Rank aggregation to predict the fundamental frequency of historic masonry towers

The fundamental frequency is a key dynamic parameter for evaluating the seismic vulnerability and structural integrity of historic masonry towers. Its estimation with empirical laws is feasible but it is often complicated by the variability in geometric features, material properties, and boundary conditions. This work proposes an original methodology that combines multiple predictive empirical models and laws using a rank aggregation approach based on the Plackett-Luce model. Rather than selecting a single law, the method considers results from empirical equations and data-driven models to produce a unified and more reliable prediction. Two distinct estimation scenarios are examined: one relying exclusively on geometric properties, and another that also takes into account mechanical features. Both are trained and validated on a broad dataset of historic masonry towers. The novelty of the approach lies in its ability to integrate different sources of knowledge while reducing individual model errors. Since many structural characteristics of the towers may be unknown, this method seeks to combine models with different input features, ranging from complex models to simpler formulations based on easily measurable parameters. By exploiting the best features of each candidate and by ranking their contributions, the method shows improved performance across different towers. This strategy can be a valuable tool in structural health monitoring and seismic assessment of heritage towers, especially when experimental dynamic data are not available and when dealing with complex modeling uncertainties.