Analyzing the viability of agro-waste for sustainable concrete: Expression-based formulation and validation of predictive models for strength performance

2.1 Dataset assembling and review

This work employed MEP and GEP approaches to anticipate the CS and TS of agro-waste derived concrete, respectively. A total of 700 data points were collected through experimental investigations, comprising values for both CS and TS [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]. This study employed seven variables to foresee CS and TS, such as corn cob ash content (CCA), palm oil fuel ash content (POA), rice husk ash content (RHA), sugarcane bagasse ash content (SBA), wheat straw ash content (WSA), water to cement ratio (WCR), and curing duration (CD). Thorough data preparation was crucial for the data collection and organization processes. An effective approach for overcoming a significant challenge is to prepare data for data mining; this fits in with the widely-used knowledge discovery from data methods. To simplify and improve the data, preparation primarily aims to remove distortion and unnecessary portions. Several descriptive statistics were calculated using these data and their results are displayed in Table 1. As an initial stage in ML investigations, descriptive statistics help us comprehend the distribution, central tendency, and variability of the input material. There are a total of 700 samples in the dataset, broken down as follows: CCA, POA, RHA, SBA, and WSA, as well as WCR, CD, and the desired outcomes CS and TS. With a mean WCR of around 0.54 and an average curing day of about 39, the data show moderate amounts of cementitious replacements. The input variables, particularly the percentages of SCMs and the CD, show a great deal of variability, as seen by the standard deviations and ranges. This variability may impact the generalizability of the model. A strong right-tailed distribution is shown by the high kurtosis and skewness values of SCMs. The clustering of most values near 0 indicates that many mixes did not have partial replacements. The construction and validation of accurate ML models depend on a thorough understanding of data behavior, which can be achieved through statistical profiling.

Figure 1(a) and (b) illustrate the Pearson correlation matrices for the datasets associated with CS and TS, respectively. These visualizations depict the linear relationships among the input variables and their corresponding strength outputs, using color-coded ellipses and numerical correlation values (ranging from −1 to +1). The red ellipses indicate positive correlations, while blue signifies negative relationships; the intensity and shape reflect the correlation magnitude. In Figure 1(a) and (b), moderate positive correlations can be seen between CD and both strength properties (CS and TS), with correlation coefficients nearing +0.25. This indicates that longer CDs generally contribute positively to strength development. WCR shows a weak but negative correlation with strength, consistent with established concrete behavior. In contrast, the five SCMs (CCA, POA, RHA, SBA, WSA) exhibit slight negative correlations with the outputs, suggesting that excessive replacement may reduce strength in some mixes. Similar patterns are observed in Figure 1(b) for the TS dataset, although minor variations in correlation values suggest differing sensitivity of compressive and TSs to certain input variables. It is important to note that low correlation values near zero do not necessarily imply independence; nonlinear effects or complex interactions may still exist. Therefore, additional interpretative tools such as SHAP values or sensitivity analysis are recommended to gain a more comprehensive understanding of input–output relationships in predictive modeling.

Figure 1

Correlation matrices highlighting key variable interdependencies for (a) CS dataset and (b) TS dataset.

2.2 ML framework

The CS and TS of agro-waste-based concrete were predicted using a dataset curated through an extensive analysis of prior research studies. Seven input features were considered essential for estimating the corresponding CS and TS values. GEP and MEP, recognized as high-performing ML methods, were employed to develop the predictive models. Typically, ML model accuracy is evaluated by comparing output predictions to actual recorded values. In this study, the dataset was split into two segments, 70% was allotted for training the models, while the rest 30% was utilized to test their generalization performance. The predictive strength of the models was primarily judged by the R ² score, where a higher value indicates close alignment between estimated and true values, whereas a lower score reveals inconsistencies and reduced reliability [60]. A number of tests, including statistical analyses and evaluations of errors, were conducted to ensure that the model was reliable. Table 2 lists the critical hyperparameters controlling the GEP and MEP models’ performance, and Figure 2 shows a scenario-based model representation.

Figure 2

Four-step ML framework for predicting CS and TS of agro-waste concrete.

2.3 Performance metrics and accuracy evaluation

The predictive capability of the GEP and MEP models was evaluated on the test dataset using a range of statistical indicators. The assessment incorporated metrics such as root mean square error (RMSE), mean absolute percentage error (MAPE), Nash–Sutcliffe efficiency (NSE), relative root mean square error (RRMSE), mean absolute error (MAE), relative squared error (RSE), and Pearson’s correlation coefficient (R), providing a comprehensive measure of the models’ accuracy and reliability [61,62,63,64,65]. Eqs. (1)–(7) outline the mathematical expressions used to quantify different statistical indicators that evaluate the predictive performance of the models.

