Abstract
This study explores the possibilities of a new binding material, i.e., marble cement (MC) made from recycled marble. It will assess how well it performs when mixed with ash from rice husks and fly ash. This research analyzes flexural strength of marble cement mortar (FR-MCM), a mortar that incorporates MC, fly ash, and rice husk ash. A set of machine learning models capable of predicting CS and FS (flexural and compressive strengths) were developed. Gene expression programming (GEP) and multi-expression programming (MEP) are crucial in creating these types of models. Statistics, Taylor’s diagrams, R 2 values, and comparisons of experimental and theoretical results were used to evaluate the models. Stress testing also showed how different input features affected the model’s outputs. The accuracy of all GEP models was shown to fall within the acceptable range (R 2 = 0.952 for CS and R 2 = 0.920 for FS), and all MEP prediction models were determined to be exceptionally accurate (R 2 = 0.970 for CS and R 2 = 0.935 for FS). The statistical testing for error validation also verified that MEP models were more accurate than GEP models. According to sensitivity analysis, curing age and rice husk ash exerted the most significant influence on the prediction of CS and FS, followed by fly ash and MC.
Graphical Abstract

1 Introduction
One to eight percent of the world’s greenhouse gas emissions arise from making regular Portland cement, widely known as OPC, and it is predicted that this figure will rise by 8% by 2050 [1,2], which casts questions on the practicality of achieving the zero-emissions objective. If the OPC sector is serious about reducing its CO2 emissions, it must find less harmful alternatives to OPC [3,4]. On the flip side, marble is a material that is gaining popularity all over the globe. Throughout the globe, people are enthused about the marble that is produced. There are about 300 billion tons of marble in the sphere. The quarrying process involves blasting, which results in the waste of over 50% of the marble that is mined [5,6]. The deficiency of a central system for waste disposal means that the quarries continue to collect trash from all over. Marble comes in huge chunks from quarries and is processed into tiles and other valuable stones. Rough blocks should not be refined and trimmed. The exact proportion varies with each processing method, but 20% of these blocks are finely powdered [7]. Companies usually dump waste in open locations. Drying into a fine powder can cause allergic reactions to the skin, cancer of the lungs, and discomfort in the eye. Sludge increases water contamination [8]. Tiny marble particles on plant shrubberies and stems cause dehydration in older hedges and trees, highlighting a drawback of plant diversity [9,10].
The composition of OPC is 60–65% CaO, 20–25% SiO2, and 4–8% Al2O3, rendering to Neville and Brooks [11]. According to the study, limestone is the primary component of cement due to its calcium oxide content. Limestone and water-soluble Portland cement (WMP) have several molecular components, one of which is the excessive content of CaO [12,13]. Marble cement (MC) was made by blending WMP with a silica-rich substance, like clay, as shown in Figure 1 [14,15]. According to the findings of an X-ray diffraction study that was carried out by Khan et al., MC encompasses 3.7% C3S, 52.51% C2S, and 23.11% free lime in its phase chemistries. Low amounts of C3S and high concentrations of C2S and CaO resulted from slow cooling. The MC pellets were gently brushed by the chilly wind. C3S reverted to C2S and CaO at around 1,100°C after that. C3S that is produced at high temperatures is retained by quickly cooling the cement clinkers during the OPC manufacturing process [16]. The decreased water demand and lack of slaking, which results in a greater concentration of free lime in MC, were the reasons for the shorter setting time of the cement when compared to OPC. Increases in the concentration of free lime are accompanied by an increase in the OPC. The immense internal pressure produced by cement grids accelerates the degradation of mortar and concrete mixed with them. As the permitted lime concentration increases, the compressive strength (CS) of cement generally decreases due to the high amount of ground-up calcium hydroxide (Ca(OH)2) [17].
![Figure 1
Process for producing MC [15].](/document/doi/10.1515/rams-2024-0049/asset/graphic/j_rams-2024-0049_fig_001.jpg)
Process for producing MC [15].
In order to increase the ingestion of free lime content, researchers suggested using pozzolanic materials as a partial substitute for MC. For a wide range of waste by-products, researchers are currently investigating pozzolanic applications [18,19,20]. Thermal coal power plants utilize coal powder as their fuel. As a result of the combustion process, fly ash (F) and bottom ash are produced. Minuscule particles of fly ash are carried in automobile emissions. By incorporating precipitators prior to the chimney, it may be extracted from the exhaust gases. Prior to the exhaust gases entering the chimney, the precipitators filter out any fly ash [21,22]. Globally, rice is also grown. “Rice husk” refers to the brittle outer covering that shields each rice grain [23]. This trash turns to ash after being burned in a controlled environment. The pozzolanic properties of rice husk ash (R) are particularly noteworthy due to the finely powdered nature of the ash [24].
Research on cement-based materials (CBMs) has been extensive due to the significance of their mechanical characteristics [25]. The flexural strength (FS) and CS of CBM offer valuable insights into its properties. These characteristics are inherently linked to a wide array of mechanical and durability properties of the mortar [26,27]. To reduce unnecessary testing, analysts are developing analytical models to determine the material strength. It is common practice to use best-fit curves and other conventional models to reproduce material properties found by regression analysis. However, conventional regression algorithms could incorrectly presume the material’s intrinsic behavior because CBMs are nonlinear [28]. The application of artificial intelligence (AI), i.e., machine learning (ML), has led to the advancement of more complex models in this domain [29,30,31,32,33]. These models must be experimentally validated for accuracy before they can produce trustworthy predictions based on input features. More and more ML algorithms are being used to forecast CBM characteristics [34,35,36].
This research utilized ML techniques, particularly multi-expression programming (MEP) and gene expression programming (GEP) to forecast the CS and FS of marble cement mortar (FR-MCM) incorporating rice husk ash and fly ash. This prediction is based on data from studies that have already been published. Statistical tests, the distribution of anticipated outcomes, and the R 2 coefficient were among the metrics used to gauge the enactment of ML algorithms. The main intent of this research was to assess the predictive capabilities of ML methods for material properties. Exploratory experiments or database analysis could provide the data needed for ML algorithms. Machine learning algorithms may be able to learn more about material properties by examining these data. Using experimental data and four input parameters, this study assessed the capability of ML approaches to forecast the FS and CS of FR-MCM. Raw material relevance was further investigated using sensitivity analysis. One possible use for the newly acquired characteristics and ML models is to aid in the creation of CBM blends or to add to the existing database for environmentally friendly materials.
2 Methods of study
2.1 Data gathering and analysis
Using a dataset from prior research [15] and applying MEP and GEP methodologies, this study intended to approximate the FS and CS of FS-MCM. The estimation of the FS and CS of FR-MCM was conducted using four input parameters: MC, fly ash (F), curing age (A), and rice husk ash (R). The images of the lab work conducted are shown in Figure 2. Initially comprising 84 data points, the dataset was expanded to 500 points. The executed Python code adhered to a specific process for adding new data points to the dataset. The script begins by launching a Tkinter-powered file dialog box for users to select a database file. Once imported into a Pandas DataFrame, the script verifies the present number of data points. A new file is then created to store the merged dataset, which includes both the synthetic data and the original DataFrame. The script makes statements that clarify the issue as the data are being enhanced. In these declarations, one can find details like how many data points were added, how many data points were synthesized, and where the stored file was located. In addition, the script accounts for cases where resampling is required or when no file is selected. Data gathering and categorization were aided by data preparation. The widely recognized task of discovering fresh insights from available data frequently faces a notable challenge. A common strategy to surmount this hurdle is the preparation of data for data mining. Data preparation is cleaning data of any extraneous or noisy information. The model analysis made use of statistical approaches such as error dispersion and regression. The models’ efficacy and reliability were also evaluated. Histograms in Figure 3(a)–(f) depict the frequency distribution of values, offering a visualization of the overall dataset frequency distribution by integrating all components’ distributions. The distribution of the collection’s value can be better understood with the use of a relative frequency distribution.
![Figure 2
Images of specimens for CS and FS within molds, dried, and during testing [15].](/document/doi/10.1515/rams-2024-0049/asset/graphic/j_rams-2024-0049_fig_002.jpg)
Images of specimens for CS and FS within molds, dried, and during testing [15].

