Developing machine learning frameworks to predict mechanical properties of ultra-high performance concrete mixed with various industrial byproducts

Kstar models

The hyperparameter tuning for the Kstar model is presented in Fig. 10. The relationship plots presented in Fig. 11 between the measured and predicted values of the Kstar model for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity illustrate the high predictive accuracy of the model. For compressive strength (Fc) in plot (a), the predicted values align closely with the measured values along the 1:1 reference line, indicating minimal deviation. The high coefficient of determination (R² = 0.98) and low root mean square error (RMSE = 3.59 MPa for training and 4.28 MPa for validation) confirm the model’s ability to accurately predict Fc. The nearly linear trend in the plot suggests a strong correlation, with only minor deviations at higher strength values. In plot (b), representing flexural strength (Ff), the measured and predicted values also exhibit a strong correlation, with an almost perfect alignment along the reference line. The model achieves an exceptional R² of 1.00 in validation, indicating near-perfect prediction accuracy. The RMSE values of 0.77 MPa (training) and 0.34 MPa (validation) further support the model’s robustness. The absence of significant scatter in the plot confirms that the model successfully captures the relationships governing Ff. For workability (Slump) in plot (c), the relationship plot again shows a tight clustering of points around the reference line, demonstrating strong predictive accuracy. The training and validation R² values of 0.94 and 0.98, respectively, highlight the model’s effectiveness. The RMSE values of 13.66 mm (training) and 7.59 mm (validation) suggest that the model performs exceptionally well in predicting Slump flow behavior. The minor dispersion in the plot at higher slump values may indicate slight underestimation in extreme cases, but overall, the predictive accuracy remains high. Plot (d), representing porosity, exhibits the strongest agreement between predicted and measured values, with the model achieving an R² of 1.00 in both training and validation. The RMSE values of 0.12 and 0.14 further reinforce the model’s near-perfect accuracy. The data points align exactly with the reference line, confirming that the model captures the porosity behavior with minimal error. Overall, the relationship plots for the Kstar model across all four parameters confirm its exceptional predictive capability, with minimal deviations from the reference line. The high R² values and low errors in all cases suggest that the model is highly reliable for predicting UHPC properties incorporating industrial byproducts.

M5Rules models

The hyperparameter tuning for the M5Rules models is presented in Fig. 12, and the rule iteration in Fig. 13. The relationship plots presented in Fig. 14 between the measured and predicted values of the M5Rules model for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity indicate moderate to good predictive performance, with noticeable deviations from the ideal 1:1 reference line. For compressive strength (Fc) in plot (a), the predicted values exhibit a scattered distribution around the reference line, reflecting a lower predictive accuracy compared to the Kstar model. The R² values of 0.61 (training) and 0.69 (validation) indicate a moderate correlation between the measured and predicted values. The RMSE values of 17.62 MPa (training) and 18.62 MPa (validation) suggest relatively higher errors, indicating that while the model captures general trends, its accuracy is lower, particularly at higher strength levels where deviations are more prominent. In plot (b), representing flexural strength (Ff), the relationship between measured and predicted values is somewhat improved, with R² values of 0.75 (training) and 0.84 (validation). While the points generally follow the reference line, there is still a noticeable spread, particularly at higher flexural strength values, indicating some level of under-prediction or over-prediction. The RMSE values of 3.31 MPa (training) and 3.33 MPa (validation) suggest a moderate predictive capability, but the spread in the relationship plot confirms that M5Rules does not capture Ff as precisely as the Kstar model. For workability (Slump) in plot (c), the measured and predicted values exhibit significant scatter around the reference line, showing a weaker correlation. The R² values of 0.54 (training) and 0.43 (validation) indicate a relatively lower accuracy, while the RMSE values of 39.20 mm (training) and 37.93 mm (validation) confirm the presence of substantial prediction errors. The relationship plot shows a considerable deviation from the ideal trend, indicating that the M5Rules model struggles with predicting workability accurately, possibly due to the complex nature of slump behavior in UHPC. Plot (d), representing porosity, exhibits a slightly stronger agreement between measured and predicted values compared to Slump, but with some noticeable scatter. The R² values of 0.96 (training) and 0.78 (validation) indicate good but inconsistent performance, with better accuracy in the training phase. The RMSE values of 0.90 (training) and 1.95 (validation) suggest an increase in prediction error in validation, reflecting a decline in generalization capability. The points in the relationship plot tend to deviate from the reference line more significantly in validation, suggesting that the model may be prone to overfitting or struggles with certain variations in porosity data. Overall, the relationship plots for the M5Rules model show moderate predictive performance across all four parameters, with relatively higher errors and noticeable deviations from the ideal reference line. The model performs better for flexural strength and porosity but struggles with compressive strength and slump, indicating that while it captures some general trends, its predictive accuracy is lower compared to Kstar, particularly in handling complex material behavior.

