Analyzing the compressive strength, eco-strength, and cost–strength ratio of agro-waste-derived concrete using advanced machine learning methods

1 Introduction

The yearly production of concrete continues to increase rapidly as a result of the worldwide need for infrastructure construction. The worldwide utilization of concrete surpasses 25 gigatons per year [1,2]. The construction sector is a main contributor to global greenhouse gas (GHG) emissions, with a major portion arising from concrete manufacture, including both the materials used and the building activities involved [3,4]. During the building process, two types of GHG CO₂ emissions are generated: embodied CO₂ and operational CO₂. The CO₂ emissions that are directly associated with transportation, manufacture of materials, maintenance, and demolition contribute to the overall carbon footprint. The operational CO₂ emissions are derived from the energy utilized during the operational period [5,6]. The primary source of CO₂ emissions in the construction sector is cement manufacturing. Specifically, the cement industries are accountable for around 7–8% of the worldwide CHG CO₂ emissions [7]. The manufacturing of 1 kg of cement results in the release of about 1 kg of CO₂ into the atmosphere, which varies depending on the type and amount of clinker [8]. The primary source of CO₂ emissions in cement manufacture occurs during the clinker-forming process. The clinker is produced by the process of calcination when limestone and clay are heated to temperatures exceeding 1,500°C in a furnace. This causes the transition of CaCO₃ into CaO and CO₂. During calcination, around 50% of the overall CO₂ generated during cement manufacturing is released into the environment [9]. Given the rising demand for cement, with a yearly manufacturing rate surpassing 4.4 billion tons and projected to surpass 5.5 billion tons by 2050 [10], reducing cement manufacture and demand will effectively decrease worldwide CO₂ emissions from the construction sector. This, in turn, will mitigate the long-term risk of global warming [11]. One method of reducing cement usage is by using supplementary cementitious materials (SCMs) derived from industrial or agricultural byproducts [12,13,14,15].

Agro-based byproducts such as eggshell powder (ESP) and date palm ash (DPA) are utilized as SCMs in cementitious composites because of their pozzolanic characteristics [16,17]. DPA is acquired by the incineration of all parts of the date tree, containing its leaves, fronds, stems, and mesh, at elevated temperatures, followed by the process of grinding them into extremely small particles [18,19]. Studies have shown that the DPA contains a significant amount of silica, which is responsible for its pozzolanic response [20]. Prior research has demonstrated the effectiveness of DPA as a pozzolanic substance in cementitious composites. It has been seen to improve the mechanical characteristics and long-lasting nature of cementitious composites [16,21]. DPA might be used with other SCMs, such as fly ash, to improve the performance of cementitious composite [20,22]. In addition, ESP has a significant amount of CaO, which enhances its cementing characteristics along with its pozzolanic characteristics [23]. ESP is acquired by the process of pulverizing poultry eggshells into a finely powdered state. Prior to grinding, eggshells are obtained from various sources such as chicken farms, bakeries, and restaurants. They undergo a thorough process of washing and drying before being further processed [24]. The ESP is typically mixed with other SCMs that have a high content of SiO₂ and Al₂O₃. CaO in the ESP facilitates the production of more Ca(OH)₂, which then combines with SiO₂ and Al₂O₃ to generate an excess of calcium silicate hydrate (C–S–H) gel [23]. The C–S–H gel is primarily important for the formation of concrete strength [25]. ESP has a role in stabilizing ettringites and mono-carbonates in the cementitious composite when it undergoes hydration. This leads to enhanced mechanical strength and resilience characteristics [26]. ESP has been used with other agricultural-based SCMs, such as straw and rice husk ashes [27,28] and DPA [29,30], and the resulting combined SCMs were observed to improve the performance of cementitious composites.

