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<p>In this study, a novel hybrid model, HMCS-WB, is proposed for concrete compressive strength (CS) prediction. The HMCS-WB integrates multiple machine learning (ML) models with optimized weights and a bias term, providing improved accuracy and stability across multiple evaluation metrics. The model employs stacking with the least squares method (LSM) to jointly estimate the weights and bias term of the meta-learner. The explicit incorporation of the bias term enhances the expressive power of the meta-learner, offering a theoretical advantage analogous to its role in neural networks (NNs). A database of 1030 concrete mix ratios was used to evaluate the proposed framework. Five tree-based models served as base learners, and extensive experiments compared various single models, the stacking variants, the weight-only variant, and the proposed HMCS-WB. Results demonstrated that HMCS-WB consistently outperformed all individual models, achieving the best performance with MSE = 16.303, MAE = 2.650, MAPE = 8.464%, and R<sup>2</sup> = 0.949, thereby surpassing the best base model (CatBoost). External validation using geopolymer concrete datasets further demonstrated the generalization of the model. Furthermore, SHAP analysis confirmed that cement and age were the most influential factors in CS prediction. Experimental findings indicate that the newly developed HMCS-WB model predicts CS with high accuracy.</p>

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HMCS-WB: a hybrid model for enhanced prediction of concrete compressive strength via weight-bias optimization

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Jiyuan Jiang,
  • Liangdong Qu

摘要

In this study, a novel hybrid model, HMCS-WB, is proposed for concrete compressive strength (CS) prediction. The HMCS-WB integrates multiple machine learning (ML) models with optimized weights and a bias term, providing improved accuracy and stability across multiple evaluation metrics. The model employs stacking with the least squares method (LSM) to jointly estimate the weights and bias term of the meta-learner. The explicit incorporation of the bias term enhances the expressive power of the meta-learner, offering a theoretical advantage analogous to its role in neural networks (NNs). A database of 1030 concrete mix ratios was used to evaluate the proposed framework. Five tree-based models served as base learners, and extensive experiments compared various single models, the stacking variants, the weight-only variant, and the proposed HMCS-WB. Results demonstrated that HMCS-WB consistently outperformed all individual models, achieving the best performance with MSE = 16.303, MAE = 2.650, MAPE = 8.464%, and R2 = 0.949, thereby surpassing the best base model (CatBoost). External validation using geopolymer concrete datasets further demonstrated the generalization of the model. Furthermore, SHAP analysis confirmed that cement and age were the most influential factors in CS prediction. Experimental findings indicate that the newly developed HMCS-WB model predicts CS with high accuracy.