Evaluating the predictive accuracy of supervised machine learning models to explore the mechanical strength of blast furnace slag incorporated concrete

Abstract

Blast furnace slag (BFS) concrete offers significant environmental and durability advantages over ordinary portland cement (OPC) concrete, including reduced CO₂ emissions, enhanced long-term strength, and stronger resistance to chemical attacks. However, refining its mix design using conventional experimental methods is time-consuming and costly. This study addresses this challenge by developing advanced machine learning (ML) models to predict the compressive strength of BFS-incorporated concrete. A large dataset of 675 samples featuring cement, BFS, fly ash, aggregates, water, superplasticizer (SP), and curing age was assembled. Six ML models—AdaBoost, Decision Tree, Gradient Boosting Regressor, K-Nearest Neighbors, LightGBM, and XGBoost were evaluated. Comprehensive hyperparameter tuning via grid search and cross-validation optimized model performance and mitigated overfitting. Predictive accuracy was assessed using R², RMSE, MAE, and MAPE metrics. Model interpretability was enhanced through SHAP analysis and partial dependence plots (PDP), revealing curing age, SP, and cement as dominant features influencing compressive strength. Results demonstrated that LightGBM (test R² = 0.946, RMSE = 4.41 MPa) and XGBoost (test R² = 0.943, RMSE = 4.52 MPa) exhibited almost comparable predictive performance; however, LightGBM achieved the highest overall accuracy, reflected in its slightly higher test R² and lower RMSE, which declares LightGBM the best model for predicting CS of BFS-concrete. PDP analysis revealed that the optimal BFS replacement was observed between 30 and 40% range. This ML framework eliminates resource-intensive experimentation, accelerating sustainable concrete design with industrial byproducts.

Introduction

Concrete remains the world’s most used construction material, valued for its cost-efficiency, mechanical strength, durability, and adaptability in a variety of structural applications^1–4. Yet this success comes at a cost that the industry can no longer ignore. The cement manufacturing process, which forms concrete’s binding foundation, causes approximately 8% of global CO₂ emissions^5–9. The magnitude of these emissions is heightened by extensive energy input, consumption of non-renewable mineral resources, and the production of associated pollutants^7,10–13. Growing recognition of the environmental costs linked to ordinary portland cement (OPC) has led to an urgent search for greener alternatives that can reduce the ecological footprint without compromising performance^14–18. One strategic intervention involves incorporating a fraction of OPC with supplementary cementitious materials (SCMs)^1,19–21. Among available SCMs, BFS offers significant advantages. This glassy granular material originates as a co-product of pig iron manufacturing²². When ground to fine particles (< 45 μm), BFS manifests latent hydraulic properties that enable it to react with portlandite (Ca(OH)₂) during cement hydration, forming additional calcium silicate hydrate (C-S-H) gel²³. This reaction mechanism delivers three combined benefits: significant carbon reduction (0.75–0.95 tons CO₂ avoided per ton of cement replaced), enhanced durability performance (40–60% lower chloride permeability compared to OPC), and improved long-term strength development through pore structure refinement^24–28. Field studies further confirm BFS-concrete’s superior durability under sulfate exposure and alkali-silica reactivity, extending service life in aggressive environments like marine structures and chemical processing plants^29,30. Despite these advantages, optimizing BFS-concrete compositions leads to ongoing challenges. The performance of BFS-concrete is governed by complex, nonlinear interactions among replacement level, slag chemistry, admixtures, and curing conditions, which are difficult to capture through conventional parametric approaches ​​³¹. Furthermore, the interaction between BFS and chemical admixtures like SP results in dual constraints between workability and strength gain³². ML techniques effectively model these multifactor interactions and can accurately map the composition–strength relationships based on experimental data³³.

Traditional methods demand experimental matrices testing dozens of variables and curing conditions. Such experimentation consumes large material volumes per mix and requires 28–90 days for strength results alone³⁴. This resource-intensive system fundamentally facilitates the need for intelligent, data-driven innovations that streamline the development and assessment of eco-efficient construction materials. The application of ML is increasingly recognized as a promising pathway to deal with the complexities inherent in modern concrete mix design and performance evaluation, among these innovations^35,36.

The availability of extensive experimental datasets, combined with increasing computational power, has enabled the deployment of ML algorithms that can capture and predict the complex relationships linking composition, processing, and resulting properties of concrete. Trained on earlier observations, these algorithms can provide rapid, accurate predictions of compressive strength (CS), enabling researchers and practitioners to efficiently identify optimum blends for both structural performance and sustainability^37–41. Numerous ML techniques have been successfully utilized for the prediction of concrete properties. Linear regression, one of the earliest strategies, is limited by its inability to capture interactions and nonlinearities characteristic in concrete systems^42–44. Subsequent models have employed regularization methods such as Ridge and LASSO regression to enhance stability and reduce overfitting, but their predictive capabilities still trail those of more sophisticated methods⁴⁵. The real breakthrough has been the adoption of non-linear and ensemble-based algorithms, such as Decision Tree (DT), Random Forests (RF), Support Vector Machines (SVM), Gradient Boosting Regressor (GBR), AdaBoost, LightGBM, and XGBoost, among others^46–50.

