Analyzing the influence of chemical components of incinerated bottom ash on compressive strength of magnesium phosphate cement using machine learning analysis

Abstract

Background

The use of incinerated bottom ash (IBA) as a sustainable construction material offers potential environmental benefits but introduces complex interactions with cement chemistry. Magnesium phosphate cement (MPC), known for its rapid hardening and superior bonding, can be optimized through the controlled incorporation of IBA. However, limited studies have addressed how the chemical components of IBA affect the compressive strength of MPC, particularly using data-driven approaches.

Methods

A database of 396 experimental samples was compiled from previous studies considering mix proportions, oxide compositions, and curing conditions. Four ensemble machine learning algorithms—Extreme Gradient Boosting (XGB), Light Gradient Boosting (LGB), Gradient Boosting Regressor (GBR), and Random Forest (RFR)—were employed to predict compressive strength. Model robustness was validated through 5-fold cross-validation. Feature interpretation was achieved using SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) to quantify individual and interactive effects of chemical and physical parameters.

Results

The XGB model achieved the highest predictive accuracy, with mean training and testing R2 values greater than 0.90 and 0.80, and the lowest mean absolute percentage error of 16.71%. SHAP analysis identified curing age as the most dominant factor, followed by FA/C, W/C, and MgO/PO4 ratios. IBA content and specific oxides such as Fe2O3 and Al2O3 contributed positively to strength within optimal ranges. PDP confirmed nonlinear dependencies, indicating a 26% reduction in strength as W/C increased from 0.1 to 0.6, while extended curing up to 28 days improved performance substantially.

Conclusion

The integration of SHAP and PDP provided a transparent interpretation of feature interactions in IBA-modified MPC. The developed XGB model demonstrated strong generalization and interpretability. The combined modeling approach offers a reliable predictive framework for optimizing IBA incorporation in sustainable binder systems and advancing eco-efficient material design.

Introduction

In recent time, the construction industry has faced mounting pressure to reduce its environmental footprint, specifically in the production and use of concrete (Hasan et al. 2023; Hossain et al. 2023; Saha et al. 2024a; Chen et al. 2024; Islam, et al. 2024; Sobuz et al. 2017). Conventional concrete relies heavily on energy-intensive Portland cement, whose production contributes significantly to global CO₂ emissions (Momshad et al. 2025; Sobuz et al. 2024a; Datta et al. 2023). To address this issue, researchers have increasingly explored the incorporation of industrial byproducts and waste materials into concrete as partial replacements for conventional binders or aggregates (Sobuz et al. 2024a; Sobuz et al. 2025a; Akid et al. 2021; Sadiqul Hasan et al. 2015; Islam et al. 2014). Furthermore, the accelerating pace of industrial development combined with rapid global population growth has led to a significant escalation in the generation of municipal solid waste (MSW). Projections indicate that this upward trend in MSW production is likely to continue in the near future, exerting pressure on existing waste management infrastructure (Gueboudji et al. 2024; Rahman et al. 2013; Habibur Rahman Sobuz et al. 2023; Sobuz et al. 2022; Sobuz et al. 1024). A 2012 World Bank report estimated global MSW generation at approximately 1.3 billion tons, with forecasts predicting a rise to 2.2 billion tons by 2025 (Cheng et al. 2024). Although landfilling remains the predominant method of MSW disposal worldwide, it poses several environmental challenges (Hasan, et al. 2024; Sobuz, et al. 2023). These include the prolonged occupation of land, potential contamination of soil and groundwater, and the emission of greenhouse gases such as methane along with unpleasant odors (Lan et al. 2025; Gebrekidan et al. 2024). As an alternative, the incineration of MSW has gained increasing recognition, particularly in densely populated urban areas with limited land availability (Cheng et al. 2024; Lu et al. 2024; Gao et al. 2024). Incineration not only reduces the physical volume of waste significantly but also recovers thermal energy through the combustion of organic components present in the waste stream (Gu et al. 2021). The byproduct of this process, incinerated bottom ash (IBA), presents a promising opportunity for reuse in construction applications (Alderete et al. 2021; Miguel et al. 2023). Utilizing BA in this context contributes to waste minimization and helps decrease the embodied energy and carbon emissions associated with traditional construction materials (Weiksnar et al. 2024; Sobuz et al. 2016; Aditto et al. 2023).

Several studies have highlighted the feasibility of integrating IBA into cement manufacturing. For example, pretreatment processes such as water or acid washing have been recommended to mitigate the presence of chlorides, which can lead to kiln corrosion during cement production (Wei et al. 2024). Moreover, certain investigations have explored the complete replacement of conventional binders with materials derived from incineration residues. Under accelerated carbonation curing, some of these novel binders have achieved compressive strengths exceeding 50 MPa within a matter of hours (Singh et al. 2025). In other research, IBA has also been processed into lightweight aggregates through cementitious binding and hydrothermal curing techniques, effectively limiting the leaching of hazardous components (Song et al. 2024; Ren et al. 2024).

Magnesium phosphate cement (MPC) has recently emerged as a compelling alternative to Portland cement (PC), owing to its rapid setting behavior, high early-age strength, and superior bonding capabilities (Zheng et al. 2025). Composed primarily of calcined magnesium oxide (MgO), phosphate solutions, and chemical retarders, MPC sets through an acid–base reaction that distinguishes it from hydration-based cements. However, the widespread adoption of MPC has been constrained by high production costs, energy-intensive processing, and reliance on non-renewable raw materials (Yan et al. 2022; Chen et al. 2025; Datta et al. 2022). Environmental assessments have further revealed that the carbon footprint of MPC often exceeds that of conventional PC, with reported emission intensities averaging around 0.60 kg CO₂-e per kilogram—undermining its sustainability potential (Shen et al. 2024; Sayed Mohammad Akid et al. 2023; Sobuz et al. 2024b; Hasan, et al. 2022). Consequently, the partial substitution of MPC with industrial waste materials has gained attention as a strategy to enhance its economic viability and reduce its environmental impact without compromising performance (Yu et al. 2021a; Dong et al. 2021).

