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AI-based prediction for the strength, cost, and sustainability of eggshell and date palm ash-blended concrete

  • Zhao Quanwei , Chen Qi EMAIL logo , Ali H. AlAteah , Abdulgafor M. Alfares , Sadiq Alinsaif and Sahar A. Mostafa EMAIL logo
Published/Copyright: May 21, 2025
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REVIEWS ON ADVANCED MATERIALS SCIENCE
From the journal REVIEWS ON ADVANCED MATERIALS SCIENCE Volume 64 Issue 1

Abstract

Eggshell powder (ESP) and date palm ash (DPA) are increasingly used as sustainable cement substitutes in cementitious composites. This study used multi-expression programming (MEP) to develop prediction models due to its advantage of yielding model equations. The attributes of ESP and DPA-modified concrete chosen for modeling include compressive strength (C-S), eco-strength (E-C-S), and cost-strength ratio (C-S-R). Hyperparameters in MEP were fine-tuned to get the maximum accuracy for predictions. The models were validated using R 2 and statistical checks and analyzing the variance among predictions and real values. The MEP models were noted to be exact in estimating C-S, C-S-R, and E-C-S with an R 2 of 95, 93, and 92%, respectively, indicating good agreement with actual data. Additionally, the ±20% index analysis indicated that all values fall within the acceptable range, validating the model’s reliability. The mathematical expression-based MEP prediction models developed in this study can be applied to future C-S, C-S-R, and E-C-S predictions in ESP–DPA-modified concrete. These models are designed to operate with a predetermined set of input parameters and are incompatible with a variable set of inputs. Additionally, it is imperative to maintain consistency in the units of inputs to obtain precise predictions from the constructed models.

Keywords: sustainable concrete material; strength, environmental, and cost parameters; eggshell and date palm ash

1 Introduction

There is an extensive quantity of date trees globally, and each tree produces about 40 kg of waste annually [1,2]. This waste is commonly gathered and incinerated. A minor portion of the trash is finely cut and mixed with some organic waste to be utilized as animal food, or it is allowed to degrade naturally for the purpose of being used as fertilizer. Nevertheless, the majority of date palm trash is disposed of in landfills, resulting in environmental issues [3]. Improper disposal of these wastes can lead to environmental and agricultural issues, including soil degradation and water contamination. Effective waste management is essential for mitigating these consequences and ensuring the long-term sustainability of the ecosystem [4]. Date palm tree debris may be incinerated and utilized as date palm ash (DPA) in building materials, addressing concerns over the discarding of date palm trash and the ecological sustainability challenges associated with cement production and use. DPA may be utilized to produce environmentally friendly cementitious composites because of its high pozzolanic properties, particularly when reduced to smaller particle sizes [5,6]. Incorporating DPA as a supplementary cementitious material (SCM) in cementitious composites might substantially reduce construction expenses and CO2 releases while also preserving the project’s service life. DPA, around 10–30% of the cement content, was used in both mortar and concrete. The addition of 10% DPA to the concrete caused an enhancement in compressive strength (C-S), resistance to water, and chloride penetration [7,8]. Also, including DPA up to 10% as a substitute for cement in mortar resulted in enhanced strength properties [9]. DPA achieved a cost reduction of up to 11% in block manufacture while maintaining its mechanical attributes. The blocks made of DPA concrete are sustainable and effectively manage and utilize DPA waste, resulting in reduced building costs during construction and operation [10].

Eggshell powder (ESP) is derived by processing waste eggshells into fine powder. Eggshells are acquired as byproducts from restaurants, poultry farms, and bakeries in large quantities, where they are disposed of in dustbins and landfills after the eggs have been utilized [11,12]. The ESP has a significant concentration of CaCO3, which facilitates the formation of extra calcium aluminate hydrate (CAH) and calcium silicate hydrate (CSH) gels when incorporated into cementitious composites [13]. In addition to ESP’s pozzolanic properties, its chemical makeup contains a significant amount of CaO, which imparts cementitious qualities to it. The suitability of the ESP as an SCM in concrete has been demonstrated in prior studies [14,15]. Several investigations have utilized ESP as SCM in cementitious composites and have observed notable improvements in the properties of the concrete [16,17]. The ESP effectively stabilizes the monocarbonates and ettringite in the cement matrix, with the optimal ESP concentration ranging from 5 to 10% of cement [18]. ESP is utilized in conjunction with other waste materials with pozzolanic properties that contain ample amounts of silica and alumina. This combination ensures optimal and improved pozzolanic reaction among the Al2O3 and SiO2, as well as the Ca(OH)2 in the ESP (derived from excessive CaO). The result is the production of an excess of CAH and CSH. A combination of ESP and fly ash (FA) in concrete was used. ESP was used in 5% of the cement and FA in 20–40% of the cement. The concrete exhibited a notable increase in both C-S and flexural strength. The mixtures with 5% ESP and 30% FA had the greatest strengths [11]. Another study replaced 20% of the cement in self-compacting concrete (SCC) with a combination of 10% ESP and 10% slag. They observed a notable enhancement in the flowability, C-S, and flexural strength of the concrete. The incorporation of both ESP and slag resulted in a higher density of the microstructure of the SCC [19]. In an experimental study, cement was substituted with a combination of ESP and bagasse ash in concrete. Cement was replaced with 5–20% bagasse ash and 2.5–7.5% ESP. The mechanical properties of the concrete were enhanced by using blends of SCMs. Compared to the control mix, the addition of 15% bagasse ash and 5% ESP resulted in a significant increase in C-S, flexural, and tensile strengths by 23.6, 19.8, and 19.5%, respectively. The mixture containing 20% bagasse ash and 5% ESP exhibited the least permeability, which was 48% lower than the control mix. This indicates that the combination of ESP and bagasse ash effectively compacted and filled the empty spaces in the microstructure of the concrete. Other studies have documented notable enhancements in the characteristics of concrete when incorporating combinations of ESP and other pozzolanic materials [20,21].

