Structural Health Monitoring (SHM) is a means of identifying damage from the structural response to environmental loads. Real-time SHM offers rapid assessment of structural safety by owners and civil defense authorities enabling more optimal response to major events. This research presents an real-time, convex, integral-based SHM methods for seismic events that use only acceleration measurements and infrequently measured displacements, and a non-linear baseline model including hysteretic dynamics and permanent deformation. The method thus identifies time-varying pre-yield and post-yield stiffness, elastic and plastic components of displacement and final residual displacement. For a linear baseline model it identifies only timevarying stiffness. Thus, the algorithm identifies all key measures of structural damage affecting the immediate safety or use of the structure, and the long-term cost of repair and retrofit. The algorithm is tested with simulated and measured El Centro earthquake response data from a four storey non-linear steel frame structure and simulated data from a two storey non-linear hybrid rocking structure. The steel frame and rocking structures exhibit contrasting dynamic response and are thus used to highlight the impact of baseline model selection in SHM. In simulation, the algorithm identifies stiffness to within 3.5% with 90% confidence, and permanent displacement to within 7.5% with 90% confidence. Using measured data for the frame structure, the algorithm identifies final residual deformation to within 1.5% and identifies realistic stiffness values in comparison to values predicted from pushover analysis. For the rocking structure, the algorithm accurately identifies the different regimes of motion and linear stiffness comparable to estimates from previous research. Overall, the method is seen to be accurate, effective and realtime capable, with the non-linear baseline model more accurately identifying damage in both of the disparate structures examined.