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Compressive strength of waste-derived cementitious composites using machine learning

  • Qiong Tian , Yijun Lu , Ji Zhou EMAIL logo , Shutong Song , Liming Yang , Tao Cheng EMAIL logo and Jiandong Huang EMAIL logo
Published/Copyright: May 15, 2024
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REVIEWS ON ADVANCED MATERIALS SCIENCE
From the journal REVIEWS ON ADVANCED MATERIALS SCIENCE Volume 63 Issue 1

Abstract

Marble cement (MC) is a new binding material for concrete, and the strength assessment of the resulting materials is the subject of this investigation. MC was tested in combination with rice husk ash (RHA) and fly ash (FA) to uncover its full potential. Machine learning (ML) algorithms can help with the formulation of better MC-based concrete. ML models that could predict the compressive strength (CS) of MC-based concrete that contained FA and RHA were built. Gene expression programming (GEP) and multi-expression programming (MEP) were used to build these models. Additionally, models were evaluated by calculating R 2 values, carrying out statistical tests, creating Taylor’s diagram, and comparing theoretical and experimental readings. When comparing the MEP and GEP models, MEP yielded a slightly better-fitted model and better prediction performance (R 2 = 0.96, mean absolute error = 0.646, root mean square error = 0.900, and Nash–Sutcliffe efficiency = 0.960). According to the sensitivity analysis, the prediction of CS was most affected by curing age and MC content, then by FA and RHA contents. Incorporating waste materials such as marble powder, RHA, and FA into building materials can help reduce environmental impacts and encourage sustainable development.

Keywords: marble cement; gene expression programming; multi-expression programming

1 Introduction

The production of ordinary Portland cement (OPC) accounts for around 5–8% of the world’s CO₂ emissions, and current predictions indicate that this percentage will increase by 8% by the year 2050 [1,2], which raises doubts about the feasibility of reaching the zero-emission target set out by the Paris Agreement. It is critical to identify less damaging alternatives to OPC to decrease CO2 emissions from the OPC industry. Conversely, marble has become an increasingly popular material around the world. About half of the marble that is mined is wasted due to blasting processes employed in quarrying [3,4]. Because no proper method of disposal is in place, waste is still dispersed throughout the quarries. Tiles and other valuable stones are created from marble, which is transported in massive blocks from quarries to processing facilities. It is wasteful to trim and refine raw blocks. Around 20% of these blocks are reduced to fine powder, while the exact percentage varies by processing method [5]. Typically, open spaces surrounding factories are used for depositing the slurry. As the mixture dries into a fine powder, it poses health risks, including skin irritation, lung cancer, and eye pain. Adding sludge to water also makes it more polluted [6,7]. One negative aspect of plant diversity is the drying out of older trees and hedges caused by small marble atoms on shrub and vegetative leaves [8,9,10].

OPC contains 60–65% CaO, 20–25% SiO2, and 4–8% Al2O3, as stated by Neville and Brooks [11]. The majority of the calcium oxide used to make cement comes from limestone, as the researcher has already mentioned repeatedly. Limestone and waste marble powder (WMP) have several molecular components, including a high CaO content [12,13]. Therefore, Khan et al. [14] created a binding material such as marble cement (MC) using WMP and a silica-rich substance such as clay, as depicted in Figure 1. The phases that make up MC were determined to be 3.7% C3S, 23.11% free lime, and 52.51% C2S, as reported by Khan et al. in an X-ray diffraction study [14]. Sluggish cooling led to low C3S concentrations and high C2S and CaO concentrations. The cold air was softly blown over the MC pallets. Then, at about 1,100°C, C3S changed back into C2S and CaO. By rapidly cooling the cement clinkers during OPC manufacture, the C3S that is generated at high temperatures is preserved [15]. The shorter setting time compared to OPC was attributed to the increased free lime content in MC, which allowed the cement to avoid slaking (the formation of Ca(OH)2) and use less water. The OPC increases as the concentration of free lime rises. The enormous pressure that develops within the cement matrix causes mortar and concrete made with this cement to deteriorate with time. Due to the pulverization of a considerable amount of Ca(OH)2, the compressive strength (CS) of cement falls as the allowed lime level increases [16,17,18].

Figure 1 Production of MC [19].
Figure 1

Production of MC [19].

As a partial substitute for MC, researchers suggested using pozzolanic materials to boost the consumption of free lime content. Various pozzolanic applications are now being explored for a variety of waste byproducts [20,21]. Powdered coal is the fuel used in thermal coal power units. Bottom ash and fly ash (FA) are the byproducts of burning it. Emissions from vehicles carry FA in its microscopic particle form. Precipitators are put in place before the chimney to extract it from the exhaust gases. Precipitators remove FA from exhaust gases before entering the chimney [22,23]. Worldwide, rice is also cultivated. “Rice husk” describes the hard outside layer that protects individual grains of rice [24]. After being burned at a controlled temperature, this waste material becomes ash. The pozzolanic properties of rice husk ash (RHA), a byproduct of finely powdered ash, are unparalleled [25].

The importance of CS has led to substantial study of cement-based materials (CBMs) [26,27,28,29]. Important information on the CBM’s characteristics may be found in its CS [30,31]. Many mechanical and durability characteristics are related to the concrete’s CS in some way [32,33,34]. By creating analytical models for material strength, analysts are aiming to reduce unnecessary testing and associated expenses. To replicate the material properties, which are obtained by regression analysis, a plethora of conventional models, including best-fit curves, are used. Traditional regression techniques may mistakenly assume the material’s intrinsic behavior when dealing with CBMs because of their non-linear nature [35,36,37]. The use of artificial intelligence (AI) methods, particularly supervised machine learning (ML), is propelling the development of more sophisticated models in this area [38,39,40]. In order to generate reliable predictions, these models rely on input features and undergo experimental verification of their accuracy. The application of ML algorithms to predict CBM properties is on the rise [41,42,43,44].