Researchers are now developing estimating models to evaluate the properties of materials and structures in order to reduce the requirement for extensive laboratory experiments [31,32,33,34]. Artificial intelligence (AI) strategies, like machine learning (ML), are presently at the forefront of the development of modeling techniques in this field [35,36,37]. In recent years, there has been a growing recognition of the application of ML approaches in evaluating the performance of building materials [38,39,40,41,42]. Gene expression programming (GEP) is an advantageous multiphysics model since it disregards previously established relationships while developing a model [43,44]. The GEP algorithm represents a program using a linear chromosome with a fixed length [45]. It can offer a mathematical formula for predicting behavior that can be applied in practical situations [46,47,48]. Unlike neural networks, GEP has several advantages. When discussing artificial neural network algorithms, they lack practical value, as they are unable to generate a functional relationship or framework. In contrast, GEP produces output in the form of an expression tree (ET), which can be decoded to obtain a mathematical relationship. This relationship is user-friendly and can be effectively utilized to make future predictions. GEP possesses the unique capability of establishing frameworks, which showcases its novelty through the provision of dependable models [49]. This characteristic enhances the reliability of GEP in generating precise predictions for the future. In contrast, all other techniques, with the exception of genetic programming (GP), are solely employed as predictors. Due to their limitations, neural networks are classified as black-box algorithms, which restrict their practical use. As a result, GEP emerges as a viable alternative to these methods, surpassing other approaches in addressing technical and complex problems, including SHapley Additive exPlanations (SHAP)-based studies, while outperforming traditional methods like LR [50,51,52].

The aim of this research is to create and evaluate GEP-based models for the compressive strength (CS), eco-strength (ECR), and cost–strength ratio (CSR) of DPA–ESP concrete while also investigating the impact of input components. The aim was accomplished by pursuing the following objectives: (i) optimizing hyperparameters for GEP using experimental data to build prediction models, (ii) verifying the accuracy of the constructed GEP prediction models using statistical measures and analyzing deviations among actual and predicted outcomes, and (iii) examining the influence of input components through SHAP analysis. Conducting studies on materials necessitates a significant investment of time, money, and effort, as it involves acquiring materials, creating samples, allowing them to cure, and subsequently assessing them through testing. These problems can be overcome using innovative techniques, such as ML, which would be advantageous for the construction sector. The characteristics of concrete are also influenced by several factors, and it is challenging to accurately measure their collective impact using experimental techniques. SHAP analysis is a valuable method for examining the influence and correlation between input characteristics and outputs. The necessary data for constructing the ML model and conducting SHAP analysis can be obtained from previous research or laboratory experiments. Consequently, the obtained database may be used to implement ML algorithms, predict material characteristics, and analyze the impact of inputs. The results of this study have the potential to enhance the flexibility of SCMs (DPA and ESP) composites in the construction sector, hence benefiting green building programs.

2 Data collection and analysis

The dataset was collected from the published literature [53] and includes five input variables: cement (C), DPA, superplasticizer (SP), ESP, and test age (A). The corresponding output variables are CS, ECR, and CSR. The ECR of DPA–ESP concrete is calculated using Eq. (1), and CSR is calculated by dividing the cost of concrete in $/m³ by CS in MPa. The dataset was increased from its initial 28 data points to 560 data points with the aid of a Python code that operated in accordance with a strategy that had been established beforehand. The user is given the opportunity to pick a database file via a Tkinter-based file dialog box, which leads to the beginning of the code. A Pandas DataFrame was used to import the file, and then the code checked the current point count once it was imported. A freshly formed file that included synthetic and original data was then used to hold the upgraded dataset after it had been created. The script provides incisive statements as it supplements the data. The declarations include a variety of information, including the precise location of the saved file, the number of synthetic data elements added, and the total number of data elements added. Furthermore, the script accommodates scenarios in which resampling is necessary, or no file is selected. This method was also utilized in earlier studies in order to enhance the number of data points included inside a database [54,55]. In order to develop models, the data are allocated as follows: 70% is allotted for the training phase, while 30% is set aside for the testing phase. Data preparation facilitated the acquisition and organization of the data. Commonly, data preparation is employed as a buffer to surmount a substantial impediment in the well-established method for deriving novel insights from old data [54]:

where F c is the CS of concrete in MPa, and E CO 2 is the embodied CO₂ release for 1 m³ of concrete.