Recent research has advanced the use of artificial intelligence (AI) technologies to develop consistent, dependable, and accurate models for solving issues in engineering [22,23,24,25]. Machine learning (ML) techniques have been widely used previously on different waste materials in the field of civil engineering, as shown in Table 1. AI strategies like support vector regression, decision tree, boosting, bagging, and artificial neural networks (ANN) involve training the existing data to solve the problem [26,27,28,29]. AI techniques are capable of identifying intricate and complex structures and providing generalized patterns [30,31,32,33]. Soft computing techniques have been widely used to predict complex engineering problems, including concrete properties and structural behavior [34,35,36]. Optimization approaches like fuzzy-based models and AI techniques, including neural networks, have demonstrated high accuracy in modeling material performance [37,38,39]. These methods effectively handle nonlinear and uncertain data, enhancing prediction reliability [40,41,42,43]. AI techniques have been increasingly applied to predict material performance and dynamic responses in concrete composites [44,45]. These approaches are particularly valuable when incorporating sustainable components like carbon-based materials and plastic waste, which enhance concrete properties [46,47]. Additionally, advanced algorithms are utilized to model structural behavior and damage prediction in reinforced concrete, supporting the development of more efficient and durable composites [48,49,50,51,52]. Thus, it is operational throughout the extensive field of engineering [53,54,55,56]. These approaches require a large number of hidden neurons, which in turn require a significant amount of memory. As a result, the ability to establish a realistic and practical relationship between the inputs and outcomes is limited [57]. These models accurately reproduce the connection in a realistic manner, but they do not provide a practical empirical expression. What sets genetic programming (GP) apart is its rejection of previously established relationships to construct a new model. In order to address the aforementioned constraints of other AI algorithms, a novel technique called multi-expression programming (MEP) has been developed. The MEP possesses a distinctive characteristic of encapsulating numerous equations (chromosomes) within a single program. The most optimal chromosome is picked from the given options and serves as the definitive solution to the problem [58]. MEP, an advanced variant of GP, surpasses existing evolutionary algorithms by its ability to produce precise results even in cases when the complexity of the target is unknown [59]. Unlike other AI approaches, MEP does not need the specification of the eventual equation’s form. During the evolution phase of MEP, any mathematical contradictions are identified and removed from the final phrase. Moreover, with MEP, the process of decoding is significantly simpler compared to other soft computing approaches. Due to its notable advantages over other evolutionary algorithms, the application of MEP in the civil engineering sector is gaining attention.

Table 1

Prior research on ML utilizing various waste materials

S. no ML techniques Dataset Waste material used in previous research Predicted properties Publication year Ref.
1 ANN 69 FA CS 2017 [60]
2 ANN 114 FA C-S 2017 [61]
3 RF 131 FA, GGBS C-S 2019 [62]
4 GEP, MLR and MNLR 65 Bagasse Ash CS 2020 [63]
5 SVM, BR 117 ESP C-S 2022 [64]
6 MLPNN, SVM, XGBoost 234 ESP Water absorption 2023 [65]
7 GEP, MEP 169 RHA, SF C-S 2023 [66]
8 MEP 275, 109 E-waste C-S, T-S 2023 [67]
9 GEP, MEP 135 Plastic waste C-S 2023 [68]
10 RSM, ANN 225 ESP, WGP F-S 2024 [69]
11 RSM, ANN 49 ESP C-S, T-S 2024 [70]

RF: random forest; GEP: gene expression programming; MLR: multi-linear regression; MLNR: multi-output non-linear regression; SVM: support vector machine; BR: bagging regressor; MLPNN: multilayer perceptron neural network; XGBoost; extreme gradient boosting; RSM: response surface methodology.

Previous studies on DPA–ESP concrete have largely relied on extensive experimental work, which demands significant time, financial resources, and energy. This process involves material procurement, sample fabrication, curing, and property evaluation through testing, making it both labor-intensive and costly. However, these studies have not fully leveraged AI-based predictive modeling to reduce this burden. Additionally, most prior research has focused on evaluating individual material properties rather than investigating the combined effects of multiple input components. Since concrete properties are influenced by several interacting factors, accurately quantifying their combined impact through experimental methods alone remains challenging. Sensitivity analysis can serve as a valuable tool to address this limitation by systematically assessing the influence of different input variables. Moreover, previous research lacks comprehensive models that integrate both experimental and AI-based approaches to enhance predictive accuracy, often relying on traditional regression-based techniques that may not effectively capture nonlinear relationships between input and output variables. A critical research gap is that MEP has not yet been explored for predicting the properties of DPA–ESP concrete, despite its ability to generate explicit mathematical expressions for predictive modeling. While other AI models have been used, MEP remains underutilized in this domain, even though it offers advantages such as improved transparency and interpretability of the prediction process. By addressing these limitations, this study not only introduces MEP-based models for predicting C-S, eco-strength (E-C-S), and cost-strength ratio (C-S-R) of DPA–ESP concrete but also optimizes hyperparameters, verifies accuracy through statistical measures, and evaluates the influence of input variables using sensitivity analysis. These contributions can significantly improve the versatility of SCM composites, promoting their application in green building initiatives while advancing AI-driven solutions for sustainable construction materials.

2 Research significance

Despite significant advancements in concrete technology, existing studies predominantly rely on traditional experimental approaches that are time-consuming, resource-intensive, and often lack predictive accuracy when applied to diverse material compositions. Furthermore, most prior research fails to integrate advanced AI-based models, such as MEP, which can capture complex nonlinear relationships between input variables and output properties. The proposed approach addresses these limitations by developing MEP-based predictive models for C-S, E-C-S, and C-S-R, offering transparent and interpretable mathematical expressions that reduce dependency on repetitive laboratory testing. By optimizing mix design and accurately predicting key performance metrics, this research advances the state of the art and contributes to sustainable concrete production. The findings significantly improve the existing knowledge base by providing efficient, data-driven solutions that promote economical and environmentally friendly construction practices.

