Predicting flexural strength of hybrid FRP-steel reinforced beams using symbolic regression and ML techniques

Hybrid fiber-reinforced polymer (FRP) and steel reinforced concrete (hybrid FRP-steel RC) beams have gained recognition for their exceptional flexural performance, surpassing that of beams reinforced exclusively with FRP bars (FRP-RC). However, current design guidelines, such as ACI 440.11-22, fail to accurately predict the flexural strength of these hybrid systems. This study aims to enhance the predictive accuracy and interpretability of flexural strength models by applying advanced computational approaches-specifically, machine learning (ML) techniques and symbolic regression. A robust dataset of 134 experimental data points was utilized to develop predictive models. The prediction results showed that both ML and symbolic regression models significantly outperformed the ACI 440.11-22 equations, achieving lower errors (MAE, MAPE, RMSE) and higher accuracy (R²). The results demonstrate that the ML models-Gaussian process regression (GPR), NGBoost, and CatBoost-achieved high predictive accuracy, with mean R² values approaching 1.0 and MAPE% as low as 5.19 (training) and 11.51 (testing) for GPR. Furthermore, symbolic regression yielded a transparent mathematical expression with a mean prediction ratio (µ) of 1.003, a CoV of 0.139, and a MAPE% of 11.08. These findings highlight the practical and technical advantages of symbolic regression in developing reliable, interpretable, and efficient design equations for hybrid FRP-steel RC beams.