STM-based symbolic regression for strength prediction of RC deep beams and corbels

This study uses symbolic regression with a strut-and-tie model to predict the shear strength of reinforced concrete deep beams (RCDBs) and corbels (RCCs). Previous studies have proposed two distinct types of models for estimating shear capacity: explainable models based on theoretical derivations and black-box models derived from machine learning (ML) methods. This study proposes a hybrid model derived from the strut-and-tie model (STM), where the performance of STM is enhanced through the ML approach using genetic programming. This model is based on a comprehensive experimental database of 810 tests for the shear strength of RC deep beams and 371 tests for RC corbels from various research papers. The developed STM-based symbolic regression (SR-STM) integrates two distinct force-transferring mechanisms: the diagonal strut mechanism utilizing concrete strength and the truss mechanism utilizing orthogonal web reinforcement. The SR-STM model is both robust and interpretable, demonstrating high prediction accuracy with mean values of the prediction-to-actual ratios of 0.999 and 1.004 and coefficient of determination values of 0.913 and 0.862 for RCDBs and RCCs, respectively, while providing explainable mathematical expressions that align with the mechanical principles of STM. The developed SR-STM model is benchmarked against several state-of-the-art models and evaluated against the CatBoost ML technique, demonstrating acceptable performance. The results highlight the SR-STM model's effectiveness in providing reliable predictions and valuable insights for practical engineering applications. Furthermore, a SHAP (Shapley Additive Explanations) analysis was performed, and its results align with the SR-STM model, confirming the model's effectiveness in accurately capturing the key factors influencing the shear strength of RCDBs and RCCs.