Frequency distribution plots illustrating the database's input and output characteristics: (a) MC, (b) fly ash, (c) rice husk ash, (d) age, (e) CS, and (f) FS.
Using Pearson’s correlation coefficient (r) is a typical approach to discovering parameter dependencies [37]. The results of the distinctive association map plot are shown in Figure 4. When looking to prove multicollinearity or parameter dependency, the R 2 test is a good tool to utilize [38]. The r-value can take values between −1 and +1; 0 indicates no connection, while +1 indicates a significant positive relationship [39]. The bottom row of Pearson’s array displays the association between the independent variables and the dependent variables, in this case, CS and FS. Multicollinearity is an important point to make about ML algorithms [40]. In order to prevent multicollinearity issues, ML models must ensure that no two variables have a correlation coefficient (r-value) greater than 0.8 [41]. As can be observed in Figure 4, the r-value falls inside the acceptable range. Therefore, multicollinearity in correlational models is highly unlikely.

Parameter correlation heat map.
2.2 ML modeling
The CS and FS of FR-MCM were tested in a supervised environment. Four inputs were used to generate the results (CS and FS). More advanced ML methods, like MEP and GEP, were used to predict the CS and FS of FR-MCM. When evaluating ML algorithms, it is a common practice to compare the results with the input data. The ML models were trained using 70% of the dataset, while the remaining 30% was held aside for testing. A high R 2 score for the expected outcome indicates that the model is correct. R 2 is low for a large fluctuation, indicating that the anticipated and actual values differ by a small amount [42]. The correctness of the model can be confirmed through various methods, including statistical analysis and error assessments. An illustration of a scenario model is depicted in Figure 5. All of the GEP and MEP model hyperparameter parameters are included in Table 1.

