Hybrid machine learning with HHO method for estimating ultimate shear strength of both rectangular and circular RC columns

This paper presents six novel hybrid machine learning (ML) models that combine support vector machines (SVM), Decision Tree (DT), Random Forest (RF), Gradient Boosting (GB), extreme gradient boosting (XGB), and categorical gradient boosting (CGB) with the Harris Hawks Optimization (HHO) algorithm. These models, namely HHO-SVM, HHO-DT, HHORF, HHO-GB, HHO-XGB, and HHO-CGB, are designed to predict the ultimate strength of both rectangular and circular reinforced concrete (RC) columns. The prediction models are established using a comprehensive database consisting of 325 experimental data for rectangular columns and 172 experimental data for circular columns. The ML model hyperparameters are optimized through a combination of cross-validation technique and the HHO. The performance of the hybrid ML models is evaluated and compared using various metrics, ultimately identifying the HHO-CGB model as the top-performing model for predicting the ultimate shear strength of both rectangular and circular RC columns. The mean R-value and mean a20-index are relatively high, reaching 0.991 and 0.959, respectively, while the mean absolute error and root mean square error are low (10.302 kN and 27.954 kN, respectively). Another comparison is conducted with four existing formulas to further validate the efficiency of the proposed HHO-CGB model. The Shapely Additive Explanations method is applied to analyze the contribution of each variable to the output within the HHO-CGB model, providing insights into the local and global influence of variables. The analysis reveals that the depth of the column, length of the column, and axial loading exert the most significant influence on the ultimate shear strength of RC columns. A user-friendly graphical interface tool is then developed based on the HHO-CGB to facilitate practical and cost-effective usage.