The primary characteristics of the dataset were summarized using descriptive statistics, and the results are summarized in Table 1. Table 1 contains critical metrics for the input and output variables, including the mean, median, standard deviation, minimum, and maximum values. These statistics reveal the central tendencies, variability, and overall distribution patterns of the variables, which provide a comprehensive overview of the data. The correlation coefficients among the variables were calculated to evaluate the intensity and direction of their linear relationships, in addition to descriptive statistics. The correlation between the variables is denoted by these coefficients, which vary from −1 to 1. A direct relationship is suggested by a positive coefficient, while an inverse relationship is indicated by a negative coefficient. The correlations between each pair of input and output variables are visually represented in Figure 1(a)–(c). This figure offers valuable insights into the interdependencies within the dataset by identifying the inputs that have the most significant impact on the outputs. For example, test age was the crucial parameter with the highest positive values of 0.71 and 0.72 for CS and ECS, respectively, and −0.69 for the CSR.

Figure 1

Correlation coefficient of the dataset: (a) CS, (b) ECR, and (c) CSR.

3 Methodology

The methodology involved the implementation of advanced modeling techniques to examine the correlations between the input variables (C, DPA, SP, ESP, and Age) and the output variables (CS, ECR, and CSR). After that, the models were fine-tuned for optimal performance by employing the modeling approach GEP to create the predictive models. This allowed for the correct prediction of output variables from each input. Figure 2 illustrates the flow chart of this study, which includes the sequential phases of data acquisition, model development, and validation. This methodical approach facilitated the identification of critical input variables and the development of predictive models that were both accurate and robust.

Figure 2

Flow chart of the study.

3.1 GEP

GEP is an expanded version of GP and genetic algorithms (GAs), which was initially presented by Koza [56,57]. In the field of domain-independent problem-solving, GP is defined as a strategy in which computer programs are progressed to resolve problems on the basis of the Darwinian principle of reproduction and fittest survival, as well as similarities of naturally occurring genetic processes like mutation crossover. The GA relies on a population of potential solutions known as individuals. Individuals are typically made up of a single chromosome, and each individual may have one or more genes that are separated into tail and head segments. The selection process continues by picking individuals based on their fitness, and genetic diversity is initiated by employing one or more genetic operators to resolve optimization problems. The majority of the genetic operators that are utilized in GAs are also capable of being executed in GEPs with very few modifications. These GEPs are composed of five primary components: fitness function, function set, control parameters, ending condition, and terminal set [58,59]. Figure 3 shows a flowchart illustrating a method for gene expression. For the purpose of representing solutions to issues, GEP makes use of character strings of a predetermined length. These solutions are then described as parse trees of varying sizes and forms. These trees are referred to as GEP ETs and other formulations that are linked to them can be created by following the approach, as shown in Figure 4. This technique is capable of performing well for the explicit formulation and predicting mechanical characteristics. In this method, all of the issues are denoted by ETs, which are made up of operators, constants, functions, and variables [60,61].

Figure 3

GEP algorithm flowchart [62].

Figure 4

Decoding of the chromosome in GEP, containing two genes [63].

4 Results

The prediction of CS, ECR, and CSR was assessed using the GEP model. ETs were constructed for each output variable, and the accuracy of the predictions was evaluated by calculating R ². The following subsections provide a detailed discussion of these evaluations, which include the derived ETs and their corresponding R ² values. These analyses offer a thorough examination of the model’s ability to exactly predict each of the output variables.

4.1 GEP CS model

The output of the ideal GEP model is represented by the ET for predicting CS, as demonstrated in Figure 5(a)–(c). The model equation for predicting CS was obtained by decoding the ET. Eq. (9) is a fundamental forecasted formula which utilizes fundamental arithmetic operators, including Ln, +, −, /, √, and ×. From Sub-ETs 1, 2, and 3, three discrete variables are extracted and used in this equation. The decoded equation provides a clear and interpretable model for prediction by effectively capturing the connection between the inputs and CS. Eq. (9a) suggests that the impact of DPA and SP on cement can be represented through a logarithmic and inverse relationship, indicating a sensitive dependence of the blend’s properties on the ratio of these components. In Eq. (9b), the nested square root term involving ESP implies that even minor variations in ESP content may have a non-linear effect on certain material characteristics, possibly related to flowability or structural integrity. Eq. (9c) reveals that the DPA-to-cement ratio, when combined with the additive effects of ESP, can significantly influence the final material properties, emphasizing a need for a careful balance in the mix design. These equations, therefore, not only capture the mathematical interactions but also offer a deeper understanding of how each component contributes to the overall behavior of the material:

(9) CS = A 1 + A 2 + A 3 ,

where

(9a) A 1 = C − Ln ( 8.06 ) ( DPA − ( − 8.27 ) − SP ) ,

(9b) A 2 = [ C − DPA − ( A − SP ) × ( − 8.27 ) ] × ESP ,

(9c) A 3 = A × DPA C − ( ESP + 8.22 ) ( 1.54 × A ) + 9.37 .

