Bayesian-Optimized Ensemble Models for Geopolymer Concrete Compressive Strength Prediction with Interpretability Analysis
Abstract
1. Introduction
- To systematically assess the effectiveness of ensemble machine learning models in predicting the compressive strength of geopolymer concretes.
- To investigate the impact of hyperparameter tuning through BO, providing insights into how model calibration affects prediction accuracy.
- To enhance model interpretability by applying SHAP, an explainable artificial intelligence (XAI) technique, for identifying the most influential variables affecting concrete strength.
- To develop reliable, accurate, fast, and interpretable predictive models supported by a user-friendly GUI, facilitating the practical implementation of AI-driven solutions in designing sustainable and eco-friendly construction materials.
2. Related Studies
3. Predictive Modeling and Explainable AI
3.1. Predictive Models
3.1.1. Extreme Gradient Boosting (XGB)
3.1.2. Random Forest (RF)
3.1.3. Light Gradient Boosting Machine (LightGBM)
3.1.4. Support Vector Regression (SVR)
3.1.5. Artificial Neural Network (ANN)
3.2. Bayesian Hyperparameter Optimization
3.3. Model Performance Evaluation
3.4. Explainable Artificial Intelligence (XAI)
4. Methods
5. Results and Discussion
6. Conclusions
- The XGB-BO model outperformed other ensemble machine learning models in terms of predictive accuracy, as demonstrated by its higher R2 and lower RMSE, MAE, and MAPE values. This model effectively captured the complex, nonlinear relationships among mixture design parameters influencing the compressive strength of geopolymer concretes, providing a robust, reliable, and explainable prediction framework.
- The integration of the XGB model with Bayesian Optimization (BO) has significantly enhanced the model’s predictive performance. The BO approach enabled a more efficient search for optimal hyperparameters, reducing the risk of overfitting and maintaining high prediction accuracy. This optimization strategy provided a notable reduction in error rates and played a key role in improving the model’s robustness and generalization capability.
- Model interpretability analysis using SHAP contribution values revealed that the most influential parameters affecting the compressive strength of geopolymer concretes are coarse aggregate, curing time, and NaOH molar concentration, with corresponding mean SHAP values of 9.109, 7.743, and 2.584, respectively. The SHAP feature importance plot provides an explicit quantification of how each variable contributes to the model’s predictions, highlighting their relative impact. In this way, ensemble learning models, which are often considered black-box approaches, were made explainable, and the model’s decision-making process was rendered more transparent.
- A user-friendly GUI was developed to enable fast and accessible prediction of the compressive strength of geopolymer concretes based on mixture design parameters. This tool facilitates the practical implementation of the proposed AI-based framework and supports its adoption in real-world engineering applications.
