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<p>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 (R<sup>2</sup>). The results demonstrate that the ML models—Gaussian process regression (GPR), NGBoost, and CatBoost—achieved high predictive accuracy, with mean R<sup>2</sup> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月25日

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  • Khaled Megahed

摘要

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.