ElasticNet models

Figure 15 shows the hyperparameter tuning of the ElasticNet models and the model has proposed Eqs. 22, 23, 24 and 25 as closed-form equations. The relationship plots presented in Fig. 16 between the measured and predicted values of the ElasticNet model for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity demonstrate relatively weak predictive performance compared to other models, with considerable scatter and deviation from the 1:1 reference line. For compressive strength (Fc) in plot (a), the ElasticNet model shows a weak correlation between measured and predicted values, with R² values of 0.28 (training) and 0.19 (validation). The RMSE values of 24.10 MPa (training) and 30.16 MPa (validation) suggest significant prediction errors, indicating that the model struggles to capture the underlying relationships governing compressive strength in UHPC. The scatter plot exhibits a large spread, particularly at higher strength values, demonstrating that ElasticNet fails to generalize well, leading to underprediction and overprediction across different strength levels. In plot (b), representing flexural strength (Ff), the predictive accuracy remains relatively poor, with R² values of 0.49 (training) and 0.64 (validation). The RMSE values of 4.74 MPa (training) and 4.60 MPa (validation) suggest notable errors, though slightly lower than for compressive strength. The relationship plot reveals significant scatter around the reference line, with ElasticNet exhibiting inconsistent prediction behavior across different strength levels. The spread indicates that the model does not effectively capture the complex interactions influencing flexural strength in UHPC. For workability (Slump) in plot (c), the relationship plot displays substantial deviation from the reference line, reinforcing the weak predictive power of ElasticNet for this parameter. The R² values of 0.32 (training) and 0.13 (validation) indicate poor correlation, with RMSE values of 48.88 mm (training) and 46.95 mm (validation) highlighting considerable prediction errors. The large scatter observed in the relationship plot suggests that ElasticNet fails to capture the variability in slump measurements, potentially due to the nonlinear and complex nature of workability in UHPC mixed with industrial byproducts. Plot (d), representing porosity, exhibits the weakest performance among all parameters, with R² values of 0.38 (training) and 0.47 (validation). The RMSE values of 3.25 (training) and 3.32 (validation) indicate substantial errors, suggesting that the model struggles to accurately predict porosity variations. The relationship plot shows a broad distribution of points around the reference line, confirming that ElasticNet fails to capture the underlying dependencies affecting porosity in UHPC. Overall, the relationship plots for the ElasticNet model reveal weak predictive capabilities for all four parameters. The model consistently exhibits high prediction errors, poor correlation, and significant scatter, indicating that it is not well-suited for modeling the mechanical and rheological properties of UHPC. The inability to effectively capture nonlinear relationships in the dataset suggests that ElasticNet lacks the flexibility required for accurate prediction of UHPC properties when mixed with various industrial byproducts.

XNV model

Figure 17 shows the hyperparameter tuning of the model technique. The relationship plots presented in Fig. 18 between the measured and predicted values of the XNV models for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity demonstrate a moderate to strong predictive performance, with relatively high accuracy compared to ElasticNet and M5Rules but lower than Kstar and Decision Tree models. For compressive strength (Fc) in plot (a), the XNV model exhibits a fairly strong correlation between measured and predicted values, with R² values of 0.69 (training) and 0.70 (validation). The RMSE values of 15.74 MPa (training) and 18.40 MPa (validation) suggest reasonable predictive accuracy, though some deviations from the reference line are noticeable. The scatter plot indicates that most points align well with the 1:1 line, but there are some outliers, particularly at higher compressive strength values, where the model slightly underestimates the actual values. In plot (b), representing flexural strength (Ff), the XNV model shows improved predictive performance compared to Fc, with R² values of 0.78 (training) and 0.92 (validation). The RMSE values of 3.13 MPa (training) and 2.20 MPa (validation) indicate lower prediction errors, demonstrating that the model captures the relationship between measured and predicted values more effectively. The relationship plot shows a tighter clustering of points along the reference line, indicating strong predictive reliability. However, some minor dispersion is observed at higher strength values, where slight underestimation occurs. For workability (Slump) in plot (c), the XNV model provides reasonable predictive accuracy, with R² values of 0.77 (training) and 0.80 (validation). The RMSE values of 27.44 mm (training) and 22.43 mm (validation) indicate moderate prediction errors. The scatter plot shows that most points are closely aligned with the reference line, but there are noticeable deviations at higher slump values. The model tends to perform better for mid-range workability values, while some mispredictions occur at extreme ends, likely due to the complex nature of slump behavior in UHPC. Plot (d), representing porosity, demonstrates strong predictive performance, with R² values of 0.95 (training) and 0.87 (validation). The RMSE values of 0.94 (training) and 1.51 (validation) suggest low prediction errors, indicating a reliable model for porosity estimation. The relationship plot shows a strong alignment of points along the reference line, with minimal scatter, highlighting the effectiveness of XNV in capturing the nonlinear dependencies affecting porosity in UHPC. Overall, the relationship plots for the XNV model show a moderate to strong correlation between measured and predicted values across all four parameters. The model performs well in predicting flexural strength and porosity, with good alignment along the reference line and low prediction errors. However, its performance for compressive strength and slump, while reasonable, shows room for improvement, particularly in capturing higher values where slight underestimation is observed. Despite these minor shortcomings, the XNV model demonstrates better predictive reliability than M5Rules and ElasticNet, making it a viable choice for modeling UHPC properties with industrial byproducts.

DT models

Figure 19 shows the hyperparameter tuning of the DT model and the tree iterations of the model are shown in Fig. 20. The relationship plots is shown in Fig. 21 between the measured and predicted values of the Decision Tree (DT) models for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity indicate strong predictive accuracy across all parameters, with DT models outperforming M5Rules, ElasticNet, and XNV while closely approaching the performance of Kstar. For compressive strength (Fc) in plot (a), the DT model demonstrates strong agreement between measured and predicted values, with R² values of 0.89 (training) and 0.87 (validation). The RMSE values of 9.13 MPa (training) and 12.12 MPa (validation) indicate relatively low prediction errors. The scatter plot shows a tight clustering of points along the reference line, with minimal dispersion. However, a few minor deviations can be observed at higher strength values, where the model slightly underestimates some data points. Overall, the DT model provides a reliable prediction of Fc with minimal overfitting, as reflected in its consistent performance across training and validation datasets. In plot (b), representing flexural strength (Ff), the DT model performs exceptionally well, with R² values of 0.81 (training) and 0.92 (validation), indicating a strong correlation between measured and predicted values. The RMSE values of 2.88 MPa (training) and 2.24 MPa (validation) highlight the model’s accuracy in capturing the variations in flexural strength. The scatter plot shows that most points align closely with the reference line, suggesting minimal errors in prediction. The model maintains high accuracy across the dataset, with only a few scattered points deviating from the trend, likely due to complex material behavior in some instances. For workability (Slump) in plot (c), the DT model provides robust predictive performance, with R² values of 0.78 (training) and 0.91 (validation). The RMSE values of 26.90 mm (training) and 14.59 mm (validation) suggest that the model captures the relationship between input parameters and slump effectively. The scatter plot reveals that most points closely align with the reference line, though some slight deviations appear at extreme values. The overall accuracy is higher than that of M5Rules and ElasticNet, indicating that the DT model can predict slump behavior with high reliability. Plot (d), representing porosity, shows the best predictive performance among the four parameters, with R² values of 0.98 (training) and 0.95 (validation). The RMSE values of 0.54 (training) and 0.91 (validation) indicate very low prediction errors, highlighting the model’s strong predictive capabilities for porosity. The relationship plot exhibits an almost perfect alignment along the reference line, with only minimal scatter. This suggests that the DT model effectively captures the underlying trends and dependencies affecting porosity in UHPC with industrial byproducts. Overall, the DT model demonstrates strong predictive accuracy across all four parameters, with particularly high reliability for flexural strength and porosity. The scatter plots show minimal deviation from the reference line, indicating a strong correlation between measured and predicted values. Compared to other models, DT outperforms M5Rules, ElasticNet, and XNV in terms of both R² and RMSE, closely matching the performance of Kstar. While minor underestimations are observed at higher compressive strength and slump values, the overall consistency and accuracy of the DT model make it a highly effective choice for predicting the properties of ultra-high-performance concrete incorporating industrial byproducts.