Furthermore, synergy of the different chemical components largely affects the CS in the IBA-modified concrete composites (Chu et al. 2024). In particular, the contribution of SiO₂ and Al₂O₃ is significant as they react with magnesium phosphate to produce secondary gel phases (Einarsrud et al. 1999). SiO₂ and Al₂O₃ in IBA normally account for 30–40%. Such oxides hasten the secondary gels by pozzolanic reactions and thereby enhance the compressive strength (Sun 2022). Therefore, the mechanical property of MPC–IBA mixtures gains greatly (10–30%) from pure MPC at 28 days curing time, depending on the IBA incorporation (Feng et al. 2022). Further, the existence of CaO in the MPC mixture produces early strength development, since CaO rapidly reacts with phosphate ions to form magnesium phosphate gels. Other MPC strength development is usually around 50–60% of the final strength value after 24–48 h of curing, whereas pure MPC without IBA has an early strength gain of 10–15% (Feng et al. 2021). On the other hand, Fe₂O₃ and MgO in the IBA component promote the crystallization of gel structure which contributes to improving the resistance to high temperature of the cement's final strength.

In recent years, the rapid evolution of machine learning (ML) has introduced advanced approaches for forecasting the mechanical behavior of cementitious composites (Alahmari et al. 2025, 2024; Kabbo et al. 2025; Sobuz et al. 2025b, c, 2024b). These data-driven models have demonstrated significant promise in improving predictive accuracy while reducing experimental dependency (Sobuz 2025; Sobuz et al. 2025d; Hossain et al. 2023; Mottakin et al. 2024; Mehedi et al. 2024; Safayet et al. 2025). For instance, studies conducted by Imran, et al. (Imran et al. 2025) utilized ML techniques to estimate the strength performance of cement pastes, mortars, and concretes modified with carbon-based nanomaterials, reporting superior results using the XGB algorithm. In another investigation conducted by Luo, et al. (Luo et al. 2023), ML was employed to simulate the compressive strength of magnesium silicate hydrate cement, where interpretability was enhanced through SHAP-based feature importance analysis. Among the conventional methods, artificial neural networks (ANN) and support vector machines (SVM) have been frequently utilized to evaluate various concrete properties, owing to their ability to capture nonlinear relationships in complex datasets (Marangu 2020). Recent advancements have introduced hybrid approaches, such as integrating ANN with nature-inspired optimization algorithms, to enhance prediction accuracy for high-performance concrete (Pan et al. 2023). These predictive models offer significant advantages in optimizing mix design and improving the overall performance of cementitious composites (Pan et al. 2023; Sobuz, et al. 2024c, d).

In particular, some investigations have successfully applied ANN models to estimate the compressive strength of lightweight concrete reinforced with steel fibers, highlighting the adaptability of neural networks in handling material variability (Ocak et al. 2024). However, Bui, et al. (Bui et al. 2018) observed that ANN models may exhibit limited generalizability when trained on small-scale datasets, thereby affecting their reliability in external validation scenarios. In response to such limitations, ensemble learning methods have gained increased attention for their robustness and superior generalization capabilities (Uddin et al. 2025; Mishra, et al. 2025; Saha et al. 2024b; Rahman Sobuz et al. 2025; Sobuz et al. 2025e). Researchers have developed both bagging-based and boosting-based frameworks to improve prediction accuracy for concrete strength, with models such as XGBoost and CatBoost consistently demonstrating reduced prediction errors compared to traditional approaches (Pranav et al. 2023; Sobuz et al. 2025; Aayaz et al. 2025). Despite the notable progress, many existing ML models still face challenges related to overfitting, limited data availability, and lack of interpretability, suggesting the need for more advanced and transparent modeling strategies (Sobuz et al. 2024c). In addition, Chou, et al. (Chou et al. 2011) conducted extensive investigations into the application of various machine learning techniques for predicting concrete compressive strength, with a particular focus on artificial neural networks and support vector machines (SVM). Aiyer, et al. (Aiyer et al. 2014) advanced this area by introducing a refined variant known as least squares support vector machine (LS-SVM), which offered improved computational efficiency.

In a more complex scenario, the application of SVM to forecast the unconfined compressive strength of cockle shell–cement–sand mixtures demonstrate the versatility of ML models in non-conventional materials. Further enhancement was made by Pham, et al. (Pham et al. 2016), who incorporated metaheuristic optimization into LS-SVM to develop a more accurate prediction model for high-performance concrete. In another comparative effort, Omran, et al. (Omran et al. 2016) evaluated multiple data mining techniques to assess their effectiveness in predicting the compressive strength of environmentally sustainable concrete, providing a broad perspective on algorithmic performance. Similarly, Naderpour, et al. (Naderpour et al. 2018) applied ANN techniques to estimate the compressive strength of green concrete compositions. In a different approach, Ashrafian, et al. (Ashrafian et al. 2018) implemented heuristic regression models to predict both compressive strength and ultrasonic pulse velocity in fiber-reinforced concrete, showcasing the potential of rule-based learning systems in multiparametric estimation. Moreover, Zhang, et al. (Zhang et al. 2019) utilized the Random Forest (RF) algorithm to model the compressive strength of concrete and conducted a detailed feature importance analysis to determine the relative contribution of each input variable, underscoring the interpretability advantages of ensemble models.

However, many of these studies have been limited in scope, focusing primarily on basic mix proportions and bottom ash content as the only variable representing waste incorporation. The influence of chemical components of IBA on the performance of magnesium phosphate cement (MPC) remains largely unaddressed. Addressing the existing research gap, the present study proposes the development of a robust ML model to predict the compressive strength of MPC incorporating incineration bottom ash (IBA). By doing so, this research advances the application of ML in sustainable construction and offers insight into the potential of multi-source waste utilization in low-carbon binder systems.

