Rank Aggregation of Fundamental Frequency Estimation Laws for Historic Towers

The estimation of the fundamental frequency in historic masonry towers remains a challenge due to uncertainties in material properties, structural configurations, and boundary conditions. Empirical formulations provided by national codes and literature are often used, in order to avoid experimental tests, which can prove costly, especially in tall towers. This study uses the concept of rank aggregation, based on the Plackett-Luce model, to enhance the prediction of fundamental frequency in bounded historic masonry towers. By integrating eight different empirical formulations based on geometric parameters, the methodology optimally combines the different laws to generate a new aggregate estimate. This rank aggregation strategy is trained on an extensive historic tower dataset and then validated through an experimental dataset coming from a number of Italian towers. The resulting reference ranking list demonstrates the effectiveness of the Plackett-Luce model in prioritizing the most reliable formulations while minimizing variance. This study further enhances fundamental frequency estimation by fitting datasets to distributions, ensuring a robust and adaptable framework for ranking empirical formulations, which is a relevant parameter for the seismic assessment of these cultural heritage assets.