3 Research methods

3.1 Data collection

The concrete mix design has been comprehensively reported, following the ACI 211.1R guidelines to obtain the constituent materials of the control concrete [71]. The design involved partially replacing cement with DPA at proportions of 0, 10, 20, and 30% by volume. Additionally, ESP was incorporated as an additive in proportions of 0, 1, 2, 3, and 4% by the weight of the binder. The mix design also included cement (C) and testing age (A), along with a superplasticizer (SP) to achieve the desired workability and strength. Moreover, the particle size gradations for both fine and coarse aggregates are presented in Figure 1, demonstrating the distribution of particle sizes within the aggregate samples. Gradation analysis is essential to ensure optimal packing density, which directly affects the concrete’s workability, strength, and durability. These gradation curves are crucial for achieving a dense and cohesive concrete matrix, minimizing voids, and enhancing the overall mechanical performance of the concrete mix.

Figure 1 Particle size distribution curves of fine and coarse aggregates [71].
Figure 1

Particle size distribution curves of fine and coarse aggregates [71].

The dataset was compiled from previously published research and contains five variables that were used as inputs: C, ESP, DPA, A, and SP [71]. The outputs are compressive strength (C-S), eco-strength (E-C-S), and cost-strength ratio (C-S-R). The original dataset consisted of 28 data points, which were later expanded to 560 through data augmentation using Python programming. The data augmentation process involved generating synthetic data points through random sampling and introducing slight variations to existing data while preserving the statistical characteristics of the original dataset. This expansion increased the robustness of the model and enhanced its ability to generalize predictions. For model development, the augmented dataset was divided into training (70%) and testing (30%) phases. The Python script employed for data augmentation starts by displaying a file dialog window using Tkinter, allowing the user to select the input file. After validation, the file is loaded into a Pandas DataFrame, and new synthetic data points are generated and merged with the original data. The enhanced dataset is then saved as a new file, with the script providing comprehensive output, including the file storage location, the number of synthetic data points generated, and the total number of data elements. In cases where no file is chosen, the script handles resampling as needed. The data preparation step not only simplifies the data acquisition process but also helps ensure the consistency and quality of the input data [55].

An extensive study was conducted on the dataset, beginning with the examination of the frequency distribution of its variables to gain insights into their dispersion and central trends, as seen in Figure 2. In this phase, the data were arranged into a frequency table, which allowed for an examination of the prevalent values and the distribution pattern of the dataset. In addition, we evaluated the correlation coefficients between the variables to evaluate the magnitude and direction of their associations, as presented in Tables 2–4. These coefficients are essential for identifying pairs of variables that exhibit substantial correlation, whether positive or negative. This is particularly important for tasks such as feature selection and gaining insight into the underlying data structure. The integration of frequency distribution and correlation analysis establishes a strong basis for further data-driven modeling and decision-making. Moreover, Table 5 presents the range and distribution of input variables, detailing their statistical properties.

Figure 2 Frequency distribution of the dataset (a) C, (b) DPA, (c) ESP, (d) SP, (e) A, (f) C-S, (g) E-C-S, and (h) C-S-R.
Figure 2

Frequency distribution of the dataset (a) C, (b) DPA, (c) ESP, (d) SP, (e) A, (f) C-S, (g) E-C-S, and (h) C-S-R.

Table 2

Correlation coefficients of the dataset with respect to C-S

Cement (kg·m−3) DPA (kg·m−3) ESP (kg·m−3) SP (kg·m−3) Test age (days) C-S (MPa)
Cement (kg·m−3) 1
DPA (kg·m−3) −0.999 1
ESP (kg·m−3) −0.157 0.157 1
SP (kg·m−3) 0.919 −0.919 0.246 1
Test age (days) 0.031 −0.031 0.058 0.053 1
C-S (MPa) 0.296 −0.296 0.220 0.379 0.706 1
Table 3

Correlation coefficients of the dataset with respect to E-C-S

Cement (kg·m−3) DPA (kg·m−3) ESP (kg·m−3) SP (kg·m−3) Test age (days) E-C-S (MPa/kgCO2/m3)
Cement (kg·m−3) 1
DPA (kg·m−3) −0.999 1
ESP (kg·m−3) −0.157 0.157 1
SP (kg·m−3) 0.919 −0.919 0.246 1
Test age (days) 0.031 −0.031 0.058 0.053 1
E-C-S (MPa/kgCO2/m3) 0.159 −0.159 0.276 0.268 0.722 1
Table 4

Correlation coefficients of the dataset with respect to C-S-R

Cement (kg·m−3) DPA (kg·m−3) ESP (kg·m−3) SP (kg·m−3) Test age (days) C-S-R ($/MPa/m3)
Cement (kg·m−3) 1
DPA (kg·m−3) −0.999 1
ESP (kg·m−3) −0.157 0.157 1
SP (kg·m−3) 0.919 −0.919 0.246 1
Test age (days) 0.031 −0.031 0.058 0.053 1
C-S-R ($/MPa/m3) −0.273 0.273 −0.005 −0.273 −0.686 1
Table 5

Range and distribution of input variables

Variable Cement (kg·m−3) DPA (kg·m−3) ESP (kg·m−3) SP (kg·m−3) Age (days)
Maximum 490 151.2 18.7 5 28
Skewness 0.12 −0.12 0.03 −0.08 0.17
Mean 396.37 72.22 8.76 4.77 16.60
Range 196 151.2 18.7 0.46 21
Mode 392 75.6 9.4 4.77 7
Standard deviation 51.75 39.92 4.96 0.12 10.47
Sample variance 2678.19 1593.79 24.68 0.0146 109.63
Minimum 294 0 0 4.54 7
Sum 221,970 40,446 4,910 2673.39 9,296
Kurtosis −0.11 −0.11 −0.10 −0.39 −1.97
Median 392 75.6 9.4 4.77 7
Standard error 2.18 1.68 0.21 0.005 0.44

3.2 Modeling methodology

ML methods are utilized in several fields to forecast and understand the characteristics of materials [33,72]. In this investigation, the C-S, E-C-S, and C-S-R containing DPA and ESP were predicted using an ML-based approach that included MEP. This approach was chosen due to its extensive usage, reliable predictive outcomes in related studies, and its representation as an exceptional data mining algorithm. The study’s flowchart is depicted in Figure 3.

Figure 3 Overview of the study methodology.
Figure 3

Overview of the study methodology.

