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<p>This investigation focuses on determining the optimal concentration of multiwalled carbon nanotubes (MWCNTs) to enhance the compressive strength of pavement-grade high-volume fly ash (HVFA) concrete. The proportion of MWCNTs was systematically varied from 0% to 2% in 0.25% intervals, with the fly ash content held constant at 55% replacement. Experimental testing demonstrated that a 2% MWCNT dosage consistently yielded the highest compressive strength across all curing durations, reaching a maximum of 48.43&#xa0;MPa at 90 days. 108 observations were recorded in the current study and was divided into training and testing sets for developing 11 different machine learning models: SVM with power, linear, and radial basis function (RBF) kernels; partial least squares (PLS); LASSO; Elastic Net; Ridge regression; gradient boosting machines (GBM); random forest (RDF); and neural networks. MWCNT dosage and curing age were used as input variable and compressive strength was the output variable. Model evaluation was conducted using parity and Taylor plots, alongside various statistical performance metrics. Among the eleven machine learning models evaluated, the SVM with radial basis function (RBF) kernel achieved the lowest test-set errors, with MAE = 0.70&#xa0;MPa and RMSE = 0.87&#xa0;MPa, outperforming Random Forest (MAE = 1.63&#xa0;MPa, RMSE = 1.89&#xa0;MPa) and Gradient Boosting models. Linear and regularized regression models showed notably higher errors (RMSE ≈ 4.5–4.7&#xa0;MPa), indicating limited capacity to capture nonlinear strength development. To assess model generalization and reliability, regression error characteristic (REC) curves and area over the curve (AOC) values were also computed. Interpretability of the best-performing model was explored using partial dependence plots (PDPs), which showed that both MWCNT concentration and curing age positively influence compressive strength. Notably, curing age exerted a more substantial and nonlinear effect. Monotonicity analysis affirmed the model’s capability to reflect the steady increase in strength with prolonged curing, while the impact of MWCNT dosage remained comparatively consistent. Perturbation analysis revealed limited variation in predicted strength due to minor changes in MWCNT levels, contrasted with greater sensitivity to alterations in curing duration. Sensitivity analysis further emphasized curing age as the dominant factor driving compressive strength predictions in MWCNT-enhanced HVFA concrete.</p>

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Comparative assessment of multiple machine learning models for predicting the compressive strength of multiwalled carbon nanotube reinforced high volume fly ash concrete

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Sameer Sen,
  • Sanjeev Sinha,
  • Anish Kumar

摘要

This investigation focuses on determining the optimal concentration of multiwalled carbon nanotubes (MWCNTs) to enhance the compressive strength of pavement-grade high-volume fly ash (HVFA) concrete. The proportion of MWCNTs was systematically varied from 0% to 2% in 0.25% intervals, with the fly ash content held constant at 55% replacement. Experimental testing demonstrated that a 2% MWCNT dosage consistently yielded the highest compressive strength across all curing durations, reaching a maximum of 48.43 MPa at 90 days. 108 observations were recorded in the current study and was divided into training and testing sets for developing 11 different machine learning models: SVM with power, linear, and radial basis function (RBF) kernels; partial least squares (PLS); LASSO; Elastic Net; Ridge regression; gradient boosting machines (GBM); random forest (RDF); and neural networks. MWCNT dosage and curing age were used as input variable and compressive strength was the output variable. Model evaluation was conducted using parity and Taylor plots, alongside various statistical performance metrics. Among the eleven machine learning models evaluated, the SVM with radial basis function (RBF) kernel achieved the lowest test-set errors, with MAE = 0.70 MPa and RMSE = 0.87 MPa, outperforming Random Forest (MAE = 1.63 MPa, RMSE = 1.89 MPa) and Gradient Boosting models. Linear and regularized regression models showed notably higher errors (RMSE ≈ 4.5–4.7 MPa), indicating limited capacity to capture nonlinear strength development. To assess model generalization and reliability, regression error characteristic (REC) curves and area over the curve (AOC) values were also computed. Interpretability of the best-performing model was explored using partial dependence plots (PDPs), which showed that both MWCNT concentration and curing age positively influence compressive strength. Notably, curing age exerted a more substantial and nonlinear effect. Monotonicity analysis affirmed the model’s capability to reflect the steady increase in strength with prolonged curing, while the impact of MWCNT dosage remained comparatively consistent. Perturbation analysis revealed limited variation in predicted strength due to minor changes in MWCNT levels, contrasted with greater sensitivity to alterations in curing duration. Sensitivity analysis further emphasized curing age as the dominant factor driving compressive strength predictions in MWCNT-enhanced HVFA concrete.