Overall performance and comparison of models

The performance analysis of the models in predicting the compressive strength (Fc) of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts highlights significant variations in accuracy, error rates, and predictive reliability (see Table 5). The Kstar model emerges as the most robust, achieving an exceptionally high accuracy of 97% for both training and validation datasets. It records the lowest errors, with RMSE values of 3.59 MPa in training and 4.28 MPa in validation, alongside strong correlation metrics (R² = 0.98, R = 0.99). These results suggest that Kstar is highly reliable in capturing the complex interactions between mix proportions and UHPC compressive strength. In contrast, the M5Rules model demonstrates moderate performance, with accuracy at 87% for both training and validation datasets. However, it exhibits significantly higher errors, with an RMSE of 17.62 MPa in training and 18.62 MPa in validation. The lower R² values (0.61 in training and 0.69 in validation) indicate that the model struggles to capture the intricate relationships within the dataset. The ElasticNet model performs the weakest, with the highest errors (RMSE = 24.10 MPa in training and 30.16 MPa in validation) and the lowest accuracy (83% in training, dropping to 79% in validation). Its R² values (0.28 in training and 0.19 in validation) indicate poor predictive ability, suggesting that the model is not well-suited for complex UHPC compositions. The XNV model performs slightly better than M5Rules but remains less reliable compared to Kstar. It achieves an accuracy of 89% in training and 87% in validation, with an RMSE of 15.74 MPa and 18.40 MPa, respectively. The model’s R² values (0.69 in training, 0.70 in validation) suggest moderate predictive reliability, though it still exhibits relatively high errors. The Decision Table (DT) model performs well, with an accuracy of 93% in training and 92% in validation. It records lower RMSE values of 9.13 MPa in training and 12.12 MPa in validation compared to M5Rules and XNV, indicating a relatively strong predictive capacity. Its high R² values (0.89 in training, 0.87 in validation) suggest that DT effectively captures the relationships governing UHPC compressive strength. Overall, Kstar is the most accurate and reliable model, offering precise predictions with minimal errors, followed by DT, which provides a balance between computational efficiency and prediction accuracy. XNV and M5Rules demonstrate moderate reliability, whereas ElasticNet is the least effective model for predicting UHPC compressive strength. The performance analysis of models in predicting the flexural strength (Ff) of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts reveals significant differences in accuracy, error rates, and predictive capabilities (see Table 6). The Kstar model demonstrates superior performance, achieving the highest accuracy of 97% in training and an exceptional 99% in validation. It has the lowest RMSE values (0.77 MPa in training and 0.34 MPa in validation), indicating minimal prediction errors. The model’s R² values (0.99 in training and 1.00 in validation) confirm its near-perfect fit, making it the most reliable choice for predicting flexural strength. The M5Rules model performs moderately well, with accuracy at 86% for both training and validation datasets. However, it exhibits significantly higher RMSE values (3.31 MPa in training and 3.33 MPa in validation) and error percentages of 14%, indicating weaker predictive ability. Its R² values (0.75 in training, 0.84 in validation) suggest that while it captures some of the relationships in the data, it lacks precision compared to Kstar. The ElasticNet model is the least effective, with the highest error rates (20% in training, 19% in validation) and an RMSE of 4.74 MPa in training and 4.60 MPa in validation. Its low R² values (0.49 in training, 0.64 in validation) indicate a weak ability to model flexural strength accurately, making it unsuitable for high-precision predictions. The XNV model offers a balanced performance, achieving 87% accuracy in training and 91% in validation. It records an RMSE of 3.13 MPa in training and a significantly improved 2.20 MPa in validation, suggesting strong generalization capabilities. The model’s R² values (0.78 in training, 0.92 in validation) indicate a good fit, making it a viable option for predicting Ff. The Decision Table (DT) model exhibits similar performance to XNV, with an accuracy of 88% in training and 91% in validation. It records RMSE values of 2.88 MPa in training and 2.24 MPa in validation, coupled with R² values of 0.81 in training and 0.92 in validation. These results suggest that DT is a reliable model, though slightly less precise than Kstar. Overall, Kstar is the most accurate and reliable model for predicting flexural strength, with near-perfect correlation and minimal errors. XNV and DT also demonstrate strong predictive capabilities, while M5Rules offers moderate reliability. ElasticNet performs the worst, struggling with high error rates and poor correlation, making it the least suitable for predicting Ff in UHPC. The performance analysis of models predicting the workability (slump) of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts reveals distinct variations in predictive accuracy and error rates (see Table 7). The Kstar model exhibits the highest accuracy, with 94% in training and 97% in validation. It has the lowest RMSE values (13.66 mm in training and 7.59 mm in validation), indicating minimal prediction errors. The R² values (0.94 in training and 0.98 in validation) confirm its strong correlation, making it the most reliable model for slump prediction. The M5Rules model performs moderately well but with a significant increase in error rates (17% in both training and validation). It records an RMSE of 39.20 mm in training and 37.93 mm in validation, indicating poor precision. The R² values (0.54 in training and 0.43 in validation) suggest weak predictive capabilities, making it less reliable compared to Kstar. The ElasticNet model is the weakest performer, with the highest error rates (21% in training and 22% in validation) and an RMSE of 48.88 mm in training and 46.95 mm in validation. Its low R² values (0.32 in training and 0.13 in validation) indicate poor correlation, making it highly unsuitable for predicting slump in UHPC. The XNV model offers a balanced performance with 88% accuracy in training and 90% in validation. It records an RMSE of 27.44 mm in training and 22.43 mm in validation, suggesting strong predictive capabilities. The R² values (0.77 in training and 0.80 in validation) indicate a reasonably good fit, making it a viable option. The Decision Table (DT) model performs similarly to XNV, with an accuracy of 88% in training and an improved 93% in validation. It records RMSE values of 26.90 mm in training and a significantly lower 14.59 mm in validation, coupled with high R² values (0.78 in training and 0.91 in validation), suggesting strong generalization. Overall, Kstar is the most accurate and reliable model for predicting slump, with minimal errors and near-perfect correlation. DT also demonstrates strong predictive capabilities, particularly in validation, while XNV provides a well-balanced alternative. M5Rules has moderate performance, whereas ElasticNet is the weakest model, struggling with high error rates and poor correlation, making it the least suitable for predicting workability in UHPC. The performance analysis of models predicting the porosity of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts shows clear distinctions in predictive accuracy and error rates (see Table 8). The Kstar model demonstrates the highest accuracy, achieving 99% in both training and validation. It has the lowest RMSE values (0.12 in training and 0.14 in validation), indicating minimal prediction errors. With an R² of 1.00 and an NSE of 1.00, it provides near-perfect correlation, making it the most reliable model for porosity prediction. The M5Rules model exhibits moderate performance, with an accuracy of 92% in training but dropping to 85% in validation. It has higher RMSE values (0.90 in training and 1.95 in validation), indicating reduced precision compared to Kstar. The R² values (0.96 in training and 0.78 in validation) suggest a decent fit but lower predictive power, especially in validation where the error increases to 15%. The ElasticNet model performs the weakest, with the highest error rates (29% in training and 26% in validation) and the highest RMSE values (3.25 in training and 3.32 in validation). Its R² values (0.38 in training and 0.47 in validation) suggest poor correlation, making it unsuitable for porosity prediction. The XNV model offers a balanced performance with 92% accuracy in training and 88% in validation. It records RMSE values of 0.94 in training and 1.51 in validation, with R² values of 0.95 in training and 0.87 in validation, indicating strong predictive capability. It is a reliable model but not as strong as Kstar. The Decision Tree (DT) model also performs well, with 95% accuracy in training and 93% in validation. It records RMSE values of 0.54 in training and 0.91 in validation, with R² values of 0.98 in training and 0.95 in validation, making it a strong alternative to Kstar. Overall, Kstar is the most accurate and reliable model for predicting porosity, with minimal errors and perfect correlation. DT also demonstrates strong predictive capabilities, particularly in validation. XNV provides a well-balanced alternative, while M5Rules shows moderate performance with increased errors in validation. ElasticNet is the weakest model, struggling with high error rates and poor correlation, making it the least suitable for predicting porosity in UHPC.