Methodology

Development of the dataset

To facilitate accurate prediction of compressive strength in MPC incorporating IBA, a comprehensive experimental dataset was compiled. The dataset consists of 386 data points collected from published available journal articles, encompassing a wide range of mix design parameters, chemical compositions, and curing ages (Magnuson et al. 2023; Dillard et al. 2025; Haque et al. 2022; Liu et al. 2020; Liu et al. 2023a; Lv et al. 2019; Su et al. 2016; Cao et al. 2020; Alnezami et al. 2024; Li et al. 2015; Zhang et al. 2023; Zheng et al. 2022; Filipponi et al. 2003; Yang et al. 2019; Bernasconi, et al. 2023; Xu et al. 2015; Hou et al. 2016; Záleská et al. 2025; Yu et al. 2021b). The dataset for this research was compiled from 19 peer-reviewed journal articles published between 2000 and 2025. Criteria for selection of the articles were established: (1) compressive strength was specified for the composites composed with or without additional IBA supplement; (2) the detailed mix proportions and chemical compositions as well as curing conditions were presented; and (3) the papers were published in a reputable, Scopus indexed journal. The data were extracted manually by hand, and all required results were cross-checked by an additional two review authors to maintain accuracy and consistency. Each data entry includes eleven variables, categorized into binder chemistry, IBA, chemical components of IBA, and curing conditions. The selected input features include the water-to-cement ratio (W/C), fine aggregate-to-cement ratio (FA/C), ratio of magnesium oxide to phosphate (MgO/PO₄) for MPC, and the content of IBA in the mix. In addition to physical proportions, chemical components of IBA—specifically silica (SiO₂), alumina (Al₂O₃), calcium oxide (CaO), iron oxide (Fe₂O₃), and other minor oxides—were also considered. These components were quantified through X-ray fluorescence (XRF) spectroscopy and included as independent variables to evaluate their influence on compressive strength development. The compressive strength of MPC was treated as the dependent output variable, recorded at varying curing ages ranging from one to 180 days.

Dataset preprocessing and statistical evaluation

Before applying the algorithms to predict CS, the dataset was preprocessed for ensuring generalizability. To minimize the influence of inconsistent testing environment, a systematic data normalization process was applied prior to model development. For curing temperature, results obtained under standard range of laboratory curing (20–27 °C) or water curing were included. Other types of curing regimes were excluded to maintain consistency. Furthermore, compressive strength tests that were conducted only by using specific guidelines of ASTM were considered similar and taken. In addition, a min–max normalization technique was employed for input features to rescale each variable to a range between 0 and 1, which ensures comparability among parameters with different measurement units and prevent dominance of variables with larger numerical scales during ML analysis.

Furthermore, descriptive statistics of the dataset revealed a wide distribution of values such as, the W/C ratio varied from 0.12 to 0.60, with a mean of 0.188, while IBA content ranged from 0 to 63.53%, averaging 15.24%. Chemical components also exhibited high variability; SiO₂ content ranged from 0 to 77.03%, CaO from 0% to 51.6%, and Fe₂O₃ from 0 to 30.9%, reflecting the heterogeneous nature of IBA derived from various municipal solid waste streams. Compressive strength values spanned from 1.6 to 99.49 MPa, with a mean of 43.49 MPa and a standard deviation of 20.22 MPa, indicating significant performance variation due to mix composition and curing conditions. The statistical attributes of dataset in tabulated in Table 1.

Table 1. Statistical attributes of the dataset

Parameter	Min	Max	Mean	Standard deviation	First quartile (25%)	Median (50%)	Third quartile (75%)
W/C	0.12	0.6	0.188	0.072	0.15	0.18	0.20
FA/C	0	1.5	0.507	0.519	0.00	0.25	1.00
MgO/PO4	0.81	12.88	6.963	2.607	5.00	7.28	8.56
IBA (%)	0	63.53	15.242	14.547	3.75	11.28	22.50
Silica (%)	0	77.03	33.659	27.250	9.45	33.48	51.62
Alumina (%)	0	64.78	19.314	18.863	0.73	16.02	35.90
Calcium (%)	0	51.6	11.478	16.469	0.07	2.67	18.48
Iron oxide (%)	0	30.9	6.139	8.408	0.12	2.26	10.61
Other (%)	0	21.2	7.947	6.969	1.29	5.92	11.70
Curing age (days)	1	180	12.887	25.710	1.00	3.00	28.00
CS (MPa)	1.6	99.49	43.487	20.223	29.15	42.40	54.98

Pearson correlation

Figure 1 illustrates the Pearson correlation heatmap that quantifies the linear relationships among the input features and the target variable, used in the modeling process. This analysis aids in understanding interdependencies between variables and identifying potential predictors with significant influence on CS. As shown in the figure, the water-to-cement ratio exhibits a moderate negative correlation (–0.31) with compressive strength, aligning with the general principle that excess water can weaken the cement matrix. Conversely, the FA/C shows a positive correlation (0.36), indicating that increased fine aggregate content will contribute positively to strength development.

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Fig. 1

Pearson heatmap

Other variables such as MgO/PO₄, bottom ash content, and silica exhibit relatively weak correlations with CS, suggesting more complex or nonlinear interactions that may not be captured through linear metrics alone. Interestingly, curing age shows a mild positive correlation (0.18) with CS, which reflects the common observation that strength typically increases over time as hydration progresses. On the other hand, oxide-based components such as calcium, iron oxide and alumina demonstrate minimal correlation with compressive strength, although they may still play synergistic roles in microstructural development. Overall, the heatmap visualizes that there’s no extremely high correlation among any of the two parameters that can affect the modeling process of the ML work.

