Generalized Local Curvature Modal Information Entropy (GLCME) for Mitigating Nodal Blindness in Beam Damage Assessment

Aiming at the inherent limitation of the curvature mode (CM) index, i.e., its insensitivity to damage near mode shape nodes, this study introduces the concept of generalized local curvature modal information entropy (GLCME) into the CM analysis framework, leveraging the significant potential of information entropy in enhancing damage identification sensitivity. The mathematical formulation of GLCME is rigorously derived, and the corresponding damage index is constructed and optimized by utilizing the characteristics of high-order mode shapes. Numerical models of a simply supported beam and a continuous beam bridge are established to extract and process structural dynamic parameters. Meanwhile, physical tests on a simply supported steel beam are conducted to obtain measured dynamic data for cross-validation. Both CM and GLCME are employed as inputs to a feed-forward neural network (NN) for damage identification, and their performance is systematically compared. The results demonstrate that GLCME enables reliable damage localization and quantification when used as the NN input. Notably, it exhibits significantly higher accuracy and sensitivity than traditional CM, especially in identifying damage near mode shape nodes. The two indices form complementary performance: CM is more suitable for damage far from nodes, while GLCME effectively addresses the challenge of damage identification in nodal regions, providing a more comprehensive technical solution for structural health monitoring of complex bridge structures.