*Article* **Damage Identification Method for Medium- and Small-Span Bridges Based on Macro-Strain Data under Vehicle–Bridge Coupling**

**Hao Zhang 1,2,\*, Zhixin Zhong 3, Junmiao Duan 4, Jianke Yang 3, Zhichao Zheng <sup>3</sup> and Guangxun Liu <sup>3</sup>**


**Abstract:** The damage identification method based on macro-strain modality has shown good results for large-span flexible bridges. However, medium- and small-span bridges have a high stiffness, and the axle system is embodied. The strong time-varying vibration characteristics, coupled with the non-stationary characteristics of vehicle loads, make it difficult to accurately determine the stable strain modes of such bridges. To solve this problem, a damage localization index in the form of an amplitude vector matrix of the mutual energy density spectrum based on macro-strain was constructed using wavelet transform de-noising and reconstruction technology and cross-correlation function. The macro-static strain and macro-dynamic strain data obtained from a vehicle–bridge coupling experiment were reconstructed through wavelet transform, and the factors influencing the damage indices were analyzed. The results showed that the proposed indicators could help realize an accurate damage localization for medium- and small-span bridge systems with different damage degrees under the action of vehicle–bridge coupling.

**Keywords:** macro-strain mode; medium- and small-span bridges; wavelet transform; crosscorrelation function