Hyperparameter optimization

In this study, hyperparameter optimization was performed to enhance the predictive performance and generalization ability of the ML models. The tuning process involved systematically exploring predefined ranges of key parameters, such as learning rate, maximum depth, number of estimators, regularization terms, and sampling strategies, using GridSearchCV. Optimizing these parameters allowed the models to balance complexity, reduce overfitting, and improve convergence efficiency. The optimal values were determined based on their ability to minimize error metrics and maximize predictive accuracy, thereby ensuring robust and reliable model performance across both training and testing datasets. The optimized value for all the models used in this study have been tabulated in Table 2.

Table 2. Optimized value of key hyperparameters

Model	Hyperparameter	Range considered	Optimal value
XGB	learning_rate	0.01–0.5	0.03
	max_depth	1–10	6
	n_estimators	100–1000	350
	reg_alpha	0–10	1
LGB	learning_rate	0.01–0.3	0.05
	max_depth	3–12	5
	num_leaves	20–150	80
	n_estimators	100–1000	600
GBR	learning_rate	0.01–0.3	0.04
	max_depth	3–12	5
	n_estimators	100–1000	300
	subsample	0.5–1.0	0.8
RFR	n_estimators	100–1000	250
	max_depth	3–20	10
	min_samples_split	2–10	4
	max_features	“Sqrt”, “log2”, “auto”	"sqrt"

Machine learning algorithm

Extreme gradient boosting (XGB)

XGB is an optimized machine learning algorithm built upon the principles of gradient boosting. It enhances model performance by sequentially developing an ensemble of weak learners—typically decision trees—that work collectively to improve prediction accuracy. In each iteration, XGB constructs a new tree that concentrates on minimizing the residual errors from the previous model. It employs a gradient descent optimization strategy to reduce the overall loss, allowing each new learner to correct the shortcomings of earlier ones. What sets XGB apart is its scalability, regularization capabilities, and handling of sparse data. It integrates both L1 and L2 regularization to prevent overfitting, which is particularly useful when dealing with high-dimensional datasets. Furthermore, the algorithm uses a sparsity-aware approach that efficiently manages missing values by assigning them to optimal branches during training. Parallel and distributed computing features accelerate training, making XGB suitable for large-scale and real-time applications. In this study, the algorithm effectively captured nonlinear relationships among variables and delivered high predictive performance due to its robust error minimization strategy and efficient computation.

Light gradient boosting (LGB)

LGB is a decision tree-based gradient boosting framework developed with a focus on efficiency and scalability. Unlike conventional boosting methods that grow trees level-wise, LGB adopts a leaf-wise growth strategy. In this approach, the algorithm identifies and expands the leaf with the maximum information gain, resulting in deeper trees and often higher model accuracy. This mechanism enables LGB to process massive datasets with reduced memory consumption and faster training times.

Another key advantage of LGB lies in its support for categorical features and histogram-based binning. By converting continuous values into discrete bins, it significantly reduces computational complexity without compromising accuracy. The model can handle data with high dimensionality and strong feature interdependence, which makes it well-suited for engineering datasets with diverse input variables. LGB also includes techniques such as gradient-based one-side sampling (GOSS) and exclusive feature bundling (EFB) to further enhance speed and performance. In this research, LGB offered a practical balance between accuracy and computational efficiency, allowing the model to generalize well across varying feature distributions.

Gradient boosting (GBR)

Gradient Boosting is a powerful ensemble learning technique that sequentially constructs a model by combining multiple weak learners, usually decision trees, to create a strong predictive system. The algorithm begins by fitting an initial tree to the training data, then builds subsequent trees that attempt to correct the prediction errors of the preceding models. This correction is guided by the gradient of a chosen loss function, which ensures that each new learner focuses on minimizing the residuals generated by the current ensemble.

This iterative refinement process enables the model to capture complex and nonlinear relationships within the dataset. One of the key strengths of gradient boosting is its flexibility in optimizing a wide range of loss functions, making it suitable for both regression and classification tasks. The model is also capable of incorporating various regularization techniques to prevent overfitting, although it typically requires careful tuning of hyperparameters such as the number of estimators, learning rate, and maximum depth of trees. In this study, gradient boosting proved effective in learning subtle patterns in the data, particularly due to its stage-wise optimization and cumulative improvement strategy that incrementally enhances model performance.

Random forest regressor (RFR)

Random Forest is an ensemble learning method that builds a large number of decision trees during training and aggregates their outputs to form a final prediction. Unlike boosting methods, where trees are built in sequence, Random Forest constructs each tree independently using a technique known as bootstrap aggregation, or bagging. This involves randomly selecting samples with replacement from the original dataset for training each tree, thereby introducing diversity among individual models. Additionally, at each split in a tree, the algorithm considers a random subset of features, which further reduces correlation between trees. This randomness and ensemble averaging lead to increased model robustness and generalization, particularly in cases involving noisy or imbalanced data. Random Forest models are generally resistant to overfitting and require minimal parameter tuning, making them an attractive choice for a wide range of predictive tasks. They also offer inherent feature importance ranking, which aids in understanding the relative influence of input variables on model output. In this investigation, Random Forest served as a reliable baseline, demonstrating consistent performance while maintaining interpretability and resilience to data variability.

Feature importance analysis

In this study, the SHAP (SHapley Additive exPlanations) framework was employed to quantify and visualize the individual effect of each input feature on the predicted compressive strength of magnesium phosphate cement. SHAP is grounded in cooperative game theory and provides a unified measure for feature attribution by calculating Shapley values, which represent the average marginal contribution of a feature across all possible feature combinations. The SHAP methodology offers a consistent and model-agnostic approach to interpret complex predictive systems. Unlike traditional feature importance metrics that may vary across algorithms or rely on heuristic assumptions, SHAP values satisfy properties such as local accuracy, consistency, and additivity. This ensures that the sum of the feature attributions equals the model output and that features with greater influence always receive higher importance scores. In the context of this research, SHAP analysis enabled a detailed breakdown of how individual variables—such as curing time, mix ratios, and oxide compositions—impacted the machine learning models’ decisions. This helped identify which features contributed positively or negatively to the predicted strength values and how these influences varied across the dataset.

