Early structural damage is often subtle and difficult to detect. To address this challenge, a damage detection method based on piezoelectric active sensing and numerical algorithms for subspace state space system identification (N4SID) is proposed. Since higher-order dynamic characteristics are more sensitive to early damage, piezoelectric active sensing in the high-frequency band is employed to test structural dynamics in the high-frequency band, since the high-frequency excitation and sensing are capabilities of the piezoelectric material. Then, the high-frequency response signals are processed by the N4SID algorithm to extract the higher-order dynamic parameters of the structure. Finally, the imaginary and real parts of the state matrix extracted by the N4SID, which contains the frequency and damping information of the structure, are derived to construct the damage index (DI). To validate the proposed method, experiments of a numerical simulation, a mass-reduced beam, and a crack in a composite fiber-reinforced polymer plate were conducted. Simulation results show that the proposed normalized DI increases monotonically as damage propagates. Results from multiple sets of repeated experiments demonstrate the same trend, confirming that the normalized DI can effectively detect the early-stage damage of structures. This demonstrates the applicability of the proposed method—extracting high-order dynamic changes via piezoelectric active sensing combined with the N4SID algorithm—in early-stage damage detection, thereby expanding the application scope of the N4SID algorithm.
Wang et al. (Mon,) studied this question.