Experimental Validation on a Real-World Truss Structure of a Damage Localization Method Based on Mode Shape Derivatives

Damage detection and localization analysis have gained increasing importance over the years, due to the growing number of catastrophic events and the associated risks that small, undetected cracks in structures may evolve into severe failures if not identified in time. In this context, vibration-based methods have been extensively investigated for structural damage detection. Among them, one of the most widely used approaches since its introduction is the curvature method. It has been successfully employed in numerous studies, consistently providing reliable results. However, the use of second-order or higher-order derivatives can be challenging when dealing with experimental data, as these are highly sensitive to measurement noise. Conversely, using the first derivative may simplify the analysis while maintaining robustness. Therefore, the present work introduces and experimentally demonstrates an extension of the curvature-based approach, focusing on the integration of the first derivative for damage localization. In particular, both methods based on the use of the second and first derivatives were applied to detect their capability in detecting and localizing the damage. This was tested on a slender truss structure, with induced damages at different locations, equal to just 1.069% of the structure volume. The results, obtained from this real-world case study, show that for certain structures, like slender ones, the use of the first derivative can achieve equal or even superior damage detection performance compared to the traditional second derivative method. Specifically, the comparison was evaluated based on the accuracy in localizing the damage with the two methods, both from a visual and quantitative point of view, since a deviation index δ was also introduced.