Performance measurement and cross-validation

To evaluate the predictive performance of the machine learning models developed in this study, three widely used statistical indicators were employed: the coefficient of determination (R²), root mean square error (RMSE), and mean absolute percentage error (MAPE). The mathematical expressions of these performance metrics are shown below-

1

2

3

In addition, a fivefold cross-validation (CV) technique was implemented to ensure the robustness and generalizability of the models. This validation strategy involved partitioning the dataset into five equal subsets, where each subset was used once as a test set while the remaining four were used for training. The process was repeated five times, and the performance metrics were averaged across the folds to mitigate overfitting and variance due to data partitioning. The application of fivefold CV yielded consistent and stable results across all four models, confirming the reliability of the training process and the reproducibility of the predictions. Furthermore, the flow diagram of the whole study has been illustrated in Fig. 2 below.

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Fig. 2

Flow diagram of the modeling

Results

Dataset analysis

A statistical visual analysis was conducted to assess the distribution characteristics and internal structure of the dataset used for modeling the compressive strength of IBA-MPC composites. The combined density and cluster plots presented in Fig. 3 illustrate the frequency distributions of both input and output variables. Most input variables demonstrated non-normal and skewed distributions, highlighting the heterogeneous nature of the dataset. As can be seen, the FA/C ratio showed a strong right-skew, indicating a predominance of mixes with relatively low FA content. Similarly, the curing age exhibited a heavily right-skewed profile, with the majority of specimens tested before 28 days, reflecting the rapid-setting behavior of MPC-based systems. Chemical components of IBA also exhibited considerable variability across the dataset. Silica content displayed a bimodal distribution, suggesting the presence of IBA sources with distinctly different mineralogical compositions. Alumina, calcium, and iron oxide similarly covered a broad range, with significant variation observed in samples derived from different incineration processes and feedstocks. Furthermore, as can be seen in the clustering plot of parameter density, chemical oxides such as CaO, Al₂O₃, and Fe₂O₃ formed a close cluster, indicating shared variance and potentially synergistic effects on mechanical performance. Meanwhile, IBA content appeared moderately associated with these chemical variables, implying its dual role as a physical filler and a chemical modifier in the MPC system. Considering the overall attributes of the data distribution, this analysis confirms the presence of complex, nonlinear relationships among the dataset variables. The broad data ranges, non-Gaussian distributions, and overlapping clusters will significantly important for advanced machine learning models to capture the intricate interactions that govern the Cs of IBA-MPC composites.

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Fig. 3

Density and histogram distribution of input features (a) W/C, (b) FA/C, (c) MgO/PO₄, (d) IBA, (e) silica, (f) alumina, (g) calcium, (h) iron oxide, (i) other oxides and (j) curing age

Accuracy of ML models

The predictive performance of four supervised ML algorithms—XGB, LGB, GBR and RFR—was evaluated by comparing their predicted compressive strength values against experimental observations. As visualized in Fig. 4, each model's accuracy is expressed through R² values for both train and test phase. As can be seen in Fig. 4a, the XGB model demonstrated the highest degree of fit, yielding an R² value of 0.981 in training stage, which indicates strong predictive capability and a robust generalization performance. Most of the data points clustered tightly along the ideal prediction line, with minimal dispersion in both low- and high-strength regions. However, comparing the R² of training stage, the performance of testing phase is slightly downgraded which indicates a rise of potential overfitting issue.

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Fig. 4

Regression plot of ML models (a) XGB, (b) LGB, (c) GBR and (d) RFR

In comparison, Fig. 4b displays the performance of the LGB model, which achieved an R² value of 0.933 and 0.845 in train and test phase. While still demonstrating satisfactory accuracy, LGB showed slightly wider deviation in medium- and high-strength ranges, suggesting a comparatively reduced ability to model certain feature interactions, potentially due to aggressive leaf-wise tree growth or sensitivity to feature noise. Figure 4c presents the results for the Gradient Boosting Regressor. The model attained an R² of 0.932 and 0.855 in train and testing stage, closely surpassing LGB. However, among all the four models the GBR exhibited the most train-test balance performance with lower overfitting issue. Finally, the Random Forest model, as shown in Fig. 4d, achieved an R² value of 0.827 in the testing stage, the lowest among the four models. Although the prediction trend followed a generally linear pattern, notable discrepancies were observed, particularly for specimens with compressive strengths ranging between 50 and 100 MPa. This behavior is likely due to RFR's limitation in extrapolation and its averaging nature, which can smooth out extreme values. Overall, XGB outperformed all other models in terms of training predictive accuracy, affirming its robustness and adaptability in modeling heterogeneous datasets with both numerical and compositional inputs. The GBR model showed most balanced performance with a lower difference between training and testing R² ensures minimal overfitting and high generalizability.

However, the XGB model achieved the highest train accuracy among the evaluated algorithms, the observed difference between the training and testing R² suggests a tendency toward overfitting. Although, hyperparameter tuning was performed for all the models, including the adjustment of learning rate, maximum tree depth, number of estimators, still, there’s remain a discrepancy between test and train R². In addition, the consistent results obtained across fivefold cross-validation indicate that the apparent train–test discrepancy is largely attributable to the intrinsic heterogeneity of the dataset, rather than uncontrolled overfitting. Further study needed of stronger regularization and more diverse datasets in future work to enhance the model’s generalizability.

Performance using fivefold CV

To ensure the reliability and generalizability of each ML model, a fivefold cross-validation (CV) approach was implemented and the outcomes are shown in Table 3 as fold-wise performance. The performance metrics—R², RMSE and MAPE—were computed for both training and testing folds. These metrics provide a comprehensive evaluation of model robustness and error stability, and the detailed results are presented in Table 3. Among all models evaluated, XGB consistently outperformed the others, achieving the highest mean train and test R² value of 0.981 and 0.843. Its average RMSE and MAPE were 7.88 MPa and 16.71%, respectively for testing phase. This result confirms the earlier single-split evaluation and further demonstrates XGB's capacity to maintain prediction stability across varying data partitions. Notably, its training R² remained exceptionally high at 0.981, with negligible overfitting observed between train and test scores.