Comparatively, for more sustainable ultra-high-performance concrete (UHPC) production, selecting the most accurate and efficient predictive model is crucial to optimizing the use of industrial byproducts while maintaining high performance. When comparing models across compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity, the Kstar model consistently outperforms the others, making it the most suitable choice for sustainable UHPC applications. For compressive strength (Fc), Kstar demonstrates the highest accuracy (97%) with the lowest error (3%) and RMSE values (3.59 MPa for training and 4.28 MPa for validation), indicating strong predictive power and minimal deviation. The Decision Tree (DT) model also performs well, with 93% accuracy and RMSE values of 9.13 MPa (training) and 12.12 MPa (validation), making it a viable alternative. Models like Elastic Net and M5Rules struggle with significantly higher errors (17–21%) and lower accuracy, making them less suitable for predicting Fc in sustainable UHPC production. For flexural strength (Ff), Kstar again delivers the best results, achieving 97–99% accuracy with minimal error (1–3%) and RMSE values of 0.77 MPa (training) and 0.34 MPa (validation). Decision Tree (DT) and XNV also perform well, maintaining over 90% accuracy and reasonable RMSE values (DT: 2.88 MPa training, 2.24 MPa validation; XNV: 3.13 MPa training, 2.20 MPa validation). Meanwhile, M5Rules and Elastic Net exhibit higher errors (14–20%) and lower R² values, making them less reliable for flexural strength prediction. For workability (Slump), Kstar continues to be the most accurate model, with 94–97% accuracy and low error rates (3–6%). Its RMSE values (13.66 mm in training and 7.59 mm in validation) are significantly lower than those of M5Rules and Elastic Net, both of which show much higher errors (17–22%) and weaker correlations. XNV and DT provide a balance between accuracy and error, making them reasonable alternatives if Kstar is unavailable. For porosity, which is critical for durability and sustainability, Kstar again outperforms all other models, achieving near-perfect accuracy (99%) with the lowest RMSE values (0.12 in training and 0.14 in validation). The Decision Tree (DT) model also delivers high accuracy (95–98%) with low RMSE values, making it another strong option. XNV and M5Rules show moderate predictive capabilities, whereas Elastic Net significantly underperforms, with a high error rate (26–29%) and poor correlation, making it the least reliable for porosity prediction. Overall, Kstar is the most reliable and accurate model across all four parameters, making it the best choice for predicting sustainable UHPC properties when incorporating industrial byproducts. The Decision Tree (DT) model is a strong alternative, especially for flexural strength, slump, and porosity, but slightly lags behind Kstar in compressive strength. XNV provides balanced performance but is not as robust, while M5Rules and Elastic Net consistently exhibit higher errors, making them less suitable for sustainable UHPC applications. By prioritizing Kstar or DT models, UHPC production can achieve greater efficiency, reduced material waste, and improved performance with industrial byproduct integration. To compare the present research models with those published in the literature, it is essential to analyze their performance in predicting ultra-high-performance concrete (UHPC) properties, including compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity. Traditional models in the literature, such as artificial neural networks (ANNs), support vector machines (SVMs), and multiple regression approaches, have been widely used, but they often face challenges in terms of computational efficiency, data dependency, and generalization ability. For compressive strength (Fc), previous studies have reported that ANN models achieve R² values between 0.85 and 0.95, with mean absolute errors (MAE) exceeding 5 MPa^24,25. In comparison, the present research demonstrates that the Kstar model achieves an R² of 0.98 with an MAE of only 1.92 MPa, significantly improving predictive accuracy. The Decision Tree (DT) model also performs well with an R² of 0.87 in validation, comparable to literature models but with lower root mean square error (RMSE). Unlike ANNs, which require extensive hyperparameter tuning, Kstar and DT models provide stable and interpretable results with reduced computational complexity. Regarding flexural strength (Ff), literature studies indicate that ANN and regression-based models report RMSE values ranging from 2.5 to 4.0 MPa, with R² values between 0.85 and 0.95^26,27. The present research shows that the Kstar model outperforms traditional models by achieving an RMSE of only 0.34 MPa in validation and an R² of 1.00. Similarly, the DT model demonstrates strong predictive capability with an R² of 0.96, aligning with the best results in the literature while offering greater interpretability and ease of implementation. For workability (Slump), previous research suggests that traditional regression models and ANNs exhibit high variance due to the complex interactions of mix proportions and material properties, often achieving R² values around 0.75 to 0.85 with errors between 10 and 20%^28,29. The present study shows a significant improvement, with the Kstar model reaching an R² of 0.98 and an error of only 3%, far surpassing conventional models. The DT model also outperforms literature-reported results, with an R² of 0.91 in validation. In contrast, models such as Elastic Net and M5Rules show lower R² values and higher RMSE, performing similarly to traditional regression models. For porosity, literature studies have found that conventional regression-based models and ANNs achieve moderate predictive accuracy, with R² values typically between 0.85 and 0.95^30,31. The present research significantly enhances prediction accuracy, with the Kstar model reaching an R² of 1.00, suggesting near-perfect prediction capabilities. Even the DT model, with an R² of 0.95, surpasses many literature-reported models. Traditional approaches often struggle with porosity prediction due to the complexity of material interactions, but the machine learning models in this study, particularly Kstar, demonstrate substantial error reduction and improved generalization ability. Overall, the present research models, especially Kstar and DT, outperform many existing models from the literature in predicting the properties of UHPC incorporating industrial byproducts. These models offer superior accuracy, lower errors, and improved robustness, making them more suitable for practical applications in sustainable UHPC production. While ANN and SVM models have been widely explored in the literature, their reliance on extensive tuning and risk of overfitting make them less efficient compared to the more adaptable and interpretable models developed in this study.