3.2.1 MEP

Oltean introduced MEP as an evolutionary algorithm that represents solutions as linear sequences of instructions or expressions [73]. Unlike conventional GP, where each individual represents a single solution, MEP encodes multiple expressions within a single chromosome, enhancing flexibility and efficiency in evolutionary computations. This unique characteristic allows MEP to simultaneously assess several potential solutions, improving the search process and reducing computational cost [74]. MEP is particularly effective for symbolic regression problems, where the objective is to derive the most accurate mathematical expression for a given dataset. By storing multiple expressions in a single chromosome, MEP efficiently explores a broader solution space, leading to faster convergence toward optimal or near-optimal solutions [75].

As shown in Figure 4, the MEP process begins with the initialization of a population of randomly generated chromosomes, each representing a potential solution. Two parent chromosomes are selected using a binary selection method, followed by crossover and mutation operations to generate offspring that inherit traits from both parents. The fitness of each progeny is then evaluated based on predefined criteria, such as minimizing error or optimizing predictive accuracy. If the termination conditions, such as reaching a predefined number of iterations or achieving an acceptable error threshold, are met, the process stops; otherwise, it continues iteratively, refining solutions over multiple generations. By integrating evolutionary strategies with an efficient representation of multiple expressions, MEP enhances predictive modeling capabilities, making it a valuable tool in engineering, materials science, and other computational applications [76].

Figure 4 Flowchart employed by the MEP technique.
Figure 4

Flowchart employed by the MEP technique.

MEP utilizes the MEPX software to generate predictive models by evolving mathematical expressions. In MEP, cross-validation is performed by dividing the dataset into multiple folds, where each fold is used as a validation set while the remaining folds form the training set. MEP generates predictive models using the training data and evaluates their performance on the validation set by calculating error metrics such as mean absolute error (MAE) or root mean square error (RMSE). This process is repeated for each fold, and the performance metrics are averaged to obtain an overall assessment of the model’s accuracy and robustness. The best-performing models from each fold are then selected for further evolution, ensuring that the final model is reliable and generalizable.

3.2.2 Modeling creation

The initial step in developing a precise AI model involves choosing the most influential input variables. Consequently, a comprehensive evaluation was carried out to determine the performance and effectiveness of several preliminary tests. The MEP modeling was initiated by configuring the subpopulation size to 20. The hyperparameters of the MEP model, as listed in Table 6, were selected based on an iterative process of experimentation and performance evaluation. Several configurations were tested, and the settings that resulted in the most accurate and consistent predictions were chosen. The selection criteria were guided by minimizing error metrics (such as MAE, RMSE, and root mean squared logarithmic error (RMSLE)) while ensuring model stability and convergence. Additionally, the chosen hyperparameters reflect a balance between computational efficiency and prediction accuracy, as evaluated through multiple replication trials. The fundamental arithmetical operations, including natural log, division, addition, square root, power, subtraction, and multiplication, were taken into account to generate a straightforward and accessible ultimate equation. The termination criterion for the model is determined by the number of generations required to attain the desired level of accuracy. A program that is run with a larger number of generations would provide outcomes with a lower margin of error. In the same way, the probability of progeny undergoing genetic functions is determined by the mutation rate and crossover rate. The crossover probability range is between 50 and 95% [77]. Various combinations were tested, and the combination that yielded the most favorable outcomes was used. The length of reviewing the generation has a significant impact on the accuracy of the suggested model. The model’s development is perpetual due to the incorporation of more variables into the system. Nevertheless, this work examines the conditions for terminating the development of the model, either after 3,000 generations or when the fitness function experiences a change of less than 0.1%. Figure 5 shows the MEP model workflow, including data preparation, feature selection, model training, validation, and prediction of C-S, E-C-S, and C-S-R.

Table 6

Parameters of MEP model

Parameters Settings
Sub-population size 300
Length of code 35
Function set Ln, +, /, pow, sqrt, −, ×
Number of generations 2,500
Population size 2,500
Crossover type Uniform
Probability of crossover 0.9
Mutation probability 0.01
Replication number 10
Figure 5 MEP model workflow.
Figure 5

MEP model workflow.

3.2.3 Model assessment

The MEP model’s performance was assessed by using statistical checks to achieve reliable and precise predictions [78,79]. The R 2 (coefficient of determination) statistic quantifies the proportion of the variation in the dependent variable that can be accurately predicted using the independent variables. It offers a deeper understanding of the extent to which the model accounts for the differences in the response data. The R 2 value ranges from 0 to 1, with higher values suggesting a stronger correlation between the variables being analyzed. The calculation is performed using the following equation:

(1) R 2 = 1 − ∑ j = 1 m ( p j − t j ) 2 ∑ j = 1 m ( t j − t ̅ ) .

The MAE is a parameter that quantifies the average magnitude of errors in a collection of predictions without taking into account their direction. This metric is beneficial for comprehending the average error in the model’s predictions. Better predictive accuracy is indicated by a lower MAE. MAE is calculated using the following equation:

(2) MAE = ∑ j = 1 m | t j − p j | n .

Another important statistic is the RMSE, which gives the square root of the average of the squared discrepancies between the actual and projected values. RMSE assigns greater importance to significant errors, therefore making it very responsive to outliers. It serves as a valuable tool for assessing the precision of the model in forecasting continuous results. The RMSE is computed by using the following equation:

(3) RMSE = ∑ j = 1 m ( t j − p j ) 2 n .

To enable comparison across various datasets and sizes, the normalized root mean square error (NRMSE) normalizes the RMSE by dividing it by the range of the observed values. This statistic is especially valuable for assessing the performance of models on datasets that have varying sizes. The NRMSE is indicated by the following equation:

(4) NRMSE = RMSE p j .

When calculating the ratio between actual and anticipated values, the RMSLE is a helpful tool for reducing the influence of outliers. This measure is especially advantageous when working with data that exhibits a large range of values or when the disparities between observed and anticipated values are more pronounced at smaller sizes. The RMSLE is a mathematical metric used to measure the accuracy of predictions in regression models. It is calculated by taking the square root of the average of the logarithmic differences between the predicted and actual values. RMSLE is calculated by using the following equation:

(5) RMSLE = ∑ j = 1 m ( log ( x + 1 ) − log ( y + 1 ) ) 2 n .