Table 3. Performance evaluation using fivefold CV

Model	k-Fold	R2		RMSE		MAPE
		Train	Test	Train	Test	Train	Test
XGB	1	0.987	0.794	2.36	8.79	1.62	14.17
	2	0.979	0.875	2.86	7.47	1.62	15.29
	3	0.978	0.893	2.97	6.60	1.57	13.24
	4	0.985	0.797	2.49	9.00	1.49	15.71
	5	0.976	0.855	3.17	7.57	1.88	25.13
	Mean	0.981	0.843	2.77	7.88	1.64	16.71
LGB	1	0.928	0.851	5.46	7.47	13.04	15.87
	2	0.929	0.858	5.32	7.96	12.27	22.03
	3	0.935	0.856	5.15	7.67	12.41	17.15
	4	0.943	0.804	4.83	8.84	12.50	20.55
	5	0.932	0.857	5.29	7.50	11.34	29.17
	Mean	0.933	0.845	5.21	7.89	12.31	20.95
GBR	1	0.934	0.839	5.25	7.77	11.24	15.59
	2	0.929	0.875	5.28	7.48	11.37	18.57
	3	0.930	0.896	5.32	6.50	12.10	15.94
	4	0.941	0.811	4.92	8.68	10.64	19.28
	5	0.927	0.854	5.47	7.60	11.67	27.41
	Mean	0.932	0.855	5.25	7.60	11.40	19.36
RFR	1	0.965	0.824	3.82	8.13	9.65	17.79
	2	0.960	0.837	3.95	8.54	9.20	19.85
	3	0.959	0.866	4.07	7.40	8.95	18.16
	4	0.966	0.794	3.75	9.07	9.08	21.98
	5	0.957	0.816	4.22	8.53	9.89	31.32
	Mean	0.961	0.827	3.96	8.33	9.35	21.82

The LGB model followed closely, with a mean test R² of 0.845, nearly matching XGB. However, its average MAPE rose to 20.95%, indicating higher relative error in certain folds, especially in samples with extreme strength values. Despite its rapid computation and leaf-wise optimization strategy, LGB showed slightly more variance across folds compared to XGB. Gradient Boosting Regressor demonstrated competitive accuracy, with a mean test R² of 0.855 and RMSE of 7.60 MPa, but the MAPE of 19.36% suggests that the model struggled with localized prediction accuracy for outliers or nonlinear regions. Interestingly, its performance consistency across all folds was relatively stable, pointing to a balanced trade-off between bias and variance. Furthermore, the RFR achieved the lowest mean test R² at 0.827, with a higher average RMSE of 8.33 MPa and MAPE of 21.82%. Despite its strong training R² of 0.961, the model's generalization to unseen data was less effective, as evidenced by the larger gap between training and testing errors. This behavior aligns with RFR’s known limitations in high-dimensional and extrapolation-sensitive datasets.

Feature importance analysis using SHAP

Global feature importance

To better interpret the inner mechanics of the machine learning model and quantify the influence of each input variable on the predicted compressive strength of IBA-MPC, SHAP analysis was employed. SHAP provides a consistent, model-agnostic framework that assigns an importance value to each feature based on its contribution to the model’s output. As shown in Fig. 5, the mean absolute SHAP values were used to rank all input features by their average impact across all data samples. Among the ten input variables, IBA content, MgO/PO₄ ratio, and Iron content emerged as the top three contributors to the prediction outcome. IBA content held the highest SHAP value, affirming its critical role as physical filler behavior and chemical contribution of the ash. Similarly, the MgO/PO₄ ratio significantly influenced setting kinetics and bonding characteristics.

[See PDF for image]

Fig. 5

Mean model output across all sample

Furthermore, Fig. 5 also dissects how each input feature pushes the predicted compressive strength away from the base value. Based on the analysis, the expected mean model output was 43.083 MPa. Notably, the FA/C exerted the strongest negative influence, reducing the predicted strength by 7.83 MPa. This aligns with the generally observed trend that higher FA content in MPC systems can reduce the active binder phase. Similarly, silica content (33.48%) and a water-to-cement ratio of 0.16 contributed modest negative effects of − 1.90 MPa and − 0.97 MPa, respectively.

Conversely, several features had a positive impact on strength prediction. The IBA content and MgO/PO₄ ratio enhanced the compressive strength by + 2.63 MPa and + 2.01 MPa, respectively, indicating that this sample had a beneficial ash dose and a chemically favorable binder stoichiometry. Other features such as iron oxide (1.4%), alumina (12.31%), and curing age (7 days) each contributed between + 1.02 and + 1.48 MPa, suggesting modest but meaningful improvements due to synergistic pozzolanic reactions and early hydration. It is worth noting that calcium and other oxides have a minor role in this sample. Overall, this force plot confirms that compressive strength prediction is not dominated by a single variable but is the net outcome of multiple features interacting both positively and negatively.

SHAP interaction between feature values and predicted strength

In Fig. 6a, the average absolute SHAP value of each input variable is plotted, quantifying its global importance in shaping the predicted compressive strength. Among all features, curing age ranked as the most influential factor, with a mean SHAP value of 8.21, indicating its consistent and dominant role in strength development. This aligns with the well-documented rapid early-age strength gain behavior of magnesium phosphate cement. The FA/C ratio also exhibited substantial importance. Other features with notable influence include the W/C ratio (3.39), silica content (2.67), MgO/PO₄ ratio (2.36), and IBA content (2.32)—each contributing to the mechanical, chemical, or rheological behavior of the matrix. In contrast, iron oxide (0.73) and other minor oxides (0.66) had relatively lower SHAP values, indicating a less consistent or indirect impact on strength.