Tree-based ensemble techniques have become a widely adopted method in concrete property prediction because they can represent complex, non-linear interactions, manage high-dimensional input spaces, and resist overfitting through mechanisms like bagging and boosting⁵¹. RF aggregates the outputs of many decision trees, each fitted to a bootstrapped sample of the training data, reducing variance and improving generalization⁵². Gradient boosting frameworks like XGBoost and LightGBM build sequential ensembles. Every added model corrects the residual error from the previous step. These models show high accuracy even on complex and noisy datasets. Furthermore, these methods are strong at inputting feature interactions and, with appropriate hyperparameter tuning, adapt well to the multifactorial nature of modern concrete systems^20,53–55. Other advanced ML models, such as artificial neural networks (ANNs), have also shown promise due to their universality in function approximation; still, they are frequently scrutinized for their ‘black-box’ nature and high data requirement for reliable convergence⁵⁶. ANNs can yield high accuracy, especially when developed on expansive, multi-domain data. However, they lack the native interpretability of tree-based or linear models. This often makes them less suitable for engineering applications, where understanding feature contributions and physical reasoning is important^57,58.

A prevailing issue in the adoption of ML in the construction materials community is the question of interpretability. Materials science requires models to be accurate and physically meaningful. These predictions must guide scientific understanding and practical application⁵⁹. To confront this challenge, recent research has embraced model-agnostic interpretability methods, most notably SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP)⁶⁰. SHAP, which derives from game‑theoretic Shapley values, allocates an additive importance value to each feature for every prediction. This enables detailed attribution of performance outcomes to attributes⁶¹. In contrast, PDP shows how the target variable changes as one input feature varies while other features are held constant. This makes PDP useful for understanding the monotonicity and shape of feature effects⁶². Alongside recent developments in modeling and interpretability, rigorous evaluation of ML solutions requires objective, standardized metrics. Metrics such as the Coefficient of Determination (R²), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) have become standard benchmarks for model assessment⁶³. Each offers specific indications: MAE and MAPE assess average predictive error, MSE and RMSE emphasize larger deviations, and R² quantifies the overall explained variance⁶⁴.

The authors are aware that only a few studies have developed ML models for the inference of the mechanical properties of concrete with BFS. Table 1 presents a synthesis of the literature on ML-based learning for assessing the characteristics of BFS concrete. From the table, previous studies have primarily employed traditional predictive models such as ANN, SVM, and RF to characterize concrete properties^65–67. Much of the current literature tends to focus on individual models or a limited suite of techniques, often relying on relatively small datasets, which can limit external validity. While XGBoost and LightGBM excel in general ML, their effectiveness for concrete mixes is unclear. This limitation is most notable when systematic feature analysis and hyperparameter optimization are applied. The majority of studies to date have not coupled prediction with reliable interpretation. Another complication is the risk of overfitting, whereby highly complex models learn the random variation of the training data rather than the underlying patterns. Advanced cross-validation strategies, grid search for hyperparameters, and careful partitioning of test/training sets are essential. They mitigate risk and generate predictions that are reliable across novel datasets⁶⁸.

Table 1.

A comprehensive review of ML approaches for predicting the properties of concrete incorporating BFS.

Objective of the study	Number of samples	ML-based models	Output parameter	Refs.
Predictive modeling of CS of concrete with BFS using ANN, ANFIS, and GEP	300	ANN, ANFIS, GEP	CS	69
Optimized XGBoost model for predicting CS of eco-friendly concrete with BFS and RCA	270	XGBoost, Bayesian Optimization	CS	70
Analyzing properties of concrete incorporating GGBFS and calcium nitrite-based corrosion inhibitor (CNI)	162	ANN and ANFIS	CS, splitting tensile strength, chloride ion permeability, durability	71
Concrete’s CS prediction with BFS and Fly Ash using Firefly Algorithm and RF	128	Firefly Algorithm, RF	CS	72
Modeling the long- term influence of GGBFS on concrete CS under wet curing	284	ANN and Fuzzy Logic	CS	73
GGBFS concrete’s CS prediction	268	RF and SVM	CS	74
Evaluation of AI methods for assessing CS of BFS concrete using multiple ML models	625	DT, RF, SVM, KNN, ANN	CS	75
Comparison of the effects of BFS and waste tire rubber powder (WTRP) on the CS of cement mortars	288	RF, AdaBoost, SVM and Naïve Bayes Classifier	CS	76

Recognizing these drawbacks and opportunities, our objective is to advance the deployment of ML in the prediction of CS for BFS-incorporated concrete. We built an extensive, curated dataset of 675 entries covering cement, BFS, and other key mix parameters. Using this, we developed and systematically compared advanced ML models: AdaBoost, DT, GBR, k-Nearest Neighbor (KNN), LightGBM, and XGBoost. The workflow integrates comprehensive hyperparameter tuning via grid search and cross-validation to ensure powerful generalization. Equally important, we employ SHAP and PDP methods to open the ‘black box’ of these models, delivering transparent, actionable insights into how mix components shape strength outcomes. Through this work, we seek to fill existing gaps in the ML-driven optimization of BFS concrete and to demonstrate that explainable, well-calibrated ML models can equip the construction materials community with faster, more transparent, and more sustainable pathways to high-performance concrete design.

Methodology

Data collection and pre-processing

In the present study, a thorough examination of existing research on BFS incorporated concrete was conducted to construct the algorithmic predictors of CS. A comprehensive database of 675 records has been curated through an in-depth analysis of published experimental studies and ML repositories, which contain verified experimental datasets on BFS incorporated concrete^77–89. The data collection involved systematically reviewing prior research that reported CS and corresponding mix composition parameters used in this research. Each dataset was extracted, cross-checked, and standardized to maintain consistency in units, mix proportions, and test conditions across different studies. Then, they were compiled into an Excel sheet, where they were systematically organized, categorized, and subjected to statistical analysis. An overview of the methodology is shown in Fig. 1.

Fig. 1.

Flowchart of the study methodology.