In this context, n represents the total number of data points, while a i and p i correspond to the observed and predicted values for each instance. The symbols a ¯ and p ¯ indicate the average of the observed and predicted values, respectively. To assess the degree to which a simulation reliably reproduces or forecasts results, the correlation coefficient (R) is frequently employed. A higher R value reflects a strong linear association between the predicted and actual results, suggesting that the model reliably captures the underlying data trends [66]. The correlation coefficient (R) remains unaffected by the scaling of data, such as multiplication or division. However, the coefficient of determination (R ²) offers a more robust and informative measure of predictive accuracy. It quantifies how well the predicted values align with the actual data. An R ² value closer to 1 indicates a highly dependable model with strong predictive capability and minimal deviation from observed outcomes [67,68]. The developed model exhibits enhanced predictive capability, evidenced by notable reductions in MAE and RMSE values. These error metrics consistently decrease as the model’s accuracy improves, ideally approaching zero when discrepancies between actual and predicted values are minimized [69,70]. On the other hand, MAE has shown to be particularly reliable when applied to datasets characterized by continuous and smooth patterns, as confirmed through comprehensive analysis [71]. A reduction in prior error values corresponds to enhanced model performance, indicating greater predictive accuracy.

A Taylor diagram serves as an effective tool for evaluating a model’s predictive performance. Among various statistical validation techniques, it stands out by visually summarizing how closely a model’s output aligns with observed data. By comparing standard deviations, correlation coefficients, and centered root-mean-square differences relative to a reference point (the actual data), the diagram provides a comprehensive assessment of model accuracy and reliability [72,73]. The Taylor diagram graphically integrates three key statistical measures to assess model performance: standard deviation is shown along the axes, correlation coefficients are displayed as angular lines, and RMSE is represented by curved contours centered on the reference point (true values). This visual layout allows for a quick and effective comparison of models. The ideal model position is one that lies nearest to the reference point, indicating minimal error, high correlation, and strong predictive reliability [72].

3.1 CS models

3.1.1 GEP predictive model

To predict the CS of agro-waste-based concrete, the models employed ETs that embed mathematical structures influenced by genome distribution patterns and head length parameters. The construction of these ETs was primarily based on fundamental arithmetic operations, including multiplication, division, addition, subtraction, and exponentiation. These operations were strategically organized to construct subcomponents within the overall model. The GEP algorithm effectively transforms these structural elements into interpretable mathematical expressions that represent the predictive behavior of the model. Eq. (8) shows that by plugging in the feature values, these methods can predict the future CS of concrete made from agro-waste. Under ideal circumstances, the resultant model can beat it, but only if there is enough data. Figure 3(a) shows that the data are correctly matched because there is a solid black line there. The dotted green line shows a 20% change, whereas the dashed red line shows a 10% variance. The degree to which the experimental results match the projected CS values is shown by this graph. With a significant correlation shown by a R ² value of 0.935, the GEP model successfully reproduced the reported CS values with little variation. Predicting CS using the GEP method was remarkably accurate; 99.1% of the values were within a 20% margin of error and 91.5% were within a 10% margin. Figure 3(b) shows the CS data vs the absolute error and may indicate a difference between the test values and the ones obtained by the GEP model. The findings demonstrated that the GEP-derived equation produced predictions that were closely aligned with the experimental outcomes, with absolute errors extending from 0.102 to 13.148 MPa. Figure 4 presents the error distribution, confirming the model’s precision. Out of all predictions, 105 values exhibited errors below 1.0 MPa, while 98 fell within the 1.0–5.0 MPa range, and only 30 readings exceeded 5.0 MPa. High-magnitude errors were infrequent, highlighting the model’s overall accuracy and reliability.

(8) CS ( MPa ) = CCA + POA + RHA + SBA + WSA + WCR + ( 6.7040 ⋅ WSA ⋅ RHA ) − ( 10.418 ⋅ WCR ) + 5.1701 WCR + 13.3633 + 1.25 ⋅ log ( CD + 1 ) + 0.005 ⋅ CD ⋅ WSA ,

where, CS: compressive strength, CCA: corn cob ash content, POA: palm oil ash content, SBA: sugarcane Bagasse ash content, RHA: rice husk ash content, WSA: wheat straw ash content, WCR: water-to-cementitious ratio, and CD: curing duration.

