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 (fc′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\text{c}}^{'}$$\end{document}), 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.

中文翻译：

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通过自然启发式元启发式优化基于混合 BART 的模型来预测 CCFST 柱的最终轴向承载力

本研究的目的是研究一种预测轴向承载圆形钢管混凝土 (CCFST) 柱极限承载力的新方法。基于贝叶斯加性回归树（BART），结合遗传算法（GA）、人工蜂群（ABC）和粒子群优化（Particle Swarm Optimization）三种自然优化算法，开发了一种混合智能系统，即GAP-BART。 PSO)，然后应用。使用从已发表的研究中收集的 504 个实验数据，构建了该系统的三个亚混合模型，分别缩写为 G-BART、A-BART 和 P-BART。编译后的数据库包含五个输入变量，包括圆形截面的直径（D）、钢管壁厚（t）、柱长（L）、混凝土的抗压强度 (fc′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{ upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\text{c}}^{'}$$\end{document}），以及钢管的屈服强度（fy ）。G-BART、A-BART 和 P-BART 模型的训练和测试分别获得了决定系数 (R2) 值（0.9971、0.9982 和 0.9986）和（0.9891、0.9923 和 0.9931）。P-BART 模型分别为 (66.85 kN 和 49.60 kN) 和 (141.24 kN 和 102.04 kN) 的训练和测试集执行了最低的 RMSE 和 MAE 值。这些结果表明，虽然所提出的模型能够高精度地估计极限轴向承载力，其中，P-BART 模型的性能最好。对于基准测试，获得的结果针对几种数学方法以及其他 AI 技术（MARS、ANN）进行了验证。比较分析的结果清楚地表明，相对于基准模型，预测 CFST 极限轴向承载力的能力更强。研究了每个预测变量的相对重要性，以找到最重要的输入变量。结果证实，混合 GAP-BART 系统可以作为设计 CCFST 柱并预测其性能的可靠且准确的工具。比较分析的结果清楚地表明，相对于基准模型，预测 CFST 极限轴向承载力的能力更强。研究了每个预测变量的相对重要性，以找到最重要的输入变量。结果证实，混合 GAP-BART 系统可以作为设计 CCFST 柱并预测其性能的可靠且准确的工具。比较分析的结果清楚地表明，相对于基准模型，预测 CFST 极限轴向承载力的能力更强。研究了每个预测变量的相对重要性，以找到最重要的输入变量。结果证实，混合 GAP-BART 系统可以作为设计 CCFST 柱并预测其性能的可靠且准确的工具。