3.3 Sensitivity analysis

Sensitivity analysis is a critical aspect of model evaluation that examines how changes in input parameters impact the model’s output, providing insights into the model’s robustness and reliability. It plays a vital role in identifying the most influential variables that significantly affect the predicted outcomes, helping researchers and engineers to better understand model behavior and the interactions between input variables. Sensitivity analysis also assists in evaluating the model’s stability by determining how variations in the input data influence the results [80]. In the context of this study, sensitivity analysis was performed to determine the impact of each input parameter on the predicted values of C-S, C-S-R, and E-C-S. This analysis is essential for identifying key factors that drive model performance and can be used to optimize the input combination for achieving desired outputs. By systematically varying one parameter at a time while keeping the others constant, the relative significance of each input variable was quantified [81]. Through the use of Eqs. (6) and (7), the extent to which each variable influences the output can possibly be determined [82].

(6) N i = f max ( x i ) − f min ( x i ) ,

(7) SA = N i ∑ n j = 1 N j ,

where the expression “ f min ( x i ) ” represents the output with the lowest model forecasting while “ f max ( x i ) ” represents the output with the greatest forecasting of the model. The variable “ i ” represents the range of the input variable, while all other variables are fixed.

This analysis highlights the input variables that have a dominant effect on the model predictions, enabling targeted efforts to improve the accuracy of the most influential parameters. Furthermore, understanding the sensitivity of the model facilitates better decision-making when prioritizing variables for data collection and model refinement. By implementing sensitivity analysis, potential vulnerabilities of the model can be identified, and adjustments can be made to improve its predictive accuracy and reliability. Consequently, the practical application of this analysis enhances the model’s robustness and confidence in real-world scenarios.

4 Results

4.1 MEP model for C-S

The MEP was employed in the study to predict and model the C-S of the mixture. Eq. (8) was derived using MEP, which describes the correlation between the input parameters and the C-S. The accuracy of the MEP model was assessed by comparing the observed values with the predicted values. This evaluation is depicted in Figure 6, which shows a high level of precision with an R 2 value of 0.95. Additional error analysis of the MEP model, depicted in Figure 7, emphasized significant error metrics, such as the maximum, minimum, and mean errors, which were measured at 4.82, 0.39, and 1.94 correspondingly. The error distribution showed that 41.7% of forecasts had errors below 1.25, 47% of predictions had errors ranging from 1.25 to 3.5, and 11.3% had errors beyond 3.5. The thorough error analysis highlights the model’s resilience and dependability in accurately forecasting C-S.

(8) C − S = 2 ( ESP − C ) − ( C ) 2 × 2 ( DPA ) + A − SP 3 × DPA 2 × SP + A − ( 2 DPA ) + ln ( C × ESP × SP × DPA + A 2 ) + ESP SP A + C 2 − 2 SP × ln DPA ,

where ESP = eggshell powder quantity in kg·m−3, C = cement quantity in kg·m−3, DPA = date palm ash quantity in kg·m−3, A = testing age in number of days, SP = superplasticizer quantity in kg·m−3, and C-S = compressive strength in MPa.

Figure 6 R 2 for the C-S model.
Figure 6

R 2 for the C-S model.

Figure 7 Error distribution of the C-S model.
Figure 7

Error distribution of the C-S model.

4.2 MEP model for E-C-S

MEP was utilized to make a prediction about the E-C-S. Eq. (9), which properly represents the link between the input variables and E-C-S, was formulated as a consequence of the procedure that was carried out. To validate the performance of the model, the actual values were plotted against the projected values, as shown in Figure 8. The model acquired an R 2 value of 0.92, which indicates that it is capable of achieving expected outcomes. Additional insights into the correctness of the model were offered by a comprehensive error analysis, which is depicted in Figure 9. According to the findings of the analysis, the errors were the most significant and the least significant, and the averages were 0.014, 0.001, and 0.005, respectively. In addition, the distribution of prediction errors revealed that about 44.1% of mistakes were lower than 0.006, 45.8% of errors were between 0.006 and 0.012, and 10.1% of errors were higher than 0.012. In terms of calculating E-C-S, this comprehensive examination reveals that the MEP model is both effective and precise.

(9) E - C - R = 3 ( C ) − 2 A DPA ln ESP 2 SP − C C DPA 2 × 2 ( SP ) × ln A C + ESP SP 2 ( C ) − 2 ( DPA ) × A 2 − A ESP SP − 2 ( ESP + C ) − A × ln ( DPA ) ,

where ESP = eggshell powder quantity in kg·m−3, C = cement quantity in kg·m−3, DPA = date palm ash quantity in kg·m−3, A = testing age in number of days, SP = superplasticizer quantity in kg·m−3, and E-C-R = eco-strength in MPa/kgCO2/m3.

Figure 8 R 2 for the E-C-S model.
Figure 8

R 2 for the E-C-S model.

Figure 9 Error distribution of the E-C-S model.
Figure 9

Error distribution of the E-C-S model.

4.3 MEP model for C-S-R

For the purpose of calculating the C-S-R, MEP was utilized, which ultimately led to the determination of Eq. (10). The correctness of this model was verified by comparing the actual values to the projected values, as shown in Figure 10. The result was a robust R 2 value of 0.93, which indicates that the model is accurate. A more comprehensive error analysis, which is represented in Figure 11, was utilized to give additional confirmation of the performance of the model. In the course of the investigation, it was discovered that the most significant error was 0.39, the least significant error was 0.019, and the average error was 0.16. In addition, the distribution of prediction errors revealed that 36.3% of errors were lower than 0.14, 47% of errors were between 0.14 and 0.28, and 16.7% of errors were equal to or higher than 0.28. These results bring to light the dependability and efficacy of the model in forecasting the C-S-R.