That the Kstar model significantly outperforms other models in this study, despite its limited adoption in concrete prediction applications, highlights an important but often overlooked aspect of model selection in engineering research—namely, the alignment between data characteristics and algorithmic capabilities³⁶. While Kstar is not commonly used in concrete materials modeling, its core strengths make it particularly well-suited for complex, nonlinear, and small-to-moderate-sized datasets, which are typical in experimental concrete studies involving multiple supplementary cementitious materials or industrial byproducts³⁶. Kstar, an instance-based learning algorithm, relies on comparing new input instances with stored historical examples using an entropy-based distance function^36,37. This localized, non-parametric approach allows the model to flexibly adapt to intricate patterns and relationships in the data without assuming any fixed functional form. Such flexibility is crucial in predicting the behavior of ultra-high performance concrete (UHPC), where performance characteristics, such as compressive strength, flexural strength, slump, and porosity are influenced by subtle and nonlinear interactions among various binder compositions, additives, and curing conditions. In traditional concrete modeling, widely adopted algorithms like decision trees, support vector machines, or neural networks may require more extensive datasets or hyperparameter tuning to generalize well. In contrast, Kstar can perform robustly on smaller datasets, provided that the data is representative and sufficiently descriptive of the underlying material behavior^36,37. This is particularly advantageous when experimental constraints limit the number of mix designs or replicates, as is often the case with high-performance or specialized concretes. Although its application in concrete prediction literature is limited, Kstar has demonstrated reliable performance in related fields, such as geotechnical engineering, environmental modeling, and materials informatics³⁷. In these domains, it has been successfully employed to predict soil strength parameters, contaminant migration, and composite material properties, problems that similarly involve nonlinear, multivariate interactions and data heterogeneity³⁸. This cross-domain evidence reinforces the validity of Kstar’s strong performance in the current study. Therefore, its inclusion is not arbitrary but rather a deliberate attempt to evaluate a broader spectrum of machine learning techniques that align with the specific data characteristics and modeling challenges of UHPC systems^36,37,38. The strong performance of Kstar in this context suggests that its capabilities may be underrecognized in civil engineering applications, and its demonstrated effectiveness here opens the door for more widespread exploration of instance-based learning in future concrete prediction research.

Furthermore, the reviewed literature demonstrates the extensive application of artificial neural networks (ANNs) in predicting the mechanical properties of concrete mixtures, including ultra-high-performance concrete (UHPC) incorporating various industrial byproducts. Studies such as those by Chou et al.⁸, Li et al.¹⁰, Alabduljabbar et al.¹⁴, and Zhang et al.¹¹ have consistently shown that ANN models can achieve high accuracy, with R² values often ranging from 0.91 to 0.94, depending on the complexity of the dataset and the inclusion of factors like curing conditions, chemical composition, or optimization via hybrid techniques. These studies validate the capability of ANN-based approaches to handle nonlinear relationships and high-dimensional data, which are typical in UHPC systems with multiple supplementary cementitious materials (SCMs). However, while ANN models have proven effective, they also come with several limitations. They typically function as “black-box” models, making them less interpretable, and often require large datasets and intensive hyperparameter tuning to achieve stable and reliable performance. Moreover, they are sensitive to issues like overfitting, especially when dealing with moderate-sized datasets, which are common in UHPC research due to the high cost and complexity of experimental trials. In comparison, the present research adopts a broader and more diversified set of machine learning models, including Kstar, M5Rules, ElasticNet, XNV, and Decision Table, to evaluate their ability to predict multiple mechanical properties of UHPC mixtures containing various industrial byproducts. Notably, the Kstar model outperforms others across most performance metrics, achieving R² values up to 1.00 in some cases on independent test data. Unlike traditional ANN models, Kstar offers a more adaptable and instance-based approach that proves particularly effective for small to medium-sized datasets with high variability and nonlinearity, as is the case in this study. The use of rule-based and ensemble models alongside Kstar also enhances the robustness of the findings by ensuring that model performance is not reliant on a single algorithmic approach.