This work aimed to forecast the CS of FA and RHA-based MC concrete (FR-MCC) using ML algorithms, specifically multi-expression programming (MEP) and gene expression programming (GEP). This forecast is based on information found in previously published works. Several measures were used to assess the efficacy of ML procedures, such as the R 2 coefficient, statistical tests, and the dispersion of expected results. Investigating the efficacy of ML techniques in reliably projecting material attributes was the driving force behind this study. An exploratory experiment or an analysis of existing databases can yield the dataset that is required by ML methods [45,46]. By examining this information, ML algorithms may gain a more accurate understanding of the material’s qualities. By combining experimental data with four input parameters, ML methods’ ability to predict the CS of FR-MCC was assessed [47,48]. Through the application of sensitivity analysis, additional exploration into the relevance of raw materials was conducted [49,50]. The newly gathered features and developed ML models could be used to improve the current sustainable materials database or to guide the formulation of CBM blends, among other potential applications.

2 Methods of research

2.1 Collecting and analyzing data

Using MEP and GEP techniques, this research analyzed a dataset comprising 500 data points from an experimental inquiry with the purpose of forecasting the CS of FR-MCC [51]. With an initial set of 84 data points amplified to 500 points, this study predicted the CS of FR-MCC using four input parameters: MC, FA, RHA, and curing age (CA). The Python code that was executed followed a certain protocol for expanding the dataset’s data points. First, it opens a file dialog box built on Tkinter so the user can choose a database file. The selection of the file is then followed by its import into a Pandas DataFrame, and the script checks the current point count. A new file is generated that contains the dataset that is the end result of merging the synthetic data with the original DataFrame. As the data are being supplemented, the script provides illuminating statements. Among the information included in these declarations are the total number of data points added, the amount of synthetic data points, and the precise location of the saved file. Furthermore, the script takes into consideration situations when either no file is chosen or resampling is necessary. With the aid of data preparation, the data were collected and organized. One popular approach to data preparation is to use it as a cushion to get past a major problem with the well-known process of getting new insights out of old data. Eliminating extraneous information and background noise from data is what data preparation is all about. The model analysis made use of regression and error-distribution approaches. Table 1 displays the outcomes of multiple descriptive statistics that were calculated using this dataset. In addition, validation was used to assess the efficacy of the models that were used. Histograms show the distribution of frequencies for different values in Figure 2(a)–(e). As a whole, the dataset’s frequency distribution can be described by combining its constituent components’ distributions. One technique to gain insight into the dataset is to construct a relative frequency distribution. This will show you how common certain values are and how often they appear.

Table 1

Data variable statistical descriptions

Statistical parameters MC (kg·m−3) FA (kg·m−3) RHA (kg·m−3) Age (days) CS (MPa)
Mean 241.48 45.62 40.90 170.32 14.38
Standard error 1.83 2.35 2.30 5.68 0.20
Median 230.00 0.00 0.00 136.50 14.70
Mode 230.00 0.00 0.00 91.00 20.05
Standard deviation 40.83 52.63 51.35 126.93 4.50
Sample variance 1667.24 2769.81 2636.97 16110.58 20.24
Kurtosis −0.05 −1.44 −1.25 −1.18 −1.06
Skewness 0.84 0.49 0.65 0.56 −0.31
Range 131.00 131.00 131.00 336.00 16.19
Minimum 197.00 0.00 0.00 28.00 5.81
Maximum 328.00 131.00 131.00 364.00 22.00
Sum 120738.00 22811.00 20451.00 85162.00 7190.66
Count 500.00 500.00 500.00 500.00 500.00
Figure 2 Frequency distribution of the input and output features of the database: (a) MC, (b) FA, (c) RHA, (d) Age, and (e) CS.
Figure 2

Frequency distribution of the input and output features of the database: (a) MC, (b) FA, (c) RHA, (d) Age, and (e) CS.

Overfitting occurs frequently in the field of mathematical dataset simulation [30,52]. This happens when a model does a good job of reproducing the input data during training and development but fails miserably when faced with input parameters that are different from both sets. While the model does a great job of mimicking the known dataset, it can produce wildly inaccurate results when asked to predict values for non-standard input parameters [53,54]. The authors used regularization (L1 and L2) and other strategies to punish complexity and discourage overemphasis on specific features in order to minimize overfitting in the constructed model. To evaluate the model on new data, the dataset was split into two parts: training and validation. In order to protect the training data from fitting noise, early stopping was instituted by keeping an eye on validation performance and ending training if there was no progress. All of these steps added up to a generalizable model that can handle new, unknown data with ease and without overfitting [55,56].

2.2 ML algorithm application

A highly controlled setting was used to test the CS of FR-MCC. In order to obtain the outcome (CS), four inputs were required. Using advanced ML methods such as GEP and MEP, predictions were made for the CS of FR-MCC. It is usual practice to evaluate outcomes by feeding them into ML algorithms. A total of 70% of the data were used to train the ML models, while 30% were set aside for testing. As a measure of the model’s effectiveness, the R 2 score of the predicted outcomes quantified the degree to which the actual values differed from the expected ones; a smaller R 2 number indicates a larger discrepancy [36,57,58]. Statistical testing and error evaluations are two of the methods used to verify the model’s accuracy [59,60]. While the hyperparameters for both the GEP and MEP models are presented in Table 2, Figure 3 gives a simple representation of a scenario model.

