Estimating compressive strength of CO₂ incorporated concrete with data augmentation and explainable regression modeling

Materials

The study utilised two cement types: Ordinary Portland Cement (OPC) and fly ash–based Portland Pozzolana Cement (PPC), adhering to IS: 269-2015 ; equivalent to ASTM C150/C150M and IS: 1489 (Part 1)–1991 equivalent to ASTM C595/C595M, respectively, with specific gravities of 3.15 and 3.06 and standard consistencies of 28% and 34%. River sand, locally sourced and classified as Zone II according to IS: 383-2016; equivalent to ASTM C33/C33M, was used as fine aggregate, exhibiting a specific gravity of 2.65, a fineness modulus of 2.82, and a water absorption of 1.60%. Coarse aggregates comprised crushed stone (20 and 10 mm), assessed in accordance with IS: 383-2016; equivalent to ASTM C33/C33M, exhibiting specific gravities of 2.68 and 2.77, fineness moduli of 6.00 and 6.95, and water absorptions of 0.17% and 0.37%, respectively. Potable tap water was used for both casting and curing. A polycarboxylic ether polymer-based superplasticizer (Fosroc Auramix 200) complying with IS: 9103-1999 ; equivalent to ASTM C494/C494M, was employed as an admixture. Furthermore, 99.9% pure industrial-grade carbon dioxide gas was supplied in high-pressure cylinders (about 300 psi or 20 bar) for the carbonation process.

Mix design and methodology

The study examined the impact of $\mathrm{C}{\mathrm{O}}_2$ incorporation during mixing on the compressive strength of concrete. The data encompassed various concrete mix proportions, binder types, and $\mathrm{C}{\mathrm{O}}_2$ dosages, facilitating an extensive assessment. The concrete mixes comprised two types of binders, OPC and PPC, with binder quantities of 500, 400, and 350 kg/m³. Additional constituents comprised water (175–193 kg/m³), coarse aggregates (1,200.63 kg/m³), fine aggregates (674.584 kg/m³), and superplasticisers (0.65% by weight of cement). $\mathrm{C}{\mathrm{O}}_2$ was injected in concentrations of 0%, 0.05%, 0.10%, 0.15%, and 0.20% by weight of cement, serving as a critical factor in assessing compressive strength. The input parameters for regression modelling were binder type, binder content, water-to-binder ratio, $\mathrm{C}{\mathrm{O}}_2$ dosage, and testing age. The concrete mixture proportions are listed in Table 1 range of parameters is listed in Table 2.

In this study, $\mathrm{C}{\mathrm{O}}_2$ was injected directly during the mixing process. High-purity $\mathrm{C}{\mathrm{O}}_2$ gas (99.9%) was supplied through a cylinder equipped with a dual-stage regulator, pressure gauge, and calibrated rotameter to ensure a regulated flow rate of 3.0 $\pm$ 0.2 L/min. The injection duration for each batch (30–45 s) was determined based on the mixer capacity and the required $\mathrm{C}{\mathrm{O}}_2$ dosage relative to cement weight, ensuring delivery within $\pm$2% of the target. The gas was injected into the concrete mixer through a 10 mm inner-diameter reinforced hose, with the mixing chamber enclosed by gasket-lined acrylic panels to reduce leakage, leaving only a narrow, sealed opening for the hose connection and a pressure relief vent equipped with a one-way valve. The measured $\mathrm{C}{\mathrm{O}}_2$ was injected consistently, enabling its reaction with the hydrating cement and promoting carbonation within the mix. Safety protocols comprised continuous laboratory ventilation to ensure ambient $\mathrm{C}{\mathrm{O}}_2$ levels remained below 1,000 ppm, using personal protective equipment (safety goggles, nitrile gloves, and $\mathrm{C}{\mathrm{O}}_2$-rated respirators), leak detection via portable monitors, and emergency shut-off valves in compliance with ASTM C1768 standards. This process was essential for achieving the intended interaction between $\mathrm{C}{\mathrm{O}}_2$ and the binder. Following the mixing process, the concrete was cast into standard moulds to assess its compressive strength. Compressive strength tests were carried out at 7, 28, and 56 days, in accordance with IS: 516-1959 norms; equivalent to ASTM C39, to evaluate the strength of the $\mathrm{C}{\mathrm{O}}_2$-incorporated concrete.