A comprehensive overview of the study’s method.
Hyperparameters for GEP and MEP models (parameters comparable to the study of Amin et al. [43])
| GEP | MEP | ||
|---|---|---|---|
| Parameters | Settings | Parameters | Settings |
| Stumbling mutation | 0.00141 | Code length | 40 |
| Chromosomes | 200 | Number of generations | 250 |
| Leaf mutation | 0.00546 | Number of runs | 15 |
| Random chromosomes | 0.0026 | Replication number | 15 |
| Data type | Floating number | Cross over probability | 0.9 |
| General | CS, FS | Mutation probability | 0.01 |
| Constant per gene | 10 | Number of generations | 500 |
| Linking function | Addition | Number of treads | 2 |
| Lower bound | −10 | Error | MSE, MAE |
| Upper bound | 10 | Operators/variables | 0.5 |
| Mutation rate | 0.00138 | Number of sub-populations | 50 |
| Genes | 4 | Sub-population size | 100 |
| Inversion rate | 0.00546 | Terminal set | Problem input |
| One-point recombination rate | 0.00277 | Function set | +, −, x, ÷, square root |
| IS transposition rate | 0.00546 | Problem type | Regression |
| Gene recombination rate | 0.00277 | ||
| Function set | +, −, x, ÷, square root | ||
| RIS transposition rate | 0.00546 | ||
| Gene transposition rate | 0.00277 | ||
| Two-point recombination rate | 0.00277 | ||
2.2.1 GEP model
J. H. Holland’s genetic algorithm (GA) is primarily founded on Darwin’s theory of evolution [44]. The chromosomal endpoint is defined by an ordered succession of GAs and contains chromosomes of a particular length. Koza came up with the phrase “gene programming” to describe one novel GA approach [45]. An evolutionary model is generated via generalized problem-solving (GP) using GAs [46]. The adaptation ability of GP is derived from its capacity to replace binary strings of fixed length with nonlinear structures like parse trees. According to Darwin’s theory, present AI programs deal with reproduction-related problems by using genetic components that occur naturally, such as procreation, crossover phenomenon, and modification [47]. With GP, wasteful programs are systematically removed from successive iterations. Just like in the previous example, removing the undesired trees is an integral part of replanting the region using the selected method. However, evolution safeguards early convergence [47,48]. Five key considerations must be settled upon before the GP approach can be put into action. Priorities by area, fitness evaluation, key functional operators (including crossovers and populace capacity), and approach-surgical incision results [47]. The majority of the parse trees were created by an integrated genomic processor, even though GP develops models frequently [48]. As a result of the fact that they must function as both genotype and phenotype, nonlinear GP forms provide expressions that are difficult to understand for desired features [48].
First proposed by Ferreira, GEP is an adaptation of GP that he developed [48]. The GEP model follows the notion of population formation and uses static-length linear chromosomes to build parse trees. Although GEP is an enhanced variant of GP, GP still employs medium-sized program development using simple chromosomes of a specific length. Among GEP’s several advantages is its high-reliability prediction capabilities for complex and nonlinear problems [49,50]. As with GP, this one has a fitness function, an end set, and specified termination criteria. The “Karva” dialect really recognizes chromosomes before they are formed, even if the GEP process produces them with seemingly random numbers. GEP is fundamentally based on a constant-length linear structure. Conversely, in GP’s data processing algorithm, parse trees of varying lengths are observable. Chromosomes with a constant length are the original name for these unique cords. Thus, dynamic manifestation/parse trees with prong morphologies of varied sizes are used to represent chromosomes [47]. Several phenol strains and genotypes have unique genetic codes [48]. GEP eliminates costly structural alterations and duplications by preserving the genome.
Normally, a chromosome will have two halves that complement each other, called the “head” and the “tail” sections. Interestingly, this can occur when a single chromosome produces many genes [47]. These genes include the instructions for performing Boolean operations, as well as mathematical reasoning and numeracy. Programmers provide genetic coding cells with specialized functions. Inferring these chromosomes’ contents using the new language Karva can establish the framework for empirical formulations. The journey starts in Karva on the ET, which is followed by a leading revolution. Rendering to Eq. (1), ET places the connected nodes in the sublayer [49]. The amount of ETs dictates two parameters: the duration and intensity of GEP gene K expression:
The independence of GEP’s results from pre-existing relationships highlights its advanced nature as an ML technique. The development of a GEP mathematical equation involves several stages, as illustrated in Figure 6. An individual’s chromosomal count remains constant at birth. After verifying these chromosomes as expression trees (ETs), a comprehensive evaluation of each individual’s fitness is performed. The most accomplished individuals undergo an iterative method to refine and achieve the optimal solution, granting reproductive rights to the fittest and strongest individuals. Ultimately, breeding, mutation, and crossover yield the final numerical expression.
![Figure 6
Methodology of the GEP flowchart [43].](/document/doi/10.1515/rams-2024-0049/asset/graphic/j_rams-2024-0049_fig_006.jpg)
Methodology of the GEP flowchart [43].
2.2.2 MEP model
There is a cutting-edge, linear-based genetic programming technology known as MEP. This technique relies on linear chromosomes. As far as their core software is concerned, GEP and MEP are completely interchangeable. A number of software components (substitutes) may be encoded into an individual’s genome using MEP, in contrast to its forerunner, the GP method. The desired result is achieved by selecting the most advantageous chromosomes through fitness evaluation [40,51]. Rendering to Grosan and Oltean [52], this hypothetical scenario occurs after a bipolar arrangement re-establishes itself, resulting in two successive generations adopting one parent as their own. Until the condition for termination is satisfied or the best program is identified, the process keeps running, as shown in Figure 7. Modifications in infants take place during this process. Similar to the GEP model, the MEP paradigm enables the combination of numerous components. Key considerations in MEP include algorithm or code length, number of subpopulations, number of functions, and the potential for crossover [53]. When there are as many bundles as there are people in a population, evaluation and management get quite complicated and time-consuming. Code length has a significant impact on the number of mathematical expressions. MEP parameters required to construct a solid model of mechanical properties are shown in Table 1.
![Figure 7
Process flow diagram for MEP operation [43].](/document/doi/10.1515/rams-2024-0049/asset/graphic/j_rams-2024-0049_fig_007.jpg)
Process flow diagram for MEP operation [43].
In both the assessment and simulation phases, both methods extensively utilize literature datasets [54,55]. There is evidence suggesting that established linear GP methods like GEP and MEP excel in estimating the attributes of ecological mortar and concrete. Grosan and Abraham asserted that a fusion of linear genomic programming and maximal entropy programming (METP) represents the utmost active neural network-based method [56]. The mode of operation utilized by the GEP is slightly more complicated than that utilized by the MEP [53]. Despite MEP’s lower density in comparison to GEP, several notable distinctions exist: (i) MEP explicitly encodes references to function arguments; (ii) there is no necessity for non-coding sections to be positioned at a fixed point within the genetic factor; and (iii) MEP permits code reprocessing [57]. Further thorough evaluations of these genetic approaches to engineering challenges are, hence, absolutely needed. Signals at the “head” and “tail” of the GEP chromosome facilitate the creation of syntactically correct software programs, leading many to believe it is more capable [52]. Therefore, comprehensive evaluations of these genomic engineering methods are essential.
2.3 Model’s validation
A test set was utilized to conduct a statistical analysis of the MEP and GEP models. From the literature [55,58,59,60,61], seven numerical measures were figured for every one of the models: Pearson’s correlation coefficient (R), relative root mean square error (RRMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), relative squared error (RSE), root mean square error (RMSE), and mean absolute percentage error (MAPE). Numerous statistical measures can be calculated using the following formulas (Eqs (2)–(8)):
In a data set with
Two of the most useful ways to evaluate a model’s predictive power are the Taylor diagram and statistical validation. This statistic helps show which models are more accurate and dependable by showing how far they are from the truth, which serves as a benchmark [68,69]. Determining the best model placement requires the integration of three essential metrics: the standard deviation, represented on the model’s horizontal and vertical axes; the correlation coefficient, shown by radial lines; and the RMSE, depicted as concentric circles centered around the point of the true value. In prediction tasks, the most reliable model is identified by its highest accuracy rate [68].
3 Results and interpretation
3.1 GEP models
3.1.1 CS-GEP model
Using mathematical conclusions based on genomic number and head dimensions, the GEP technique (as shown in Figure 8(a)–(d)) created models that calculated the CS using ETs. Most sub-ETs in predicting FR-MCM’s CS utilized fundamental arithmetic operations such as dot product, multiplication, subtraction, addition, and square root. Deciphering these sub-ETs through the GEP approach yields equations. By inputting data into Eq. (9), future CS values of FR-MCM can be predicted. The resulting model outperforms an ideal model under perfect conditions when sufficient data are available. As demonstrated in Figure 9(a), the continuous line signifies a seamless fit to the data, whereas broken lines indicate variations of up to 20% from this line, visually demonstrating the arrangement between trial and estimated CS findings. Predicted CS values from the GEP model closely matched measured values, indicating its effectiveness. An R 2 of 0.952 and a CS prediction inside the 20% threshold 96% of the time indicate that the model achieved significantly improved accuracy. Figure 9(b) plots the absolute error compared to trial data, showing how the GEP model aligns with experimental results. The predictions showed minimal deviation, with an absolute error ranging from 0.00 to 3.477 MPa and an average error of 1.01 MPa. Additionally, Figure 10 illustrates that the distribution of error values closely resembles that of a bell-shaped curve. The pressure measurements ranged from 54 (<0.5 MPa) to 75 (>1.0 MPa). The range from 37 to 54 was between 0.5 and 1.0 MPa. It is important to note that maximal error frequencies occur very seldom:
where MC represents the marble cement, A represents the curing age, R represents the rice husk ash, F represents the fly ash, and CS represents the compressive strength.