For the ML simulations, the compiled dataset was partitioned using a random split into train/test sets. A total of 80% of the data was designated for the training set, utilized to develop the model, and validated through cross-checking for optimal hyperparameter adjustment. The data cross-checking process involved two authors independently re-entering 10% of the rows sampled at random and comparing them against the compiled sheet (acceptance threshold: ≤0.5% relative deviation per field). Discrepancies triggered a full re‑check of the source paper. A third author validated all unit conversions. The leftover 20% of the compiled data was reserved as the testing set, employed to assess the effectiveness and accuracy of the developed models. The laboratory data referenced from the literature were collected in a randomized manner to ensure an unbiased representation. Although the dataset encompassed numerous variables, only those parameters with a significant influence on the mechanical properties were chosen and subsequently processed. While many of these experimental studies also assess other concrete properties, this research focused solely on CS related data points, which were selectively gathered in sufficient quantity to support model development.

Eight input variables were used to develop the models, including the amount of cement, BFS, fly ash, coarse aggregate, fine aggregate, water, SP, and curing period, while CS was the output variable. To ensure consistency and minimize potential errors introduced during the simulation process, all data values were meticulously transformed and standardized to a uniform scale ranging from 0 to 1. This normalization step was integral to the model construction, facilitating enhanced computational efficiency and improved accuracy in the simulation outcomes. Data manipulation and preprocessing employed data analysis libraries of Pandas v2.2 and NumPy v1.26, with statistical computations facilitated by SciPy v1.12.

The additional data processing steps encompassed data cleaning, handling missing values, encoding categorical data and treating outliers. The statistical summary of all variables is presented in Table 2. Outliers were detected using the interquartile range (IQR) method, where values below or above were identified as extremes. Rather than deleting these values, they were winsorized to the nearest valid limit to maintain the full dataset size. Figure 2 illustrates the variable distributions and the IQR-based outlier detection process applied to each parameter. Together, these steps ensured a validated and balanced dataset suitable for reliable model training.

Table 2.

Statistical summary of input and output variables used for model development.

Parameters	Mean	Std.	Min.	25%	50%	75%	Max.
Cement	290.74	100.63	102	212.5	266	375	540
BFS	67.99	84.45	0	0	20	128.5	359.4
Fly ash	56.66	63.14	0	0	0	118.8	174.7
Coarse aggregate	981.21	72.21	801	936.2	971.8	1043.6	1145
Fine aggregate	780.93	82.40	594	746.6	780.7	845	992.6
Water	177.33	23.11	121.8	159.35	175.5	192	228
SP	6.74	6.27	0	0	6.7	11.1	32.2
Curing age	49.69	69.30	3	7	28	56	365
Compressive strength	38.16	17.52	4.57	24.6	37.4	50.735	82.6

Fig. 2.

Boxplots of input and output variables.

Data representation

Data representation is an essential tool for understanding complex datasets. It allows for the effective communication of patterns, relationships, and trends that may not be obvious through experimental data alone⁹⁰. In this study, we employ histograms with overlaid density plots and a correlation heatmap to explore the frequency profiles of input and output features and their interrelationships. A comprehensive summary presented in Table 2 enumerates the key distribution statistics for each input and output variable in the dataset, including mean, standard deviation, quartiles, and observed ranges.

In addition, the boxplot visualization referred to as Fig. 2 concisely displays the central tendency, dispersion, and outlier distribution for all variables. Cement content has a mean of 290.74 kg/m³, with values spreading from 102 kg/m³ to 540 kg/m³, indicating a wide variety of mix designs. Figure 2 highlights a concentration of values around 266 kg/m³, with some extreme outliers. BFS shows similar variability, with a mean of 67.99 kg/m³ ranging from 0 to 359.4 kg/m³ with frequent outliers. Water content ranges from 121.8 kg/m³ to 228 kg/m³, while SP is typically used in small amounts, showing less variability. Coarse and fine aggregates show extensive interquartile ranges, with means of 981.21 kg/m³ and 780.93 kg/m³, respectively, are more consistent across the samples.

CS ranges from 4.57 MPa to 82.6 MPa with a median of 37.4 MPa and several high‑strength outliers, features that the whiskers and mean markers in Fig. 2 display clearly. This wide range can be linked to the variations in input materials. Higher cement content and the presence of BFS seem to positively affect the CS. Concrete mixes with higher cement content and optimal amounts of slag generally show stronger CS. The consistent use of water, SP and aggregates further influences the overall strength, showing that the mix design directly impacts the concrete’s performance.

Figure 3 presents a series of histograms with density plots for each input variable. These visualizations highlight key aspects of the data distribution and provide a clearer understanding of how each variable behaves. Cement shows a relatively normal distribution, with values mostly centered around 200 kg/m³ to 400 kg/m³. This suggests that cement content is fairly consistent across the dataset, although a few higher values indicate mixes that use a larger proportion of cement.

Fig. 3.

Histograms and density plots of dataset variables.

BFS results in a more prominent distribution. The histogram reveals a concentration of values between 0 and 150 kg/m³, followed by a gradual decrease as slag content increases. This indicates that lower amounts of BFS are more commonly used in the mixes, although there are some concrete designs containing higher levels of slag. The density plot clarifies that while most mixes contain low slag, a smaller subset uses high quantities. This difference may impact cost and material properties (e.g., strength, durability). Fly Ash follows a similar behavior to slag but shows a slightly more skewed distribution, with values ranging from 0 to 174.7 kg/m³. Water content is near symmetric around 175 to 190 kg/m³. Its slight upward skew indicates a common trend toward higher-water mixes. SP usage, with a strong right-skewed distribution, is consistent with dosage-on-demand practice. Curing age is multi-modal with peaks at standard curing times (notably 28 days) and secondary modes at extended ages. Finally, CS is unimodal with a slight positive skew, indicating more mid-strength than very high-strength mixes.