Compressive strength test results

This study examines the impact of $\mathrm{C}{\mathrm{O}}_2$ incorporation during mixing on the compressive strength of concrete, assessed at 7, 28, and 56 days to determine both early-age and long-term strength development. The findings demonstrate that the incorporation of $\mathrm{C}{\mathrm{O}}_2$ at regulated dosages during mixing significantly improves the compressive strength of concrete, especially at reduced water-to-cement (w/c) ratios. The optimum $\mathrm{C}{\mathrm{O}}_2$ concentration ranges from 0.05% to 0.10% for the majority of mixes, beyond which a reduction in strength is observed. This behaviour can be attributed to the carbonation reactions between $\mathrm{C}{\mathrm{O}}_2$ and calcium hydroxide ( $\mathrm{C}\mathrm{a}(\mathrm{O}\mathrm{H}{)}_2$), which leads to the formation of calcium carbonate ( $\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{O}}_3$). This reaction optimally refines the pore structure and enhances the density of the concrete matrix, consequently augmenting strength. However, excessive $\mathrm{C}{\mathrm{O}}_2$ exposure may lead to premature carbonation, hindering the hydration process and reducing the availability of $\mathrm{C}\mathrm{a}(\mathrm{O}\mathrm{H}{)}_2$ for further strength development (Monkman et al., 2018; Monkman & MacDonald, 2016). For the w/c = 0.45 mixes, OPC-based concrete exhibited enhanced compressive strength with increasing $\mathrm{C}{\mathrm{O}}_2$ dosage up to 0.10%. The control mix demonstrated compressive strengths of 24.25, 37.62, and 39.12 MPa at 7, 28, and 56 days, respectively. The highest strength (50.58 MPa at 56 days) was observed at 0.10% $\mathrm{C}{\mathrm{O}}_2$, indicating that moderate carbonation positively impacted the microstructure. Nevertheless, beyond 0.10%, a reduction in strength was noted, likely due to excessive carbonation impeding further hydration (Monkman & MacDonald, 2017). Similarly, for PPC mixes, the compressive strength improved up to 0.05% $\mathrm{C}{\mathrm{O}}_2$, to a maximum of 55.87 MPa at 56 days, after which the strength began to decrease, especially at 0.15% and 0.20% $\mathrm{C}{\mathrm{O}}_2$ concentrations. The presence of pozzolanic materials in PPC would have facilitated early strength development, but prolonged exposure to $\mathrm{C}{\mathrm{O}}_2$ would have reduced the efficacy of the long-term pozzolanic reaction (Samniang et al., 2021).

For the w/c = 0.35 mixes, with a reduced water content and inevitably higher strength, a more significant improvement due to $\mathrm{C}{\mathrm{O}}_2$ incorporation was observed. The control OPC mix exhibited compressive strengths of 32.63, 50.19, and 53.20 MPa at 7, 28, and 56 days, respectively. The highest strength (60.09 MPa at 56 days) was attained at 0.10% $\mathrm{C}{\mathrm{O}}_2$, indicating the improved densification effect resulting from controlled carbonation. A similar trend was seen for PPC, where 0.05% $\mathrm{C}{\mathrm{O}}_2$ yielded the highest strength of 59.53 MPa at 56 days. However, beyond this concentration, strength began to decrease, indicating that excessive carbonation would have led to the formation of a dense outer layer that impeded further hydration of the cementitious matrix (Xu et al., 2022). Conversely, the w/c = 0.55 mixes exhibited a comparatively lower strength enhancement due to $\mathrm{C}{\mathrm{O}}_2$ incorporation. The control OPC mix had compressive strengths of 18.19, 26.33, and 28.47 MPa at 7, 28, and 56 days, respectively. The compressive strength attained a maximum of 31.25 MPa at 56 days with 0.05% $\mathrm{C}{\mathrm{O}}_2$; however, with higher $\mathrm{C}{\mathrm{O}}_2$ dosages, the increase in strength was negligible. A similar pattern was noted in PPC, with the highest strength (30.95 MPa at 56 days) obtained at 0.05% $\mathrm{C}{\mathrm{O}}_2$, followed by a decrease in strength. This limited strength improvement can be attributed to the higher porosity of w/c = 0.55 mixes, which would have reduced the effectiveness of $\mathrm{C}{\mathrm{O}}_2$-induced densification. Furthermore, at high w/c ratios, carbonation may progress more rapidly. However, it does not substantially enhance overall strength development due to the extensive availability of pore water (Wang et al., 2019).

