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After a damaging earthquake, assessment of the residual seismic capacity is required for large parts of the building stock. Increased vulnerability of structures together with the threat of immediate aftershocks call for rapid and objective decision making. Structural identification has the potential to reduce parameter-value uncertainties of physics-based models through interpreting measurement data. Significant amounts of uncertainty are associated with the non-linear behaviour of structures during extreme events such as earthquakes. Therefore, a structural identification methodology that accommodates multiple sources of systematic modelling uncertainties is used. Error-domain model falsification (EDMF) enables structural identification through combining damage grades observed by visual inspection with fundamental frequencies that are derived from ambient vibrations. Parametric uncertainties of a hysteretic model are reduced with the two information sources in order to extrapolate the vulnerability of the building regarding future earthquakes. The applicability of the methodology is shown using measurements made on a mixed reinforced-concrete unreinforced-masonry building tested on a shaking table. Based on nonlinear time-history analyses involving single-degree-of-freedom models, EDMF leads to more precise, yet robust, vulnerability predictions of earthquake-damaged buildings when compared with prediction ranges that are obtained without data interpretation.