Vibration-based methods for damage detection have been widely used, particularly those relying on ambient excitations. These methods are based on the principle that changes in a structure's physical properties, such as mass, stiffness, and damping, will lead to changes in its vibration characteristics. A promising area of research focuses on utilizing operational loads, such as vehicular traffic, instead of ambient excitations. Dynamic responses generated by operational loads, such as trains, induce higher levels of vibration compared to those caused by temperature variations or ambient vibrations. The consistent and repeatable nature of this load can also reduce the time required for training predictive models. Furthermore, as vehicles cross the bridge from end to end, structural damage, even if localized, will generate anomalies in the dynamic responses, which may be detectable by sensors installed in the structure. With a higher signal-to-noise ratio, this approach enables more efficient and cost-effective monitoring systems. This paper presents a data-driven approach for identifying damage in railway bridges based on train-induced dynamic responses. In this methodology, nonlinear autoregressive models with exogenous inputs (NARX) are developed for different sensor clusters, using the structure's free response after train excitations. The damage index is defined based on the prediction errors of each NARX. The effectiveness of the proposed methodology is validated using real acceleration data from a long-span steel-concrete composite bowstring arch railway bridge. Changes in the longitudinal stiffness of the bearing devices were identified through acceleration data recorded during the passage of Alfa Pendular trains.