Figure 3

CS modeling with GEP: (a) Estimated vs observed CS relationship and (b) dataset-level error dispersion.

Figure 4

Residual error distribution of the CS-GEP model.

3.1.2 MEP predictive model

An analytical expression for predicting the CS of agro-waste-based concrete was derived using the results obtained from the MEP model. This model takes into consideration the cumulative impact of seven independent factors. The finalized mathematical representation generated through this modeling process is presented in Eq. (9).

(9) CS ( MPa ) = 2 ⋅ WCR ⋅ ( CD + 1 ) ⋅ WCR 2 + ( CD + 1 ) ⋅ WCR ⋅ ( 2 ⋅ WCR ) ⋅ POA ( 2 ⋅ WCR ) − 2 ⋅ log 10 ( CD ) + WCR + ( CD + 1 ) ⋅ WCR + CCA + WSA + SBA + RHA ⋅ 2 ⋅ log 10 ( CD ) ( 2 ⋅ WCR ) − 2 ⋅ log 10 ( CD ) + CD + ( CD + 1 ) ⋅ WCR 2 ⋅ log 10 ( CD + 1 ) − 1 ( 2 ⋅ WCR ) − 2 ⋅ log 10 ( CD ) ,

where, CS: compressive strength, CCA: corn cob ash content, RHA: rice husk ash content, POA: palm oil ash content, SBA: sugarcane Bagasse ash content, WSA: wheat straw ash content, WCR: water-to-cementitious ratio, and CD: curing duration.

Figure 5(a) provides evidence of the MEP model’s resilience to simplification and proficiency; the figure also boasts an impressive R ² value of 0.964. The CS model developed using MEP demonstrated greater reliability than the GEP model, as evidenced by its higher R ² value. The solid black line in Figure 5(a) displays a perfect one-to-one connection between the anticipated and actual values, whereas the dashed red and dotted green lines indicate variances of ±10 and ±20%, respectively. The predicted CS values from the MEP model align closely with the experimental data, indicating strong predictive performance and minimal deviation across the majority of observations. The MEP approach consistently produced precise CS calculations for agro-waste derived concrete. Its forecasts met or exceeded the 10% requirement in 97% of cases and the 20% barrier in 100% of cases, highlighting its remarkable accuracy.

Figure 5

CS modeling with MEP: (a) Estimated vs observed CS relationship and (b) dataset-level error dispersion.

Figure 5(b) illustrates the absolute error distribution between the measured and predicted CS values generated by the MEP model. This analysis highlights the model’s ability to minimize prediction deviations, providing a clear depiction of how closely the estimated results align with experimental outcomes across the dataset. There is a wide variation in the MEP calculations, from 0.006 to 5.869 MPa, with an average error of 1.245 MPa. Nevertheless, the average inaccuracy is lower than 5.869 MPa; 137 of them are less than 1.0 MPa, 85 are between 1.0 and 5.0 MPa, and just 11 are greater than 5.0 MPa. Figure 6 shows a distribution plot comparing the MEP and GEP models. The MEP model has lower prediction variability, especially when outlier values are taken into consideration. This indicates a more stable and consistent performance of MEP in estimating CS. The GEP and MEP models both demonstrate great potential as accurate forecasters. In contrast, lowering the correlation coefficient and error standard deviations is achieved by utilizing the MEP equation. The MEP equation’s popularity stems from its widespread use and adaptability.

Figure 6

Residual error distribution of the CS-MEP model.

3.2 TS models

3.2.1 GEP predictive model

The TS was computed by the models using ETs by utilizing mathematical correlations that emerged from the relationship between genome frequency and head size. Once the GEP method encodes the subexpression trees, it results in a complete algebraic equation as shown in Eq. (10), which can be utilized to estimate the TS of concrete incorporating agro-waste materials. When sufficient input data are provided, this model has the potential to perform even better than a theoretically ideal model. The solid black line in Figure 7(a) shows that the predicted and actual values are perfectly aligned. The red dashed line indicates a 10% deviation while the green dotted line represents a 20% variation. This figure highlights a strong correlation between the measured TS values and those predicted by the GEP model. The technique proved highly effective in estimating TS, achieving an R squared value of 0.946. Additionally, 82% of the predictions fell within a 10% error margin and 96% within a 20% range, demonstrating the model’s high level of precision. Figure 7(b) displays the absolute errors between the experimental and predicted values, revealing a close match between them. The model achieved an average absolute error of 0.253 MPa, with errors ranging from 0.002 to 2.519 MPa. Figure 8 shows that the error values have a dome-shaped distribution. In all, 189 of the erroneous values are between 0.2 and 0.5 MPa, with 123 of those being below 0.2 MPa and 21 beyond 0.5 MPa, according to the error distribution. It is rare for maximal error incidences to occur.