Table 2

Predefined model factors for MEP and GEP (parameters similar to [61])

MEP GEP
Parameters Settings Parameters Settings
Number of generations 250 Stumbling mutation 0.00141
Problem type Regression Constant per gene 10
Terminal set Problem input Inversion rate 0.00546
Replication number 15 Head size 8
Operators/variables 0.5 Data type Floating number
Number of treads 2 Two-point recombination rate 0.00277
Number of generations 500 Chromosomes 200
Mutation probability 0.01 Linking function Addition
Error MSE, MAE Lower bound −10
Cross-over probability 0.9 Upper bound 10
Number of subpopulations 50 Mutation rate 0.00138
Subpopulation size 100 Genes 4
Number of runs 15 Leaf mutation 0.00546
Function set +, −, ×, ÷, square root General CS
Code length 40 IS transposition rate 0.00546
RIS transposition rate 0.00546
One-point recombination rate 0.00277
Function set +, −, ×, ÷, square root
Gene recombination rate 0.00277
Gene transposition rate 0.00277
Random chromosomes 0.0026
Figure 3 Comprehensive overview of the studied method.
Figure 3

Comprehensive overview of the studied method.

2.2.1 GEP model

Taking cues from Darwin’s idea of evolution, Holland created the genetic algorithm (GA) [62]. The genomic process, which is defined by the order of GAs, is followed by the observation of chromosomes of persistent length. One unique GA approach is that Koza coined the term “gene programming” [63,64]. Generalized problem-solving (GP) uses GAs to generate an evolutionary model [65]. The ability to substitute non-linear structures, such as parse trees, for binary strings of fixed length gives GP its flexibility. By leveraging naturally occurring genetic components, including reproduction, crossover, and alteration, AI software tackles reproductive difficulties, drawing inspiration from Darwin’s theory [66]. By progressively removing inefficient programs from succeeding iterations, GP aims to achieve its purpose. Similar to the previous example, cleaning the area by removing trees that do not match properly is an important part of implementing the chosen plan. Nevertheless, early convergence is protected by the evolutionary process [66,67]. It is necessary to specify five critical factors before using the GP approach. Among these, you may find the following: a list of mandatory domain tasks, an assessment of fitness, a list of primary functional operators (including population size and crossover), and the establishment of outcomes according to the method-specific criteria [66]. Although GP incorporates recurrent model building, a crossover genetic processor is mostly responsible for parse tree formation [48]. The need for non-linear GP forms to serve as both genotype and phenotype has resulted in the development of intricate expressions that stand in for desirable features [67].

GEP is a variation on GP that Ferreira initially proposed [67]. The GEP model incorporates static-length-lined chromosomes into parse trees in accordance with the population-generation theory. GP employs simple, fixed-length chromosomes to encrypt medium-sized software; GEP is an improved version of that. The ability to predict complicated and non-linear issues with high reliability is one of GEP’s many benefits [68,69]. The fitness function, the last set, and the conditions for termination are defined in the same way as in GP. Chromosomes are generated at random by the GEP technique; however, they are designated as such before they are produced using the “Karva” dialectal. GEP relies on a fixed-length line as its fundamental basis. On the other hand, GP’s code processing of data displays parse trees of varying lengths. Initially, these unique cords are described as genomes of static length. Subsequently, they stand in for chromosomes by means of non-linear manifestation/parse trees that have pronged morphologies varying in size [66]. These genotypes and the small number of phenol strains each have their own unique genetic code [67]. The necessity for expensive structural changes or duplications is eradicated by GEP’s capacity to maintain the genome from one generation to another.

In a typical chromosome, the “head” and the “tail” are the two complementary regions. Surprisingly, this phenomenon can occur when multiple genes are produced by a single chromosome [66]. Logic, mathematics, arithmetic, and Boolean operations are encoded in these genes. A programmer assigns specific functions to cells in the genetic code. Karva, a novel language, can decipher the contents of these chromosomes and use that information to build empirical formulas. A basic revolution marks the beginning of the trip on the Expression Tree (ET), which starts at Karva. According to Eq. (1), ET arranges the nodes in the underlying layer [68]. In terms of both amount and duration, the total number of ETs can affect GEP gene K-expression:

(1) ET GEP = log i − 3 j .

The fact that GEP’s findings are not dependent on any previous relationships makes it a sophisticated ML method. A GEP mathematical equation goes through a number of steps, as seen in Figure 4. There is no change to a person’s chromosomal count at delivery. Upon confirmation that these chromosomes are ETs, a thorough assessment of the health of every individual can be conducted. Reproductive privileges are bestowed upon the healthiest and strongest individuals. The best solution is found by taking the most skilled people through an iterative process. Reproduction, alteration, and overlap are the three generations of genetic processes that have resulted in the ultimate numerical expression once they have been applied.

Figure 4 GEP procedure’s method flowchart [61].
Figure 4

GEP procedure’s method flowchart [61].

2.2.2 MEP model

Due to its reliance on linear chromosomes, the MEP represents a state-of-the-art, model linear-based GP technique. In terms of their core software, the GEP and MEP are very similar to one another. MEP’s capacity to encode numerous software components (substitutes) into a sole chromosome sets it apart from its predecessor, the GP method. Using fitness analysis to choose the optimal chromosome yields the desired result [70,71]. According to Oltean and Grosan, this happens when a bipolar system recombines to form two new offspring, with each offspring choosing one parent [72]. Figure 5 demonstrates that the process will keep running until the termination condition is met or until the best program is found. Mutations in newborns happen here. A number of components can be combined using the MEP model, much as with the GEP model. Criteria that are important in MEP include the number of functions, the number of subpopulations, the length of the algorithm or code, and the possibility of crossover [73]. Assessing and accounting for a population when its size equals the total number of packages is a time-consuming and complex process. Mathematical expression sizes are heavily impacted by the code length. The amount of MEP parameters needed to build a trustworthy model of rheological properties is shown in Table 2.

Figure 5 Process flow diagram for MEP operation [61].
Figure 5

Process flow diagram for MEP operation [61].

