Identification and Localization of Structural Damage Using the Second-Largest Eigenvalue of the Mutative-Scale Symbolic Matrix as the Damage Indicator

Time series–related methods in structural damage detection have gained increasing recognition due to their effectiveness, yet they face limitations in accuracy and efficiency for data processing, particularly in damage localization. In this study, we propose a novel method that utilizes a mutative-scale symbolic matrix, which extracts the second-largest eigenvalue as a damage indicator, to address the difficult problems of damage detection under random excitation. Unlike the conventional symbolized time series method, the mutative-scale symbolic matrix method selects data from the virtual impulse response function series at specific intervals, based on the Pearson correlation coefficient, and uses these data with the intervals to construct the mutative-scale symbolic matrix through joint occurrence entropy. The second-largest eigenvalue of the matrix is identified as an effective damage indicator which significantly magnifies the variations in structural characteristics. Damage localization is achieved by exploring damage occurrence between different reference and measurement points, and the flexibility in selecting these points enables a more precise determination of the damaged area according to the technology process based on dichotomy. A 10-DOF numerical model subjected to random Gaussian white noise is initially employed to validate the accuracy of the damage indicator for damage identification and localization. Subsequently, upon experimental application to a testbed structure, the proposed method exhibited super robustness in data selection under different damage types, with higher computational efficiency than conventional methods.