(10) C - S - R = DPA + ESP ESP + C 2 + SP A − ln A + ESP C × ( SP + DPA ) 2 2 ( C ) × DPA ESP − SP − ln DPA ESP + A + SP C ,

where ESP = eggshell powder quantity in kg·m−3, C = cement quantity in kg·m−3, DPA = date palm ash quantity in kg·m−3, A = testing age in number of days, SP = superplasticizer quantity in kg·m−3, and C-S-R = cost-strength ratio in $/MPa/m3.

Figure 10 R 2 for the C-S-R model.
Figure 10

R 2 for the C-S-R model.

Figure 11 Error distribution of the C-S-R model.
Figure 11

Error distribution of the C-S-R model.

4.4 Statistical checks for all models

It is essential to conduct statistical checks to validate the accuracy and dependability of predictive models. This helps to ensure that the models function well across a wide range of settings and datasets. The results of their analysis give a full grasp of the model’s strengths and flaws, which in turn guides further developments. For the purpose of assessing the effectiveness of the models, statistical checks were carried out, and the outcomes are depicted in Figure 12 through the use of a spider plot. The details are found in Table 7. All three parameters, C-S-R, and E-C-S were taken into consideration during the study. In the case of C-S, the MAE was 1.941 MPa, the RMSE was 2.302 MPa, the RMSLE was 0.051 MPa, and the NRMSE was 0.057 MPa. The values that corresponded to C-S-R were determined to be 0.169, 0.198, 0.06, and 0.066, respectively. In the case of E-C-S, the values were 0.007, 0.008, 0.071, and 0.075, respectively. The results of these statistical assessments offer a complete assessment of the correctness and reliability of the models across a variety of measures.

Figure 12 Statistical checks of all output models.
Figure 12

Statistical checks of all output models.

Table 7

Statistical checks for all the output models

C-S C-S-R E-C-S
MAE 1.941 0.169 0.007
RMSE 2.302 0.198 0.008
RMSLE 0.051 0.06 0.071
NRMSE 0.057 0.066 0.075

4.5 Impact of input parameters

A sensitivity analysis was carried out to ascertain the influence that a number of different input factors had on the predictions made by the model. The research findings indicated that Age had the greatest impact on C-S, contributing 52.9% of the total effect, as shown in Figure 13. This was followed by DPA (15.7%), ESP (13.8%), SP (11.1%), and cement (6.5%). Similarly, age remained the most influential factor for E-C-S, accounting for 61.1% of the total impact. Other factors that had an impact were ESP (20.2%), SP (7.1%), DPA (6.2%), and cement (5.4%). In the C-S-R, age remained the most significant factor at 50.7%, while SP, cement, ESP, and DPA also made significant contributions at 17.8, 10.3, 12.4, and 8.8%, respectively. In each and every instance, age demonstrated the greatest influence on the predictions made by the model, demonstrating that it plays a crucial part in defining the qualities of the concrete. The variations in ESP and DPA content had a relatively lower impact on the prediction accuracy of the models compared to the influence of age. While changes in ESP and DPA content did affect the model outcomes, their contributions were limited, as shown by sensitivity analysis results, where ESP and DPA accounted for 13.8 and 15.7% of the impact on C-S, respectively. No significant limitations were observed regarding prediction accuracy related to variations in ESP and DPA content; however, future studies may further investigate these factors under diverse conditions to enhance model robustness and generalizability. This illustrates how important it is to correctly measure and regulate the age parameter to generate reliable and exact predictions of the model.

Figure 13 Sensitivity analysis of all the output models.
Figure 13

Sensitivity analysis of all the output models.

5 Discussion

MEP was selected in this study to develop forecast models for the C-S, C-S-R, and E-C-S of ESP–DPA-modified concrete because of its ability to yield mathematical expressions as model outcomes, which makes it particularly effective for predictive modeling tasks. The developed prediction models demonstrated high accuracy, with R 2 values of 0.95, 0.93, and 0.92 for C-S, C-S-R, and E-C-S, respectively, verifying the precision and reliability of the constructed MEP models. These high R 2 values reflect the strong correlation between the predicted and actual outcomes, indicating that MEP can efficiently capture the complex relationships between the input variables and the target properties. In addition to R 2 values, statistical measures such as MAE, RMSE, RMSLE, and NRMSE further validated the models’ performance, confirming their robustness and consistency. As highlighted in Table 8, previous studies also demonstrated that MEP outperforms other predictive techniques, thereby reinforcing its suitability for developing mathematical models in concrete mix optimization. The practical implications of the results for concrete mix design are the development of accurate predictive models that eliminate the need for repetitive laboratory testing, saving time, effort, and resources. The MEP-based models can be effectively used to optimize mix proportions for ESP–DPA-modified concrete, ensuring the desired strength and performance while minimizing costs and environmental impact. These models provide a reliable tool for engineers to make informed decisions during the design phase, ultimately contributing to more efficient and sustainable concrete production. Furthermore, the developed models offer practical utility by providing an efficient means of calculating C-S, C-S-R, and E-C-S using the input variables employed in this study, including cement, ESP, DPA, testing age, and SP. However, it is important to acknowledge that these models are limited to the specified input variables and will not function if more or fewer variables are used. Additionally, unit consistency must be maintained, as variations in input units could alter model outputs. Despite these limitations, the proposed models hold potential for practical applications by reducing the need for repetitive laboratory testing during concrete mix design, significantly minimizing human effort, time, and expenses associated with experimental procedures.

Table 8

Comparison of the current study’s findings to past studies using ML

Ref. Waste material used ML algorithms applied Properties predicted Best model
Present study ESP, DPA MEP C-S, E-C-S, C-S-R MEP
[83] Metakaolin GEP and MEP C-S MEP
[84] Alkali activated GEP and MEP C-S, slump MEP
[85] RHA GEP and MEP C-S MEP
[30] Marble waste GEP and MEP C-S MEP
[86] Limestone, chalk MEP, LGP, and GEP C-S, T-S LGP and MEP
[87] ESP, GP GEP and MEP C-S loss MEP
[88] FA M5P-tree, NLR, ANN, and MEP C-S MEP

RHA: rice husk ash; T-S: tensile strength; GP: glass powder; FA: fly ash; LGP: linear genetic programming; NLR: non-linear regression.