Illustration of the CS-GEP model’s ET: (a) sub-ET 1, (b) sub-ET 2, (c) sub-ET 3, and (d) sub-ET 4.

GEP model for CS-FR-MCM: (a) trial-projected CS correlation and (b) trial-projected CS error spread.

Violin diagram for CS-GEP error dispersion.
3.1.2 FS-GEP model
Figure 11(a)–(d) illustrates how the GEP method utilizes arithmetical associations based on genomic number and head dimension to construct ET-based models for FS. In FR-MCM’s FS forecasts, the majority of sub-ETs are constructed using basic arithmetic operations (÷, ×, −, +, and square root). Deciphering these sub-ETs through the GEP method yields arithmetic formulas. By inputting data into Eq. (10), the future FS of FR-MCM can be estimated. Predicted FS values from the GEP model closely matched the measured values, highlighting its effectiveness. The model achieved an R 2 of 0.920 and predicted FS inside the 20% limits 97% of the time, representing significantly improved exactness. Figure 12(b), which plots the absolute error versus the experimental data, shows the GEP model. The absolute error range for the test findings and the predictions provided by the GEP equation was 0.001–0.476 MPa, with an average of 0.207 MPa. A bell-curve distribution was observed for the error value (Figure 13). Overall, 45 values were more than 0.3 MPa, 70 values were in the range of 0.1–0.3 MPa, and 51 values were lower than 0.1 MPa. Note that maximal error frequencies are extremely rare occurrences:

Illustration of the FS-GEP model’s ET: (a) sub-ET 1, (b) sub-ET 2, (c) sub-ET 3, and (d) sub-ET 4.

GEP model for FS-FR-MCM: (a) correlation between trial and projected FS and (b) error spread between trial and projected FS.

Violin plot for FS-GEP error dispersion.
where MC represents marble cement, A represents curing age, R represents rice husk ash, F represents fly ash, and CS represents compressive strength.
3.2 MEP models
3.2.1 CS-MEP model
To ascertain the CS of FR-MCM, an empirical formula was derived based on MEP findings that incorporate the effects of the four primary constituents. The final set of formulated equations is presented in Eq. (11):
where MC represents the marble cement, A represents the curing age, R represents the rice husk ash, F represents the fly ash, and CS represents the compressive strength.
Figure 14(a) illustrates that the MEP model exhibits robustness and is well-trained, as indicated by its high R 2 value of 0.971. To top it all off, it works fine with new, untested data. The R 2 value of the CS-MEP model is higher than that of the CS-GEP model, indicating that the former is more accurate. Figure 14(a) displays a line that is perfectly in line with the data, which is the solid black line, and dotted lines that are off by as much as 20%. With very similar predicted and observed values of CS, the MEP model was able to accurately predict the CS of FR-MCM. The MEP method successfully detected CS, with 100% of its predictions falling inside the 20% cutoff, showing remarkable precision. The results of comparing the target and actual values in the MEP simulations are shown in Figure 14(b). The data indicate that MEP estimate error margins ranged from 0.016 to 2.806 MPa, with an average of 0.841 MPa. To be more specific, 59 errors were less than 0.5 MPa, 47 were in the range of 0.5–1 MPa, and 73 were higher than 1 MPa. The MEP model is superior to the GEP model in predicting values that are deemed outliers. The MEP model decreases error correlation and standard deviation, as shown in Figure 15’s violin figure. Due to its generalizability and ease of use, the MEP equation is a popular tool. With fewer mistakes and a greater correlation coefficient, the MEP model beats the GEP model.

MEP model for CS-FR-MCM: (a) correlation between trial and projected CS and (b) error spread between trial and projected CS.

An error distribution violin plot for CS-MEP models.
3.2.2 FS-MEP model
An empirical formula was developed based on MEP findings to predict the FS of FR-MCM and incorporate the effects of the four primary constituents. The final set of formulated equations is presented in Eq. (12):
where MC represents the marble cement, A represents the curing age, R represents the rice husk ash, F represents the fly ash, and CS represents the compressive strength. Figure 16(a) demonstrates a well-trained MEP model with an R 2 value of 0.935, indicating its capability to handle complexity effectively. With a higher R 2 value, the FS-MEP model also proves to be more accurate than the FS-GEP model. The predicted values of FS are closely aligned with the measured values, highlighting the MEP model’s efficiency in predicting the FS of FR-MCM. The MEP method achieved remarkable accuracy in predicting FS, which was consistently inside the 20% benchmark. Figure 16(b) compares the target and actual values calculated in MEP simulations. The results showed that 0.001–0.419 MPa were the values that made up the MEP forecasts, with a standard deviation of 0.172 MPa. Specifically, 56 errors occurred at pressures below 0.1 MPa, 71 at pressures between 0.1 and 0.3 MPa, and 39 at pressures over 0.3 MPa. The MEP model outperformed the other in terms of predicting outlier values. The MEP model reduced the standard deviation of errors, as shown in the violin plot in Figure 17. The MEP equation has received a lot of praise for being both simple and widely used. It is evident that the MEP model works better than the GEP model due to its greater R 2 and reduced error levels.

