Nonlinear Mixture Signal Separation With the Extended Slow Feature Analysis (xSFA) in Fiber-Optic Distributed Acoustic Sensor (DAS)

Fiber-optic distributed acoustic sensor (DAS) has been applied to various large-scale infrastructure monitoring areas in smart cities, leading to a new generation of fiber-optic Internet of Things for ground listening. However, its single-source detection and recognition methods may fail in unpredictable multi-source interfering environments in urban. When an unknown number of sources are nonlinearly mixed at the DAS's fiber receiver, it increases the difficulty of multiple source separation further. Therefore, in this paper, it is proposed a novel multi-source separation method in fiber-optic DAS to separate individual vibration signals from the unidentified nonlinear mixing procedure with unknown number of sources. Firstly, the mixed source number is blindly estimated by utilizing the Gerschgorin disk estimator (GDE), which is effective and robust in real-field applications of DAS. Secondly, the statistically independent sources are separated with the extended slow feature analysis (xSFA) according to the nonlinear instantaneous mixing model constructed for DAS in this paper, which considers the complexity of the vibration wave propagation to the subsurface fiber. It relies on the temporal correlation to recover structure of the source signals that has been destroyed in the nonlinear mixing procedure. Finally, evaluation indices for separation are studied and the effectiveness of both the multi-source separation and the source number estimation are verified through simulation experiments and field tests. Compared with the two benchmark methods of fast independent component analysis (FastICA) and the independent slow feature analysis (ISFA), it shows the complicated nonlinear mixture of DAS signals can be separated with higher reliability in both the artificially and the real-field mixed cases.