Source identification of propagating waves inside a network
Résumé
The localization of short events arising within a network subsequently leading to wave propagation into it, is of interest in many applications. This work extend (Caputo et al. , 2019) which demonstrated the identifiability of a source from two detectors in a N nodes graph. We show that, rather than a source, a boundary condition identification is also possible and demonstrate a generalyzed unicity result. Furthermore, we extend the identification algorithm proposed in (Caputo et al. , 2019) to an arbitrary number of sensors, and estimate its complexity which depends on sensors number Ns and time dicretisation Nt . Increasing detectors number increases source identification robustness to noise up to a cut-off number being a small raction of N . This cutt-off detector density for efficiency in noise reduction is of practical significance. We also analyze and discuss the method sensitivity to total recording time Te , sampling frequency, and signal to noise ratio. Finally we propose a pre-sectorisation to improve the systematic exploration algorithm proposed in (Caputo et al. , 2019) and we show a O(N) drop in complexity leading to a O(N ³) cost for the source identification. Several tests of the method on model and real graphs confirm and support the presented results.
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