Development of Hybrid Machine Learning Models for Predicting the Critical Buckling Load of I-Shaped Cellular Beams

The principal purpose of this work is to develop three hybrid machine learning (ML) algorithms, namely ANFIS-RCSA, ANFIS-CA, and ANFIS-SFLA which are a combination of adaptive neuro-fuzzy inference system (ANFIS) with metaheuristic optimization techniques such as real-coded simulated annealing (RCSA), cultural algorithm (CA) and shuffled frog leaping algorithm (SFLA), respectively, to predict the critical buckling load of I-shaped cellular steel beams with circular openings. For this purpose, the existing database of buckling tests on I-shaped steel beams were extracted from the available literature and used to generate the datasets for modeling. Eight inputs, considered as independent variables, including the beam length, beam end-opening distance, opening diameter, inter-opening distance, section height, web thickness, flange width, and flange thickness, as well as one output of the critical buckling load of cellular steel beams considered as a dependent variable, were used in the datasets. Three quality assessment criteria, namely correlation coefficient (R), root mean squared error (RMSE) and mean absolute error (MAE) were employed for assessment of three developed hybrid ML models. The obtained results indicate that all three hybrid ML models have a strong ability to predict the buckling load of steel beams with circular openings, but ANFIS-SFLA (R = 0.960, RMSE = 0.040 and MAE = 0.017) exhibits the best effectiveness as compared with other hybrid models. In addition, sensitivity analysis was investigated and compared with linear statistical correlation between inputs and output to validate the importance of input variables in the models. The sensitivity results show that the most influenced variable affecting beam buckling capacity is the beam length, following by the flange width, the flange thickness, and the web thickness, respectively. This study shows that the hybrid ML techniques could help in establishing a robust numerical tool for beam buckling analysis. The proposed methodology is also promising to predict other types of failure, as well as other types of perforated beams.