Structural Health Monitoring faces several challenges. Among them, especially for the quantification of damage, are (1) the uncertainty in the boundary conditions, (2) the need for a calibrated numerical model, or measurements, of the structure in its healthy state, (3) the variability in the structure properties and boundary conditions due to environmental and operational conditions and (4) the possibility of damage in the virgin structure due to construction defects. Based on the sparsity condition of structural damage, this work presents a method that tackles these challenges simultaneously. The method consists in synthesising the response of a healthy-structure model, which is valid in the current environmental and operational conditions, only inside a region of interest (ROI) that excludes the boundaries and the rest of the full structure. This is accomplished by means of a robust regression of the solution of an analytical model of the healthy structure, and its loading, only using testing data of the (possibly) damaged structure in that ROI. Under ideal conditions, the method showed to be exact in detecting, locating and quantifying damage, in some cases much better than using measurements of the virgin structure. Finally, the method was tested by numerical simulations and using experimental data, under realistic conditions, which evidences its practical applicability.Fil: Garrido, Carlos Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería. Instituto de Mecánica Estructural y Riesgo Sísmico; ArgentinaFil: Domizio, Martin Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería. Instituto de Mecánica Estructural y Riesgo Sísmico; ArgentinaFil: Curadelli, Raul Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería. Instituto de Mecánica Estructural y Riesgo Sísmico; ArgentinaFil: Ambrosini, Ricardo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería. Instituto de Mecánica Estructural y Riesgo Sísmico; Argentina