Structural Health Monitoring (SHM) techniques are key to monitor the health state of engineering structures, where damage type, location and severity are to be estimated by applying sophisticated techniques to signals measured by sensors. However, very localized damage detection algorithms applied to dynamics problems when dealing with rigid structures at low-frequency range remains still a big challenge. The last due to the low influence of very localized damage on the overall response of the structure (Saint-Venant principle). In this context, in the present work, we propose a methodology for locally correcting the models from collected data for elastodynamics problems at low-frequency range which is able to predict very localized damage. The proposed technique consists in enriching the structural model in a sparse way and solving the identification problem in the frequency domain, where the influence of damage over a large frequency band is exploited to improve the prediction of the damage location. The advantages and potential of the proposed technique are illustrated for the damage detection in a plate problem, demonstrating the advantages of the method in detecting very localized damage. The proposed technique is limited to a methodological description, and further developments should be considered to approach its applicability in an industrial scenario.