Furthermore, the present study distinguishes itself by not only focusing on compressive strength but also incorporating flexural strength, slump, and porosity into the modeling framework. This multi-target approach allows for a more comprehensive assessment of concrete performance, something that is often overlooked in studies that utilize ANN models to predict only a single mechanical property. The interpretability of results is further supported through SHAP analysis and Hoffman & Gardener sensitivity techniques, enabling the identification of key features and their influence on each performance metric. This level of interpretability is often lacking in standard ANN implementations. In conclusion, while ANN-based models have shown strong predictive capabilities in prior studies, the present research expands the modeling scope, enhances interpretability, and achieves superior predictive performance using models like Kstar. It highlights the importance of aligning the machine learning technique with the specific characteristics of the dataset and prediction task, demonstrating that less commonly used models like Kstar can provide significant advantages over traditional ANN models in UHPC prediction tasks.

In addition, studies presented in the literature^{32,33,34,35,36,37,38} provide significant contributions to the field of concrete strength prediction using machine learning and hybrid optimization methods. For instance, Parhi and colleagues^32,34,35 utilized metaheuristic techniques such as Dolphin Echolocation and Spotted Hyena Optimization to optimize model performance, achieving improved predictions in specialized concrete compositions like PET fiber-reinforced or ASR-affected concretes. Similarly, Singh et al.³³ emphasized the importance of evolutionary hyperparameter tuning in achieving accurate strength predictions for high-performance concrete. These models demonstrated considerable accuracy; however, they often targeted specific material configurations or single performance metrics. The current study distinguishes itself by applying a broader range of machine learning models including KStar, M5Rules, ElasticNet, XNV, and Decision Table to predict multiple mechanical properties of ultra-high-performance concrete (UHPC) incorporating various industrial byproducts. Unlike many of the cited works which focus on a single mechanical property, this study addresses compressive strength, flexural strength, slump, and porosity collectively, providing a more comprehensive prediction framework. In addition, the KStar model used here achieved exceptionally high predictive accuracy (R² values up to 1.00), outperforming the models reported in the comparative literature which typically reported R² values in the range of 0.90–96. Furthermore, recent works by Onyelowe et al.^36,37,38 introduced advanced machine learning frameworks for predicting mechanical properties of concrete using hybrid fibers and industrial waste, and employed physics-informed modeling approaches. While these works contribute valuable methodologies, the present study integrates both performance prediction and feature interpretability using Hoffman & Gardner and SHAP analyses, offering an in-depth understanding of material influences. Overall, the present research expands the scope and performance benchmark of existing literature by not only offering higher model accuracy across multiple UHPC properties but also integrating detailed interpretability and sustainability considerations into model development.

The Taylor chart for the Fc (compressive strength) model (see Fig. 22) provides a statistical visualization of the model’s performance by comparing predicted and measured values in terms of three key metrics: correlation coefficient, standard deviation, and root-mean-square error (RMSE). For the training phase, the Taylor chart likely indicates a high correlation coefficient (close to 1), signifying a strong agreement between predicted and actual Fc values. The standard deviation of the model’s predictions should be close to that of the measured values, indicating that the model captures the variability in the data effectively. A low RMSE value suggests minimal prediction errors, confirming the model’s accuracy in training. During the validation phase, the Taylor chart might show a slightly lower correlation coefficient compared to training, reflecting some loss of prediction accuracy on unseen data. The standard deviation of the predicted values could deviate more from the actual values, signifying potential overfitting if the difference is significant. An increase in RMSE during validation would indicate higher prediction errors compared to training, but if the values remain close, it confirms that the model generalizes well. Overall, the Taylor chart effectively illustrates the predictive performance of the Fc model, highlighting its reliability during both training and validation phases. If the validation performance remains strong with minimal deviation from training metrics, it indicates a well-generalized model suitable for practical applications in UHPC mix optimization. The Taylor diagram for the Ff (flexural strength) models (see Fig. 23) provides an in-depth statistical assessment of the model’s predictive accuracy by evaluating correlation coefficient, standard deviation, and root-mean-square error (RMSE). In the training phase, the Taylor diagram likely demonstrates a high correlation coefficient, indicating a strong linear relationship between the predicted and actual Ff values. The standard deviation of the model’s predictions should align closely with the standard deviation of the measured data, confirming that the model effectively captures the variability in flexural strength. A low RMSE further supports the model’s accuracy, demonstrating minimal deviations between predictions and actual values. During the validation phase, the correlation coefficient may slightly decrease compared to training, reflecting the model’s ability to generalize to unseen data. If the standard deviation of the predicted values remains close to that of the measured data, it suggests that the model retains its predictive capability. However, a noticeable increase in RMSE during validation could indicate higher errors, potentially suggesting overfitting or model limitations in handling new data. The Taylor diagram provides a concise visualization of the Ff model’s performance, allowing for direct comparison between training and validation. If the validation metrics remain strong and closely aligned with the training performance, the model can be considered reliable for predicting the flexural strength of UHPC incorporating industrial byproducts. The Taylor diagram for the Slump model (see Fig. 24) provides a comprehensive statistical evaluation of the model’s predictive accuracy, highlighting the correlation coefficient, standard deviation, and root-mean-square error (RMSE). In the training phase, the correlation coefficient should ideally be high, indicating a strong agreement between the predicted and measured slump values. A close match between the standard deviation of the predicted values and that of the actual data signifies that the model accurately represents the variations in workability. A low RMSE further supports the model’s ability to make precise predictions, suggesting minimal deviation from actual slump measurements. During the validation phase, the correlation coefficient might decrease slightly compared to training, reflecting the model’s generalization capability on unseen data. If the standard deviation of the predictions remains close to that of the actual slump values, it suggests the model effectively captures the distribution of the data. However, an increase in RMSE during validation could indicate that the model struggles with new data, potentially pointing to overfitting or insufficient generalization. The Taylor diagram visually represents how well the model performs in both training and validation, allowing direct comparison. If the validation performance remains close to the training metrics, it confirms the model’s reliability for predicting the slump of UHPC incorporating industrial byproducts. If discrepancies arise, further optimization or additional training data may be required to improve robustness. The Taylor diagram for the Porosity models (see Fig. 25) evaluates the predictive performance by analyzing the correlation coefficient, standard deviation, and root-mean-square error (RMSE). In the training phase, a high correlation coefficient indicates a strong agreement between the predicted and measured porosity values. The standard deviation of the predictions should align closely with that of the actual data, demonstrating that the model effectively captures variability in porosity. A low RMSE suggests minimal error in the predictions, reinforcing the model’s accuracy in capturing the porosity characteristics of UHPC. During the validation phase, the correlation coefficient may slightly decrease, reflecting the model’s performance on unseen data. If the standard deviation of the predicted values remains close to the actual porosity values, it indicates that the model generalizes well. An increase in RMSE compared to training could signify reduced accuracy and potential overfitting, suggesting the need for further model refinement. The Taylor diagram provides a visual comparison of training and validation performance, illustrating how well the model generalizes. If the validation metrics closely match the training performance, the model demonstrates strong reliability for porosity prediction. However, significant discrepancies could indicate the need for additional training data, hyperparameter tuning, or feature engineering to enhance predictive capabilities.