Figure 4, a correlation heatmap, provides visibility into the interactions between these variables, illustrating both positive and negative correlations. The heatmap illustrates that cement shows a positive correlation of about 0.48 with CS, confirming that higher cement content generally produces stronger concrete. BFS exhibits a weak positive correlation of around 0.19 with CS, suggesting that slag provides a modest improvement in strength. In contrast, fly ash, coarse aggregate, fine aggregate and water show slight to moderate negative correlations with CS. SP and curing age demonstrate strong positive correlations of 0.46 and 0.30, respectively, emphasizing their substantial role in strength enhancement.

Fig. 4.

Correlation heatmap of concrete mix parameters and CS.

Model development

This research investigated a range of algorithms to select the best-performing model for concrete incorporating BFS. In this study, classical regression models such as linear and polynomial regression were not adopted because they rely on rigid functional assumptions that struggle to represent the complex, nonlinear interactions inherent in BFS-incorporated concrete. Relationships among binder, aggregate, SCMs, and curing kinetics with CS are highly non-linear and exhibit interdependent effects that cannot be adequately captured through linear combinations of parameters or simple transformations. In contrast, ensemble tree-based methods and gradient boosting frameworks can model nonlinear feature interactions without prespecifying functional forms, which makes them more appropriate for accurately learning composition-strength relationships. Therefore, classical regression approaches were excluded at the model selection stage to ensure methodological alignment with the underlying material behavior.

The evaluated algorithms included AdaBoost, DT, GBR, XGBoost, KNN and LightGBM. Each model was evaluated using a random 80:20 train-test split and a statistical metrics approach to ensure the generation of the most reliable results. The analysis incorporated eight input variables and a single output variable, as detailed in the preceding sections. All computational analyses were performed on a Windows 11 64-bit system using Python 3.11. Model development and validation were conducted using scikit-learn version 1.7, while XGBoost version 2.0 and LightGBM version 4.3 enabled advanced ensemble modeling. Visualization outputs were generated using Matplotlib v3.8, Seaborn v0.13, and SHAP v0.45.

Adaptive boosting (AdaBoost/ADB)

AdaBoost is an ensemble algorithm that facilitates predictive accuracy by concentrating on tough examples⁹¹. For regression, AdaBoost combines multiple weak learners by reweighting samples according to their relative absolute error⁹². For iteration with sample weights ,

The weighted error and stage parameter are,

Weights are updated and normalized as,

Each learner receives weight, . The final ensemble prediction is the weighted median of all weak learners,

Decision tree (DT)

DT is widely utilized for classification and regression tasks. They work by repeatedly splitting the data based on features, attempting to reduce variance at each node⁹³. DT for regression splits the data to minimize the sum of squared errors (SSE) at each node⁹⁴. For a node containing samples are,

A candidate split on a feature produces child nodes . The reduction (gain) in impurity is,

The algorithm chooses the split that maximizes and continues recursively until a stopping criterion (e.g., maximum depth, minimum samples per leaf) is satisfied. The final leaf prediction is the mean of targets in that leaf,

Gradient boosted regression (GBR)

GBR is a highly effective ML algorithm that combines the principles of boosting and regression to deliver accurate predictive models⁹³. At the start, it creates a simple model ​ (often a constant) that minimizes the chosen loss function . In each round , it calculates the “pseudo-residuals” ​ for each data point,

where ​ is the model from the previous step, and is the true target. It then trains a weak regressor (commonly a shallow tree) on these residuals. Next, the algorithm finds the multiplier that best fits the new weak regressor to reduce the loss. Finally, it updates the model:

where is the learning rate that controls how quickly the model learns. Repeating this process for iterations yields a final model that sums all weak regressors. By continually adjusting for past errors, GBR steadily boosts predictive accuracy⁴⁶.

k-Nearest neighbors (KNN)

KNN is based on the principle of proximity, where the outcome for a given data point is determined by the modal class or mean value of its -nearest neighbors in the predictor space. It is a model-free method that makes no specific assumptions about the underlying distribution⁹⁵. KNN predicts CS for a query point ​ as the average strength of its nearest neighbors,

where distance is typically Euclidean,

Here, is a training instance described by features. The closest samples (i.e., those with the smallest distances) form the “neighborhood.” In classification, KNN typically chooses the highest frequency data among these neighbors; for regression, it often takes the mean of their target values. The parameter significantly influences performance, small values may overfit to local noise, while large values risk over-smoothing predictions. Because KNN postpones its core calculations until it needs to predict a query point⁹⁶.

Light gradient boosting machine (LightGBM/LGB)

LightGBM is a powerful and sample-efficient algorithm for gradient boosting tasks. It builds decision trees by focusing on the leaf that achieves the greatest improvement in the loss function. Instead of adding a tree layer by layer, LightGBM performs leaf-wise growth, which enables it to capture more complex patterns in the data⁹⁷. To update the model, LightGBM adds a new tree to the previous model with a learning rate :

Defining first- and second-order gradients of the loss,

For any node, the gradient and Hessian sums are defined as,

The gain for a split into left (L) and right (R) children is,

where represents the regularization term for leaf weights and is a complexity penalty that discourages overfitting. LightGBM continues leaf-wise growth until the stopping criteria are met.

Extreme gradient boosting (XGBoost/XGB)

XGBoost assembles a series of decision trees, where each iteration corrects the residual errors of previous ones. XGBoost applies a second-order Taylor expansion to optimize the objective function, which allows for faster convergence and more accurate models⁹⁸.