The results validate that the inclusion of $\mathrm{C}{\mathrm{O}}_2$ during mixing improves concrete strength at optimal dosages (0.05–0.10%) owing to the beneficial effects of early-age carbonation. The regulated formation of $\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{O}}_3$ enhances the packing density of the cement matrix and decreases porosity, thereby enhancing strength. However, when $\mathrm{C}{\mathrm{O}}_2$ concentration exceeds a critical threshold (beyond 0.10%), the carbonation reaction consumes excessive $\mathrm{C}\mathrm{a}(\mathrm{O}\mathrm{H}{)}_2$, which may interfere with long-term hydration and strength development (Rashid & Singh, 2023). The impact of the w/c ratio, as shown in Figs. 1A and 1B, is also evident in the findings, as reduced w/c ratios (0.35 and 0.45) demonstrate a significant increase in strength. This is attributed to the denser microstructure of low w/c ratio mixes, which enables regulated carbonation to enhance the pore structure without substantially reducing hydration (Li et al., 2019). Conversely, high w/c ratio mixes (0.55), as shown in Fig. 1C exhibit increased porosity, hence limiting the efficacy of $\mathrm{C}{\mathrm{O}}_2$-induced densification. The comparison between OPC and PPC indicates that PPC typically has superior long-term strength due to the pozzolanic reaction. However, PPC appears more sensitive to excessive $\mathrm{C}{\mathrm{O}}_2$ exposure, as seen from the more pronounced decline in strength at 0.15% and 0.20% $\mathrm{C}{\mathrm{O}}_2$ concentrations. The delayed pozzolanic reaction may be impeded by early carbonation, hence influencing the formation of additional cementitious compounds (Šavija & Luković, 2016). The study indicates an optimal $\mathrm{C}{\mathrm{O}}_2$ range of 0.05–0.10% for strength enhancement, beyond which carbonation impacts hydration. The effect is more pronounced at lower water-to-cement ratios (0.35 and 0.45) and with OPC in comparison to PPC. These insights can be valuable for developing sustainable cementitious composites through the integration of regulated $\mathrm{C}{\mathrm{O}}_2$ utilisation while ensuring optimal performance.

Problem formulation

The primary objective of this study is to develop an Artificial Intelligence (AI) model $\mathcal{M}$ that can accurately forecast the compressive strength of concrete ( $y\in \mathbb{R}$) based on its mix proportions. The dataset $D\in {\mathbb{R}}^{n\times m}$, where $n$ is the number of samples and $m$ represents the features, poses challenges due to its limited size ( $n=270$) and the complex, non-linear relationships. Moreover, the lack of interpretability in traditional ML models requires methods to explain predictions, ensuring trust and usability in real-world applications. This study addresses these challenges through a comprehensive framework that integrates data augmentation, ML, and model explainability.

The first step in the proposed framework involves addressing data scarcity by generating synthetic samples using both CTGAN and TVAE. The CTGAN model ${\mathcal{G}}_{CTGAN}$ and the TVAE model ${\mathcal{G}}_{TVAE}$ are independently trained on the original dataset D to generate synthetic datasets $D_{\mathrm{s}\mathrm{y}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}^{\mathrm{C}\mathrm{T}\mathrm{G}\mathrm{A}\mathrm{N}}$ and $D_{\mathrm{s}\mathrm{y}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}{\mathrm{c}}^{\prime }}^{\mathrm{T}\mathrm{V}\mathrm{A}\mathrm{E}}$ respectively, each consisting of $k\cdot n$ samples, where $k>1$ is the augmentation factor. A quantitative and qualitative comparison of the synthetic datasets is then conducted using evaluation metrics and model performance metrics when trained on the synthetic data. The framework selects the synthetic dataset characterised by superior quality and the most representative samples based on this comparison. The final augmented dataset is then constructed as:

(1) $$D_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{d}}=D\cup D_{\mathrm{s}\mathrm{y}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}},$$where $D_{\mathrm{s}\mathrm{y}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}}^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}$ is the superior synthetic dataset from either CTGAN or TVAE. This approach ensures that only the best-quality synthetic data is utilised, leading to improved model performance and robustness. The ML model $\mathcal{M}$ is trained on $D_{\mathrm{f}\mathrm{i}\mathrm{l}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}$ with the objective of minimising prediction errors for compressive strength. The training process is governed by the following mathematical objective function:

