Simply Supported Bridge Damage Identification Using a Generalized Information Entropy Index of Rotation Difference: Theoretical and Experimental Study

Accurate identification of damage in simply supported girder bridges and the timely implementation of protective measures are crucial to preventing structural failure. Rotation influence line-based methods offer a straightforward and cost-effective approach for bridge monitoring; however, their validation has primarily relied on numerical simulations, with a lack of rigorous theoretical explanation. To address this limitation, an analytical relationship between the rotation difference at cross-sections before and after damage and the moving load position is first derived using the principle of virtual work, thereby clarifying the theoretical mechanism underlying damage identification. On this theoretical basis, a novel generalized information entropy index of rotation difference is proposed by incorporating information entropy theory to quantify the local nonlinear response induced by damage. The proposed method is validated through numerical simulations conducted on a simply supported steel girder bridge model developed in ANSYS, as well as through comparisons with existing experimental datasets. The results demonstrate that the proposed index can accurately and stably identify both single and multiple damage locations in bridges, while requiring only two inclination sensors installed at the supports. Under varying damage locations and severity levels, the entropy response curves consistently exhibit distinct peaks corresponding to the actual damage positions, thereby confirming the physical consistency and practical applicability of the method. The strategy of combining a minimal sensor configuration with information entropy analysis significantly reduces system complexity and cost while maintaining identification accuracy, providing an efficient and economical solution for practical bridge health monitoring.