Both approaches rely heavily on literature datasets during the modeling and evaluation stages [74,75]. Famous linear GP approaches such as the GEP and the MEP are superior at predicting the properties of ecological concrete, according to certain studies. According to Grosan and Abraham, the optimal neural network-based strategy was a hybrid of lined genomic programming and maximum entropy programming (MEP) [76]. The GEP’s method of operation is marginally more intricate than that of the MEP [73]. Notwithstanding MEP’s lower density compared to GEP [77], there are a few key differences: (i) MEP explicitly encodes function argument references, (ii) non-coding units are not required to be presented at a set point in the genes, and (iii) MEP allows code reprocess. It is commonly believed that the GEP chromosome has greater competence due to the signs found at its “head” and “tail” that facilitate the writing of syntactically accurate software programs [72]. Therefore, additional comprehensive assessments of these genomic strategies for engineering problems are urgently required.

2.3 Validation of models

A test set was used to statistically test the models that were created using GEP and MEP. Using equations from previous studies [75,78–81], seven arithmetical measures were computed for each of the models: relative root mean square error (RRMSE), mean root mean square error (RMSE), mean absolute error (MAE), relative squared error (RSE), Nash–Sutcliffe efficiency (NSE), Pearson’s correlation coefficient (R), and mean absolute percentage error (MAPE). Eqs. (2)–(8) provide the formulas for several statistical measurements:

(2) R = ∑ i = 1 n ( a i − a ¯ i ) ( p i − p i ¯ ) ∑ i = 1 n ( a i − a i ¯ ) 2 ∑ i = 1 n ( p i − p ¯ i ) 2 ,

(3) MAE = 1 n ∑ i = 1 n | a i − p i | ,

(4) RMSE = ∑ ( a i − p i ) 2 n ,

(5) MAPE = 100 % n ∑ i = 1 n | a i − p i | p i ,

(6) RSE = ∑ i = 1 n ( a i − p i ) 2 ∑ i = 1 n ( a ¯ − a i ) 2 ,

(7) NSE = 1 − ∑ i = 1 n ( a i − p i ) 2 ∑ i = 1 n ( a i − p i ¯ ) 2 ,

(8) RRMSE = 1 | a ¯ | ∑ 1 = 1 n ( a i − p i ) 2 n .

“R” is a useful metric for assessing the model’s predictive capability, where “ n ” stands for the overall count of data points, “ a i ” and “ p i ” denote the ith tangible and projected values, and “ a i ̅ ” and “ p i ̅ ” denote the mean tangible and projected values, correspondingly. A strong correlation between expected and actual production volumes is indicated by a high value of R [10,82,83]. No matter how you divide or multiply, the component R will stay the same. The R 2 statistic, which provides a more accurate estimation of the actual value, was computed between the actual results and the expected outcomes. When R 2 values are close to 1, it indicates that the process of developing the model is quite successful [84,85]. Just as MAE and RMSE showed great improvement with progressively larger mistakes, the proposed model shows even greater performance with smaller errors, and both approach zero with larger errors [86,87]. However, upon closer inspection, it became apparent that continuous and smooth databases are where MAE truly excels [88,89]. When the computed error numbers are reduced, it is generally believed that the model is performing effectively:

(9) a 20 - index = m 20 M .

This takes into consideration an expected or experimental value between 0.80 and 1.20, where M is the number of specimens in the dataset and m 20 is the number of entries, as provided in Eq. (9) [90]. The optimal a20-index values, according to the prediction model, would be 1%. The proposed 20-index offers the advantage of a physical engineering approach, revealing the percentage of samples that correspond to expected values within a ±20% uncertainty range of experimental data.

The Taylor diagram, in conjunction with statistical validation, is one of the most useful tools for evaluating the predictive power of a model. In order to determine which models are more credible and accurate, this figure plots their divergence from the truth, which serves as the reference point [91,92]. Three metrics can be used in order to ascertain the optimal location for a model. These metrics are the standard deviation, which is depicted by the axis, the correlation coefficient, which is represented by the radial lines, and the RMSE, which is represented by the circular lines that are centered at the actual value point. The most reliable model is the one that has the best track record of accurately predicting outcomes [91,93].

3 Results and analysis

3.1 CS-GEP models

Figure 6(a)–(d) shows how the GEP technique predicts FR-MCC’s CS using ET models based on chromosomal number and head size data. The ÷, ×, −, +, and square root mathematical operations are used to create most CS sub-ETs in FR-MCC. The output is a mathematical formula once the sub-ETs have been encrypted. The equations that are produced as a result of these models (Eqs. (10)–(14)) can be used to make predictions regarding the future CS of FR-MCC by making use of the presented input values. Under ideal conditions and with sufficient observations, the resulting model performs better than a perfect model would. Figure 7(a) illustrates the use of lines of statistical significance (CS) for the purpose of comparing the predicted values of the model with the values that were observed in the testing set. According to the great degree of agreement between the expected and observed values (R 2 = 0.95), the GEP approach is effective in estimating the CS of FR-MCC. Figure 7(b) shows the absolute error plotted against experimental data to show that there can be a difference between the GEP model and actual outcomes. The fact that the absolute errors range from 0.001 to 3.040 MPa shows that the experimental data agree well with the predictions made by the GEP equation. An average of 0.792 MPa is the inaccuracy. Figure 8 shows that the error values follow a bell-shaped distribution, with 49 measurements over 1.0 MPa, 56 readings between 0.5 and 1.0 MPa, and 61 readings below 0.5 MPa. The occurrence of maximal error frequencies is extremely rare:

(10) CS ( MPa ) = A + B + C + D ,

(11) A = ( 3 FA − 2 CA ) ( RHA + MC ) − CA 4.723 ,

(12) B = ( CA + ( RHA − MC ) ) − CA ,

(13) C = RHA ( ( − 11.714 + RHA ) − 9.883 ) + ( − 11.714 − FA ) − RHA ,

(14) D = RHA − 11.364 CA + 1.299 + CA + 4.580 ,

where MC is the marble cement, FA is the fly ash, RHA is the rice husk ash, CA is the curing age, and CS is the compressive strength.

