Circular structures are used in a wide variety of engineering mechanisms and devices. In this paper, an effective algorithm on the basis of the complex mappings is proposed to identify defects in circular structures using Cartesian damage detection techniques. The efficacy of the proposed algorithm is demonstrated through damage identification in circular plates using the Cartesian wavelet analysis. The vibration and thermal responses of the structure, as two important structural signals, are imported into the proposed algorithm to evaluate the abilities of the signals in identifying the damage location and severity. Finally, two experimental tests are conducted to explore the efficacy of the proposed algorithm in real applications.