Figure 5

ETS of the GEP model for CS. (a) Sub-ET 1; (b) Sub-ET 2; (c) Sub-ET 3.

The GEP model’s ability to predict CS was demonstrated by an R ² value of 0.94, which suggests that the model accurately predicted the data, as illustrated in Figure 6. An error analysis was also performed to compare the experimental values with the predicted values, as illustrated in Figure 7. According to the analysis, 40.5% of the forecasts had an error of less than 1 MPa, while 45.2% of the predictions were within the range of 1–4 MPa. A total of 14.3% of the results were predictions, with errors exceeding 4. The error statistics consist of an average error of 1.92 MPa, a lowest error of 0.47 MPa, and a maximum error of 5.41 MPa. The model’s efficacy is underscored by this exhaustive error analysis, which also pinpoints potential areas for enhancement. The high R ² value confirms that, overall, the model is well-tuned for CS predictions, though certain cases may still benefit from additional fine-tuning to improve consistency across all data points.

Figure 6

Correlation among the actual and predicted CS for the GEP model.

Figure 7

Error analysis for the CS.

4.2 GEP ECR model

Figure 8(a)–(c) illustrates the ET for ECR. This ET is the output of the optimal GEP model and was decoded to create a mathematical equation for predicting ECR, as shown in Eq. (10). Basic arithmetic operations and specific variables obtained from the ETs are incorporated into the derived equation, as was done in the previous case. A transparent and comprehensible model for ECR prediction is provided by this mathematical formula, which encapsulates the interactions between input variables to accurately forecast ECR. Eq. (10a) suggests that the interaction between SP, C, and A relative to ESP and DPA affects the material properties in a non-linear fashion. Eq. (10b) reveals a logarithmic relationship involving the combination of SP and DPA with cement, modified by the presence of SP and A. This implies that changes in the ratios between these components can significantly influence the material’s behavior, possibly affecting flowability or bonding. Eq. (10c) indicates a complex interplay between cement, SP, and ESP relative to DPA, where the interaction between these parameters and a logarithmic term involving A can have substantial implications for the material’s stability and performance. Together, these equations highlight the intricate relationships among these components, emphasizing the importance of the precise mix design to achieve the desired material properties.

(10) ECR = B 1 + B 2 + B 3 ,

where

(10a) B 1 = SP + C + A 0.74 − ESP − DPA ,

(10b) B 2 = Ln ( SP + DPA ) C × SP × ( 7.67 + A ) − DPA ,

(10c) B 3 = C C + SP ESP − ( DPA − ESP ) − Ln ( 8.66 × A ) .

Figure 8

ETS of the GEP model for ECR. (a) Sub-ET 1; (b) Sub-ET 2; (c) Sub-ET 3.

As shown in Figure 9, the performance of the GEP model for predicting ECR resulted in an R ² value of 0.91, which indicates that the model’s predictions are accurate to a high degree. In addition, an error analysis was carried out in order to compare the values obtained from the experiment with those predicted, as shown in Figure 10. According to the findings of the investigation, 39.8% of the forecasts had errors that were less than 0.003, and 36.3% of the forecasts had errors between 0.003 and 0.010. A total of 23.9% of the findings were composed of predictions that had errors greater than 0.10. According to the data on errors, the highest error is 0.015, the lowest error is 0.001, and the average error is 0.006, respectively. Similarly, the predominance of green markers in the figure aligns with this high R ², showing that the model can reliably predict ECR in most cases. The few red markers representing error-prone cases are relatively isolated, suggesting the model effectively handles ECR predictions overall, with minor opportunities for improvement under special conditions.

Figure 9

Correlation among the actual and predicted ECR for the GEP model.

Figure 10

Error analysis for the ECR.

