to separate the independent sources in the transformed domain. Finally, inverse Fourier transform is employed to transform the sources back into the time domain. The application of this algorithm is demonstrated using simulation examples. © The Society for Experimental Mechanics, Inc. 2012.