Probabilistic Shear Strength Prediction for Deep Beams Based on Bayesian-Optimized Data-Driven Approach

Abstract

To ensure the safety of buildings, accurate and robust prediction of a reinforced concrete deep beam’s shear capacity is necessary to avoid unpredictable accidents caused by brittle failure. However, the failure mechanism of reinforced concrete deep beams is very complicated, has not been fully elucidated, and cannot be accurately described by simple equations. To solve this issue, machine learning techniques have been utilized and corresponding prediction models have been developed. Nevertheless, these models can only provide deterministic prediction results of the scalar type, and the confidence level is uncertain. Thus, these prediction results cannot be used for the design and assessment of deep beams. Therefore, in this paper, a probabilistic prediction approach of the shear strength of reinforced concrete deep beams is proposed based on the natural gradient boosting algorithm trained on a collected database. A database of 267 deep beam experiments was utilized, with 14 key parameters identified as the inputs related to the beam geometry, material properties, and reinforcement details. The proposed NGBoost model was compared to empirical formulas from design codes and other machine learning methods. The results showed that the NGBoost model achieved higher accuracy in mean shear strength prediction, with an R2 of 0.9045 and an RMSE of 38.8 kN, outperforming existing formulas by over 50%. Additionally, the NGBoost model provided probabilistic predictions of shear strength as probability density functions, enabling reliable confidence intervals. This demonstrated the capability of the data-driven NGBoost approach for robust shear strength evaluation of RC deep beams. Overall, the results illustrated that the proposed probabilistic prediction approach dramatically surpassed the current formulas adopted in design codes and machine learning models in both prediction accuracy and robustness.