Figure 6 ET schematic for CS-GEP model: (a) sub-ET 1, (b) sub-ET 2, (c) sub-ET 3, (d) sub-ET 4. d0: MC, d1: FA, d2: RHA, and d3: CA.
Figure 6 ET schematic for CS-GEP model: (a) sub-ET 1, (b) sub-ET 2, (c) sub-ET 3, (d) sub-ET 4. d0: MC, d1: FA, d2: RHA, and d3: CA.
Figure 6

ET schematic for CS-GEP model: (a) sub-ET 1, (b) sub-ET 2, (c) sub-ET 3, (d) sub-ET 4. d0: MC, d1: FA, d2: RHA, and d3: CA.

Figure 7 GEP model for CS in FR-MCC: (a) the relationship between tested and predicted CS and (b) the error distribution in tested and predicted CS.
Figure 7

GEP model for CS in FR-MCC: (a) the relationship between tested and predicted CS and (b) the error distribution in tested and predicted CS.

Figure 8 Violin plot for GEP models’ error distribution.
Figure 8

Violin plot for GEP models’ error distribution.

3.2 CS-MEP model

After analyzing the MEP data and taking into account the impact of the four independent components, an empirical method was created to estimate the CS of FR-MCC. The final mathematical model that comes out of this procedure is shown in Eq. (15):

(15) CS ( MPa ) = CA + RHA + CA − MC CA + 2 FA − MC FA + MC + CA + RHA MC ,

where MC is the marble cement, FA is the fly ash, RHA is the rice husk ash, CA is the curing age, and CS is the compressive strength.

Figure 9(a) shows that the MEP model is well trained, capable of handling oversimplification, and performs adequately on novel, untested data, with an R 2 of 0.96. It appears that the CS-MEP model is marginally more accurate than the CS-GEP model, according to its higher R 2 value. Figure 9(b) displays the results of an analysis of absolute differences between the goal and observed values performed in MEP simulations. The presented data show that the error margin for MEP estimations ranged from 0.002 to 3.264 MPa, with an average of 0.647 MPa. With 86 values below 0.5 MPa, 50 values between 0.5 and 1.0 MPa, and 30 values over 1.0 MPa, the mean error values were also below 3.500 MPa. Remember that the MEP model predicts less degree of outcome variability than the GEP model when considering the most extreme values. Both the MEP and GEP models might be incredibly accurate predictors. Implementing the MEP equation leads to a decrease in both the correlation coefficient and the error standard deviations. There has been much use of the MEP equation because of its generalizability and its condensed form. The MEP model appears to be better than the GEP model because it has a higher correlation coefficient and lower error levels (as shown in Figure 10), comparable to earlier research of a similar kind [94,95]. Some researchers have also developed prediction models using different ML techniques for various properties of concrete [96–98].

Figure 9 MEP model for CS in FR-MCC: (a) the relationship between tested and predicted CS and (b) the error distribution in tested and predicted CS.
Figure 9

MEP model for CS in FR-MCC: (a) the relationship between tested and predicted CS and (b) the error distribution in tested and predicted CS.

Figure 10 Violin plot for MEP models’ error distribution.
Figure 10

Violin plot for MEP models’ error distribution.

3.3 Validation of model

Based on the previously described Eqs. (2)–(8), Table 3 displays the results of effectiveness and error computations (RMSE, MAE, R, RSE, NSE, and RRMSE). The created models’ prediction accuracy is higher when their error values are smaller. The CS-GEP model’s MAE values were 0.792 MPa, while the counterpart CS-MEP model’s values were 0.646 MPa, a little reduction. CS-GEP model’s MAPE value of 6.60% was significantly reduced to 4.60% in the corresponding CS-MEP model. Additionally, additional error-based statistical metrics, such as RMSE, RSE, and RRMSE, showed an analogous trend. Additionally, error-based validation was used in order to evaluate the effectiveness of the constructed models. The Pearson’s coefficient (R) and the NSE were the two measures that were used. An increase in a model’s efficiency indicates an improvement in its forecast accuracy. The CS-GEP model had an NSE of 0.953, whereas the matching CS-MEP model had a slightly higher NSE of 0.960. When measured with Pearson’s coefficient (R), the models that were constructed produced findings that were comparable to one another. As can be seen in Figure 11, a Taylor diagram is used to compare all of the different forecasting models. As far as predicting the CS of FR-MCC is concerned, the MEP models are relatively near, whereas the GEP models are relatively far away. The MEP model outperformed other ML-based techniques in predicting the CS of FR-MCC, according to prior study, since it had the lowest standard deviation, highest efficiency, lowest error, and best R 2.

Table 3

Findings gained by statistical examination

Property CS (MPa)
GEP MEP
MAE 0.792 0.646
MAPE 6.50 4.60
RMSE 0.992 0.900
R 0.977 0.980
RSE 0.297 0.229
NSE 0.953 0.960
RRMSE 0.642 0.342
a20-index 0.840 0.940
Figure 11 Taylor diagram for CS models.
Figure 11

Taylor diagram for CS models.

3.4 Sensitivity analysis

The research aims to investigate the effect of different input parameters on CS prediction for FR-MCC. The input factors are strongly correlated with the expected output [99]. Figure 12 shows how each variable affects the CS of FR-MCC, giving us a glimpse into the future of concrete and building materials in general. The highest impact, 65%, on predicting the CS of FR-MCC came from CA, followed by MC (23.0%), RHA (9.0%), and FA (3%). The amount of model parameters and data points used in sensitivity studies was directly related to the results. The results of the analysis were shown to be affected differentially by various input parameters, such as the quantities of concrete mix when the ML technique was applied. The relative importance of the model’s input parameters was determined using Eqs. (16) and (17):

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

(17) S i = N i ∑ j − i n N j ,

where f max ( x i ) represents the highest predicted value across all ith outputs and f min ( x i ) represents the lowest.

Figure 12 Sensitivity analysis radar plot.
Figure 12

Sensitivity analysis radar plot.