4.3 GEP CSR model

The optimal GEP model generates the ETs for predicting the CSR, as illustrated in Figure 11(a)–(c). The model equation for CSR prediction was obtained by decoding the ET, as illustrated in Eq. (11). The formula that results from this process employs fundamental arithmetic operations and variables from the decoded ET. The cost-effectiveness of the ESP–DPA concrete formulations can be accurately and interpretably predicted by this equation, which depicts the relationship between CSR and the input factors. Eq. (11a) describes a non-linear interaction involving DPA, C, SP, ESP, and A, affecting the resulting CSR. Eq. (11b) emphasizes the role of cement relative to SP and A, where the ratio of cement to a modified SP term directly impacts CSR. Eq. (11c) introduces a logarithmic dependency on DPA, modulated by the combination of C, A, ESP, and SP, suggesting that these components collectively influence CSR through sensitive variations. Together, these equations provide a structured approach to predicting CSR:

(11) CSR = C 1 + C 2 + C 3 ,

where

(11a) C 1 = DPA C − ( SP × ESP ) + A ,

(11b) C 2 = C 7.67 − A SP × ( 0.74 + A ) ,

(11c) C 3 = Ln ( DPA ) C × A ESP × SP + 0.74 .

Figure 11

ETS of the GEP model for CSR. (a) Sub-ET 1; (b) Sub-ET 2; (c) Sub-ET 3.

Figure 12 illustrates that the GEP model’s CSR predictions were highly accurate, as evidenced by an R ² value of 0.92. In order to compare the experimental values with the predicted values, an error analysis was also performed, as illustrated in Figure 13. Based on the analysis, 47% of the predictions had errors of less than 0.15, while 41.7% of the predictions had errors in the range of 0.15–0.4. Only 11.3% of the results were predictions, with errors exceeding 0.4. In terms of error statistics, the highest error is 0.58, the lowest error is 0.02, and the average error is 0.17. The distribution of red markers indicates certain complexities in predicting CSR accurately, possibly due to fluctuating cost factors. These error-prone areas suggest that while the model effectively captures the overall relationship, enhancing it to account for specific cost variations could further reduce prediction discrepancies and improve accuracy across all cases.

Figure 12

Correlation among the actual and predicted CSR for the GEP model.

Figure 13

Error analysis for the CSR.

4.4 Model validation

The GEP model’s predictions for CS, CSR, and ECR were thoroughly evaluated using an extensive variety of statistical checks to determine their accuracy and reliability. The checks that were included in this analysis were MAE, RMSE, and RMSLE. The specifics of the statistical tests are illustrated in Figure 14. The GEP model for CS achieved an MAE of 1.915, indicating that the average absolute variance among the estimated and actual values was 1.915. The RMSE for CS was 2.37, which was used to determine the standard deviation of the prediction errors. This value highlights the squaring effect, which results in greater discrepancies. The RMSLE value for CS was 0.063, and its primary focus was on the relative differences between predicted and actual values. These results suggest that the model is capable of reliably predicting CS with relatively low errors. The CSR GEP model demonstrated an MAE of 0.177, which suggests a small average absolute variance between the predicted and actual values. An RMSLE of 0.073 and an RMSE of 0.23, which indicate a low standard deviation of the prediction errors, exemplify the model’s ability to effectively manage both small and large values. These metrics assure the reliability of cost-effectiveness assessments of the ESP-DPA concrete mixtures, underscoring the model’s capacity to accurately predict CSR. The GEP model achieved an MAE of 0.04, which is an exceptionally low value for ECR. This value denotes the smallest average absolute variance among the predicted and actual values. An RMSE of 0.073 for ECR, which indicates very small standard deviations of the prediction errors, and an RMSLE of 0.072 demonstrated the model’s precision in capturing the relative differences between the predicted and actual values. These findings support the model’s robustness and accuracy in predicting ECR. The results demonstrated low error values across these metrics, indicating strong predictive accuracy and reinforcing the reliability of the models. In general, the statistical evaluations for CS, CSR, and ECR suggest that the GEP model produces predictions that are both precise and dependable, with negligible errors in all metrics. This comprehensive evaluation underscores the model’s capacity to accurately represent the complex relationships among the input variables and their corresponding output variables, ensuring confidence in their predictive capabilities.