MEP model for FS-FR-MCM: (a) correlation between trial and projected FS and (b) error spread between trial and projected FS.

FS-MEP error dispersion violin plot.
3.3 Model’s validation
Table 2 presents the results of efficacy and inaccuracy metrics (R, RSE, RMSE, NSE, MAE, and RRMSE) derived from calculations using Eqs (2)–(8). A lower error score indicates that the produced models are more accurate in their predictions. The performance metrics of the GEP and MEP models for predicting the properties of FR-MCM highlight notable differences. The FS-GEP model achieved an MAE of 0.207 MPa, while the CS-GEP model recorded a higher MAE of 1.011 MPa, with corresponding RMSE values of 7.10 and 6.50%, respectively. In contrast, the MEP models demonstrated improved accuracy, with the FS-MEP model achieving a lower MAE of 0.172 MPa and the CS-MEP model showing an MAE of 0.841 MPa. These results indicate that the MEP approach consistently outperformed the GEP method in both flexural and CS predictions for FR-MCM. However, the RMSE values of the CS-MEP and FS-MEP models were significantly reduced to 5.70 and 5.90%, respectively. There was a surprising similarity between the CS and FS models, as demonstrated by additional error-based statistical metrics. These metrics encompassed RSE, RMSE, and relative root-squared error (RRMSE). Alongside error-based validation, two measures, namely NSE and Pearson’s coefficient (R), were employed to assess the effectiveness of the constructed models. If a model can become more efficient, it indicates that it can make more accurate predictions. With respect to the CS-GEP model, the NSE value was 0.948, whereas that of the FS-GEP model was 0917. Nevertheless, these values considerably increased to 0.969 and 0.929, respectively, in the CS-MEP and FS-MEP models. When examining the generated CS and FS models using Pearson’s coefficient (R), the outcomes were comparable. Figure 18(a) and (b) illustrates the Taylor diagram comparing all the different prediction models. MEP models exhibit notably higher accuracy compared to GEP models in calculating the CS and FS of FR-MCM, which holds across the various types of models. Previous research has established that MEP models are the most accurate ML-based analysis technique for forecasting the CS and FS of FR-MCM. Their R 2 values are the highest, their error rates are the lowest, their efficiency is the highest, and their standard deviation is the lowest.
Results of statistical analysis
| Property | CS model | FS model | ||
|---|---|---|---|---|
| GEP | MEP | GEP | MEP | |
| MAE (MPa) | 1.011 | 0.841 | 0.207 | 0.172 |
| MAPE (%) | 6.50 | 5.70 | 7.10 | 5.90 |
| RMSE (MPa) | 1.305 | 0.987 | 0.244 | 0.210 |
| R | 0.976 | 0.985 | 0.960 | 0.967 |
| RSE (MPa) | 0.284 | 0.244 | 0.266 | 0.248 |
| NSE | 0.948 | 0.969 | 0.917 | 0.929 |
| RRMSE (MPa) | 0.602 | 0.322 | 0.548 | 0.372 |

Taylor diagrams: (a) CS-models and (b) FS-models.
3.4 Sensitivity analysis
Examining how various input parameters impact CS and FS prediction for FR-MCM is the primary objective of this research. The predicted outcomes are highly associated with the input variables [70]. Figure 19 illustrates the impression of various variables on the CS and FS of FR-MCM, offering insights into the long-term development of mortar and construction materials. The extrapolation of CS for FR-MCM was most influenced by a curing age of 86%, followed by 2.0% fly ash, 4% MC, and 8% rice husk ash. Similarly, for FS prediction, the curing age (A) had the greatest impact at 80%, followed by fly ash at 5.0%, MC at 3.0%, and rice husk ash at 12.0%. The outcomes were proportional to the number of model parameters and data points utilized in the sensitivity analyses. It was discovered that varied input parameters, including the amounts of mortar mix used while applying the ML approach, had distinct effects on the analytical outcomes. By comparing the values of the data input features in Eqs (13) and (14) their relative significance was determined.
where