(2) $$\underset{\mathcal{M}}{min}{\mathbb{E}}_{(x,y)\in D_{\mathrm{f}\mathrm{i}\mathrm{l}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}}\left[\mathcal{L}(y,\mathcal{M}(x))\right],$$where $\mathcal{L}$ denotes the loss function, chosen as Mean Squared Error (MSE):

(3) $$\mathcal{L}(y,\mathcal{M}(x))=\frac{1}{n}\sum _{i=1}^n{(y_i-{\hat{y}}_i)}^2,$$with ${\hat{y}}_i=\mathcal{M}(x_i)$ representing the predicted strength for input $x_i$. The framework incorporates Explainable AI (XAI) techniques to enhance model interpretability. SHAP is used to decompose predictions into feature contributions, providing insights into the relative importance of each feature. The SHAP decomposition is given by:

(4) $$\mathrm{S}\mathrm{H}\mathrm{A}\mathrm{P}(f(x))={\varphi }_0+\sum _{i=1}^m{\varphi }_i,$$where ${\varphi }_0$ is the base value representing the average prediction, and ${\varphi }_i$ quantifies the contribution of feature $i$ to the prediction for input $x$. This interpretability ensures transparency and trust in the model’s predictions, making it suitable for practical applications. Further, the model undergoes iterative optimisation to improve its performance. This includes hyperparameter tuning and retraining to ensure the model achieves the best possible accuracy and generalisation. The optimisation process is reinforced through 10-fold cross-validation, which splits the dataset into 10 subsets, iteratively training the model on nine subsets while validating on the remaining subset. This method mitigates overfitting and yields a reliable assessment of the model’s efficacy. The evaluation metrics used to assess the model’s performance include Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and $R^2$, which are defined as follows:

$$\begin{array}{rl}& \mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n|y_i-{\hat{y}}_i|,\\ & \mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{n}\sum _{i=1}^n{(y_i-{\hat{y}}_i)}^2},\\ & R^2=1-\frac{\sum _{i=1}^n{(y_i-{\hat{y}}_i)}^2}{\sum _{i=1}^n{(y_i-\overline{y})}^2}\end{array}$$where $\overline{y}$ is the mean of the true values $y_i$. The final output is an optimised model ${\mathcal{M}}_{\mathrm{o}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{s}\mathrm{e}\mathrm{d}}$ that delivers accurate predictions for compressive strength while providing interpretable insights into the underlying factors. This framework effectively addresses the challenges of data scarcity, complexity, and model transparency in concrete strength forecasting.

Algorithm

The proposed Algorithm 1 integrates synthetic data generation to address data scarcity in concrete strength prediction. It combines real and synthetic data and trains ML models. Explainable AI methods, specifically SHAP, are employed to interpret feature contributions, enhancing model transparency.

Data preprocessing and analysis

The original dataset consists of 270 rows and includes the crucial factors affecting concrete compressive strength. The dataset comprises variables including the Water-to-Binder Ratio (WBRatio) between 0.350 and 0.550, OPC and PPC with values between 0.000 and 500.0 kg/m³, curing days (DAYS) spanning from 7 to 56 days, and $\mathrm{C}{\mathrm{O}}_2$ dose varying from 0.000 to 0.200. Every row in the data shows a unique concrete mix configuration that relates these input variables to the measured compressive strength. The small size of the dataset and the complexity of the relationships among variables emphasise the need for synthetic data augmentation to support the training process of ML models and predictive accuracy. The variable WBRatio exhibits a narrow and consistent distribution, indicating minimal variability across the samples. Similarly, $\mathrm{C}{\mathrm{O}}_2$ levels show a tightly clustered distribution, suggesting well-regulated conditions with limited variability. In contrast, DAYS, representing the curing age, displays a broader distribution, indicating diverse sample ages included in the dataset. The cement variables, OPC and PPC, also show consistent distributions, with OPC spanning a slightly wider range compared to PPC. Lastly, STRENGTH, representing material strength, exhibits significant variability between 20 and 60, reflecting the range of structural performance observed.