Figure 14

Comparative analysis of statistical check results for CS, CSR, and ECR.

5 Outcomes of SHAP analysis

The SHAP study offers a thorough approach for evaluating ML models [65]. The Shapely score is an approach used to quantify the comparative impact and influence of each input parameter on the final model outcome. It is similar to parametric evaluation, where all parameters, excluding one, are kept continual, and the effect of the parameter in a query on the output characteristic is noted. The model generates a predicted result for each expected sample, and the SHAP score represents the amount assigned to each feature in the supplied sample [66]. This study investigated how input factors affect the CS, CSR, and ECR of DPA–ESP concrete. The entire data sample utilizes the SHAP tree explainer to provide a detailed depiction of localized SHAP explanations and the overall impact of characteristics.

The SHAP plot results are illustrated in Figure 15, which illustrates the impact of input parameters on the CS of DPA–ESP concrete. The x-axis of the SHAP diagram indicates the impact of each factor, while the values of each input element are displayed using a color spectrum. The analysis establishes that the specimen’s age (test age) is the primary determinant of CS, with cement quantity, ESP, SP, and DPA following in that order. The CS is positively influenced by the test age and cement quantity, indicating that an increase in either factor can increase the strength. ESP and SP, on the other hand, demonstrate both positive and negative effects, suggesting that their impact on CS can fluctuate based on their interactions and levels. The impact of DPA, however, remains uncertain as a result of the dataset’s limited variation, which implies that additional research may be necessary to gain a comprehensive understanding of its role. These insights emphasize the potential of ESP and DPA as partial cement replacements, which may have a beneficial impact on environmental sustainability and concrete performance.

Figure 15

SHAP values for the CS.

Figure 16 illustrates the SHAP plot for the ECR of DPA–ESP concrete. The most significant factors in this study were test age and ESP, which suggest a primarily positive influence on ECR. This influence may be associated with the curing process and material properties. The order of influencing factors is as follows: test age, ESP, cement, SP, and DPA. Cement and SP have both positive and negative effects on ECR, indicating that their impact may be contingent upon specific conditions. It is important to note that the limited variation in DPA data hindered the ability to draw definitive conclusions regarding its influence on ECR. The results of this analysis emphasize that, although test age and ESP have a positive impact on ECR, it is crucial to balance other components, particularly cement and SP, in order to optimize ECR performance in DPA–ESP concrete.

Figure 16

SHAP values for the ECR.

The test age is once again the most influential factor in the SHAP plot for CSR of DPA–ESP concrete, as illustrated in Figure 17. This finding is consistent with its significance in CS and ECR. In descending order of impact, the remaining influencing factors are SP, DPA, ESP, and cement. It is intriguing that the test age and cement exhibit a more negative correlation with CSR, indicating that, despite their importance, their impact may potentially diminish CSR under specific circumstances. The impacts of SP and ESP on CSR are both positive and negative. The DPA dataset’s impact was equivocal due to its limited variation. It is evident from this analysis that the substitution of cement with ESP and DPA in DPA–ESP concrete can result in economic and environmental benefits in addition to its performance benefits.

Figure 17

SHAP values for the CSR.

6 Discussion

This study aimed to develop ML forecast models for the CS, ECR, and CSR of DPA-ESP concrete. In cases where the R ² value is low, experimental validation should be preferred over model predictions, as a lower R ² suggests that the model may not fully capture the complexity of the data, leading to potential inaccuracies. For applications requiring precise predictions, especially in high-stakes or safety-critical environments, validation through experimental testing can ensure accuracy and mitigate risks associated with model limitations. However, in this case, the R ² values for all three models are high (0.94 for CS, 0.91 for ECR, and 0.92 for CSR), indicating strong predictive reliability. Also, the statistical check values are lower. Thus, the models can be applied confidently, although conservative interpretation is recommended in cases where larger deviations may impact critical decisions. The GEP ML method is used for this purpose as it provides model equations for future use. Additionally, the SHAP analysis method was employed to determine the importance of different features on the model outputs. The results of this study yielded GEP estimation models that closely aligned with experimental findings. These models can be utilized to calculate the CS, ECR, and CSR of DPA–ESP concrete using various input components, thereby decreasing the time, effort, and cost required for further experiments. Furthermore, the SHAP study showed the effect of input features on the CS, ECR, and CSR of DPA–ESP concrete, providing valuable insights for academics and industry in selecting the quantity of raw ingredients during DAP–ESP concrete production. The prediction models will be limited to the CS, ECR, and CSR of DPA–ESP concrete since the GEP models developed in this research can only receive values from a certain set of five inputs. The dependability of predictions is guaranteed due to the utilization of uniform units and test techniques across all models in the database. To gain a deeper understanding of the mix proportions and the impact of each aspect, the models yielded mathematical equations. The output models will not work if the analysis has less or more than five inputs. The accuracy of the model’s predictions in this study relies on the consistency of input units. Previous studies using experimental and ML approaches to analyze alternative materials emphasize the importance of precise inputs and robust methodologies to ensure reliable and insightful results [67,68,69].