At boosting stage , adding a new tree to the current prediction gives,

with tree complexity,

where is the number of leaves and is the weight of leaf . Using the second-order expansion around with,

Collecting samples of leaf in the index set , the stage objective (up to constants) becomes,

The optimal leaf weight and the corresponding gain are,

After fitting , the model is updated with learning rate ,

Hyperparameter tuning

We tuned hyperparameters to improve model accuracy and prevent overfitting. For the DT model, Fig. 5 illustrates RMSE versus tree depth that tested different tree depths. As depth increased, training RMSE dropped sharply, showing the model fit the training data better. However, after a certain depth, the testing RMSE stopped decreasing and even started to rise slightly. This indicated that the model was initializing to track the training data rather than learning general patterns. We selected the tree depth where the testing RMSE became stable. This approach gave us a model that was accurate on unseen data without being too complex.

Fig. 5.

Variation of RMSE with tree depth in the DT model.

Similarly, for the KNN regressor, Fig. 6 displays mean error versus K value. At low k values, the model had low training error but higher validation error, suggesting overfitting. As we increased k, the training error rose, but the validation error initially decreased, reaching its lowest point at k = 3. Beyond this, the validation error started to climb, indicating underfitting as the model became too simple. The U-shaped curve of validation error across k values helped us clearly identify the optimal k. We chose the k value that gave the lowest validation error, ensuring the model could generalize well. Throughout the tuning process, we relied on trends in both training and validation errors. This helped us avoid both underfitting and overfitting. The final hyperparameter choices for each model were based on the points where validation performance was best.

Fig. 6.

Mean prediction with different values of in the KNN algorithm.

Model accuracy assessment

In this study, a comprehensive set of performance metrics was used to assess the predictive accuracy of the ML models applied to concrete strength prediction. The chosen metrics—MAE, MAPE, MSE, RMSE, R² provide a thorough evaluation of model accuracy, reliability, and generalizability across various datasets.

MAE calculates the average absolute differences between the predicted and actual values. This straightforward metric offers a clear interpretation of how far off the model’s predictions are on average, without giving excessive weight to outliers⁹⁹. MAPE provides a measure of prediction accuracy that is easy to interpret across datasets with different scales¹⁰⁰. MSE reflects the average squared difference between actual and predicted values. It gives more importance to larger errors than MAE and provides insight into prediction errors¹⁰¹. RMSE, a derived metric from MSE, further emphasizes larger discrepancies by taking the square root. A lower RMSE indicates better model accuracy by reducing the deviation from actual values¹⁰². Finally, R² measures how well the model explains the variance in the target variable. A higher R-squared value demonstrates better model fit, with values closer to 1, meaning a stronger predictive relationship¹⁰³.

These metrics are instrumental in comparing model performance. In this study, they are used to evaluate how well each ML model fits the data and how accurately it predicts CS in BFS-incorporated concrete. A combination of these metrics covers multiple model performance aspects. These include error magnitude, accuracy, and the proportion of variance. The equations for each metric are as follows:

where ​ is the actual value, is the predicted value, and ​ is the mean of the observed values.

Model interpretation with SHAP

SHAP values are used to analyze ML models by linking each feature a contribution to the prediction¹⁰⁴. For a model with features, the prediction can be decomposed as,

where is the baseline (mean prediction over the dataset), and is the contribution of the feature for sample . The Shapley value for each feature is computed as,

where represents a subset of all features, excluding , and is the expected model output when only the features in are fixed to their observed values.

For overall global importance, the mean absolute SHAP value is calculated as,

The model’s overall performance mainly depends on features with higher average SHAP values. This allows for the identification of the key factors behind the model’s predictions¹⁰⁵. SHAP values explain the specific contribution of each feature to an individual prediction by local interpretation. Positive SHAP values indicate that the feature increases the predicted outcome, whereas negative values suggest a reducing effect on the prediction¹⁰⁶. This interpretation helps in understanding the model’s decision-making process and enhances its usability in practical applications.

Model interpretation with PDP

PDP displays the effect of a single feature on model predictions while keeping other features constant. PDP offer a clear view of how a feature influences the output across its entire range by visualizing the relationship¹⁰⁷. For a feature , the partial dependence is measured by averaging the predictions over the dataset, while fixing the values of all other features through this formula:

This plot illustrates how the prediction changes as the value of varies. PDPs are especially effective for examining non-linear relationships between features and the target variable¹⁰⁸. In this study, PDPs provide a clear and visual way to explore the role of each feature in guiding model predictions. They help clarify complex relationships and improve the model’s transparency and interpretability.

Results and discussion

Exploratory data analysis

Exploratory Data Analysis (EDA) gives a foundational understanding of the dataset by analyzing how features are spread out and how they are related to each other before utilizing ML models¹⁰⁹. Figure 7 displays scatter plots showing the correlation between essential input variables—cement, BFS, fly ash, coarse aggregate, fine aggregate, water, SP, and curing age against CS. In the plots, red circular markers represent individual data points, with each marker indicating the CS value corresponding to a specific feature level. The Cement plot indicates a clear positive correlation, confirming cement’s essential role in enhancing CS. Conversely, an inverse relationship is observed in the Water plot, aligning with the recognized impact of higher water content weakening concrete. Curing age shows a strong positive relationship, highlighting the strength improvements with extended curing periods. SP content also exhibits a positive relationship with CS, due to enhanced workability and lower water usage.

Fig. 7.

Scatter plots of key input features against CS.

Scatter plots for BFS and fly ash reveal scattered distributions, suggesting their influence on CS depends significantly on interactions with other mix parameters. Aggregate contents, both coarse and fine, display inconsistent patterns, indicating that the aggregate alone does not primarily dictate CS outcomes. These graphical representations in Fig. 7 provide valuable insights into the dataset’s structure, helping identify key influencing factors before predictive modeling.

