Deep symbolic regression for numerical formulation of fundamental period in concentrically steel-braced RC frames

Abstract

This research explores the use of Deep Symbolic Regression (DSR) to develop a sophisticated predictive model for the fundamental period of vibration in concentrically steel-braced reinforced concrete (RC) frames. Traditional empirical models often overlook complex interactions within structural dynamics during seismic events, a gap this study addresses by deriving tailored equations for various bracing configurations such as Cross bracing, Diagonal bracing, and Chevron bracing. The model development incorporates an iterative refinement process utilizing DSR techniques to enhance accuracy and applicability in predicting seismic responses. Further refinement and optimization are achieved using the L-BFGS-B algorithm, ensuring robustness and adherence to safety standards. Validation against actual structural data reveals that our proposed equations achieve high predictive accuracy, with R-squared values up to 0.8247 and RMSE values as low as 0.2119, consistently presenting lower error metrics across various configurations compared to those found in established seismic design standards, such as ASCE, Eurocode, and Japan’s Building Standards. Comparative analyses and Bland–Altman plots confirm that the models not only match but often surpass the accuracy of traditional formulas, validating their potential as reliable tools in structural engineering for earthquake resilience planning. The findings demonstrate DSR’s potential to revolutionize traditional practices in formulating empirical equations, offering a scientifically rigorous, data-driven methodology for more accurately predicting the dynamic responses of structures under seismic loads.