4 Discussions

The GEP and MEP models that were used in this investigation ensure that the predictions will be specific to FR-MCC. This is due to the fact that these models are only able to accept values from a limited range of four input parameters. Since all of the models employ the same unit measurements and testing technique, the CS predictions they produce are reliable. These models use mathematical equations to help us better understand mix design and how each input parameter affects it. The projected models might not work well if the composite analysis uses more than the four inputs. Their intended purpose must be well aligned with the inputs used to train these models; otherwise, they might not yield the expected results. If the input parameters’ units are changed or inconsistent, the models could under- or over-predict the outcomes. The models can only work if the unit sizes remain constant. There are numerous applications of ML models in the construction industry, including strength prediction, quality assurance, risk assessment, predictive maintenance, and energy efficiency improvements. Still, there are a few problems with these models. One is that they use human input, which can lead to inaccurate results and inaccurate data. To address these limitations and improve ML-based solutions, future research could look into integrating internet of things devices, creating hybrid models, using explainable AI techniques, considering sustainability, and customizing data generation and distribution for specific industries, among other things. Technological improvements have the potential to revolutionize the construction industry. By enhancing efficiency, interpretability, transparency, and informed decision-making, these advancements could reduce project delays, increase safety, and promote more sustainable practices. The findings of this study may lead to a shift toward greener construction methods and an increase in the usage of long-term, eco-friendly materials.

5 Study limitations and suggestions for future research

Taking four variables into account, this study used a dataset of 500 records to forecast CS. One potential strategy to improve the models’ performance in future research is to add more records from experiments to the dataset. With a larger dataset, the model can make more accurate predictions, which boosts confidence in the results. While GEP and MEP models were used in this study, hybrid ML approaches such as genetic algorithm-particle swarm optimization and random forest-artificial neural network should be investigated in future analyses. In addition, there is hope for enhancing model performance with individual and ensemble techniques, including support vector machine, decision tree, bagging, and boosting. It makes sense to combine these hybrid approaches, and doing so might greatly improve prediction abilities. Even though they were not used in this work, post hoc explanatory techniques such as SHapely Additive exPlanations, local interpretable model-agnostic explanations, and partial dependence plot can provide valuable insights into the ML model’s predictions. Additional information about the interpretability of models can be gleaned from future studies that use similar methods. Much of the current research on using ML to forecast concrete qualities has focused on mechanical considerations. On the other hand, research into important aspects, including concrete microstructure, dynamic properties such as fatigue, and durability, is noticeably inadequate. For a more complex understanding of concrete performance, additional study is needed to use ML approaches to thoroughly investigate these elements affecting durability.

6 Conclusions

The objective of this study was to examine the CS of FR-MCC using MEP and GEP. The models underwent training, testing, and validation using 500 sets of CS data collected from laboratory tests. The following are the key findings that were discovered by the study:

  • To estimate CS for FR-MCC, the GEP method was sufficiently accurate (R 2 = 0.95), but the MEP method was more exact (R 2 = 0.96).

  • For the GEP method, the average discrepancy between the predicted and actual CS (errors) was 0.792 MPa, while for the MEP method, it was 0.647 MPa. With these error rates, it was clear that the MEP technique was better at predicting the CS of FR-MCC than the GEP model.

  • The models’ efficacy has been validated statistically. In contrast to the MEP model’s 4.60% MAPE, the GEP model’s MAPE was 6.50%. The MEP model was more predictable than the GEP model, which had an MAE of 0.792 MPa, with a value of 0.646 MPa.

  • Sensitivity analysis showed that the prediction of CS of FR-MCC was most affected by CA at 65%, followed by MC at 23%, RHA at 9%, and FA at 3%.

What makes GEP and MEP so crucial for feature prediction in other databases is the unique mathematical method they provide. Quickly evaluating, improving, and rationalizing the proportioning of concrete mixtures is possible with the mathematical models that scientists and engineers can apply to this work.

Acknowledgments

The authors gratefully acknowledge the support of the Natural Science Foundation of Hunan and Hunan Provincial Transportation Technology Project.

  1. Funding information: This research was supported by the Natural Science Foundation of Hunan (Grant No. 2023JJ50418) and Hunan Provincial Transportation Technology Project (Grant No. 202109). The authors are grateful for this support.

  2. Author contributions: Q.T.: conceptualization, methodology, formal analysis, writing-original draft. Y.L.: data acquisition, software, methodology, writing, reviewing, and editing. J.Z.: investigation, funding acquisition, supervision, writing, reviewing, and editing. S.S.: formal analysis, resources, methodology, writing, reviewing, and editing. L.Y.: formal analysis, visualization, writing, reviewing, and editing. T.C.: validation, investigation, supervision, writing, reviewing, and editing. J.H.: conceptualization, supervision, project administration, writing, reviewing, and editing. 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 datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2023-12-19
Revised: 2024-02-17
Accepted: 2024-03-11
Published Online: 2024-05-15

© 2024 the author(s), published by De Gruyter

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

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  4. Powder metallurgy processing of high entropy alloys: Bibliometric analysis and systematic review
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  10. Advances in processing and ablation properties of carbon fiber reinforced ultra-high temperature ceramic composites
  11. Advancing auxetic materials: Emerging development and innovative applications
  12. Revolutionizing energy harvesting: A comprehensive review of thermoelectric devices
  13. Exploring polyetheretherketone in dental implants and abutments: A focus on biomechanics and finite element methods
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  34. Enhancement of hardness and wear strength of pure Cu and Cu–TiO2 composites via a friction stir process while maintaining electrical resistivity
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  36. Research on the strength prediction for pervious concrete based on design porosity and water-to-cement ratio
  37. Development of a new damping ratio prediction model for recycled aggregate concrete: Incorporating modified admixtures and carbonation effects
  38. Exploring the viability of AI-aided genetic algorithms in estimating the crack repair rate of self-healing concrete
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  40. Numerical investigations on constitutive model parameters of HRB400 and HTRB600 steel bars based on tensile and fatigue tests
  41. Research progress on Fe3+-activated near-infrared phosphor
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  43. Ultrasonic resonance evaluation method for deep interfacial debonding defects of multilayer adhesive bonded materials
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https://doi.org/10.1515/rams-2024-0008
Keywords for this article
marble cement; gene expression programming; multi-expression programming
Creative Commons
BY 4.0

