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Equation-driven strength prediction of GGBS concrete: a symbolic machine learning approach for sustainable development Cover

Equation-driven strength prediction of GGBS concrete: a symbolic machine learning approach for sustainable development

REVIEWS ON ADVANCED MATERIALS SCIENCE
Volume 64 (2025): Issue 1 (January 2025)
By: Muhammad Nasir Amin,  Asad Naeem,  Muhammad Iftikhar Faraz and  Muhammad Tahir Qadir  
Open Access
|Dec 2025

Figures & Tables

Figure 1:

Research strategy and steps involved in the study. “Model coding, Python (Spyder), and scikit-learn” denote the implementation environment for model development rather than a separate step.
Research strategy and steps involved in the study. “Model coding, Python (Spyder), and scikit-learn” denote the implementation environment for model development rather than a separate step.

Figure 2:

Box plots showing the distribution and variability of input parameters used for predicting CS of GGBS-based concrete.
Box plots showing the distribution and variability of input parameters used for predicting CS of GGBS-based concrete.

Figure 3:

Pairplot of the GGBS concrete dataset showing the distribution and pairwise relationships among input variables and CS.
Pairplot of the GGBS concrete dataset showing the distribution and pairwise relationships among input variables and CS.

Figure 4:

Graphical representation of the model’s pipeline adopted for the presented research work.
Graphical representation of the model’s pipeline adopted for the presented research work.

Figure 5:

The adopted 5-fold validation approach for the research work indicates the process.
The adopted 5-fold validation approach for the research work indicates the process.

Figure 6:

Flowchart indicating the execution process of the GEP model [69].
Flowchart indicating the execution process of the GEP model [69].

Figure 7:

Steps involved for the final prediction by AdaBoost model [70].
Steps involved for the final prediction by AdaBoost model [70].

Figure 8:

Schematic workflow of the MLP model showing the flow of data from input parameters through hidden layers to the output node responsible for compressive strength prediction [71].
Schematic workflow of the MLP model showing the flow of data from input parameters through hidden layers to the output node responsible for compressive strength prediction [71].

Figure 9:

Relationship of the forecasted and actual CS of the GGBS-based concrete using the GEP model.
Relationship of the forecasted and actual CS of the GGBS-based concrete using the GEP model.

Figure 10:

Evaluation of the GEP model performance through actual versus predicted CS of GGBS concrete.
Evaluation of the GEP model performance through actual versus predicted CS of GGBS concrete.

Figure 11:

Relationship of the forecasted and actual CS of the GGBS-based concrete using the AdaBoost model.
Relationship of the forecasted and actual CS of the GGBS-based concrete using the AdaBoost model.

Figure 12:

Evaluation of the AdaBoost model performance through actual versus predicted CS of GGBS concrete.
Evaluation of the AdaBoost model performance through actual versus predicted CS of GGBS concrete.

Figure 13:

Relationship of the forecasted and actual CS of the GGBS-based concrete using the MLP model.
Relationship of the forecasted and actual CS of the GGBS-based concrete using the MLP model.

Figure 14:

Evaluation of the MLP model performance through actual versus predicted CS of GGBS concrete.
Evaluation of the MLP model performance through actual versus predicted CS of GGBS concrete.

Figure 15:

3D surface plot illustrating the nonlinear relationship between GGBS content, curing age, and compressive strength.
3D surface plot illustrating the nonlinear relationship between GGBS content, curing age, and compressive strength.

Figure 16:

2D contour plot showing compressive strength zones as a function of GGBS content and age.
2D contour plot showing compressive strength zones as a function of GGBS content and age.

Figure 17:

Comparison of average performance metrics (MAE, RMSE, and R2) across the GEP, MLP, and AdaBoost models based on 5-fold cross-validation.
Comparison of average performance metrics (MAE, RMSE, and R2) across the GEP, MLP, and AdaBoost models based on 5-fold cross-validation.