The correlation matrix in Fig. 3 reveals key relationships among the variables in the dataset. A strong negative correlation (−0.72) between the WBRatio and material strength (STRENGTH) indicates that higher water content reduces structural strength, aligning with known material science principles. Similarly, the strong inverse relationship (−0.96) between OPC and PPC reflects their complementary roles in material composition. The moderate positive correlation (0.54) between curing time (DAYS) and strength highlights the beneficial impact of extended curing on material performance. These findings emphasise the critical role of controlling the water-binder ratio and curing time to optimise material strength while highlighting the interplay between OPC and PPC in mixtures.

Data augmentation

The original dataset undergoes preprocessing, ensuring consistency and compatibility for subsequent steps. Small datasets often lead to models that are prone to overfitting, where the model learns specific patterns in the data rather than general trends, resulting in suboptimal performance. This can compromise the reliability of insights and predictions. To overcome data scarcity, CTGAN and TAVE are employed to generate synthetic data, which expands the dataset by producing samples that mimic the statistical properties of the original data. The process commenced with metadata detection using the Metadata method from the SDV library. Metadata serves as a critical component in preserving the structural integrity of synthetic data by capturing schema definitions, data types, and interdependencies among variables. This ensures that the generative model adheres to the logical and statistical constraints inherent in the original dataset. Both models were subsequently trained on the original data using 1,000 epochs to ensure convergence and learning of the underlying data distributions. The model generated 10,000 synthetic samples; the samples are filtered, and substantially high-quality data augment the dataset to enable more robust model development. The filtering process utilised Cook’s Distance to ensure the reliability of the generated synthetic data. Following the application of a linear regression model to the integrated real and synthetic dataset, we calculated Cook’s Distance for each synthetic sample to assess its impact on the model fit. Samples exhibiting a Cook’s Distance value exceeding 4/n were classified as high-influence outliers and subsequently excluded. This enabled the removal of synthetic samples that, although not definitive statistical outliers, had the potential to distort learning and diminish model robustness.

Synthetic data quality was evaluated through diagnostic and statistical similarity measures as shown in Table 3. Through data quality assessment reports for CTGAN and TVAE, it is evident that both models attain perfect scores in data validity, data structure, and general basic data quality, each scoring 100%. However, on closer examination of data structure elements, one finds notable variations. In both column shapes (97.42% vs. 85.79%) and column pair trends (94.59% vs. 62.97%), the TVAE model outperforms CTGAN. As a result, TVAE’s (96.01%) general data structure score is rather better than CTGAN’s (74.38%). Although both models preserve fundamental data integrity, TVAE generates synthetic data with a more accurate representation of feature distributions and relationships. Further, Column-wise data quality assessments, as in Table 4, confirm that TVAE consistently outperforms CTGAN across all evaluated criteria. The TVAE model demonstrates exceptional capability in maintaining the distributional integrity of the WBRatio (0.9978), OPC (0.9890), and CO₂ (0.9823), achieving nearly perfect scores across the majority of columns. Conversely, CTGAN demonstrates challenges in capturing intricate relationships among these variables, evidenced by its relatively poor performance, particularly in the CO₂ (0.7147) and STRENGTH (0.749) columns. The WBRatio exhibits the most significant disparity (0.656 vs. 0.9978), indicating that TVAE provides a more authentic synthetic representation of this crucial attribute. TVAE’s a superior ability to generate high-quality synthetic data that closely mirrors the statistical properties of the actual dataset. However, recognising that not all synthetic samples may accurately represent the original distribution. In such cases, outliers are removed, and only synthetic samples closely aligned with the original data distribution are retained.

Machine learning modelling

Once the data preparation is complete, the final dataset obtained is split into training and testing sets in a (80:20) ratio. We utilised a 10-fold cross-validation strategy during the training phase to ensure robust model evaluation and prevent overfitting. This approach involves dividing the training data into ten subsets of equal size. In each iteration, nine folds are allocated for training, while the remaining fold serves for validation. This procedure is executed ten times, guaranteeing that each data point is utilised for validation precisely once. The resulting data is analysed using regression models, including a diverse range of ML models, including advanced algorithms such as Light Gradient Boosting Machine (LGBM), Gradient Boosting Regressor (GBR), RF, and K-nearest Neighbors Regressor (KNN). Ensemble techniques like AdaBoost Regressor (ADA) and Extra Trees Regressor (ET), along with Extreme Gradient Boosting (XGBoost), were also evaluated for their predictive performance. Traditional tree-based models, such as the Decision Tree (DT), were considered alongside linear models, including Linear Regression (LR) and Elastic Net (EN), to accurately estimate the compressive strength of $\mathrm{C}{\mathrm{O}}_2$-incorporated concrete. The models are rigorously evaluated using performance metrics, including MAE, RMSE, and ${\mathrm{R}}^2$.