(10) TS ( MPa ) = [ log 10 ( CD + 7.6427 ) ⋅ ( CCA + 7.6427 + SBA − 3.1907 ) + WCR ] ⋅ ( RHA + CD + WCR ) ⋅ WCR ⋅ POA ( ( WSA − WCR + CD ) ⋅ ( POA + WCR ) + POA ) ,

where, TS: tensile strength, CCA: corn cob ash content, RHA: Rice husk ash content, POA: palm oil ash content, SBA: sugarcane Bagasse ash content, WSA: wheat straw ash content, WCR: water-to-cementitious tatio, and CD: curing duration.

Figure 7

TS modeling with GEP: (a) Estimated vs observed TS relationship and (b) dataset-level error dispersion.

Figure 8

Residual error distribution of the TS-GEP model.

3.2.2 MEP predictive model

An empirical formula was developed using the MEP results and the impacts of the seven independent components to determine the TS of agro-waste derived concrete. The final set of mathematical equations derived from modeling is shown in Eq. (11).

(11) TS (MPa) = log 10 ( RHA 2 + ( SBA + WSA ) ⋅ CD + ( SBA + WSA ) + ( SBA − CD 2 + CD 3 + ( POA + CCA − CD ) ( POA + CCA ) ) ) ,

where, TS: tensile strength, CCA: Corn cob ash content, RHA: rice husk ash content, POA: palm oil ash content, SBA: sugarcane Bagasse ash content, WSA: Wheat straw ash content, WCR: water-to-cementitious ratio, and CD: curing duration.

The MEP model demonstrated outstanding predictive capability for TS, as evidenced by its high R squared value of 0.961, shown in Figure 9(a). This strong correlation suggests that the model is robust and effectively captures the underlying complexity of the data without oversimplifying it. The MEP model for TS is more accurate than the GEP model, just as it is for CS. A perfect one-to-one correspondence between anticipated and actual values is shown by the solid black line in Figure 9(a), whereas lines representing 10 and 20% variances, respectively, are shown by the red and green lines. The predicted TS values closely followed the experimental results, showing strong consistency. Notably, 86% of the predicted values were within a 10% deviation and all predictions fell within the 20% range, confirming the exceptional accuracy and reliability of the MEP approach for modeling the TS of agro-waste-based concrete.

Figure 9

TS modeling with MEP: (a) Estimated vs observed TS relationship and (b) dataset-level error dispersion.

The MEP model simulation results are shown in Figure 9(b), with an emphasis on the absolute discrepancies between the actual and anticipated TS values. The data show that the model is very accurate, with an average error of only 0.239 MPa and individual errors ranging from 0.003 to 0.821 MPa. Further analysis in Figure 10 illustrates the distribution of these errors: 125 values fall below 0.2 MPa, 83 are between 0.2 and 0.5 MPa, and only 25 values exceed 0.5 MPa. Even when considering outlier values, the MEP model exhibits lower variability in results compared to the GEP model. Overall, both modeling techniques, MEP and GEP, have proven effective for predictive modeling, but MEP offers a distinct advantage. The reduced standard deviation in prediction errors and stronger correlation coefficients confirm that the MEP model delivers greater reliability and predictive accuracy than the GEP model.

Figure 10

Residual error distribution of the TS-MEP model.

