Efficient Bayesian Updating with Physics-Based Reduced Models for Heritage Structure Monitoring

The preservation of Cultural Heritage structures demands reliable and non-invasive strategies to assess their structural integrity and support sustainable conservation. Structural health monitoring (SHM) through operational modal analysis (OMA) is a wide extended technique, due to its no invasiveness and relatively low cost. In many advanced applications, the identified modal data are used to update a finite element (FE) model so that damage- or deterioration-sensitive mechanical parameters can be tracked over time. However, embedding this model-updating process into a rigorous probabilistic framework to account for uncertainties is often prohibitive, since Bayesian inference requires a large number of FE evaluations. A common workaround is to replace the FE model with a data-driven surrogate, but this may weaken the physical interpretability of the results. This study proposes a physics-informed reduced-order FE model that preserves the essential dynamic features of the structure while significantly lowering computational burden. The methodology is applied to the Hospital Real in Granada (Spain), a sixteenth-century masonry complex currently monitored within the European BUILDCHAIN project. Ambient vibration data from a permanent monitoring system are combined with Bayesian inference to update the model parameters and assess uncertainty in the modal properties. The results demonstrate that physically interpretable reduced models can bridge the gap between data-driven and physics-based approaches, enabling efficient and transparent uncertainty quantification.