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The concept behind electromechanical impedance spectroscopy is to use variable high-frequency structural vibrations with piezoelectric elements to monitor the local area of a structure for changes in mechanical impedance that may indicate imminent damage. Various mathematical models that correlate the structural impedance with the electric response of the piezoelectric sensors are presented. Several algorithms and metrics are introduced to detect, localize, and characterize damage when using electromechanical impedance spectroscopy. Applications of electromechanical impedance spectroscopy to study adhesive joints are described. Research and development of alternative hardware for electromechanical impedance spectroscopy is presented. 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