An increase in the number of incidents involving steel bridges in recent years, has made it necessary to analyze their safety. So far, researchers have proposed several methods to determine the dynamic behavior of steel bridges, distinguish changes in their behavior, extract dynamic specification, and detect damage in them. In the present study, an applied algorithm and a new damage index based on the time-frequency matrix and least-square distance have been proposed and used to determine the damage and detect its location. The performance of the suggested index to identify the damage in the numerical model of two steel beam with 31 damage scenarios were investigated. In addition, the LS-index was assessed for damage diagnosis in the analytical model of the College Bridge. The finite element model (FEM) of College Bridge was created based on extensive in-situ measurements and laboratory tests, and 10 different damage scenarios were considered. The results showed the ability of the proposed index to identify damage in the girder of the bridge. The obtained results suggested that the index can also report the damage simultaneously. The performance of the proposed method was also investigated using noise-polluted signals with 3 different SNRs. Based on the calculations, the index had a good performance. To diagnose damage, there is no need to measure the input loading. Besides, it is not necessary to create a numerical model. Owing to the applicability, accuracy, and high ability, the damage index can be used to detect damage in the steel girders of bridge decks.