Predictive model performance and error metrics

The performance of the ML models in predicting the CS of BFS-incorporated concrete varied significantly. The tested models included AdaBoost, DT, GBR, XGBoost, KNN, and LightGBM. Figure 8 (a-f) illustrates the predicted vs. experimental CS values for each model. Red dots represent training data, while blue dots represent test data. The dashed black line (X = Y) indicates perfect predictions where predicted values match experimental ones. The green-shaded region marks the 10% error margin, showing how closely predictions align with actual values.

Fig. 8.

(a-f) Comparison of predicted and actual CS for each model.

Among all models, XGBoost and LightGBM delivered the best results. XGBoost achieved an R² of 0.993 for training and 0.943 for testing, while LightGBM recorded R² values of 0.975 and 0.946 for training and testing, respectively. These high values indicate that both models captured complex relationships within the data. Their predictions were closely clustered around the ideal X = Y line, highlighting their accuracy. The effectiveness of these models is attributed to their ability to handle non-linear interactions and large datasets efficiently^103,110. AdaBoost showed moderate performance, with R² values of 0.835 for training and 0.842 for testing. Its predictions followed the overall trend but had more deviations compared to XGBoost and LightGBM. GBR, with R² values of 0.960 for training and 0.934 for testing, performed well but was slightly less accurate than the leading boosting models.

KNN and DT models had the weakest performances. KNN had an R² of 0.782 for training and 0.707 for testing, indicating significant prediction errors, particularly for high CS. DT performed well on training data, achieving an R² of 0.993, but its test performance dropped significantly to 0.877. The wider spread of points in Fig. 8-(b) for DT indicates overfitting, where the model performed well on known data but failed to generalize for unseen cases.

Figure 9 presents a boxplot comparing the predicted CS values for each model against the actual experimental data. The blue boxes represent the interquartile range of predictions, while the green horizontal line within each box indicates the median. The black whiskers represent the range of values within an acceptable spread. The boxplot confirms that XGBoost and LightGBM produced predictions closest to the experimental values. Their median values are well-aligned, with minimal variation. In contrast, KNN and DT exhibit wider distributions, suggesting inconsistency in their predictions.

Fig. 9.

Boxplots of predicted versus actual CS values.

Residual analysis and model stability

Residual analysis is essential for assessing the generalization capability of ML models¹¹¹. Residuals, defined as the difference between observed and predicted CS, were plotted for each model in Fig. 10 (a-f). In these plots, black lines represent observed data, while blue and red lines indicate predictions for training and testing datasets, respectively. Residuals for each data point are depicted by green dots.

Fig. 10.

(a-f) Residual distributions for training and testing sets of ML models.

AdaBoost (Fig. 10-a) shows close agreement with training data but reveals larger deviations for the test set, especially at higher CS. AdaBoost achieved average errors of 5.7 MPa (train) and 6.015 MPa (test), with a notable maximum test error of 26.23 MPa. Similarly, DT (Fig. 10-b) exhibits extremely low training errors of an average of 0.18 MPa, yet larger test residuals of an average of 4.67 MPa and a high maximum test error of 24.04 MPa, indicating overfitting. GBR (Fig. 10-c) displays improved generalization with lower residuals for test data. GBR’s average test error was 3.72 MPa, with a maximum error of 22.18 MPa, outperforming AdaBoost and DT in stability. LightGBM (Fig. 10-d) further reduced residuals, indicating strong model stability, with average errors of 1.72 MPa (train) and 3.17 MPa (test). Its maximum test error 17.85 MPa was significantly lower, confirming good predictive reliability. XGBoost (Fig. 10-e) demonstrated the best stability among the tested models, having minimal residuals across both datasets. It achieved an average test error of 3.21 MPa and a maximum error of 18.54 MPa. KNN (Fig. 10-f) exhibited moderate stability, with training predictions closely matching the observed data. However, the residual plot indicates greater variability and dispersion for the test dataset, particularly at higher CS values¹¹². KNN produced average errors of 6.05 MPa (train) and 7.76 MPa (test), alongside a maximum test error of 37.99 MPa. This variability suggests KNN’s limitation in consistently generalizing predictions for new, unseen data. Error metrics summarized in Table 3 reinforce these observations. Boosting algorithms (GBR, LightGBM, XGBoost) consistently provided lower residuals and superior generalization compared to AdaBoost and DT, highlighting their effectiveness in predicting CS of BFS-incorporated concrete.

Table 3.

Residual error statistics of ML models for training and testing datasets.

Model	Max error (MPa)		Min error (MPa)		Avg error (MPa)
	Train	Test	Train	Test	Train	Test
ADB	16.82968	26.233	0.002222	0.076857	5.696488	6.015032
DT	24.75	24.04	0	0	0.18466	4.674037
GBR	26.7807	22.18315	0.010305	0.124604	2.49949	3.723731
LGB	26.18629	17.85596	0.000479	0.039685	1.721064	3.176309
XGB	24.8166	18.54782	0.000704	0.007422	0.337398	3.209919
KNN	36.566	37.992	0.016	0.06	6.051385	7.764815

Comparative analysis of model performances

The five complementary metrics in Table 4 (R², RMSE, MSE, MAE, MAPE) and the radar charts in Fig. 11 together provide a balanced view of accuracy and generalization. On the test set, XGBoost and LightGBM form the tightest profiles on the error axes while extending furthest on R², indicating a strong fit with low dispersion of residuals. XGBoost attains R² of 0.943 (test) and 0.993 (train), RMSE of 4.523 MPa (test) and 1.425 MPa (train), MAPE of 10.365% and 1.033% for test and train, respectively. LightGBM records R² of 0.946 (test) and 0.975 (train), RMSE of 4.414 MPa (test) and 2.719 MPa (train), MAPE of 9.792% (test) and 5.397% (train). These values are consistent with the clustered predicted–observed points near the 1:1 line in Fig. 12 and the narrow residual bands in Fig. 10.