- In this study, R-Ag showed the highest linear correlation with compressive strength (CS); however, CoAg was the most influential feature in the SHAP importance ranking. This indicates that despite its strong linear correlation, the prediction model for R-Ag has a limited impact on actual decision-making. Therefore, using not only correlation coefficients but also model-based explainability methods when selecting parameters for experimental designs offers a more comprehensive and reliable basis for parameter choice and process optimization in complex concrete systems.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
ABR | Adaptive boosting regressor |
AD | Alkali dosage |
ADA | ADAboost |
AF | Alccofine |
Ag | Aggregate |
ANFIS | Adaptive neuro-fuzzy inference system |
ANN | Artificial neural networks |
AS | Alkaline solution |
ASC | Alkaline solution concentration |
ASM | Aluminosilicate material |
B | Binder |
BC | Basicity coefficient |
BDT | Boosted decision tree |
BNN | Bayesian neural network |
BO | Bayesian Optimization |
BPNN | Back-propagation neural network |
BR | Bagging regresor |
CatBoost | Categorical boosting regressor |
CCA | Corncob ash |
CD | Curing duration |
CFV | Compaction factor value |
CG | Coal gangue |
CN2 | CN2 Rule induction |
CNN | 1 D Convolution neural network |
CoAg | Coarse aggregate |
CoS | Copper slag |
CS | Compressive strength |
CSG | Concrete strength grade |
CSO | Cat swarm optimization |
CT | Curing temperature |
CuMe | Curing method |
CuTi | Curing time |
Dmax | Maximum size of coarse aggregate |
DNN | Deep neural network |
DT | Decision tree |
ECSO | Enhanced cat swarm optimization |
EL | Ensemble learning |
ELM | Extreme learning machine |
EN | Elastic net |
ESA | Eggshell ash |
ET | Elevated temperature |
ETR | Extra trees regressor |
EW | Extra water |
FA | Fly ash |
FAR | Fibre aspect ratio |
FD | Fibre diameter |
FE | Elastic modulus of fibre |
FiAg | Fine aggregate |
FL | Fibre length |
Fs | Fineness modulus of fine aggregate |
FTS | Fibre tensile strength |
FV | Fibre volume |
GA | Genetic algorithm |
GB | Gradient boosting |
GEP | Gene expression programming |
GGBFS | Ground granulated blast furnace slag |
GMDH | Group method of data handling |
GP | Glass powder |
GPR | Gaussian process regression |
GUI | Graphical user interface |
H | Humidity |
HCD | High-temperature curing duration |
HD | Heating duration |
HM | Hydration modulus |
HO | Hyperparameter optimization |
HR | Heating rate |
HT | Heating temperature |
HTT | Heat treatment time |
KNN | K-nearest neighbour |
L | Liquid |
LightGBM | Light gradient boosting machine |
LI | Loss on ignition |
LoR | Logistic regression |
LR | Linear regression |
LSTM | Long short-term memory |
M | NaOH molar concentration |
MAE | Mean Absolute Error |
MAPE | Mean Absolute Percentage Error |
MARS | Multivariate adaptive regression splines |
MEP | Multi-expression programming |
MK | Metakaolin |
ML | Machine learning |
MLP | Multilayer perceptron regressor |
MLR | Multiple linear regression |
MP | Mixing procedure |
MR | Mole ratio |
Ms | Silica module (SiO2/Na2O) |
NB | Naive bayes |
NH | NaOH |
NS | Na2SiO3 |
PM | Pozzolanic material |
PSO | Particle swarm optimization |
PT | Pretreatment temperature |
R | Recycled |
R2 | Coefficient of determination |
RA | Rubber aggregate |
RAWA | Recycled aggregate water absorption |
ResNet | Deep residual network |