Sensitivity analysis

A sensitivity index of 1.0 indicates complete sensitivity, a sensitivity index less than 0.01 indicates that the model is insensitive to changes in the parameter. Figure 26 shows the sensitivity analysis with respect to Fc, Ff, Slump and Porosity. The sensitivity analysis results based on Hoffman & Gardener’s method provide insights into the relative importance of various input parameters on the models for Fc, Ff, Slump, and Porosity. For the Fc model, the most influential variable is MK/B, with a 14% importance, followed by S/B at 12% and FA/B at 10%. Other notable parameters include CAGS (9%), LS/B (6%), and NS/B (6%). The lowest impact is observed for SF/B (1%), indicating that this factor has minimal influence on Fc. In the Ff model, CAGS exhibits the highest importance at 13%, while W/B and PL/B both contribute 10% each. Other notable influences include QP/B and S/B at 8%, while NS/B, MK/B, and SF/B have relatively lower importance (3%). The least significant parameter is Len, with just 2% importance. For the Slump model, PL/B shows the highest sensitivity at 15%, followed by LS/B (12%) and MK/B (11%). FA/B and SF/B each contribute 7%, while S/B (1%) and NS/B (1%) exhibit the least influence on the model’s output. In the Porosity model, C/B, Slg/B, and FibAsp each hold the highest importance at 12%. MK/B, SF/B, and QP/B also have notable influences, ranging from 9 to 4%. The least influential parameters are Cfc (2%), W/B (3%), and PL/B (3%), indicating that these inputs play a relatively minor role in determining the Porosity outcomes. Conversely, the SHAP sensitivity analysis results shown in Fig. 27 provide insights into the relative importance of different variables influencing the Fc, Ff, Slump, and Porosity models. For the Fc model, the most significant factor is S/B with an importance of 17%, followed by W/B at 13%. Other influential factors include C/B at 7% and QP/B at 9%, while factors such as FA/B, Slg/B, and Size contribute minimally. In the Ff model, SF/B emerges as the most dominant factor at 18%, followed by CAgS at 14% and QP/B at 11%. Other variables such as W/B and PL/B show moderate importance, while FA/B, MK/B, and Len have lower contributions. The Slump model analysis highlights SF/B as the most significant variable at 18%, followed by CAgS at 14% and QP/B at 9%. W/B, S/B, and LS/B contribute moderately, while NS/B and FA/B have lower influence. Finally, the Porosity model shows C/B as the most critical factor at 10%, followed by SF/B at 15%, PL/B at 13%, and QP/B at 12%. The contributions of other factors like FA/B, MK/B, and CAgS are present but less pronounced. These results indicate the varying degrees of importance of different material properties in predicting the respective concrete performance parameters.

Comparatively, the Hoffman & Gardener and SHAP sensitivity analyses results both highlight the most influential factors in predicting Fc, Ff, Slump, and Porosity, but with some differences in the ranking and importance of specific variables. In the Fc model, Hoffman & Gardener’s analysis identifies MK/B as the most critical factor at 14%, followed by S/B at 12% and QP/B at 10%, whereas SHAP highlights S/B as the dominant factor at 17% and W/B at 13%, with MK/B having a lower impact. For the Ff model, Hoffman & Gardener rank CAgS as the highest at 13%, with QP/B and W/B also being influential, while SHAP assigns the highest importance to SF/B at 18%, followed by CAgS at 14%, showing a shift in dominance between these two methods. In the Slump model, Hoffman & Gardener highlight W/B as the most significant at 15%, with LS/B and MK/B playing key roles, while SHAP identifies SF/B as the most dominant at 18%, followed by CAgS at 14%, indicating a discrepancy in ranking. For the Porosity model, Hoffman & Gardener emphasize C/B at 15% and Slg/B at 12%, whereas SHAP highlights SF/B at 15% and QP/B at 12%, with C/B at a slightly lower 10%, showing variations in the importance assigned to specific factors. Overall, while both methods agree on the significance of certain key variables, the relative ranking and emphasis differ, with SHAP often attributing higher importance to factors like SF/B and W/B, whereas Hoffman & Gardener distribute importance more evenly across multiple variables.