3.3 Performance metrics and accuracy evaluation

Table 3 provides a comprehensive statistical comparison of GEP and MEP models for predicting the CS and TS of agro-waste-based concrete. Across all key performance indicators including MAE, MAPE, RMSE, R, RSE, NSE, and RRMSE, the MEP model consistently outperforms GEP, demonstrating its superior predictive capability. For CS prediction, MEP shows notably lower error values such as MAE of 1.245 MPa, RMSE of 1.845 MPa, and MAPE of 2.70%, along with a higher correlation coefficient of 0.982 and improved NSE of 0.963. It also exhibits reduced RSE and RRMSE values, indicating closer alignment between predicted and actual outcomes. In TS prediction, MEP again performs slightly better with lower MAE of 0.239 MPa, RMSE of 0.301 MPa, and MAPE of 6.20%, accompanied by stronger correlation and efficiency values. These findings highlight the robustness of MEP in capturing the complex nonlinear relationships inherent in material behavior, making it a more accurate and dependable modeling approach than GEP for strength prediction in sustainable concrete studies. The Taylor diagram in Figure 11 offers a widespread association of all predictive models, demonstrating the close alignment of MEP models in forecasting the CS and TS of agro-waste derived concrete, while GEP models are relatively more divergent. Consistent with earlier research, the MEP model stands out as the best ML method for CS and TS prediction of agro-waste derived concrete, exhibiting the fewest outliers, most efficiency, and highest R ² value. In conclusion, the analysis of error metrics and correlation efficiency statistics confirms that MEP is the more precise and efficient ML technique for predicting both CS and TS. The consistently lower prediction errors, stronger correlation coefficients, and superior efficiency metrics highlight its advantage over GEP, confirming its robustness and reliability for accurately predicting strength in material modeling applications.

Figure 11

Taylor plots comparing predictive accuracy of models for (a) CS models and (b) TS models.

3.4 SHAP-based feature interpretation

The aim of this study is to explore the factors influencing the mechanical performance of concrete by analyzing its composition in detail. To understand both the overall and individual effects of input features, the SHAP tree explainer was utilized, which is widely adopted for interpreting model predictions globally. Figure 12 of the SHAP diagram shows that various input features affect agro-waste derived concrete’s CS and TS. On the X-axis, the proportion of SHAP value associated with each raw material is shown, whereas the Y-axis represents the independent variables. As illustrated in the SHAP summary plot in Figure 12(a), the agro-waste content and the WCR emerge as the dominant factors influencing the prediction of CS in agro-waste-based concrete, whereas CD contributes the least. Higher agro-waste content generally contributes positively to CS due to its pozzolanic reactivity, which enhances the concrete matrix; however, an excessive amount may negatively affect strength, indicating a nonlinear relationship. In contrast, a lower WCR consistently leads to higher predicted CS, aligning with the fundamental principle that reduced water content enhances concrete density and strength by minimizing porosity. On the other hand, CD displays negligible variation in SHAP values, suggesting its limited influence within the dataset, possibly due to saturation in curing effect or a narrow range of CDs. A similar SHAP plot in Figure 12(b) for TS also reflects a comparable trend, where WCR and agro-waste remain dominant contributors. Specifically, low WCR values positively influence TS due to improved matrix cohesion, while moderate levels of agro-waste enhance TS via refined pore structure and better particle packing. However, excessive agro-waste still tends to reduce TS, highlighting the need for an optimal balance in mix design. CD again appears to have a minimal effect on TS prediction, reinforcing its secondary role in the model. The SHAP analysis provides engineers with a transparent understanding of how individual input variables, such as WCR, agro-waste content, and supplementary materials, influence CS and TS predictions. This interpretability allows engineers to identify optimal ranges of critical variables, diagnose poor-performing mix designs, and justify decisions with quantitative evidence.

Figure 12

Influence of input variables: (a) CS predictions and (b) TS predictions.

3.5 Sensitivity analysis

This research looks into how different input characteristics affect the CS and TS predictions in agro-waste concrete. The input variables have a high correlation with the predicted outcome [74]. The sensitivity analysis in Figure 13 reveals that agro-waste is the most influential input, contributing 52% to the model’s estimation of CS and TS. This highlights its critical role in enhancing mechanical performance, likely due to its pozzolanic and filler effects. WCR follows with a 38% impact, reflecting its importance in controlling hydration and porosity. CD has the least influence at 10%, suggesting that while it supports strength development, its effect is comparatively modest. Overall, the model is most sensitive to agro-waste and WCR, emphasizing their importance in optimizing strength outcomes. The results were greatly affected by the amount of input data points and the parameters used in the model. Keep in mind that the ML approach had varying effects on the study’s results according to certain input variables, like the amounts of concrete mix. By focusing on the most sensitive parameters, engineers can design more efficient, reliable, and sustainable concrete mixes incorporating agro-waste materials. Eqs. (12) and (13) were used to determine the weights of the model’s input parameters.

where the expression ( f min ( x i ) describes the anticipated value with the lowest ith output, while the expression ( f max ( x i ) represents the maximum.

Figure 13

Proportional impact of inputs on prediction results.