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Effective damage identification is paramount to evaluating safety conditions and preventing catastrophic failures of concrete structures. Although various methods have been introduced in the literature, developing robust and reliable structural health monitoring (SHM) procedures remains an open research challenge. This study proposes a new approach utilizing a 1-D convolution neural network to identify the formation of cracks from the raw electromechanical impedance (EMI) signature of externally bonded piezoelectric lead zirconate titanate (PZT) transducers. Externally bonded PZT transducers were used to determine the EMI signature of fiber-reinforced concrete specimens subjected to monotonous and repeatable compression loading. A leave-one-specimen-out cross-validation scenario was adopted for the proposed SHM approach for a stricter and more realistic validation procedure. The experimental study and the obtained results clearly demonstrate the capacity of the introduced approach to provide autonomous and reliable damage identification in a PZT-enabled SHM system, with a mean accuracy of 95.24% and a standard deviation of 5.64%.