MEP-based prediction models in engineering offer significant advantages over traditional AI-based approaches, particularly in forecasting material characteristics, conducting predictive maintenance, evaluating risk, overseeing quality management, and optimizing energy efficiency. Unlike conventional models that often struggle with data availability, model accuracy, and the need for human involvement, MEP efficiently handles complex relationships through its ability to generate mathematical expressions directly from data. This unique capability reduces dependency on large datasets and minimizes human intervention, making it a more practical and accurate solution. To further enhance the effectiveness of MEP-driven solutions, future studies could focus on integrating the Internet of Things, creating hybrid techniques, implementing explainable AI methods, incorporating sustainability considerations, and standardizing data curation and dissemination in the industry. By embracing these advancements, MEP models can significantly improve data quality and timeliness, boost productivity, increase transparency, and support well-informed decision-making. As a result, this approach may lead to reduced project delays, improved safety, and increased environmental sustainability in the construction sector.

Potential sources of error and uncertainty in MEP predictions can arise from data quality issues, such as noise or outliers, which may affect model training and accuracy. The selection of hyperparameters and model configuration may also introduce uncertainties, as suboptimal choices can impact prediction performance. Additionally, the inherent assumptions within the MEP algorithm may not always align with complex real-world conditions, leading to discrepancies. Variability in experimental conditions and measurement errors during data collection further contribute to prediction uncertainty. To mitigate these factors, careful data preprocessing and robust model validation are essential.

6 Conclusions

This study successfully developed MEP-based predictive models to estimate the C-S, E-C-S, and C-S-R of ESP–DPA-modified concrete. The primary contribution of this research lies in formulating accurate mathematical expressions that enable reliable predictions of these properties based on input parameters such as cement, ESP, DPA, testing age, and SP. These models offer practical utility by reducing the need for repetitive laboratory testing, saving time, effort, and resources, and enabling engineers to make data-driven decisions for mix optimization and performance enhancement. This study’s outcomes were as follows:

  • The MEP-based models demonstrated high predictive accuracy, with R 2 values of 0.95 for C-S, 0.92 for E-C-S, and 0.93 for C-S-R. These values indicate the models’ strong ability to capture the variability in each parameter, showcasing their robust predictive capabilities.

  • The mathematical equations derived through MEP provided a quantitative framework for forecasting C-S, E-C-S, and C-S-R. These equations offer a reliable means of estimating the properties of ESP–DPA-modified concrete, making them valuable for both research and practical applications in civil engineering.

  • The models’ reliability was validated through statistical tests, yielding low error metrics, including MAE (1.941), RMSE (2.302), RMSLE (0.051), and NRMSE (0.057) for C-S. Similar low error values were obtained for C-S-R and E-C-S, confirming the models’ accuracy and consistency.

  • Sensitivity analysis identified testing age as the most significant input parameter, accounting for 52.9, 61.1, and 50.7% of the influence on C-S, E-C-S, and C-S-R, respectively. This finding highlights the critical role of testing age in determining concrete strength and related properties, emphasizing its importance in predictive modeling and experimental setups.

  • Other input factors, including DPA, ESP, SP, and cement, had comparatively lower impacts on the model’s output. These variations reflect the differing levels of significance that each parameter holds in determining the properties of ESP–DPA-modified concrete, providing essential insights for mixture optimization and guiding the selection of input variables for improved model performance.

Despite the promising results, these models are limited to the specified input variables and may not perform well when applied to scenarios with different material compositions or environmental conditions. Practitioners should validate model predictions using field data before implementation and ensure unit consistency to maintain accuracy, as variations in input units can significantly alter the output. Additionally, changes in raw materials, mix proportions, or environmental conditions could affect model accuracy, requiring recalibration and updates. The developed MEP models offer practical applications in real-world construction projects by providing reliable predictions of C-S, E-C-S, and C-S-R. These models can assist engineers in optimizing concrete mix designs, reducing experimental efforts, and making data-driven decisions for sustainable construction practices. To enhance model applicability and robustness, future research should focus on incorporating additional variables and evaluating model performance using diverse datasets. Moreover, integrating advanced techniques such as IoT-based monitoring, hybrid modeling approaches, and explainable AI methods could improve model adaptability and support practical decision-making in concrete mix design and optimization.

Acknowledgments

This work was supported by the Jinhua Science and Technology Planning Project: Jinhua Public Welfare Technology Application Research Projects (2023-4-046, 2023-4-047), Zhejiang Provincial College Students’ Scientific and Technological Innovation Activity (2024R479A008).

  1. Funding information: Jinhua Science and Technology Planning Project: Jinhua Public Welfare Technology Application Research Projects (2023-4-046, 2023-4-047), Zhejiang Provincial College Students' Scientific and Technological Innovation Activity (2024R479A008).

  2. Author contributions: Z.Q.: conceptualization, methodology, formal analysis, writing – original draft. C.Q.: supervision, project administration, resources, writing, reviewing, and editing. A.H.A.: data acquisition, validation, writing, reviewing, and editing. A.M.A.: software, formal analysis, writing, reviewing, and editing. S.A.: software, visualization, formal analysis, and validation. S.A.M.: conceptualization, supervision, resources, and methodology. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The dataset generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Received: 2025-01-17
Revised: 2025-03-16
Accepted: 2025-04-28
Published Online: 2025-05-21

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/rams-2025-0113
Keywords for this article
sustainable concrete material; strength, environmental, and cost parameters; eggshell and date palm ash
Creative Commons
BY 4.0

