As civil engineering structures are growing in dimension and longevity, there is an associated increase in concern regarding the maintenance of such structures. Bridges, in particular, are critical links in today's transportation networks and hence fundamental for the development of society. In this context, the demand for novel damage detection techniques and reliable structural health monitoring systems is currently high. This paper presents a model-free damage detection approach based on machine learning techniques. The method is applied to data on the structural condition of a fictitious railway bridge gathered in a numerical experiment using a three-dimensional finite element model. Data are collected from the dynamic response of the structure, which is simulated in the course of the passage of a train, considering the bridge in healthy and two different damaged scenarios. In the first stage of the proposed method, artificial neural networks are trained with an unsupervised learning approach with input data composed of accelerations gathered on the healthy bridge. Based on the acceleration values at previous instants in time, the networks are able to predict future accelerations. In the second stage, the prediction errors of each network are statistically characterized by a Gaussian process that supports the choice of a damage detection threshold. Subsequent to this, by comparing damage indices with said threshold, it is possible to discriminate between different structural conditions, namely between healthy and damaged. From here and for each damage case scenario, receiver operating characteristic curves that illustrate the trade-off between true and false positives can be obtained. Lastly, based on the Bayes' Theorem, a simplified method for the calculation of the expected total cost of the proposed strategy, as a function of the chosen threshold, is suggested.