A new evolutionary polynomial regression technique to assess the fundamental periods of irregular buildings

The main seismic design codes propose simplified formulations to evaluate the fundamental period of regular structures based on the total height. Indeed, the fundamental period depends on several parameters directly connected to the mass and stiffness of the structure and on its geometrical characteristics, including also irregularities. This paper proposes a set of mathematical formulations to evaluate the longitudinal and transversal fundamental period of vibration of 3D Reinforced Concrete (RC) frames, which have various vertical and plan irregularities and for different mechanical and geometrical design parameters. Several types of Reinforced Concrete Bare Moment Resisting Frame (RC-BMRF) buildings have been designed according to the different versions of the Italian codes starting from 1916 to nowadays and then used as case studies. Modal analysis is performed on the entire building dataset to assess the fundamental periods in both longitudinal and transversal directions. Then, cluster analysis is carried out to classify the buildings based on similar design characteristics and construction details. Finally, a robust Evolutionary Polynomial Regression (EPR) technique is used to find the optimal polynomial forms of the natural period. Numerical results show a better performance of the proposed formulation compared with the existing methodologies available in the literature.