Structural damage detection based on coherence-statistical analysis of Volterra kernels

Nonlinear characteristics in structural dynamic behavior may impair the effectiveness of damage detection methods reliant on linearity assumption. This article introduces a truncated Volterra-Wiener model for system identification, employing Volterra kernels as distinctive features to detect both linear and nonlinear structural damage. The short-time temporal coherence (STC) is utilized to evaluate the alterations in the Volterra kernels resulting from damage. Based on the statistical analysis on STC characteristic parameters of Volterra kernels, two innovative damage detection approaches are proposed: the threshold-based approach and the statistical indicators-based approach. The former involves determining damage threshold values using a statistical hypothesis testing based on the STC-statistical properties of the kernels for the intact structure. Alternatively, the latter employs the statistical indicators of STC characteristic parameters to perform damage identification, utilizing the kernels identified from multiple tests. To demonstrate the system identification process and investigate the two damage detection approaches, numerical studies were conducted on a cantilever beam. The results show that both approaches can effectively identify the linear and nonlinear damage, and the STC characteristic parameters and statistical indicators clearly reflecting the damage severity. The threshold-based approach boasts higher detection efficiency, as it requires only one set of measurement signals for a given structure; however, it may occasionally encounter reliability issues. In contrast, the statistical indicators-based approach demands more testing and computation but provides superior accuracy in damage identification. Therefore, the threshold-based approach is ideal for preliminary and rapid damage alerting, while the statistical indicators-based approach is better suited for confirmed diagnosis.