Articles in the same Issue

  1. Review Articles
  2. Effect of superplasticizer in geopolymer and alkali-activated cement mortar/concrete: A review
  3. Experimenting the influence of corncob ash on the mechanical strength of slag-based geopolymer concrete
  4. Powder metallurgy processing of high entropy alloys: Bibliometric analysis and systematic review
  5. Exploring the potential of agricultural waste as an additive in ultra-high-performance concrete for sustainable construction: A comprehensive review
  6. A review on partial substitution of nanosilica in concrete
  7. Foam concrete for lightweight construction applications: A comprehensive review of the research development and material characteristics
  8. Modification of PEEK for implants: Strategies to improve mechanical, antibacterial, and osteogenic properties
  9. Interfacing the IoT in composite manufacturing: An overview
  10. Advances in processing and ablation properties of carbon fiber reinforced ultra-high temperature ceramic composites
  11. Advancing auxetic materials: Emerging development and innovative applications
  12. Revolutionizing energy harvesting: A comprehensive review of thermoelectric devices
  13. Exploring polyetheretherketone in dental implants and abutments: A focus on biomechanics and finite element methods
  14. Smart technologies and textiles and their potential use and application in the care and support of elderly individuals: A systematic review
  15. Reinforcement mechanisms and current research status of silicon carbide whisker-reinforced composites: A comprehensive review
  16. Innovative eco-friendly bio-composites: A comprehensive review of the fabrication, characterization, and applications
  17. Review on geopolymer concrete incorporating Alccofine-1203
  18. Advancements in surface treatments for aluminum alloys in sports equipment
  19. Ionic liquid-modified carbon-based fillers and their polymer composites – A Raman spectroscopy analysis
  20. Emerging boron nitride nanosheets: A review on synthesis, corrosion resistance coatings, and their impacts on the environment and health
  21. Mechanism, models, and influence of heterogeneous factors of the microarc oxidation process: A comprehensive review
  22. Synthesizing sustainable construction paradigms: A comprehensive review and bibliometric analysis of granite waste powder utilization and moisture correction in concrete
  23. 10.1515/rams-2025-0086
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  26. Study on dynamic response of cushion layer-reinforced concrete slab under rockfall impact based on smoothed particle hydrodynamics and finite-element method coupling
  27. Study on the mechanical properties and microstructure of recycled brick aggregate concrete with waste fiber
  28. Multiscale characterization of the UV aging resistance and mechanism of light stabilizer-modified asphalt
  29. Characterization of sandwich materials – Nomex-Aramid carbon fiber performances under mechanical loadings: Nonlinear FE and convergence studies
  30. Effect of grain boundary segregation and oxygen vacancy annihilation on aging resistance of cobalt oxide-doped 3Y-TZP ceramics for biomedical applications
  31. Mechanical damage mechanism investigation on CFRP strengthened recycled red brick concrete
  32. Finite element analysis of deterioration of axial compression behavior of corroded steel-reinforced concrete middle-length columns
  33. Grinding force model for ultrasonic assisted grinding of γ-TiAl intermetallic compounds and experimental validation
  34. Enhancement of hardness and wear strength of pure Cu and Cu–TiO2 composites via a friction stir process while maintaining electrical resistivity
  35. Effect of sand–precursor ratio on mechanical properties and durability of geopolymer mortar with manufactured sand
  36. Research on the strength prediction for pervious concrete based on design porosity and water-to-cement ratio
  37. Development of a new damping ratio prediction model for recycled aggregate concrete: Incorporating modified admixtures and carbonation effects
  38. Exploring the viability of AI-aided genetic algorithms in estimating the crack repair rate of self-healing concrete
  39. Modification of methacrylate bone cement with eugenol – A new material with antibacterial properties
  40. Numerical investigations on constitutive model parameters of HRB400 and HTRB600 steel bars based on tensile and fatigue tests
  41. Research progress on Fe3+-activated near-infrared phosphor
  42. Discrete element simulation study on effects of grain preferred orientation on micro-cracking and macro-mechanical behavior of crystalline rocks
  43. Ultrasonic resonance evaluation method for deep interfacial debonding defects of multilayer adhesive bonded materials
  44. Effect of impurity components in titanium gypsum on the setting time and mechanical properties of gypsum-slag cementitious materials
  45. Bending energy absorption performance of composite fender piles with different winding angles
  46. Theoretical study of the effect of orientations and fibre volume on the thermal insulation capability of reinforced polymer composites
  47. Synthesis and characterization of a novel ternary magnetic composite for the enhanced adsorption capacity to remove organic dyes
  48. Couple effects of multi-impact damage and CAI capability on NCF composites
  49. Mechanical testing and engineering applicability analysis of SAP concrete used in buffer layer design for tunnels in active fault zones
  50. Investigating the rheological characteristics of alkali-activated concrete using contemporary artificial intelligence approaches
  51. Integrating micro- and nanowaste glass with waste foundry sand in ultra-high-performance concrete to enhance material performance and sustainability
  52. Effect of water immersion on shear strength of epoxy adhesive filled with graphene nanoplatelets
  53. Impact of carbon content on the phase structure and mechanical properties of TiBCN coatings via direct current magnetron sputtering
  54. Investigating the anti-aging properties of asphalt modified with polyphosphoric acid and tire pyrolysis oil
  55. Biomedical and therapeutic potential of marine-derived Pseudomonas sp. strain AHG22 exopolysaccharide: A novel bioactive microbial metabolite
  56. Effect of basalt fiber length on the behavior of natural hydraulic lime-based mortars
  57. Optimizing the performance of TPCB/SCA composite-modified asphalt using improved response surface methodology
  58. Compressive strength of waste-derived cementitious composites using machine learning
  59. Melting phenomenon of thermally stratified MHD Powell–Eyring nanofluid with variable porosity past a stretching Riga plate
