Masonry structures represent a substantial portion of the built environment in Italy and across Europe, often embodying considerable historical, cultural, and architectural value. Their preservation is increasingly challenging due to material degradation, inadequate maintenance, the climate change impact but most importantly as a consequence of recurrent seismic events. In this context, Structural Health Monitoring (SHM) represents a valuable strategy for achieving this objective. Additionally, given the specific peculiarities characterizing masonry structures, static monitoring emerges as a particularly suitable approach for the SHM of historical buildings. Nevertheless, environmental and operational conditions variability can introduce undesired trends in measured strain time series, potentially concealing structural response alteration associated with damage.

To address this, the proposed work presents a methodological comparison between two innovative static monitoring strategies aimed at such structures. The first is a fully data-driven approach integrating neural networks within the theoretical framework of nonlinear cointegration, enabling the extraction of monitoring features that are insensitive to environmental variability and sensitive to the onset of damage. These features allow the implementation of global as well as sensor-level control charts, enabling not only the identification of the damage occurrence but also the estimation of its magnitude and location, as well as the precise identification of damage occurrence through change-point analysis techniques. The second strategy, model-based, is rooted in the theory of model class selection: by employing numerical and surrogate models associated with different damage scenarios, structural identification is performed via inverse calibration, pinpointing the most probable damage scenario occurred on the monitored building, according to a proper selection criterion, and estimating its severity and localization. The comparison between these complementary methodologies provides valuable insights for the advanced monitoring and safeguarding of masonry-built heritage.