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<p>In recent years, with the explosion of the 4.0 industrial revolution, terms such as machine learning (ML) have become familiar and are increasingly widely applied in the engineering field. This study focuses on proposing two new hybrid models named exponential-trigonometrie optimized extreme gradient boosting (ETO-XGBoost) and whale optimization algorithm extreme gradient boosting (WOA-XGBoost), which are developed based on extreme gradient boosting combined with exponential-trigonometric optimization and whale optimization algorithm. A data set has been built and analyzed using ABAQUS software, and combined with data from the empirical formula to construct a training data set for the proposed models. The two proposed hybrid models are compared with the available models including Kolmogorov-Arnold networks (KAN), artificial neural networks (ANN) and Eurocode 4 standard through important statistical indices such as mean absolute error (<i>MAE</i>), mean absolute percentage error (<i>MAPE</i>), root mean square error (<i>RMSE</i>) and correlation coefficient <i>R.</i> The analysis results show that the ETO-XGBoost model and the WOA-XGBoost model are the most effective ML models when compared with other models. The correlation index <i>R</i> of both models reached very high values (0.9963 for ETO-XGBoost and 0.9956 for WOA-XGBoost, respectively). At the same time, the error indexes of the ETO-XGBoost model were the smallest among the compared models, with <i>MAPE</i> = 63.3738, <i>MAE</i> = 47.4643 and <i>RMSE</i> = 1.8221; meanwhile, the WOA-XGBoost model had corresponding indexes of <i>MAPE</i> = 67.8956, <i>MAE</i> = 49.1825 and <i>RMSE</i> = 1.9040. Besides, the predicted data from the ETO-XGBoost model and the WOA-XGBoost model showed the highest similarity with the actual data in predicting the axial strength of concrete-filled steel tubular (CFST) columns. Therefore, the ETO-XGBoost model and the WOA-XGBoost model can be considered as a powerful and accurate tool in predicting the compressive strength of CFST columns.</p>

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Development of optimized XGBoost model for accurate prediction of concrete-filled steel tubular column bearing capacity

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Tran Minh Luan,
  • Samir Khatir,
  • Timon Rabczuk,
  • Nicholas Fantuzzi,
  • Thanh Cuong-Le

摘要

In recent years, with the explosion of the 4.0 industrial revolution, terms such as machine learning (ML) have become familiar and are increasingly widely applied in the engineering field. This study focuses on proposing two new hybrid models named exponential-trigonometrie optimized extreme gradient boosting (ETO-XGBoost) and whale optimization algorithm extreme gradient boosting (WOA-XGBoost), which are developed based on extreme gradient boosting combined with exponential-trigonometric optimization and whale optimization algorithm. A data set has been built and analyzed using ABAQUS software, and combined with data from the empirical formula to construct a training data set for the proposed models. The two proposed hybrid models are compared with the available models including Kolmogorov-Arnold networks (KAN), artificial neural networks (ANN) and Eurocode 4 standard through important statistical indices such as mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE) and correlation coefficient R. The analysis results show that the ETO-XGBoost model and the WOA-XGBoost model are the most effective ML models when compared with other models. The correlation index R of both models reached very high values (0.9963 for ETO-XGBoost and 0.9956 for WOA-XGBoost, respectively). At the same time, the error indexes of the ETO-XGBoost model were the smallest among the compared models, with MAPE = 63.3738, MAE = 47.4643 and RMSE = 1.8221; meanwhile, the WOA-XGBoost model had corresponding indexes of MAPE = 67.8956, MAE = 49.1825 and RMSE = 1.9040. Besides, the predicted data from the ETO-XGBoost model and the WOA-XGBoost model showed the highest similarity with the actual data in predicting the axial strength of concrete-filled steel tubular (CFST) columns. Therefore, the ETO-XGBoost model and the WOA-XGBoost model can be considered as a powerful and accurate tool in predicting the compressive strength of CFST columns.