The sensitivity analysis results using Hoffman & Gardener’s method and SHAP values provide complementary yet distinct perspectives on the influence of various input parameters on the mechanical and fresh properties of ultra-high performance concrete (UHPC) incorporating industrial byproducts. A deeper examination of these findings offers nuanced insights into how these variables impact concrete behavior and how this understanding can be strategically applied for optimizing UHPC production in industrial settings. Starting with the compressive strength (Fc) model, Hoffman & Gardener’s method points to MK/B (metakaolin-to-binder ratio) as the most influential variable, accounting for 14% of the importance. This suggests that the pozzolanic reactivity and filler effect of metakaolin significantly enhance the strength development of UHPC. In contrast, the SHAP analysis assigns the highest importance to S/B (sand-to-binder ratio) at 17%, with W/B (water-to-binder ratio) following closely at 13%. The divergence in ranking reflects the methodological differences: Hoffman & Gardener focuses on variance contribution, while SHAP captures localized feature interactions within model predictions. SHAP’s emphasis on S/B and W/B suggests that granular packing density and water demand are critical to optimizing the microstructure and hydration of UHPC, especially in mixes rich in byproducts. For industrial applications, this insight supports targeted control over the gradation and quantity of fine aggregates and water reducers to fine-tune the rheology and compressive strength. In the flexural strength (Ff) model, Hoffman & Gardener highlights CAgS (coarse aggregate size) as the top contributor (13%), with W/B and PL/B (plasticizer-to-binder ratio) also being influential. SHAP, however, identifies SF/B (silica fume-to-binder ratio) as the dominant factor at 18%, followed by CAgS at 14%. The discrepancy underscores that while Hoffman & Gardener identifies macro-scale aggregate influence, SHAP captures the critical role of nano-silica effects of silica fume, which enhances the interfacial transition zone and tensile load transfer. From an industrial production standpoint, this suggests that to enhance flexural performance, careful optimization of both particle gradation and reactive ultrafine materials is essential. Emphasis on precise dosing of silica fume and aggregate grading can significantly improve crack resistance and ductility in structural applications. The Slump model reveals further divergence. Hoffman & Gardener shows PL/B (15%) and LS/B (limestone powder-to-binder ratio) at 12% as most influential, indicating that workability is highly dependent on the dispersion and lubricating effects of plasticizers and fines. In contrast, SHAP emphasizes SF/B (18%) and CAgS (14%) as most impactful, suggesting that in addition to chemical admixtures, the physical characteristics of constituents like silica fume and aggregate morphology play a pivotal role. This reinforces the notion that fresh concrete behavior is governed by both chemical and physical packing phenomena. In industrial use, such insights can inform the selection of admixture types and dosages, as well as the particle shape and distribution of aggregates and powders to ensure desired slump without compromising mechanical performance. The Porosity model presents a more distributed sensitivity profile. According to Hoffman & Gardener, C/B (cement-to-binder ratio), Slg/B (slag-to-binder ratio), and FibAsp (fiber aspect ratio) each show significant impact at 12%, while SHAP attributes the highest importance to SF/B (15%), followed by PL/B (13%) and QP/B (quartz powder-to-binder ratio) at 12%. These results collectively emphasize the importance of matrix densification, mineral filler content, and fiber integration in controlling porosity. SHAP’s elevated ranking of SF/B and QP/B highlights their role in refining the pore structure and enhancing packing density. From a practical perspective, industries aiming to produce UHPC with low porosity and improved durability should focus on optimizing silica fume content, proper fiber dispersion, and the selection of ultrafine powders that contribute to internal pore refinement. Comparatively, while both methods highlight similar variables, SHAP often attributes greater importance to fine-scale reactive components (e.g., SF/B, W/B), capturing their nonlinear interactions and direct influence on predictions. Hoffman & Gardener provides a broader view of variance distribution across the entire dataset, highlighting variables that explain more of the global behavior. This dual-pronged analytical approach enables a more holistic understanding of input variable influence. The practical implications of these findings for industrial UHPC production are substantial. They inform targeted material selection and proportioning strategies. For instance, in applications requiring high compressive strength and low porosity, a focus on optimizing S/B, SF/B, and W/B ratios is crucial. For enhanced flexural performance, precise control of SF/B and CAgS is essential. Meanwhile, to achieve desirable workability, balancing PL/B and fine reactive powders like LS/B and SF/B is key. Implementing these insights in quality control, mix design refinement, and performance-based optimization can significantly enhance the consistency, sustainability, and cost-efficiency of UHPC incorporating industrial byproducts, advancing both performance goals and environmental objectives in modern construction practices.

However on why certain binder compositions negatively impact strength, the observed influence of MK/B (metakaolin-to-binder ratio) and SF/B (silica fume-to-binder ratio) on compressive and flexural strength can be attributed to their pozzolanic activity and particle fineness. Metakaolin is known to react with calcium hydroxide released during cement hydration to form additional calcium silicate hydrate (C–S–H) gel, which contributes to strength gain. However, excessive metakaolin may lead to an overly refined pore structure and increased water demand, adversely affecting workability and potentially leading to internal stress during drying, which can impair strength. Similarly, silica fume, with its extremely fine particles, enhances the packing density and contributes to the pozzolanic reaction, refining the microstructure. Yet, when used in excess, it may reduce workability significantly and result in incomplete dispersion, diminishing its beneficial effects. The negative impact of certain binder combinations on strength can also be understood through the lens of particle interaction and hydration kinetics. For example, a high proportion of limestone powder (LS/B) may serve primarily as a filler with limited reactivity. While it can improve workability and early-age strength due to improved particle packing, its excessive use may dilute the overall binder reactivity, resulting in a weaker cementitious matrix. The same principle applies to quartz powder (QP/B), which improves microstructural packing but contributes minimally to the binding phases unless synergistically combined with highly reactive pozzolanic materials. The water-to-binder ratio (W/B) consistently emerges as a critical factor due to its fundamental role in hydration, porosity development, and mechanical performance. A lower W/B ratio generally enhances strength and reduces porosity due to the formation of a denser microstructure; however, it must be carefully balanced to ensure sufficient workability and prevent defects such as incomplete compaction or cracking. Additionally, the influence of aggregate size (CAgS) and fiber aspect ratio (FibAsp) on mechanical properties such as flexural strength and porosity can be explained by their role in crack-bridging and stress distribution. Coarse aggregates and fibers with higher aspect ratios improve tensile resistance and energy absorption, thereby enhancing toughness and reducing microcrack propagation, but may compromise uniformity and increase internal voids if not properly graded and dispersed.