Articles in the same Issue

  1. Review Articles
  2. Utilization of steel slag in concrete: A review on durability and microstructure analysis
  3. Technical development of modified emulsion asphalt: A review on the preparation, performance, and applications
  4. Recent developments in ultrasonic welding of similar and dissimilar joints of carbon fiber reinforcement thermoplastics with and without interlayer: A state-of-the-art review
  5. Unveiling the crucial factors and coating mitigation of solid particle erosion in steam turbine blade failures: A review
  6. From magnesium oxide, magnesium oxide concrete to magnesium oxide concrete dams
  7. Properties and potential applications of polymer composites containing secondary fillers
  8. A scientometric review on the utilization of copper slag as a substitute constituent of ordinary Portland cement concrete
  9. Advancement of additive manufacturing technology in the development of personalized in vivo and in vitro prosthetic implants
  10. Recent advance of MOFs in Fenton-like reaction
  11. A review of defect formation, detection, and effect on mechanical properties of three-dimensional braided composites
  12. Non-conventional approaches to producing biochars for environmental and energy applications
  13. Review of the development and application of aluminum alloys in the nuclear industry
  14. Advances in the development and characterization of combustible cartridge cases and propellants: Preparation, performance, and future prospects
  15. Recent trends in rubberized and non-rubberized ultra-high performance geopolymer concrete for sustainable construction: A review
  16. Cement-based materials for radiative cooling: Potential, material and structural design, and future prospects
  17. A comprehensive review: The impact of recycling polypropylene fiber on lightweight concrete performance
  18. Research Articles
  19. Investigation of the corrosion performance of HVOF-sprayed WC-CoCr coatings applied on offshore hydraulic equipment
  20. A systematic review of metakaolin-based alkali-activated and geopolymer concrete: A step toward green concrete
  21. Evaluation of color matching of three single-shade composites employing simulated 3D printed cavities with different thicknesses using CIELAB and CIEDE2000 color difference formulae
  22. Novel approaches in prediction of tensile strain capacity of engineered cementitious composites using interpretable approaches
  23. Effect of TiB2 particles on the compressive, hardness, and water absorption responses of Kulkual fiber-reinforced epoxy composites
  24. Analyzing the compressive strength, eco-strength, and cost–strength ratio of agro-waste-derived concrete using advanced machine learning methods
  25. Tensile behavior evaluation of two-stage concrete using an innovative model optimization approach
  26. Tailoring the mechanical and degradation properties of 3DP PLA/PCL scaffolds for biomedical applications
  27. Optimizing compressive strength prediction in glass powder-modified concrete: A comprehensive study on silicon dioxide and calcium oxide influence across varied sample dimensions and strength ranges
  28. Experimental study on solid particle erosion of protective aircraft coatings at different impact angles
  29. Compatibility between polyurea resin modifier and asphalt binder based on segregation and rheological parameters
  30. Fe-containing nominal wollastonite (CaSiO3)–Na2O glass-ceramic: Characterization and biocompatibility
  31. Relevance of pore network connectivity in tannin-derived carbons for rapid detection of BTEX traces in indoor air
  32. A life cycle and environmental impact analysis of sustainable concrete incorporating date palm ash and eggshell powder as supplementary cementitious materials
  33. Eco-friendly utilisation of agricultural waste: Assessing mixture performance and physical properties of asphalt modified with peanut husk ash using response surface methodology
  34. Benefits and limitations of N2 addition with Ar as shielding gas on microstructure change and their effect on hardness and corrosion resistance of duplex stainless steel weldments
  35. Effect of selective laser sintering processing parameters on the mechanical properties of peanut shell powder/polyether sulfone composite
  36. Impact and mechanism of improving the UV aging resistance performance of modified asphalt binder
  37. AI-based prediction for the strength, cost, and sustainability of eggshell and date palm ash-blended concrete
  38. Investigating the sulfonated ZnO–PVA membrane for improved MFC performance
  39. Strontium coupling with sulphur in mouse bone apatites
  40. Transforming waste into value: Advancing sustainable construction materials with treated plastic waste and foundry sand in lightweight foamed concrete for a greener future
  41. Evaluating the use of recycled sawdust in porous foam mortar for improved performance
  42. Improvement and predictive modeling of the mechanical performance of waste fire clay blended concrete
  43. Polyvinyl alcohol/alginate/gelatin hydrogel-based CaSiO3 designed for accelerating wound healing
  44. Research on assembly stress and deformation of thin-walled composite material power cabin fairings
  45. Effect of volcanic pumice powder on the properties of fiber-reinforced cement mortars in aggressive environments
  46. Analyzing the compressive performance of lightweight foamcrete and parameter interdependencies using machine intelligence strategies
  47. Selected materials techniques for evaluation of attributes of sourdough bread with Kombucha SCOBY
  48. Establishing strength prediction models for low-carbon rubberized cementitious mortar using advanced AI tools
  49. Investigating the strength performance of 3D printed fiber-reinforced concrete using applicable predictive models
  50. An eco-friendly synthesis of ZnO nanoparticles with jamun seed extract and their multi-applications
  51. The application of convolutional neural networks, LF-NMR, and texture for microparticle analysis in assessing the quality of fruit powders: Case study – blackcurrant powders
  52. Study of feasibility of using copper mining tailings in mortar production
  53. Shear and flexural performance of reinforced concrete beams with recycled concrete aggregates
  54. Advancing GGBS geopolymer concrete with nano-alumina: A study on strength and durability in aggressive environments
  55. Leveraging waste-based additives and machine learning for sustainable mortar development in construction
  56. Study on the modification effects and mechanisms of organic–inorganic composite anti-aging agents on asphalt across multiple scales
  57. Morphological and microstructural analysis of sustainable concrete with crumb rubber and SCMs
  58. Structural, physical, and luminescence properties of sodium–aluminum–zinc borophosphate glass embedded with Nd3+ ions for optical applications
  59. Special Issue on Recent Advancement in Low-carbon Cement-based Materials - Part II
  60. Investigating the effect of locally available volcanic ash on mechanical and microstructure properties of concrete
  61. Flexural performance evaluation using computational tools for plastic-derived mortar modified with blends of industrial waste powders
  62. Foamed geopolymers as low carbon materials for fire-resistant and lightweight applications in construction: A review
  63. Autogenous shrinkage of cementitious composites incorporating red mud
  64. Special Issue on AI-Driven Advances for Nano-Enhanced Sustainable Construction Materials
  65. Advanced explainable models for strength evaluation of self-compacting concrete modified with supplementary glass and marble powders
  66. Special Issue on Advanced Materials for Energy Storage and Conversion
  67. Innovative optimization of seashell ash-based lightweight foamed concrete: Enhancing physicomechanical properties through ANN-GA hybrid approach
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