## 3 Results and Discussions
### Damage Identification Method Based on Boundary Modes  
Based on the analysis in Section 3.3, the boundary modal characteristics exhibit a significant correlation with structural sealant damage. Based on this observed pattern, an optimization scheme for the modal test procedure was proposed: the number of data collection points was reduced from 49 in the full-plate distribution to 24 key nodes in the boundary region (a reduction of 51.02%), and the test time was shortened by 50% per condition, significantly improving testing efficiency.  
The comparative analysis in Figures 10 and 11 demonstrates that the peak of FCMD for the boundary damage nodes closely aligns with the results of the global modal analysis in terms of both damage localization effectiveness and sensitivity to the degree of damage. This further validates the superiority of the boundary modes for structural sealant damage identification. According to the analysis of engineering applicability, this scheme offers two main advantages: it reduces test time and improves efficiency, and it enhances operational feasibility by extracting only the panel boundary modes, excluding internal nodes, thus reducing experimental error. Additionally, it provides a valuable reference for practical engineering applications.  
While this study focused on unilateral debonding to establish fundamental detection thresholds, future work will extend validation to multi-edge and irregular damage patterns to further verify generalizability. The boundary-mode approach is theoretically adaptable to such scenarios through localized threshold calibration.  
The single-stage first-order curvature mode difference (FCMD) approach streamlines the curvature mode difference method, minimizing computational demands and error risks by employing a single, direct metric for damage identification. The introduction of a  
Figure 10: First-order curvature mode difference under identical damage degree (**a–d**) at the boundary of (**a**) Condition 2; (**b**) Condition 3; (**c**) Condition 4; (**d**) Condition 5.  
statistically derived, quantitative FCM threshold enhances the method's objectivity and reproducibility. By focusing on boundary FCM extraction, the approach significantly reduces experimental effort. Furthermore, the method shows potential for detecting both boundary and internal damage in thin-plate structures.  
The derived damage threshold (FCMD > 0.1205) achieved 100% accuracy in boundary damage identification across all tested conditions. However, two limitations emerged. The experimental scope did not include damage threshold calculations for diverse sample categories or configurations with varied layout sampling point densities. Furthermore, the current threshold determination methodology lacks comprehensive validation for universal applicability across different experimental conditions. The threshold was calibrated exclusively for boundary damage scenarios. Internal debonding (e.g., mid-panel damage) may require adaptive threshold adjustments, as suggested by [PERSON] et al. [39] for slab structures, where curvature mode sensitivity varies with spatial stiffness distribution. Laboratory conditions minimized ambient vibrations, but field applications may introduce noise. Integrating noise-suppression techniques, such as the Tikhonov regularization method [40], could enhance signal-to-noise ratios in practical settings.  
Although curvature modes are sensitive to noise, the boundary-focused FCM method demonstrates empirical robustness, as damage-induced peaks (e.g., 0.272 for 100% debonding) significantly exceed noise levels in undamaged regions (FCMD \(\leq\) 0.11). The 0.1205 threshold further safeguards against noise interference. Comparative studies with noise-robust alternatives [32; 33] remain a valuable future direction.