[See PDF for image]

Fig. 6

SHAP value and model output value SHAP value and model output value using (a) mean SHAP plot and (b) tree SHAP plot

Figure 6b further visualizes the collective decision path for the entire dataset using a SHAP decision plot. Each polyline represents the cumulative SHAP contribution from each feature to a given prediction, ordered by their importance. As seen from the plot, the lines originate near the expected model mean (~ 43 MPa) and diverge depending on the specific sample’s feature values. For predictions in the higher strength range (above 60 MPa), curves generally show positive cumulative effects from features such as curing age, IBA content, MgO/PO₄, and silica. These lines appear to trend upward sharply after the influence of curing age, confirming its crucial role in enabling higher mechanical performance. Conversely, curves that end in the lower strength region (below 30 MPa) often descend early due to negative contributions from high FA/C or W/C ratios, reinforcing their inhibitory impact on strength gain when used in excess.

Comprehensive SHAP beeswarm interpretation

Figure 7 visualizes the impact of input parameter on the model output using beeswarm plot. As can be seen, Curing age emerges as the most influential feature, with higher values generally contributing positively to the model's prediction, pushing the output higher. The FA/C and W/C also exhibit substantial effects. Notably, an increased W/C ratio often results in a lower SHAP value, indicating a negative impact on the model’s prediction. Interestingly, some of the input features display both positive and negative SHAP values depending on the magnitude of the input, suggesting nonlinear relationships with the target output. For example, MgO/PO₄ and Alumina show mixed influence, where both high and low values may either enhance or diminish the prediction, depending on the context of other variables.

[See PDF for image]

Fig. 7

Bees-warm plot illustrating impact of features on input

SHAP interaction plots among critical features

Figure 8 visualizes the SHAP feature interaction plots of how the critical chemical and mix design parameters interact to influence the CS of MPC incorporating IBA. As seen in Fig. 8a and b, the interaction with the FA/C, represented by the color gradient, reveals that higher FA/C levels amplify the positive contribution of W/C, which confirms the combined optimization of these ratios is critical for strength development. Similarly, in Fig. 8c underscores the importance of the MgO/PO₄ ratio, where higher values strongly enhance CS. The interaction with minor other oxides indicates that their presence further supports strength development when the MgO/PO₄ ratio is optimized. In Fig. 8d, IBA content largely shows a negative contribution to strength, particularly when it exceeds 20%. However, its interaction with MgO/PO₄ suggests that adequate MgO availability can mitigate some of the adverse effects of higher IBA, pointing toward the critical balance between binder chemistry and ash incorporation. Figure 8e illustrates the role of silica, where higher silica contents (> 40%) reduce the SHAP values. The interaction with curing age highlights that the negative effect of silica becomes more pronounced at longer curing times.

[See PDF for image]

Fig. 8

SHAP feature interaction plot among critical features SHAP feature interaction plot among critical features focusing (a) W/C, (b) FA/C, (c) MgO/PO₄, (d) IBA, (e) silica, (f) alumina, (g) calcium, and (h) iron oxide

Furthermore, Fig. 8f reveals that the interactions of alumina content with FA/C enhance alumina’s positive impact, highlighting a synergistic effect between these two features. In Fig. 8g, calcium demonstrates a moderate positive influence on CS, with the interaction with curing age reinforcing the notion that calcium-rich mixes gain additional benefits over time. Conversely, Fig. 8h shows that iron oxide exerts predominantly negative contributions, particularly when interacting with higher IBA content, suggesting limited reactivity of iron phases in MPC.

Optimization of materials quantity using PDP

Figure 9 illustrates the partial dependence plots of all input variables on the CS of MPC. As can be seen, the W/C exerts a strong negative influence on compressive strength. As W/C increases from 0.1 to 0.6, the strength significantly drops from around 47.5 MPa to below 35 MPa. This observation is consistent with fundamental concrete science, where a higher W/C ratio tends to reduce strength due to increased porosity. In the context of FA/C the compressive strength initially decreases slightly and then increases sharply as FA/C rises, peaking at higher values. Furthermore, a nonlinear trend is evident in the MgO/PO₄ ratio. Compressive strength rises with MgO/PO₄ up to around 4, stabilizes briefly, and then exhibits minor fluctuations with a slight decline at higher values. This behavior suggests a threshold after which excess MgO or phosphate might no longer benefit the matrix structure.

[See PDF for image]

Fig. 9

Partial dependency of all input parameters Partial dependency of input parameters (a) W/C, (b) FA/C, (c) MgO/PO₄, (d) IBA, (e) silica, (f) alumina, (g) calcium, (h) iron oxide, (i) other oxides and (j) curing age

On the other hand, CS starts above 43 MPa and declines marginally as IBA increases, reflecting a possible reduction in packing density or interaction with the binder phase. Silica (%) and alumina (%) show a nearly identical pattern as both exhibit a flat response at lower contents, followed by a steep rise in compressive strength. However, once a specific threshold is crossed, the CS gradually reduced. Comparing to them, calcium content also displays a similar threshold behavior. Below 5%, CS remains constant, but above this point, it sharply increases and stabilizes. The response of iron oxide content is relatively flat, indicating minimal impact on compressive strength across its range. This suggests iron oxide plays a negligible role in the mechanical performance within the studied composition range. The other chemical components, likely comprising trace chemical components, shows a non-linear but modest positive effect on strength. As the content increases from 0 to 20%, the strength gently rises and then levels off, hinting at the potential influence of minor constituents in the mix. Lastly, curing age significantly affects CS. A sharp increase is observed from day 1 to about 28 days, where the strength surges from approximately 25 MPa to nearly 48 MPa and then remains steady. This trend strongly reflects the time-dependent hydration process that governs strength gain in cementitious materials.

