Optimal Dimensions of Post-Tensioned Concrete Cylindrical Walls Using Harmony Search and Ensemble Learning with SHAP

Abstract

The optimal design of prestressed concrete cylindrical walls is greatly beneficial for economic and environmental impact. However, the lack of the available big enough datasets for the training of robust machine learning models is one of the factors that prevents wide adoption of machine learning techniques in structural design. The current study demonstrates the application of the well-established harmony search methodology to create a large database of optimal design configurations. The unit costs of concrete and steel used in the construction, the specific weight of the stored fluid, and the height of the cylindrical wall are the input variables whereas the optimum thicknesses of the wall with and without post-tensioning are the output variables. Based on this database, some of the most efficient ensemble learning techniques like the Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Categorical Gradient Boosting (CatBoost) and Random Forest algorithms have been trained. An R-2 score greater than 0.98 could be achieved by all of the ensemble learning models. Furthermore, the impacts of different input features on the predictions of different machine learning models have been analyzed using the SHapley Additive exPlanations (SHAP) methodology. The height of the cylindrical wall was found to have the greatest impact on the optimal wall thickness, followed by the specific weight of the stored fluid. Also, with the help of individual conditional expectation (ICE) plots the variations of predictive model outputs with respect to each input feature have been visualized. By using the genetic programming methodology, predictive equations have been obtained for the optimal wall thickness.