Data-Driven Approaches for Predicting the Natural Frequencies of Masonry Minarets

Historical masonry minarets are particularly susceptible to earthquake-induced damage because their slender configuration is combined with the inherently low tensile capacity and limited ductility of masonry. Reliable characterization of their dynamic properties is therefore an important prerequisite for seismic evaluation and the planning of appropriate conservation measures. In this study, a data-driven methodology is developed to estimate the first and second natural frequencies of masonry minarets. A database comprising 1146 finite element models with different mechanical properties, representing 191 unique geometry groups, was developed through parametric modal analyses in Abaqus. The predictor set comprised total height H, lower and upper inner diameters D0 and Dtop, wall thickness t, base dimension B, and the stiffness–density-related parameter E/ρ. Random Forest, XGBoost, LightGBM, and CatBoost models were evaluated using geometry-grouped nested five-fold cross-validation, while explicit equations were derived using linear and symbolic regression. CatBoost achieved the best overall machine-learning performance, with mean outer-test R2 values of 0.9597 and 0.9610 for f1 and f2, respectively. SHAP analyses identified total height and E/ρ as the dominant predictors. Symbolic regression provided substantially more accurate explicit equations than linear regression and achieved predictive performance comparable to the best machine-learning-based models. An additional mechanically scaled geometry-only baseline achieved mean outer-test R2 values of 0.8222 and 0.8217 for the first and second frequencies, respectively, improving on ordinary additive linear regression while remaining less accurate than the more flexible models. The proposed framework provides an accurate, interpretable, and computationally efficient surrogate for predicting finite element-derived natural frequencies within the investigated parameter domain. However, the reported predictive performance reflects agreement with the numerical reference models, and experimental validation is required before applying the proposed models to existing masonry minarets.