Analytical Equations for the Prediction of the Failure Mode of Reinforced Concrete Beam-Column Joints based on Interpretable Machine Learning and SHAP values

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Abstract
One of the most critical components of reinforced concrete structures are the beam-column joint systems, which greatly affect the overall behavior of the structure during a major seismic event. According to modern design codes, if the system fails, it should fail due to flexural yielding of the beam and not due to shear failure of the joint, which occurs suddenly and can lead to collapse, endangering human lives. Thus, a reliable tool is required for the prediction of the failure mode of the joints in a preexisting population of structures. In the present paper, a novel methodology for the derivation of analytical equations for this task is presented. The formulation is based on SHapley Additive exPlanations values, which is commonly employed as an explainability tool in Machine Learning. Instead, in the present paper, they are also utilized as a transformed target variable on which the analytical curves are fitted, which approximate the predictions of an underlying Machine Learning model. A dataset comprised of 478 experimental results is utilized and the eXtreme Gradient Boosting algorithm is initially fitted. This achieved an overall accuracy of ≈84%. The derived analytical equations achieved an accuracy of ≈78%. The corresponding metrics of Precision, Recall, and F1-Score ranged from ≈76% to ≈80% and were close across the two modes, indicating an unbiased model.
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