RF | Random forest |
RHA | Rice husk ash |
RM | Red Mud |
RMSE | Root Mean Square Error |
Rub | Rubber |
S | Solid |
SC | Slag cement |
SF | Silica fume |
SGD | Stochastic gradient descent |
SHAP | SHapley Additive exPlanations |
SHO | Spotted hyena optimization |
SP | Superplasticizer |
SS | Silica sand |
SSA | Specific surface area |
StF | Steel fiber |
SVM | Support vector machine |
TA | Test age |
UPV | Ultrasonic pulse velocity |
W | Water |
WR | Water reducer |
XAI | Explainable artificial intelligence |
XGB | Extreme gradient boosting |
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References | Sample Size | Inputs | ML Method | HO | Best Model | R/R2 | XAI |
---|---|---|---|---|---|---|---|
Ghosh, A. et al. [13] | - | FA, CuTi, CuMe | LR, DT, RF, SVM | × | DT, RF | -/0.9879 | × |
Wang, Y. et al. [14] | 156 | FA, GGBFS, FiAg, CoAg, NH, NS, SP, CT | ANN, ANFIS, GEP | × | GEP | 0.99/- | × |
Revathi, B. et al. [15] | 37 | FA, GGBFS, AF, CoAg, FiAg, NH, NS, W | RF | √ | RF | -/0.79 | √ |
24 | PM, FA, M, Na/Si, Si/Al, H2O/Na2O, Na/Al | -/0.81 | |||||
28 | NH, NS, NS/NH, M, CT, ET | -/0.88 | |||||
Nguyen, K. T. et al. [16] | 335 | FA, NH, NS, CaAg, FiAg, W, Molarity, CuTi, CT | DNN, ResNet | × | ResNet | 0.9927/- | × |
Peng, Y. et al. [17] | 110 | FA, SiO2, Al2O3, CoAg, FiAg, NH, Molarity, NS, NS/NH, AA/FA, W, SP | BPNN, SVM, ELM | × | BPNN | -/0.8221 | × |
Shen, J. et al. [18] | 328 | Ms, Na2O, SiO2/Al2O3, Na2O/SiO2, L/S, PT, HTT, TA | RF, GB, XGB | √ | XGB | -/0.939 | √ |
Zhang, M. et al. [19] | 616 | Si/Al, Na/Al, Ca/Si, CT, CuTi, H, W | BPNN, LoR, MLR, SVM, RF | √ | RF | 0.9322/- | × |
Dash, P. K. et al. [20] | 192 | GGBFS, CoAg, FiAg, AS/GGBFS, NH, NS, NS/NH, CuTi, CT | ELM, ELM-CSO, ELM-ECSO | √ | ELM-ECSO | -/0.957 | × |
Gad, M. A. et al. [21] | 132 | FA, GGBFS, SF, NH, NS, SS, EW, WR, CuMe | CatBoost, XGB, ETR, DT, RF, GB | √ | GB | -/0.9651 | √ |
Gomaa, E. et al. [22] | 180 | CoAg, FiAg, SiO2, Al2O3, Fe2O3, CaO, MgO, Na2O, K2O, TiO2, P2O5, MnO, LI, W, SSA-FA, MP, CuMe, CT, CuTi, TA | RF | √ | RF | 0.972/0.944 | × |
Afzali, S. A. E. et al. [23] | 235 | MK, NH, Molarity, NS, EW, W/S, SiO2/Al2O3, H2O/Na2O, Na2O/ Al2O3, CoAg/FiAg, SP, TA, CT | GB, RF, DT, ANN, SVM | √ | GB | -/0.983 | √ |
Golafshani, E. et al. [24] | 314 | FA, SC, CoAg, R-CoAg, FiAg, NH, NS, SP, RAWA, M, CT, HCD, TA | RF, BR, ETR, ABR, GB, XGB, CatBoost, LightGBM | √ | XGB | -/0.955 | √ |
Liu, L. et al. [25] | 235 | SiO2/Al2O3, Na2O/Al2O3, H2O/Na2O, CoAg/FiAg, SP, W/S, EW, NH, NS, Molarity, MK, TA, CT | GEP, MEP | √ | MEP | 0.98/0.96 | √ |
Zeng, Y. et al. [26] | 206 | AD, SiO2/Na2O, W/B, SiO2/Al2O3, CaO/SiO2, Al2O3/Na2O, CaO/Al2O3, CaO/(SiO2+Al2O3), CG | RF, XGB, MLP, DT | √ | XGB | -/0.882 | × |
Parhi, S. K. et al. [27] | 240 | FA, GGBFS, SiO2, Al2O3, Fe2O3, CaO, CoAg, FiAg, NH, Molarity, NS, NS/NH, AS/B, EW, SP, CuTi, CT | ABR, RF, XGB, Hybrid | √ | Hybrid | -/0.97 | × |
Ji, H. et al. [28] | 795 | FA, Na2O, Ms, W/FA, CoAg/FA, FiAg/FA, Fs, Dmax, BC, HM, CT, CuTi, TA | XGB | √ | XGB | -/0.95 | × |
Ranasinghe, R. S. S. et al. [29] | 260 | GGBFS, CCA, FiAg, CoAg, W, NH, NS, CuTi, Molarity, CSG | ANN, DNN, CNN | × | DNN | -/0.972 | √ |
Bypour, M. et al. [30] | 161 | SiO2, Al2O3, Fe2O3, CaO, P2O5, SO3, K2O, TiO2, MgO, Molarity, Na2O, MnO, CoAg, FiAg, StF, Rub | DT, ETR, RF, GB, XGB, ADA | √ | ADA | -/0.86 | √ |