The model performance using the original dataset is initially assessed to obtain the overall improvement in the model predictability after data augmentation. The Table 5 presents a comprehensive comparison of various regression models. The results highlight LGBM as the best-performing model across metrics, achieving the lowest MAE (2.5954) and RMSE (3.1579), as well as the highest R² score (0.9356). This suggests LGBM’s superior ability to capture patterns in the data with minimal error. This suggests that LGBM not only reduced errors but also accounted for the greatest percentage of variance in the target variable, thereby illustrating its generalisation and robustness. GBR and RF also demonstrate strong performance, though slightly less optimal compared to LGBM. Ensemble models, such as ADA and ET, show moderate performance. On the other hand, simpler models like LR and EN exhibit significantly higher errors and lower R² scores, indicating their limited capability. These results suggest that linear models struggled to capture the underlying relationships within the dataset.

The LGBM model’s robust performance is collectively illustrated by the Fig. 4 that has been presented. The model’s performance is illustrated by the learning curve Fig. 4A, which demonstrates strong generalisation capability with minimal overfitting as the number of training epochs increases. This is evidenced by the convergence of training and validation scores. This equilibrium implies that the model is neither overfitting nor underfitting. The model’s strong predictive accuracy and calibration are further emphasised by the high $R^2$ value (0.913) and the tight clustering around the identity line in the prediction error plot Fig. 4B, which compares the predicted values ( $\hat{y}$) to the actual values ( $y$). By visualising the distribution of prediction errors, the residuals diagram Fig. 4C provides an additional layer of diagnostic analysis. The model predictions show no significant bias, as evidenced by the random dispersion around the zero line. The histogram’s roughly normal error distribution suggests that the model performs well without systematic deviations. The validation curve Fig. 4D offers a comprehensive understanding of the impact of the max_depth hyperparameter on the model’s performance. It illustrates that the model obtains optimal performance at a max depth of approximately 4–6, the parameters utilised are presented in Table 6.

In comparison to the original dataset, the performance of ML models on the augmented dataset exhibits a significant improvement in all evaluation metrics, as illustrated in Table 7. The augmented dataset improved the ${\mathrm{R}}^2$ of the majority of models and reduced estimation errors. LGBM maintains its lead in performance, with an MAE of 1.1847, an RMSE of 1.3833, and an ${\mathrm{R}}^2$ of 0.9872. In the same way, other ensemble models, including ET, GBR, and RF, exhibit robust performance, with ${\mathrm{R}}^2$ values that are nearly identical, ranging from 0.9872 to 0.9848. Interestingly, KNN also demonstrates improved performance (MAE = 1.2665, RMSE = 1.5335, ${\mathrm{R}}^2$ = 0.9843), which is a significant improvement from its original dataset performance. However, ADA exhibits less improvement, with an increase in ${\mathrm{R}}^2$ from 0.9079 to 0.9616, but it continues to lag behind the dominant models. The weakest performers are linear models, including LR and EN, despite the augmentation of the dataset. Although the R² of LR has slightly improved from 0.7850 to 0.8458, EN continues to struggle with an ${\mathrm{R}}^2$ of 0.5851. This validates the idea that the data’s complexity still necessitates more advanced, non-linear modelling methods.

The LGBM model exhibits a significant improvement in performance against the original dataset on the augmented dataset, as illustrated in Fig. 5. The learning curve Fig. 5A emphasises a robust generalisation capability as the training and cross-validation scores closely converge. This improved performance is further substantiated by the prediction error plot Fig. 5B, which displays an ${\mathrm{R}}^2$ value of 0.988. This enhancement suggests that the model trained on the augmented data is capable of predicting values with a significantly higher degree of precision. The model calibration is improved by the denser and more consistent distribution of points along the diagonal, which implies a reduced number of outliers. The distribution of residuals is more densely concentrated around the zero line in the residuals plot Fig. 5C than in the original dataset. Further, demonstrates a more concentrated and symmetrical distribution, while the residuals exhibit less variance. The validation curve Fig. 5D suggests that the model’s performance is less susceptible to fluctuations in the max-depth hyperparameter on the augmented dataset. The validation score remains high across a broader range of max-depth values, indicating that the augmented data not only enhanced performance but also increased model robustness and reduced the risk of overfitting.

