Machine-Learning-Aided First Natural Frequency Estimation for Masonry Building Archetypes

Masonry buildings represent a significant portion of the existing building stock and are particularly vulnerable to seismic actions, making their reliable dynamic characterization essential for seismic assessment, risk mitigation, and retrofit prioritization. Among their global dynamic properties, the first natural frequency is especially relevant, as it reflects the combined influence of geometry, stiffness, mass distribution, material properties, and boundary conditions. However, its estimation often requires experimental testing or detailed numerical modeling, which may not be practical for preliminary or large-scale applications. This study presents a data-driven framework for predicting the first natural frequency of linear-elastic, fixed-base unreinforced masonry (URM) building archetypes using finite element modeling, machine learning algorithms, and regression-based formula development. A parametric database composed of 147 masonry structural models was generated in Abaqus, considering plan width, plan length, structural height, modulus of elasticity, and wall density as input variables. Modal analyses were performed to obtain the corresponding frequency values, which were then used to train and evaluate random forest (RF), XGBoost, LightGBM, CatBoost, and multilayer perceptron models. Because several numerical realizations shared the same underlying geometry, model performance was assessed using group-based nested five-fold cross-validation, with Group-K-Fold applied in both the inner hyperparameter-optimization loop and the outer performance-evaluation loop. Linear and symbolic regression were also implemented to derive explicit equations for practical use. The main contributions of the study are the development of a parametric FE-based database for URM frequency prediction, the use of geometry-grouped nested cross-validation to assess generalization to unseen configurations, and the derivation of explicit regression-based equations as interpretable alternatives to black-box machine-learning models. The multilayer perceptron achieved the best predictive performance for previously unseen geometry groups within the adopted FE-generated database, with an average outer-test R2 of 0.9567±0.0114, MAE of 0.4602±0.1470 Hz, and RMSE of 0.6706±0.1967 Hz, followed by CatBoost. In addition, symbolic regression provided an explicit nonlinear equation with a favorable balance between prediction accuracy and interpretability. The reported performance therefore reflects prediction within the considered numerical archetype space and should not be interpreted as independent validation against real masonry buildings.