Radar plot for the sensitivity analysis.
4 Discussion
The findings of this research are specific to FR-MCM because the GEP and MEP models employed are tailored to handle values within a defined range of four input parameters. The accuracy of CS and FS projections is ensured by the use of consistent unit measurements and testing procedures across all models. MEP achieves higher accuracy than GEP due to its linear representation of multiple expressions within a single chromosome, which simplifies the evolutionary process. MEP’s efficient genetic operations and ability to simultaneously evaluate multiple solutions enhance its optimization capabilities and predictive performance, leading to more accurate outcomes. For the most part, the models can only understand the mix’s design and the impact of each input component by consulting mathematical formulas. All four inputs to the composite analysis, when used in any combination, will make the predicted models meaningless. Incorrect pairing with the training data could cause these models to fail to perform as anticipated. Inconsistent or out-of-date units of the input parameters put the models in danger of under or over-predicting the results. Consistently maintaining the unit sizes is crucial for the models to perform successfully. Improvements in energy efficiency, risk assessment, quality control, predictive maintenance, and material strength prediction are just a few of the many construction-related uses for ML models. These models must, however, conquer certain challenges. One potential pitfall is relying on human input, which might lead to erroneous outcomes due to human error. Possible directions for future study include incorporating IoT gadgets, creating hybrid models, making sustainability a top priority, using explainable AI techniques, and tailoring data collection and delivery to certain businesses. These strategies could significantly enhance ML-based solutions and address existing limitations. These efforts aim to enhance ML-based solutions and address current limitations effectively. Emerging technology has the potential to radically alter the construction industry by facilitating more efficient, transparent, and interpretable processes and better-informed decision-making. These enhancements have the potential to promote more sustainable practices, lessen project delays, and increase safety precautions. The results of this study have the potential to promote the use of more sustainable building practices and materials in the future.
5 Conclusions
This work aims to assess and predict the FS and CS of marble cement mortar (FR-MCM) that contains fly ash and rice husk ash using GEP and MEP. Using 500 CS and FS data sets from lab studies, the models were built, tested, and validated. A summary of the main points from the study is as follows:
The research showed that compared to other GEP models, MEP models had the best data prediction accuracy. The most effective model, MEP, achieved an R 2 value of 0.971 for the mechanical properties of FR-MCM.
The efficiency and predictability of the created models were confirmed by statistical testing; the MEP models were determined to be the most accurate in estimating the mechanical properties of FR-MCM.
MEP models had a lower standard deviation compared to GEP models, indicating that the MEP approach was more precise according to Taylor’s diagram evaluation. Specifically, for CS prediction, the standard deviation for MEP models was 5.80 compared to 5.94 for GEP models, and for FS prediction, the standard deviation for MEP models was 0.865 compared to 0.868 for GEP models.
The sensitivity study revealed that curing age was the most important input parameter positively correlated with FR-MCM’s mechanical properties.
The unique mathematical methodologies offered by GEP and MEP are essential for predicting features in other databases. Engineers and scientists leverage the mathematical models derived from this study to optimize, improve, and evaluate mortar mixture proportions effectively. These models serve to refine and enhance the formulation process, ensuring optimal performance and reliability in construction applications.
Acknowledgments
This work was supported by the Henan Province Science and Technology Research Project (No. 242102321100) and the National Natural Science Foundation of China (No. 41877251). The authors acknowledge the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia (Grant No. KFU241384). The authors extend their appreciation for the financial support that made this study possible.
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Funding information: This research was funded by Henan Province Science and Technology Research Project (No. 242102321100); the National Natural Science Foundation of China (No. 41877251) and the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia (Grant No. KFU241384).
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Author contributions: H.S.: conceptualization, data acquisition, methodology, visualization, and writing – original draft. D.S.: supervision, resources, formal analysis, validation, writing, reviewing, and editing. M.N.A.: funding acquisition, investigation, supervision, project administration, writing, reviewing, and editing. S.U.A.: software, methodology, data acquisition, formal analysis, and writing – original draft. M.T.Q.: visualization, project administration, conceptualization, writing, reviewing, and editing. K.K.: validation, resources, writing, reviewing, and editing. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Data availability statement: The datasets generated and/or analyzed during the current study are available as supplementary materials to this article.
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- Effect of fly ash on properties and hydration of calcium sulphoaluminate cement-based materials with high water content
- Analyzing the efficacy of waste marble and glass powder for the compressive strength of self-compacting concrete using machine learning strategies
- Experimental study on municipal solid waste incineration ash micro-powder as concrete admixture
- Parameter optimization for ultrasonic-assisted grinding of γ-TiAl intermetallics: A gray relational analysis approach with surface integrity evaluation
- Producing sustainable binding materials using marble waste blended with fly ash and rice husk ash for building materials
- Effect of steam curing system on compressive strength of recycled aggregate concrete
- A sawtooth constitutive model describing strain hardening and multiple cracking of ECC under uniaxial tension
- Predicting mechanical properties of sustainable green concrete using novel machine learning: Stacking and gene expression programming
- Toward sustainability: Integrating experimental study and data-driven modeling for eco-friendly paver blocks containing plastic waste
- A numerical analysis of the rotational flow of a hybrid nanofluid past a unidirectional extending surface with velocity and thermal slip conditions
- A magnetohydrodynamic flow of a water-based hybrid nanofluid past a convectively heated rotating disk surface: A passive control of nanoparticles
- Prediction of flexural strength of concrete with eggshell and glass powders: Advanced cutting-edge approach for sustainable materials
- Efficacy of sustainable cementitious materials on concrete porosity for enhancing the durability of building materials
- Phase and microstructural characterization of swat soapstone (Mg3Si4O10(OH)2)
- Effect of waste crab shell powder on matrix asphalt
- Improving effect and mechanism on service performance of asphalt binder modified by PW polymer
- Influence of pH on the synthesis of carbon spheres and the application of carbon sphere-based solid catalysts in esterification
- Experimenting the compressive performance of low-carbon alkali-activated materials using advanced modeling techniques