Sathiparan, N. et al. [31] | 189 | ESA, RHA, NH, UPV | LR, ANN, BDT, RF, KNN, SVM, XGB | × | KNN | -/0.958 | √ |
Le, Q. H. et al. [32] | 375 | CoAg, FiAg, NH, NS, ASM, CT, CuTi, TA | DNN, KNN, SVM | √ | DNN | 0.8903/- | × |
Khan, A. Q. et al. [33] | 149 | FA, SiO2, Al2O3, CoAg, FiAg, NH, Molarity, NS, NS/NH, (NH+NS)/FA, W, CT, CuTi | BPNN, RF, KNN | × | BPNN | -/0.948 | × |
Yeluri, S. C. et al. [34] | 186 | FA, Molarity, NH, NS, FiAg, CoS, CoAg, RA, CuTi | MARS, GMDH, M5P, LR | × | MARS | 0.9634/- | √ |
Philip, S. et al. [35] | 309 | FA, CoAg, FiAg, NH, NS, Molarity, NS/NH, (NH+NS)/FA, TA, CT, EW, SP | LR, ADA, RF, SVM, ANN | × | RF | -/0.96 | × |
Onyelowe, K. C. et al. [36] | 132 | GGBFS, FA, NH, NS, TA | GB, CN2, NB, SVM, SGD, KNN, DT, RF | × | KNN | -/0.99 | × |
Philip, S. et al. [37] | 110 | GGBFS, CoAg, FiAg, NH, Molarity, NS, NS/NH, (NH+NS)/GGBFS, TA, CT, FV, FL, FD, FAR, FTS | LR, DT, RF, XGB, GB, ADA | × | XGB | -/0.938 | × |
Yang, H. et al. [38] | 206 | Size, W, NS, Molarity, NH, GGBFS, FA, FiAg, CoAg, CT, HR, HD, HT, CuTi | SVM, EN, GB, XGB, GA-RF, PSO-DNN, BNN, ELM | √ | GA-RF | -/0.937 | √ |
Diksha, Dev, N. and Goyal, P. K. [39] | 144 | AF/FA, Molarity, L/B, Ag/B, L/Ag, EW, EW/L, CFV, CT, TA | LR, GPR, EL, SVM, ANN | √ | GPR | 0.9951/- | × |
Metric | Formula | Description |
---|---|---|
R2 | It is a measure of how well the model explains the variance of the dependent variable(s), typically ranging between 0 and 1. A value of 1 indicates that the model fits the data perfectly; a value of 0 indicates that the model has no success in explaining the data. The model may take negative values when it predicts worse than the mean value of the target variable [54]. | |
RMSE | RMSE measures the square root of the mean square differences between the model-predicted values and the actual values. This metric evaluates the overall accuracy of the model by penalizing large errors more. Lower RMSE values indicate better model performance [6,58]. | |
MAE | It measures the average of the absolute differences between actual and predicted values. Lower MAE values indicate that the model makes more accurate predictions. Unlike squared error metrics, MAE does not disproportionately penalize large errors, making it less sensitive to outliers [58]. | |
MAPE | It is an error metric that measures the average of the absolute percentage differences between the predicted values and the actual values. MAPE provides a percentage-based measure of how accurately the model makes predictions. MAPE is especially useful for understanding model performance when the dataset contains very large or values close to zero. Low MAPE values indicate that the model makes more accurate predictions [58]. |
Model | Parameter | Parameter Intervals | Best Value |
---|---|---|---|
XGB | learning_rate | 0.01–0.3 | 0.1495 |
max_depth | 3–10 | 7 | |
Subsample | 0.5–1.0 | 0.9591 | |
colsample_bytree | 0.5–1.0 | 0.7033 | |
n_estimators | 50–500 | 319 | |
RF | max_depth | 3–20 | 10 |
min_samples_split | 2–20 | 2 | |
min_samples_leaf | 1–20 | 1 | |
n_estimators | 50–500 | 479 | |
max_features | 0.1–1.0 | 0.8485 | |
LightGBM | learning_rate | 0.01–0.2 | 0.1926 |
