Hybrid BART-based models optimized by nature-inspired metaheuristics to predict ultimate axial capacity of CCFST columns

Abstract

The goal of this study was to investigate a novel approach of predicting the ultimate capacity of axially loaded circular concrete-filled steel tube (CCFST) columns. A hybrid intelligent system, namely GAP-BART, was developed based on the Bayesian additive regression tree (BART) combining with three nature-inspired optimization algorithms such as Genetic Algorithm (GA), Artificial Bee Colony (ABC), and Particle Swarm Optimization (PSO), and then applied. Three sub-hybrid models of the system were built, abbreviated as G-BART, A-BART, and P-BART, respectively, using 504 experimental data collected from published research. The compiled database covered five input variables, including the diameter of the circular cross-section—section (D), the wall thickness of the steel tube (t), the length of the column (L), the compressive strength of the concrete ( $$f_{\text{c}}^{'}$$ ), and the yield strength of the steel tube (fy). The coefficient of determination (R2) values of (0.9971, 0.9982, and 0.9986) and (0.9891, 0.9923 and 0.9931) were achieved for training and testing of G-BART, A-BART, and P-BART models, respectively. The P-BART model performed the lowest RMSE and MAE values for the training and testing set of (66.85 kN and 49.60 kN) and (141.24 kN and 102.04 kN), respectively. These results indicated that although the proposed models were able to estimate ultimate axial capacity with high accuracy, the P-BART model had the best performance among them. For benchmarking, the obtained results were validated against several mathematical approaches as well as other AI techniques (MARS, ANN). The findings of the comparative analysis clearly showed superior ability to predict the CFST ultimate axial capacity relative to the benchmark models. The relative importance of each predictor was investigated to find the most significant input variables. The results confirmed that the hybrid GAP-BART system can serve as a reliable and accurate tool for the design of CCFST columns and to predict their performance.