- Thermogravimetric (TG/DTG) characterization of cold-pressed oil blends and Saccharomyces cerevisiae-based microcapsules obtained with them
- Investigation of temperature effect on thermo-mechanical property of carbon fiber/PEEK composites
- Computational approaches for structural analysis of wood specimens
- Integrated structure–function design of 3D-printed porous polydimethylsiloxane for superhydrophobic engineering
- Exploring the impact of seashell powder and nano-silica on ultra-high-performance self-curing concrete: Insights into mechanical strength, durability, and high-temperature resilience
- Axial compression damage constitutive model and damage characteristics of fly ash/silica fume modified magnesium phosphate cement after being treated at different temperatures
- Integrating testing and modeling methods to examine the feasibility of blended waste materials for the compressive strength of rubberized mortar
- Special Issue on 3D and 4D Printing of Advanced Functional Materials - Part II
- Energy absorption of gradient triply periodic minimal surface structure manufactured by stereolithography
- Marine polymers in tissue bioprinting: Current achievements and challenges
- Quick insight into the dynamic dimensions of 4D printing in polymeric composite mechanics
- Recent advances in 4D printing of hydrogels
- Mechanically sustainable and primary recycled thermo-responsive ABS–PLA polymer composites for 4D printing applications: Fabrication and studies
- Special Issue on Materials and Technologies for Low-carbon Biomass Processing and Upgrading
- Low-carbon embodied alkali-activated materials for sustainable construction: A comparative study of single and ensemble learners
- Study on bending performance of prefabricated glulam-cross laminated timber composite floor
- Special Issue on Recent Advancement in Low-carbon Cement-based Materials - Part I
- Supplementary cementitious materials-based concrete porosity estimation using modeling approaches: A comparative study of GEP and MEP
- Modeling the strength parameters of agro waste-derived geopolymer concrete using advanced machine intelligence techniques
- Promoting the sustainable construction: A scientometric review on the utilization of waste glass in concrete
- Incorporating geranium plant waste into ultra-high performance concrete prepared with crumb rubber as fine aggregate in the presence of polypropylene fibers
- Investigation of nano-basic oxygen furnace slag and nano-banded iron formation on properties of high-performance geopolymer concrete
- Effect of incorporating ultrafine palm oil fuel ash on the resistance to corrosion of steel bars embedded in high-strength green concrete
- Influence of nanomaterials on properties and durability of ultra-high-performance geopolymer concrete
- Influence of palm oil ash and palm oil clinker on the properties of lightweight concrete
Artikel in diesem Heft
- Review Articles
- Effect of superplasticizer in geopolymer and alkali-activated cement mortar/concrete: A review
- Experimenting the influence of corncob ash on the mechanical strength of slag-based geopolymer concrete
- Powder metallurgy processing of high entropy alloys: Bibliometric analysis and systematic review
- Exploring the potential of agricultural waste as an additive in ultra-high-performance concrete for sustainable construction: A comprehensive review
- A review on partial substitution of nanosilica in concrete
- Foam concrete for lightweight construction applications: A comprehensive review of the research development and material characteristics
- Modification of PEEK for implants: Strategies to improve mechanical, antibacterial, and osteogenic properties
- Interfacing the IoT in composite manufacturing: An overview
- Advances in processing and ablation properties of carbon fiber reinforced ultra-high temperature ceramic composites
- Advancing auxetic materials: Emerging development and innovative applications
- Revolutionizing energy harvesting: A comprehensive review of thermoelectric devices
- Exploring polyetheretherketone in dental implants and abutments: A focus on biomechanics and finite element methods
- Smart technologies and textiles and their potential use and application in the care and support of elderly individuals: A systematic review
- Reinforcement mechanisms and current research status of silicon carbide whisker-reinforced composites: A comprehensive review
- Innovative eco-friendly bio-composites: A comprehensive review of the fabrication, characterization, and applications
- Review on geopolymer concrete incorporating Alccofine-1203
- Advancements in surface treatments for aluminum alloys in sports equipment
- Ionic liquid-modified carbon-based fillers and their polymer composites – A Raman spectroscopy analysis
- Emerging boron nitride nanosheets: A review on synthesis, corrosion resistance coatings, and their impacts on the environment and health
- Mechanism, models, and influence of heterogeneous factors of the microarc oxidation process: A comprehensive review
- Synthesizing sustainable construction paradigms: A comprehensive review and bibliometric analysis of granite waste powder utilization and moisture correction in concrete
- 10.1515/rams-2025-0086
- Research Articles
- Coverage and reliability improvement of copper metallization layer in through hole at BGA area during load board manufacture
- Study on dynamic response of cushion layer-reinforced concrete slab under rockfall impact based on smoothed particle hydrodynamics and finite-element method coupling
- Study on the mechanical properties and microstructure of recycled brick aggregate concrete with waste fiber
- Multiscale characterization of the UV aging resistance and mechanism of light stabilizer-modified asphalt
- Characterization of sandwich materials – Nomex-Aramid carbon fiber performances under mechanical loadings: Nonlinear FE and convergence studies
- Effect of grain boundary segregation and oxygen vacancy annihilation on aging resistance of cobalt oxide-doped 3Y-TZP ceramics for biomedical applications
- Mechanical damage mechanism investigation on CFRP strengthened recycled red brick concrete
- Finite element analysis of deterioration of axial compression behavior of corroded steel-reinforced concrete middle-length columns
- Grinding force model for ultrasonic assisted grinding of γ-TiAl intermetallic compounds and experimental validation
- Enhancement of hardness and wear strength of pure Cu and Cu–TiO2 composites via a friction stir process while maintaining electrical resistivity
- Effect of sand–precursor ratio on mechanical properties and durability of geopolymer mortar with manufactured sand
- Research on the strength prediction for pervious concrete based on design porosity and water-to-cement ratio
- Development of a new damping ratio prediction model for recycled aggregate concrete: Incorporating modified admixtures and carbonation effects
- Exploring the viability of AI-aided genetic algorithms in estimating the crack repair rate of self-healing concrete
- Modification of methacrylate bone cement with eugenol – A new material with antibacterial properties
- Numerical investigations on constitutive model parameters of HRB400 and HTRB600 steel bars based on tensile and fatigue tests
- Research progress on Fe3+-activated near-infrared phosphor
- Discrete element simulation study on effects of grain preferred orientation on micro-cracking and macro-mechanical behavior of crystalline rocks
- Ultrasonic resonance evaluation method for deep interfacial debonding defects of multilayer adhesive bonded materials
- Effect of impurity components in titanium gypsum on the setting time and mechanical properties of gypsum-slag cementitious materials
- Bending energy absorption performance of composite fender piles with different winding angles
- Theoretical study of the effect of orientations and fibre volume on the thermal insulation capability of reinforced polymer composites
- Synthesis and characterization of a novel ternary magnetic composite for the enhanced adsorption capacity to remove organic dyes