max_depth | 3–20 | 8 | |
num_leaves | 20–100 | 54 | |
n_estimators | 50–500 | 485 | |
min_child_samples | 5–50 | 13 | |
Subsample | 0.6–1.0 | 0.6604 | |
colsample_bytree | 0.6–1.0 | 0.8689 | |
SVR | C | 1–500 | 299 |
epsilon | 0.001–0.5 | 0.0789 | |
gamma | 0.0001–1 | 0.1561 | |
ANN | hidden1 (neurons) | 16–128 | 109 |
hidden2 (neurons) | 8–64 | 19 | |
alpha (L2 penalty) | 1 × 10−6–1 × 10−4 | 0.0018 | |
learning_rate_init | 1 × 10−4–1 × 10−2 | 0.0019 |
Parameter | Abbr. | Unit | Mean | Std | Min | 25% | 50% | 75% | Max |
---|---|---|---|---|---|---|---|---|---|
Fly ash | FA | kg/m3 | 350 | 50 | 300 | 300 | 350 | 400 | 400 |
Ground granulated blast furnace slag | GGBFS | kg/m3 | 50 | 50 | 0 | 0 | 50 | 100 | 100 |
NaOH molar concentration | M | - | 11 | 2.2 | 8 | 9.5 | 11 | 12.5 | 14 |
NaOH | NH | kg/m3 | 70 | 0 | 70 | 70 | 70 | 70 | 70 |
Na2SiO3 | NS | kg/m3 | 120 | 0 | 120 | 120 | 120 | 120 | 120 |
Extra water | EW | kg/m3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Coarse aggregate | CoAg | kg/m3 | 873.3 | 217.2 | 620 | 620 | 850 | 1150 | 1150 |
Fine aggregate | FiAg | kg/m3 | 650 | 0 | 650 | 650 | 650 | 650 | 650 |
Recycled aggregate | R-Ag | kg/m3 | 366.7 | 330.2 | 0 | 0 | 300 | 800 | 800 |
Curing temperature | CT | °C | 49.7 | 11.9 | 24 | 48 | 48 | 60 | 60 |
Curing time | CuTi | hrs | 44.6 | 20 | 24 | 24 | 48 | 72 | 72 |
Testing age | TA | Days | 13 | 9.5 | 3 | 6 | 10.5 | 17.5 | 28 |
Compressive Strength | CS | MPa | 44.7 | 17.2 | 23.4 | 32.7 | 39.9 | 52.1 | 102 |
Model | R2 | RMSE (MPa) | MAE (MPa) | MAPE (%) |
---|---|---|---|---|
XGB-Default | 0.9990 ± 0.0006 | 0.4956 ± 0.1477 | 0.2845 ± 0.0601 | 0.64 |
XGB-BO | 0.9997 ± 0.0001 | 0.3100 ± 0.0616 | 0.2191 ± 0.0368 | 0.50 |
RF-Default | 0.9965 ± 0.0020 | 0.9523 ± 0.2365 | 0.6113 ± 0.1314 | 1.39 |
RF-BO | 0.9966 ± 0.0020 | 0.9462 ± 0.2449 | 0.6222 ± 0.1522 | 1.39 |
LightGBM-Default | 0.9977 ± 0.0009 | 0.7959 ± 0.1305 | 0.5287 ± 0.0561 | 1.15 |
LightGBM-BO | 0.9996 ± 0.0001 | 0.3567 ± 0.0599 | 0.2480 ± 0.0426 | 0.57 |
SVR-Default | 0.9993 ± 0.0003 | 0.4367 ± 0.1075 | 0.2746 ± 0.0468 | 0.59 |
SVR-BO | 0.9995 ± 0.0002 | 0.3705 ± 0.0863 | 0.2274 ± 0.0287 | 0.51 |
ANN-Default | 0.9824 ± 0.0073 | 2.1965 ± 0.3982 | 1.6265 ± 0.3104 | 3.66 |
ANN-BO | 0.9961 ± 0.0012 | 1.0493 ± 0.1222 | 0.8054 ± 0.0908 | 1.87 |
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Cihan, M.T.; Cihan, P. Bayesian-Optimized Ensemble Models for Geopolymer Concrete Compressive Strength Prediction with Interpretability Analysis. Buildings 2025, 15, 3667. https://doi.org/10.3390/buildings15203667
Cihan MT, Cihan P. Bayesian-Optimized Ensemble Models for Geopolymer Concrete Compressive Strength Prediction with Interpretability Analysis. Buildings. 2025; 15(20):3667. https://doi.org/10.3390/buildings15203667
Chicago/Turabian StyleCihan, Mehmet Timur, and Pınar Cihan. 2025. "Bayesian-Optimized Ensemble Models for Geopolymer Concrete Compressive Strength Prediction with Interpretability Analysis" Buildings 15, no. 20: 3667. https://doi.org/10.3390/buildings15203667
APA StyleCihan, M. T., & Cihan, P. (2025). Bayesian-Optimized Ensemble Models for Geopolymer Concrete Compressive Strength Prediction with Interpretability Analysis. Buildings, 15(20), 3667. https://doi.org/10.3390/buildings15203667