Table 4.

Prediction performance metrics of the developed ML models.

Model	R 2		RMSE (MPa)		MSE (MPa)		MAE (MPa)		MAPE (%)
	Train	Test	Train	Test	Train	Test	Train	Test	Train	Test
XGB	0.993	0.943	1.425	4.523	2.030	20.458	0.337	3.209	1.033	10.365
LGB	0.975	0.946	2.719	4.414	7.396	19.489	1.721	3.176	5.397	9.792
DT	0.993	0.859	1.403	7.129	1.970	50.826	0.184	4.860	0.522	15.978
GBR	0.960	0.934	3.405	4.876	11.597	23.777	2.499	3.695	8.067	11.003
KNN	0.782	0.707	7.996	10.261	63.937	105.288	6.051	7.764	21.544	27.073
ADB	0.835	0.842	6.855	7.426	46.993	55.148	5.760	6.093	21.895	22.543

Fig. 11.

(a-e) Radar charts of model evaluation metrics for both training and testing phases.

Fig. 12.

PDP showing effects of key input variables on model predictions.

Models with single learners or instance-based rules show wider error envelopes. DT maintains a very high training R² of 0.993 but drops to 0.859 on the test set, with RMSE rising to 7.129 MPa at test, and an effect visible as a broader spread around the identity line and larger test residuals in Fig. 10-b, characteristic of overfitting to training partitions. KNN presents the lowest test R² of 0.707 and the highest RMSE on test of 10.261 MPa and MAPE of 27.073%, with dispersion increasing at higher strengths; this pattern matches the wider boxes and whiskers in the comparative plots and indicates limited capacity to capture nonlinearities across diverse mixes.

Boosting methods other than LightGBM and XGBoost follow similar but less pronounced trends. GBR achieves test R² of 0.934 and RMSE of 4.876 MPa, aligning closely with the leading ensemble models in the radar plots. AdaBoost reaches test R² of 0.842 with RMSE of 7.426 MPa and MAPE of 22.543%, showing moderate fit with larger residual tails. The relative ordering across metrics is coherent: methods that minimize RMSE and MSE on the test set also yield lower MAE and MAPE, and they sustain smaller train–test gaps in R², signaling better bias–variance trade–offs.

Feature importance and interpretability

Partial dependence plots (PDP) analysis

Figure 12 presents the PDP for various features such as cement, BFS, fly ash, coarse aggregate, fine aggregate, water, SP, and curing age. The plots clearly indicate non-linear relationships between certain features and CS. For cement, Fig. 12 demonstrates that strength rises steadily with increasing cement content, then shows a gentle taper, indicating diminishing returns at higher dosages. The early slope is steep, which explains why small increases in cement near the lower range produce noticeable gains. The taper suggests that past a practical threshold, other factors begin to govern paste quality.

The PDP of BFS indicates that the CS increases steadily as the BFS content rises from low to moderate levels. Beyond this range, the response curve becomes almost horizontal, suggesting that further addition of slag produces little improvement in strength. Quantitatively, the turning point appears around 140–160 kg/m³ of BFS, which corresponds to roughly 30–40% replacement of cement in the mixtures. This pattern confirms that moderate incorporation of BFS optimizes the pozzolanic and filler effects while avoiding dilution of cementitious constituents¹¹³. Although the scatter distribution of BFS in the dataset may initially look like random noise, it actually reflects a nonlinear, interaction-dependent relationship between slag content and CS. However, as shown here, BFS contributes positively to strength only within a moderate replacement level (approximately 30%–40%), after which its influence declines. When BFS levels fall outside this favorable range, their effect becomes highly sensitive to other parameters, which are not possible to simultaneously represent in the two-dimensional scatter plot. Therefore, the apparent dispersion of BFS data in the data analysis section primarily arises from these multidimensional interactions, rather than a lack of underlying trend, and is consistent with the nonlinear feature behavior captured by the interpretable ML models.

Furthermore, SP shows a clear positive trend that is most pronounced at the lower end of the dosing range, followed by a mild plateau. This shape is consistent with improved workability and packing at modest dosages and reduced incremental benefit at higher dosages once dispersion is adequate. The curve of fly ash is flat to mildly negative over much of the range, especially at shorter curing periods, reflecting slower pozzolanic activity. Where curing age is high and water is low, the decline lessens, which suggests interaction effects that a one-way PDP only partly captures. On the other hand, water exhibits an inverse relationship with CS, as seen in its plot where an increase in water content results in a noticeable drop in strength. This behavior is in line with the widely known phenomenon in concrete mix design, where the water-cement ratio plays a critical role in determining strength. Fine aggregate and coarse aggregate display complex trends, where strength rises initially with increasing aggregate content, but the effect plateaus at higher values.

SHAP values analysis

Figure 13 displays the SHAP bar plot, which quantifies the importance of each feature in predicting CS. Curing age is the most influential feature, with a SHAP value of + 10.38, meaning it has the most substantial positive impact on CS. This aligns with concrete science, as curing time is critical for the hydration process and the development of strength. The SP feature follows closely with a SHAP value of + 6.79, reflecting the significant role of SP in improving workability and achieving higher strength at lower water content. Other features, such as cement of + 3.93, fine aggregates of + 1.94, and BFS of + 1.57, also show positive contributions, though to a lesser extent. The effect of BFS is showing that its optimal use depends on the mix composition and curing regimen.