- Couple effects of multi-impact damage and CAI capability on NCF composites
- Mechanical testing and engineering applicability analysis of SAP concrete used in buffer layer design for tunnels in active fault zones
- Investigating the rheological characteristics of alkali-activated concrete using contemporary artificial intelligence approaches
- Integrating micro- and nanowaste glass with waste foundry sand in ultra-high-performance concrete to enhance material performance and sustainability
- Effect of water immersion on shear strength of epoxy adhesive filled with graphene nanoplatelets
- Impact of carbon content on the phase structure and mechanical properties of TiBCN coatings via direct current magnetron sputtering
- Investigating the anti-aging properties of asphalt modified with polyphosphoric acid and tire pyrolysis oil
- Biomedical and therapeutic potential of marine-derived Pseudomonas sp. strain AHG22 exopolysaccharide: A novel bioactive microbial metabolite
- Effect of basalt fiber length on the behavior of natural hydraulic lime-based mortars
- Optimizing the performance of TPCB/SCA composite-modified asphalt using improved response surface methodology
- Compressive strength of waste-derived cementitious composites using machine learning
- Melting phenomenon of thermally stratified MHD Powell–Eyring nanofluid with variable porosity past a stretching Riga plate
- Development and characterization of a coaxial strain-sensing cable integrated steel strand for wide-range stress monitoring
- Compressive and tensile strength estimation of sustainable geopolymer concrete using contemporary boosting ensemble techniques
- Customized 3D printed porous titanium scaffolds with nanotubes loading antibacterial drugs for bone tissue engineering
- Facile design of PTFE-kaolin-based ternary nanocomposite as a hydrophobic and high corrosion-barrier coating
- Effects of C and heat treatment on microstructure, mechanical, and tribo-corrosion properties of VAlTiMoSi high-entropy alloy coating
- Study on the damage mechanism and evolution model of preloaded sandstone subjected to freezing–thawing action based on the NMR technology
- Promoting low carbon construction using alkali-activated materials: A modeling study for strength prediction and feature interaction
- Entropy generation analysis of MHD convection flow of hybrid nanofluid in a wavy enclosure with heat generation and thermal radiation
- Friction stir welding of dissimilar Al–Mg alloys for aerospace applications: Prospects and future potential
- Fe nanoparticle-functionalized ordered mesoporous carbon with tailored mesostructures and their applications in magnetic removal of Ag(i)
- Study on physical and mechanical properties of complex-phase conductive fiber cementitious materials
- Evaluating the strength loss and the effectiveness of glass and eggshell powder for cement mortar under acidic conditions
- Effect of fly ash on properties and hydration of calcium sulphoaluminate cement-based materials with high water content
- Analyzing the efficacy of waste marble and glass powder for the compressive strength of self-compacting concrete using machine learning strategies
- Experimental study on municipal solid waste incineration ash micro-powder as concrete admixture
- Parameter optimization for ultrasonic-assisted grinding of γ-TiAl intermetallics: A gray relational analysis approach with surface integrity evaluation
- Producing sustainable binding materials using marble waste blended with fly ash and rice husk ash for building materials
- Effect of steam curing system on compressive strength of recycled aggregate concrete
- A sawtooth constitutive model describing strain hardening and multiple cracking of ECC under uniaxial tension
- Predicting mechanical properties of sustainable green concrete using novel machine learning: Stacking and gene expression programming
- Toward sustainability: Integrating experimental study and data-driven modeling for eco-friendly paver blocks containing plastic waste
- A numerical analysis of the rotational flow of a hybrid nanofluid past a unidirectional extending surface with velocity and thermal slip conditions
- A magnetohydrodynamic flow of a water-based hybrid nanofluid past a convectively heated rotating disk surface: A passive control of nanoparticles
- Prediction of flexural strength of concrete with eggshell and glass powders: Advanced cutting-edge approach for sustainable materials
- Efficacy of sustainable cementitious materials on concrete porosity for enhancing the durability of building materials
- Phase and microstructural characterization of swat soapstone (Mg3Si4O10(OH)2)
- Effect of waste crab shell powder on matrix asphalt
- Improving effect and mechanism on service performance of asphalt binder modified by PW polymer
- Influence of pH on the synthesis of carbon spheres and the application of carbon sphere-based solid catalysts in esterification
- Experimenting the compressive performance of low-carbon alkali-activated materials using advanced modeling techniques
- Thermogravimetric (TG/DTG) characterization of cold-pressed oil blends and Saccharomyces cerevisiae-based microcapsules obtained with them
- Investigation of temperature effect on thermo-mechanical property of carbon fiber/PEEK composites
- Computational approaches for structural analysis of wood specimens
- Integrated structure–function design of 3D-printed porous polydimethylsiloxane for superhydrophobic engineering
- Exploring the impact of seashell powder and nano-silica on ultra-high-performance self-curing concrete: Insights into mechanical strength, durability, and high-temperature resilience
- Axial compression damage constitutive model and damage characteristics of fly ash/silica fume modified magnesium phosphate cement after being treated at different temperatures
- Integrating testing and modeling methods to examine the feasibility of blended waste materials for the compressive strength of rubberized mortar
- Special Issue on 3D and 4D Printing of Advanced Functional Materials - Part II
- Energy absorption of gradient triply periodic minimal surface structure manufactured by stereolithography
- Marine polymers in tissue bioprinting: Current achievements and challenges
- Quick insight into the dynamic dimensions of 4D printing in polymeric composite mechanics
- Recent advances in 4D printing of hydrogels
- Mechanically sustainable and primary recycled thermo-responsive ABS–PLA polymer composites for 4D printing applications: Fabrication and studies
- Special Issue on Materials and Technologies for Low-carbon Biomass Processing and Upgrading
- Low-carbon embodied alkali-activated materials for sustainable construction: A comparative study of single and ensemble learners
- Study on bending performance of prefabricated glulam-cross laminated timber composite floor
- Special Issue on Recent Advancement in Low-carbon Cement-based Materials - Part I
- Supplementary cementitious materials-based concrete porosity estimation using modeling approaches: A comparative study of GEP and MEP
- Modeling the strength parameters of agro waste-derived geopolymer concrete using advanced machine intelligence techniques
- Promoting the sustainable construction: A scientometric review on the utilization of waste glass in concrete
- Incorporating geranium plant waste into ultra-high performance concrete prepared with crumb rubber as fine aggregate in the presence of polypropylene fibers
- Investigation of nano-basic oxygen furnace slag and nano-banded iron formation on properties of high-performance geopolymer concrete
- Effect of incorporating ultrafine palm oil fuel ash on the resistance to corrosion of steel bars embedded in high-strength green concrete
- Influence of nanomaterials on properties and durability of ultra-high-performance geopolymer concrete
- Influence of palm oil ash and palm oil clinker on the properties of lightweight concrete