ML-based prediction models have various practical applications in the construction sector, such as predicting the strength of materials, conducting predictive maintenance, assessing risks, ensuring quality control, and optimizing energy efficiency. However, ML models do have certain limitations, including challenges related to accessing data, achieving high accuracy, managing costs, and requiring human interaction. Future research should prioritize the incorporation of the Internet of Things, the creation of hybrid models, the implementation of Explainable AI methods, the inclusion of sustainability aspects, and the establishment of standardized data collection and sharing practices within the industry. These efforts will help overcome existing limitations and enhance the efficiency of ML-based results. These advancements have the potential to provide more precise and up-to-date information, improve productivity, increase transparency, facilitate understanding, and enable well-informed decision-making. As a consequence, they may help reduce project delays, enhance safety, and promote sustainability in the construction sector.

7 Conclusions

GEP was implemented in this research to generate predictive models for three critical performance metrics of DPA and ESP-modified concrete, including CS, ECR, and CSR. The selection of GEP, a type of evolutionary algorithm, was based on its capacity to develop mathematical expressions that accurately represent the intricate relationships between numerous input variables. Moreover, the SHAP analysis yielded the impact of each input on model outputs. The main findings of this study are as follows:

• The mathematical equation-based GEP models for the CS, ECR, and CSR of DPA-ESP concrete agreed well with the experimental findings and can be used for future predictions, thereby reducing the time, effort, and cost required for further experiments.

• The model’s accuracy was confirmed with an R ² value of 0.94 for CS and similarly high values of 0.91 for ECR and 0.92 for CSR.

• The absolute error analysis for CS revealed that 45.2% of the predictions were between 1 and 4, 14.3% were greater than 4, and 40.5% had errors of less than 1. The error distribution for CSR was similarly low, and for ECR, the errors were minimal, suggesting robust predictive performance across all variables.

• The reliability and accuracy of the models for CS, CSR, and ECR were also verified through statistical evaluations such as MAE, RMSE, and RMSLE. For example, MAE, RMSE, and RMSLE for the CS GEP model were 1.915, 2.37, and 0.063 MPa, respectively.

• SHAP study exhibited that the age of the specimen (test age) was the crucial factor for all outputs (CS, ECR, and CSR), exhibiting a positive impact on CS and ECR and a negative impact on CSR. The impact of cement was found to be more positive with the CS, more negative with the CSR, and both negative and positive with the ECR. This implies that cement replacement with ESP and DPA may have both cost and environmental benefits.

The model predictions are adapted to the dataset and five input variables, predicting DPA–ESP concrete CS, ECR, and CSR in this structured input framework. Nevertheless, this specificity also implies that the model may become ineffective or lose accuracy if it is used with fewer or additional variables or if inconsistent units are applied to the inputs. Although the model exhibits high R ² values (0.94 for CS, 0.91 for ECR, and 0.92 for CSR), which suggest strong reliability within these constraints, future research could seek to broaden the model to include additional SCMs or environmental factors. The model’s adaptability to various concrete compositions would be enhanced by the inclusion of SCMs such as fly ash, silica fume, and slag cement. Furthermore, customizing the model to suit a variety of geographical regions would take into account environmental factors such as temperature, humidity, and the availability of raw materials. This would increase the model’s efficacy in a variety of construction settings and climates, thereby expanding its application to a wider range of contexts.