  60. Development and characterization of a coaxial strain-sensing cable integrated steel strand for wide-range stress monitoring
  61. Compressive and tensile strength estimation of sustainable geopolymer concrete using contemporary boosting ensemble techniques
  62. Customized 3D printed porous titanium scaffolds with nanotubes loading antibacterial drugs for bone tissue engineering
  63. Facile design of PTFE-kaolin-based ternary nanocomposite as a hydrophobic and high corrosion-barrier coating
  64. Effects of C and heat treatment on microstructure, mechanical, and tribo-corrosion properties of VAlTiMoSi high-entropy alloy coating
  65. Study on the damage mechanism and evolution model of preloaded sandstone subjected to freezing–thawing action based on the NMR technology
  66. Promoting low carbon construction using alkali-activated materials: A modeling study for strength prediction and feature interaction
  67. Entropy generation analysis of MHD convection flow of hybrid nanofluid in a wavy enclosure with heat generation and thermal radiation
  68. Friction stir welding of dissimilar Al–Mg alloys for aerospace applications: Prospects and future potential
  69. Fe nanoparticle-functionalized ordered mesoporous carbon with tailored mesostructures and their applications in magnetic removal of Ag(i)
  70. Study on physical and mechanical properties of complex-phase conductive fiber cementitious materials
  71. Evaluating the strength loss and the effectiveness of glass and eggshell powder for cement mortar under acidic conditions
  72. Effect of fly ash on properties and hydration of calcium sulphoaluminate cement-based materials with high water content
  73. Analyzing the efficacy of waste marble and glass powder for the compressive strength of self-compacting concrete using machine learning strategies
  74. Experimental study on municipal solid waste incineration ash micro-powder as concrete admixture
  75. Parameter optimization for ultrasonic-assisted grinding of γ-TiAl intermetallics: A gray relational analysis approach with surface integrity evaluation
  76. Producing sustainable binding materials using marble waste blended with fly ash and rice husk ash for building materials
  77. Effect of steam curing system on compressive strength of recycled aggregate concrete
  78. A sawtooth constitutive model describing strain hardening and multiple cracking of ECC under uniaxial tension
  79. Predicting mechanical properties of sustainable green concrete using novel machine learning: Stacking and gene expression programming
  80. Toward sustainability: Integrating experimental study and data-driven modeling for eco-friendly paver blocks containing plastic waste
  81. A numerical analysis of the rotational flow of a hybrid nanofluid past a unidirectional extending surface with velocity and thermal slip conditions
  82. A magnetohydrodynamic flow of a water-based hybrid nanofluid past a convectively heated rotating disk surface: A passive control of nanoparticles
  83. Prediction of flexural strength of concrete with eggshell and glass powders: Advanced cutting-edge approach for sustainable materials
  84. Efficacy of sustainable cementitious materials on concrete porosity for enhancing the durability of building materials
  85. Phase and microstructural characterization of swat soapstone (Mg3Si4O10(OH)2)
  86. Effect of waste crab shell powder on matrix asphalt
  87. Improving effect and mechanism on service performance of asphalt binder modified by PW polymer
  88. Influence of pH on the synthesis of carbon spheres and the application of carbon sphere-based solid catalysts in esterification
  89. Experimenting the compressive performance of low-carbon alkali-activated materials using advanced modeling techniques
  90. Thermogravimetric (TG/DTG) characterization of cold-pressed oil blends and Saccharomyces cerevisiae-based microcapsules obtained with them
  91. Investigation of temperature effect on thermo-mechanical property of carbon fiber/PEEK composites
  92. Computational approaches for structural analysis of wood specimens
  93. Integrated structure–function design of 3D-printed porous polydimethylsiloxane for superhydrophobic engineering
  94. 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
  95. Axial compression damage constitutive model and damage characteristics of fly ash/silica fume modified magnesium phosphate cement after being treated at different temperatures
  96. Integrating testing and modeling methods to examine the feasibility of blended waste materials for the compressive strength of rubberized mortar
  97. Special Issue on 3D and 4D Printing of Advanced Functional Materials - Part II
  98. Energy absorption of gradient triply periodic minimal surface structure manufactured by stereolithography
  99. Marine polymers in tissue bioprinting: Current achievements and challenges
  100. Quick insight into the dynamic dimensions of 4D printing in polymeric composite mechanics
  101. Recent advances in 4D printing of hydrogels
  102. Mechanically sustainable and primary recycled thermo-responsive ABS–PLA polymer composites for 4D printing applications: Fabrication and studies
  103. Special Issue on Materials and Technologies for Low-carbon Biomass Processing and Upgrading
  104. Low-carbon embodied alkali-activated materials for sustainable construction: A comparative study of single and ensemble learners
  105. Study on bending performance of prefabricated glulam-cross laminated timber composite floor
  106. Special Issue on Recent Advancement in Low-carbon Cement-based Materials - Part I
  107. Supplementary cementitious materials-based concrete porosity estimation using modeling approaches: A comparative study of GEP and MEP
  108. Modeling the strength parameters of agro waste-derived geopolymer concrete using advanced machine intelligence techniques
  109. Promoting the sustainable construction: A scientometric review on the utilization of waste glass in concrete
  110. Incorporating geranium plant waste into ultra-high performance concrete prepared with crumb rubber as fine aggregate in the presence of polypropylene fibers
  111. Investigation of nano-basic oxygen furnace slag and nano-banded iron formation on properties of high-performance geopolymer concrete
  112. Effect of incorporating ultrafine palm oil fuel ash on the resistance to corrosion of steel bars embedded in high-strength green concrete
  113. Influence of nanomaterials on properties and durability of ultra-high-performance geopolymer concrete
  114. Influence of palm oil ash and palm oil clinker on the properties of lightweight concrete
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