Fig. 13.

SHAP feature importance for input variables in strength prediction.

In Fig. 14, the SHAP summary plot provides a detailed view of how the feature values impact the predicted CS. The plot uses color coding, where the blue and purple colors represent low feature values, and the red and pink colors represent high feature values. The SHAP values for curing age are mostly positive, as high values of curing age lead to stronger predictions. Cement and fine aggregates follow similar trends, where higher values lead to stronger predictions. Notably, fly ash and coarse aggregate show a more varied impact, with both low and high values having different influences on the predicted CS.

Fig. 14.

SHAP summary plot illustrating the distribution of feature impacts.

This detailed analysis from SHAP values helps uncover not only the most important features but also their direction of influence. The model comparison confirms that booster-driven algorithms, such as XGBoost, outperform simpler models in capturing both feature importance and nuanced interactions. Their SHAP profiles display clean separation of dominant factors, making interpretation straightforward. The consistent pattern across SHAP values and PDP plots for features like cement, curing age, and SP supports the interpretability of the model. The relative importance of features, such as curing age and SP, suggests that these features should be carefully considered when designing a concrete mix, as they have the most significant impact on the strength predictions.

Conclusion

This research focused on developing accurate and interpretable ML models to predict the compressive strength of concrete incorporating BFS. The goal was to reduce the need for repetitive laboratory testing and promote sustainable concrete mix designs using industrial byproducts. A total of 675 data samples were collected from published experimental studies. The dataset included eight input variables: cement, BFS, fly ash, coarse aggregate, fine aggregate, water, SP, and curing age. CS was used as the output. The data was split into 80% training and 20% testing. Six ML models—XGBoost, LightGBM, GBR, AdaBoost, DT, and KNN—were developed using Python-based frameworks. Model evaluation employed R², RMSE, MAE, and MAPE as performance metrics. In addition, SHAP and PDP were used to interpret model behavior and understand the influence of individual features on predictions. The findings of this study lead to the following conclusions:

• Among all tested models, the ensemble boosting algorithms (LightGBM, XGBoost, GBR & AdaBoost) demonstrated superior performance and generalization capability compared to single-tree (DT) and instance-based (KNN) approaches.

• The LightGBM model achieved the highest accuracy with a test R² of 0.946, a test RMSE of 4.41 MPa, and a test MAPE of 9.79%. XGBoost produced very similar results with a test R² of 0.943, RMSE of 4.52 MPa, and a test MAPE of 10.73%.

• KNN had the lowest accuracy with a test R² of 0.707, a test RMSE of 10.261 MPa, and a test MAPE of 27.073%.

• Optimal CS range was observed when BFS replaced 30% to 40% of the total cement mass, especially when paired with 28-day or longer curing periods. Higher replacement levels (> 50%) reduced early-age strength.

• Model interpretation with SHAP & PDP showed that curing age, SP, and cement content were the most influential positive contributors to strength, water content exerted a strong negative influence, and BFS contributed positively with effects that depended on curing age.

• Classical regression models were not included in this study due to their limited ability to capture the nonlinear and complex relationship. Relationships between binder, aggregate, and SCM dosage with CS, as well as curing kinetics, are very complex. They show interconnected effects that simple combinations of parameters or straightforward changes cannot represent well.

• The models serve as fast, cost-effective tools for mix design optimization in engineering practice. This supports eco-friendly construction by optimizing the use of BFS.

Limitations and future studies

Although this study gathered a large dataset from earlier experiments, relying on published literature introduces differences that may affect the model’s reliability. Variations in the chemical compositions of BFS from different steel industries, the use of different types of cement, different aggregate materials, and variations in testing procedures or curing standards at different labs can all add noise to the dataset. These inconsistencies can hide true material-property relationships and partially affect how well the ML models predict and generalize. While ensemble learning techniques are robust against such variability, it is necessary to interpret model performance with care, especially for extreme mix proportions beyond the main data ranges. Future studies should focus on creating standardized datasets with BFS concrete mixes designed, made, and tested under controlled conditions. Data from the lab would allow for stricter benchmarks, support hybrid ML-mechanistic modeling methods, and ultimately improve how models transfer to real engineering scenarios and mix design optimization.

Author contributions

Md. Habibur Rahman Sobuz: Conceptualization, Methodology, Validation, Formal analysis, Supervision, Writing - original draft, Writing - review & editing. Simanta Majumder: Conceptualization, Methodology, Validation, Formal analysis, Writing - original draft, Writing - review & editing. Mst. Suraiya Afrin: Methodology, Formal analysis, Investigation, Writing - original draft, Writing - review & editing. Abdullah Alzlfawi: Methodology, Formal analysis, Data curation, Validation, Writing - original draft, Writing - review & editing. Md. Kawsarul Islam Kabbo: Validation, Formal analysis, Writing - original draft, Writing - review & editing.  Mohammed Jameel: Validation, Formal analysis, Writing - original draft, Writing - review & editing. Sani Aliyu Abubakar: Project administration, Resources, Writing - review & editing. Mohammad Alharthai: Data curation, Writing - review & editing. 

Funding

There is no specific funding for this manuscript.

Data availability

Our objective is to maintain control over unsupervised usage that may lead to unintentional duplication of research efforts or reduced novelty in future studies. however, the dataset will be provided upon request. Please contact Dr. Md. Habibur Rahman Sobuz (email: habib@becm.kuet.ac.bd) if anyone needs the data for this study.

Competing interests

The authors declare no competing interests.