Using deep generative-based machine and ensemble learning framework for predicting ultimate bending capacity of circular steel tubes

Avoiding steel tubes from reaching their ultimate bending capacity is critical for civil and structural engineers in order to avoid substantial deformations that cause failures. However, conducting pure bending experimental tests on all types of steel tubes is a difficult task due to the associated high costs. This paper proposes a novel two-stage framework that combines deep generative learning, machine and ensemble learning models to accurately predict the ultimate bending capacity of circular steel tubes. In the first stage, the Copula Generative Adversarial Network is used to generate large synthetic databases of ultimate bending capacity for cold-formed and fabricated steel tubes based on limited experimental datasets, while the second stage uses various machine and ensemble learning models to accurately predict the ultimate bending capacity. The performance of each stage is examined using numerous numerical and graphical metrics, during the training, testing, and validation phases. Using the global performance indicator, the proposed Extreme Gradient Boosting model demonstrated the highest performance among the other models with PI=0.7979 for fabricated circular tubes and PI =0.8176 for cold-formed circular tubes, and coefficient of determination values of R f a b r i c a t e d 2 = 0.9853 and R c o l d − f o r m e d 2 = 0.9663 , in the same respect. SHapley Additive exPlanations approach is then utilized to describe the best performing model behavior and the role of each variable in determining the ultimate bending capacity. The results of model explanation-based SHAP analysis revealed that steel tube thickness and diameter are the most influential variables in ultimate bending capacity predictions. The proposed framework indicates the importance of deep learning-based data generation in enhancing prediction outcomes in the situation of limited experimental results, as is the case of various materials science and engineering challenges.