Figure 18:

Taylor diagram comparing the predictive performance of the MLP, AdaBoost, and GEP models for compressive strength prediction of GGBS-based concrete.
Taylor diagram comparing the predictive performance of the MLP, AdaBoost, and GEP models for compressive strength prediction of GGBS-based concrete.

Figure 19:

Local feature contribution to the predicted CS of a GGBS-based concrete mix using LIME.
Local feature contribution to the predicted CS of a GGBS-based concrete mix using LIME.

Figure 20:

Permutation sensitivity analysis with the MLP model revealed the global influence of each input feature.
Permutation sensitivity analysis with the MLP model revealed the global influence of each input feature.

Predictive accuracy measure for the employed models_

MetricFormulaDescription
Mean Absolute Error (MAE)MAE = 1 n ∑ i = 0 n y i − ŷ i $\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=0}^{\mathrm{n}}\left\vert {\mathrm{y}}_{\mathrm{i}}-{\hat{\mathrm{y}}}_{\mathrm{i}}\right\vert $ Average magnitude of prediction errors;measures absolute deviation between predicted and experimental values.
Mean Squared Error (MSE)MSE = 1 n ∑ i = 0 n y i − ŷ i 2 $\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=0}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\hat{\mathrm{y}}}_{\mathrm{i}}\right)}^{2}$ Penalises larger deviations more strongly by squaring error terms.
Root Mean Squared Error (RMSE)RMSE= 1 n ∑ i = 0 n y i − ŷ i 2 $\sqrt{\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=0}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}}-{\hat{\mathrm{y}}}_{\mathrm{i}}\right)}^{2}}$ Square root of MSE;interpretable in the same units as the target variable.
Adjusted R2Adj.R2 = 1 − 1 − R 2 n − 1 n − p − 1 $-\frac{\left(1-{\mathrm{R}}^{2}\right)\left(\mathrm{n}-1\right)}{\mathrm{n}-\mathrm{p}-1}$ Adjust R2 for the number of predictors (ρ) to account for model complexity and avoid overfitting.

Statistics obtained for the parameters used in forecasting the CS of concrete material_

ParametersCement (Kg/m3)Water/BinderW/CementAggregate (Kg/m3)Sand (Kg/m3)GGBS Kg/m3 Admixture (kg/m3)Age (days)
Mean253.360.440.88912.78818.47177.475.164.07
Standard error3.7200.023.345.332.530.243.42
Median2400.410.759328001731.7528
Mode4250.30.67932594189028
Standard deviation104.390.130.4793.73149.5971.096.6596.06
Skewness0.190.431.24−0.260.50.471.52.27
Range4050.512.21461.3560.2532232.2362
Lower700.240.29683.75943803
Higher4750.752.51,1451,154.2536032.2365
Confidence level (95.0 %)7.30.010.036.5610.474.970.476.72

Statistical results of the 5-fold cross-validation for all the employed models_

K-foldGEPMLPAdaBoost
MAE (MPa)RMSE (MPa)R2 MAE (MPa)RMSE (MPa)R2 MAE (MPa)RMSE (MPa)R2
15.647.350.864.746.250.905.866.920.88
25.166.810.905.437.760.876.118.090.86
35.417.160.904.906.220.926.698.060.87
46.408.020.854.686.030.927.529.040.81
55.937.760.864.375.540.936.708.090.84
DOI: https://doi.org/10.1515/rams-2025-0183 | Journal eISSN: 1605-8127
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Language: English
Submitted on: Aug 14, 2025
Accepted on: Oct 31, 2025
Published on: Dec 11, 2025
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Keywords:
ground granulated blast-furnace slag-based concrete,
compressive strength,
machine learning prediction models
Related subjects:
Chemistry,
Chemistry, other,
Engineering,
Introductions and overviews,
Engineering, other,
Materials sciences,
Porous materials,
Physics,
Physics, other

© 2025 Muhammad Nasir Amin, Asad Naeem, Muhammad Iftikhar Faraz, Muhammad Tahir Qadir, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 License.

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