During the last decades, extensive research has been conducted on structural health monitoring (SHM) techniques based on the changes of coupled structure properties, e.g. piezoelectric impedance, which enjoys high detection sensitivity due to high-frequency actuation/sensing nature. However, the actual identification of fault locations and severities remains to be challenging owing to underdetermined underling mathematics. Recently, compressed sensing, a signal processing technique originally developed to recover signals from the compressed measurements, has shown its potential to address some of the mathematical challenges encountered in SHM practices. In this research, we morph the impedance-based SHM problem into a compressed sensing scheme such that the impedance change are used as measured data to reconstruct the damage locations and severities through convex optimization, e.g. l1 optimization. The proposed approach offers practical attractions of only requiring a small number of measurements and a short amount of computational time, and the results are promising if certain properties are fulfilled. Finally, the proposed approach is applied to and validated by several test problems.

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