Explainable artificial intelligence

The SHAP summary graphs from both the original Fig. 6 and augmented data Fig. 7 provide a comprehensive visualisation of the significance of features and their influence on the model’s predictions. Consistency in the model’s interpretation of feature influences is indicated by the identical feature rankings and SHAP value distributions in the analysis of both plots. The most influential features of PPC, OPC, $\mathrm{C}{\mathrm{O}}_2$, DAYS, and WBRatio were analysed. The strong predictive power of the model is demonstrated by the broad distribution of SHAP values. OPC and $\mathrm{C}{\mathrm{O}}_2$ exhibit substantial impacts, as evidenced by the extensive SHAP value ranges that indicate their critical roles in shaping the model output. In contrast, the SHAP value distributions of DAYS and WBRatio are more restricted, which indicates a more modest impact on predictions and potentially less predictive strength.

The uniform influence of features on model predictions in both scenarios is underscored by the consistent SHAP value range of −10 to 10 across plots. The correlation between the magnitude of the feature and the direction of the prediction is facilitated by the colour gradient from low to high feature values. For instance, positive SHAP values, indicated by darker colours, indicate a direct relationship with the model’s output. The vertical dispersion observed in PPC and OPC suggests potential feature interactions or non-linear influences effectively represented by the model, while the balanced SHAP value spread for $\mathrm{C}{\mathrm{O}}_2$ suggests a linear or consistently influential relationship across its value range. The model’s feature attributions remain unaltered, as evidenced by the identical nature of both SHAP plots. This consistency suggests that the data augmentation procedure maintained the same feature distributions and relationships.

The interpretability and predictive capacity of the model, as illustrated in Fig. 8A, are considerably enhanced, as demonstrated by the feature importance plot for the augmented dataset. The $\mathrm{C}{\mathrm{O}}_2$ feature’s dominance is the most significant observation, as it has a variable importance score of approximately 300, indicating that it has a substantial impact on the model’s predictions. Other features, including DAYS, WBRatio, OPC, and PPC, also influence the model’s decision-making to a lesser extent. The model’s comprehensive visualisation of the contribution of individual features to a specific estimation is illustrated in the SHAP force plot in Fig. 8B. The model anticipates a value of 24.72, which is significantly lower than the base value of approximately 35.25. The estimated value is substantially reduced by the most influential feature in this prediction, DAYS, which has a value of 7. The estimation is pushed toward a lower outcome as a result of the significant negative impact indicated by the blue bar associated with DAYS. This implies that the estimation value is significantly reduced by higher values of DAYS, underscoring the model’s sensitivity to this feature. Furthermore, the estimation is also adversely affected by the $\mathrm{C}{\mathrm{O}}_2$ feature, which has a value of 0, although to a lesser extent than DAYS. The predicted value is further reduced by the narrower blue bar associated with $\mathrm{C}{\mathrm{O}}_2$, which reinforces its modest yet tangible impact.

The plot effectively distinguishes the direction of influence, with blue indicating features that contribute to a reduced estimation error. The absence of red bars indicates that no features in this instance influenced the prediction to a higher value, indicating a cumulative downward influence on the estimated output. The model’s prediction is reduced from the base value of 35.25 to 24.72 as a result of the combined effects of DAYS = 7 and $\mathrm{C}{\mathrm{O}}_2$ = 0, which highlights the extent of these features’ influence. The plot improves the interpretability of the model by clarifying the impact of feature values on specific predictions from a practical standpoint. A DAYS value of 7 is indicative of an early-stage curing period, which is typically associated with lower strength values in applications such as concrete strength estimation. This value is consistent with the reduced estimation. Likewise, a $\mathrm{C}{\mathrm{O}}_2$ value of 0 indicates that the environmental or compositional conditions are additional factors that contribute to the lower strength outcomes. The insights obtained from this force plot not only enhance comprehension of the model’s decision-making process but also offer practitioners actionable information. For example, strategies that involve changing feature values, such as optimising curing time (DAYS) or managing $\mathrm{C}{\mathrm{O}}_2$ exposure, have the potential to enhance predicted outcomes.