In the context of incinerated ash, the large SiO₂ and Al₂O₃ trigger the pozzolanic reaction, which forms aluminosilicate gels. These gels are responsible for optimizing the pore structure of the cement matrix, which increases the mechanical properties of the concrete by 15–25% as opposed to the MPC without IBA. In addition, an extra amount of CaO (about 10–20% in IBA) as compared to the stoichiometric CaO: P₂O₅ ratio will speed up the binding of phosphate to Mg by a fast increase in strength (Reed 2025; Díaz-Pérez et al. 2021). This rapid hardening could lead to 40–60% attainment of the final compressive strength after 2 days of curing. The products of the carbonation process may, however could be causing an increased brittleness of cements with a reduction of 5–10% of their mechanical strength over time as a result of overhydration of their matrix. The heavy metal oxides in IBA, for instance, Fe₂O₃ (5–10%), facilitate the densifying of the cement microstructure by assisting the formation of crystalline phases, resulting in increased thermal stability and enhanced high-temperature resistance (Liu et al. 2023b).

Furthermore, based on the analysis results it can be highlighted that certain variables, such as W/C, MgO/PO₄, and curing age, exert dominant control on strength development, while others like iron oxide show negligible influence. Based on these observations, the optimum dosage ranges and their corresponding strength responses are systematically summarized in Table 4.

Table 4. Optimum range of input features based on the PDP analysis

Input feature	Optimum range	Remarks
W/C	0.1–0.3	Strong negative influence; higher W/C leads to sharp reduction in strength due to increased porosity
FA/C	Moderate to higher values (0.3–1.2)	Initial slight decrease followed by sharp increase in strength at higher FA/C values
MgO/PO4	~ 3.5–5.0	Strength increases up to ~ 4, stabilizes, then slightly fluctuates with a minor decline at higher ratios
IBA	Up to 15%	Compressive strength declines marginally as IBA increases, likely due to reduced packing density
Silica content	Increase up to 60%	Flat at low values, then steep rise in strength, followed by gradual decline after exceeding threshold
Alumina content	Moderate range beyond threshold	Similar to silica; initial flat response, steep rise, then gradual reduction in strength beyond threshold
Calcium content	More than 5%	Constant strength below 5%; sharp increase beyond this point, then stabilizes
Iron Oxide content	Less than 5%	Minimal influence; strength response remains relatively flat across dosage levels
Other oxides	0–12%	Non-linear but modest positive effect; gradual rise in strength up to ~ 12%, then levels off
Curing Age	Gradual increase	Sharp increase from ~ 25 MPa at day 1 to ~ 48 MPa at 28 days, then the sharpness of the curve became minimal

Conclusions

This study successfully developed and validated machine learning models for predicting the compressive strength of MPC incorporating incinerated bottom ash, using a comprehensive dataset containing 396 experimental data points. The most important findings of this study are highlighted below-

• Among all models tested, the Extreme Gradient Boosting (XGB) algorithm exhibited the highest predictive accuracy, achieving a mean train and test R² greater than 0.90 and 0.80 and lowest test RMSE comparing other models in the fivefold cross-validation test phase, confirming its high capability in handling complex datasets with nonlinear patterns.

• SHAP-based feature importance analysis revealed that curing age, FA/C ratio, and W/C ratio were the most influential parameters, with curing age demonstrating the highest average SHAP value. The IBA content also showed a significant positive contribution, enhancing the predicted compressive strength.

• The SHAP force and beeswarm plots illustrated that higher curing durations, optimal MgO/PO₄ ratios, and moderate IBA contents contributed positively, while excessive FA/C and W/C ratios had the strongest negative impacts, reducing strength significantly.

• Partial dependency plots confirmed nonlinear trends in input-parameter influence. Compressive strength dropped almost 26% as W/C increased from 0.1 to 0.6. In addition, silica and alumina exhibited threshold effects by boosting strength initially and then gradually reduce it.

Overall, the integration of SHAP and partial dependence analysis enriched the interpretability of ML models and provided deeper insights into the role of chemical constituents in MPC systems, establishing data-driven pathways for optimizing low-carbon binder formulations.

Limitations and future studies

Despite the promising outcomes, this study is not without limitations. Firstly, the dataset, though extensive, was derived from previously published experimental results, which may introduce variability in measurement standards, testing procedures, and material sourcing across studies. Such inconsistencies could affect the generalizability of the machine learning models beyond the current dataset. However, experimental evaluation based on MPC were not possible for our current laboratory conditions due to limitations on laboratory access and material availability. Moreover, the models were developed based on input features limited to physical mix ratios and major chemical oxide components; the exclusion of microstructural characteristics or environmental exposure conditions may overlook influential factors affecting long-term performance. Additionally, while XGB and GBR demonstrated strong predictive performance, the slight overfitting observed between training and testing phases suggests the need for further model refinement or regularization. These limitations indicate that future research should incorporate more diverse datasets, experimental validation, and multi-target modeling frameworks to enhance prediction reliability and broaden application scope.

Acknowledgements

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through large group project under grant number (RGP2/33/46). The computational simulation work took place at KUET’s BIM laboratory at the Department of BECM, Khulna, Bangladesh.

Author contributions

Md. Kawsarul Islam Kabbo: Conceptualization, Methodology, Investigation, Formal analysis, Writing—original draft, Writing—review & editing. Md. Habibur Rahman Sobuz: Conceptualization, Methodology, Data curation, Validation, Supervision, Writing—original draft, Writing—review & editing. Mita Khatun: Formal analysis, Data curation, Validation, Data curation, Writing—original draft, Writing—review & editing. Mohamed Ghalla: Formal analysis, Data curation, Validation, Writing—original draft, Writing—review & editing. M Jameel: Methodology, Validation, Investigation, Writing—original draft, Writing—review & editing. Noor Md. Sadiqul Hasan: Methodology, Validation, Investigation, Writing—review & editing. Sani Aliyu Abubakar: Validation, Investigation, Writing—review & editing.

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: [email protected]) if anyone needs the data for this study.

Declarations

Competing Interests

The authors declare no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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