A comprehensive comparison of different regression techniques and nature-inspired optimization algorithms to predict carbonation depth of recycled aggregate concrete

Abstract

The utilization of recycled aggregates (RA) for concrete production has the potential to offer substantial environmental and economic advantages. However, RA concrete is plagued with considerable durability concerns, particularly carbonation. To advance the application of RA concrete, the establishment of a reliable model for predicting the carbonation is needed. On the one hand, concrete carbonation is a long and slow process and thus consumes a lot of time and energy to monitor. On the other hand, carbonation is influenced by many factors and is hard to predict. Regarding this, this paper proposes the use of machine learning techniques to establish accurate prediction models for the carbonation depth (CD) of RA concrete. Three types of regression techniques and meta-heuristic algorithms were employed to provide more alternative predictive tools. It was found that the best prediction performance was obtained from extreme gradient boosting-multi-universe optimizer (XGB-MVO) with R² value of 0.9949 and 0.9398 for training and testing sets, respectively. XGB-MVO was used for evaluating physical laws of carbonation and it was found that the developed XGB-MVO model could provide reasonable predictions when new data were investigated. It also showed better generalization capabilities when compared with different models in the literature. Overall, this paper emphasizes the need for sustainable solutions in the construction industry to reduce its environmental impact and contribute to sustainable and low-carbon economies.

Graphical abstract

Keywords

recycled aggregate concrete / carbonation depth / nature-inspired optimization algorithms / extreme gradient boosting technique / parametric analysis

1 Introduction

Currently, countries around the world are actively working toward developing sustainable and low-carbon economies, recognizing the need to address climate change and reduce their environmental impact [1–5]. As a major contributor to energy consumption and carbon emissions, the construction industry has placed a significant emphasis on improving its energy efficiency and economic and environmental performance [6,7].

One of the key areas of focus has been the use of concrete, which is the most widely used material in the construction industry. However, the production of concrete requires large amounts of natural sand and gravel, leading to significant depletion of natural resources. It is estimated that over 400 million tons of natural aggregates (NA) are consumed each year, and this number is projected to increase to an astonishing 800 million tons in the next 20 years [8]. The excessive exploitation of NA can have a severe and lasting impact on the ecological environment. Another significant challenge facing the construction industry is the staggering amount of waste generated by urban renewal and expansion. According to 2014 statistics, the United States, the European Union, and China, which are three of the world’s largest economies, generate more than 530 million, 850 million, and 1.13 billion tonnes of demolition waste respectively [9,10]. This not only puts a strain on the environment but also on the economies.

One solution to this problem is recycling waste concrete from construction and demolition waste to produce recycled aggregate (RA). The RA can then be used as a replacement for NAs in the production of RA concrete.

Studies have shown that the incorporation of RA can lead to a diminution of the mechanical properties of concrete [11,12]. In addition, researchers have found that the addition of RA can have an impact on the durability of concrete, particularly with respect to carbonation [13–16]. Concrete carbonation refers to the chemical reaction between carbon dioxide in the air and the calcium compounds within the concrete. This reaction decreases the pH value of the concrete, which can increase the corrosion of reinforcement and ultimately lead to the deterioration of reinforced concrete structures [5]. In addition, carbonation products (mainly CaCO₃) may cause microcracks within the concrete [13]. Xiao et al. [13] concluded that RA content (RAC) has a direct impact on the carbonation depth (CD) of RA concrete. They found that when the threshold value of the substitution rate of NA by RA is lower than 70% the CD of RA concrete increases with the increase of RAC. When the substitution rate exceeds 70%, further substitution leads to a reduction in the CD. Silva et al. [15] found that adding more RAC causes an increase in the CD. They also found that using all coarse grains of RA may lead to CDs that are up to twice those occurring in normal concrete. Additionally, they observed that the age and curing conditions of the concrete had little effect on the CD. Balayssac et al. [16] and Atiş [17] observed that the longer the curing time, the lower the degree of carbonation. Leemann and Loser [18] conducted a study and discovered that the high water absorption properties of RA had a significant impact on the compressive strength of RA concrete. However, a comparison between concrete made from dry aggregates and pre-saturated aggregates revealed minimal disparities in their carbonation resistance. Additionally, when the proportion of RA was increased from 25% to 50% by mass, there was no discernible enhancement in the concrete’s carbonation factor [18]. A similar finding, that the appropriate addition of RA had little effect on the CD, can be found in Ref. [19]. The depth of carbonation of RA concrete was also related to the type of superplasticizer (SP) [20]. Zega and di Maio [21] examined the effect of exposing RA concrete samples containing 20% and 30% fine RA to air over periods of 310 and 620 d. Despite the extended exposures, there was little difference in the CDs.

From the literature review, it can be seen that the carbonation resistance of RA concrete is affected by various factors. And it can be indicated that the carbonation behaviors of RA concrete vary significantly among previous studies. Furthermore, most of the studies on RA concrete carbonation property were conducted through experimental trial-and-error methods, which are highly variable for different laboratories and different environments. The research is also time-consuming and expensive. Therefore, it is vital to establish accurate prediction models. Several mathematical theoretical models have been proposed to predict the carbonation resistance of RA concrete (see below). However, these models have limited ability to specifically discuss the effects of different factors on the carbonation results.

It has become increasingly common to use machine learning algorithms to predict various aspects of concrete performance, on the grounds that these techniques possess superior predictive capabilities compared to traditional mathematical models [22–26]. Nunez and Nehdi [22] proposed a gradient boosting regression tree (GBRT) model to predict the CD of RA concrete containing different mineral additives. Through a comprehensive analysis of the results, they found that the GBRT model achieved a high level of accuracy, as demonstrated by its low Root Mean Squared Error (RMSE) of 1.5139, Mean Absolute Error (MAE) of 0.948, and high coefficient of determination (R²) of 0.9707. These results indicate that the GBRT model performed significantly better than traditional mathematical equations for predicting CDs. Furthermore, Liu et al. developed an Artificial Neural Network (ANN) model using 593 RA concrete CD data sets [23]. The ANN model was shown to have high accuracy and robustness in its predictions. However, it should be noted that ANN models are known to be “black boxes”, meaning they lack interpretability in terms of understanding the relationships between the input and output variables. Despite the promising results of previous studies, the use of machine learning to predict CD of RA concrete is still relatively limited.

In this study, three representative regression techniques were employed, i.e., support vector regression (SVR), kernel extreme learning machine (KELM), and extreme gradient boosting (XGB). The role of SVR was mainly to find the best separation hyperplane in the feature space. KELM is mainly based on the theory of neural network and XGB is mainly inspired by the regression tree. Meanwhile, three types of nature-inspired meta-heuristic algorithms were adopted to optimize the hyper-parameters in these regression techniques, i.e., genetic algorithm (GA), multi-universe optimizer (MVO) and sparrow search algorithm (SSA). GA is inspired by evolutionary theory, MVO is from physics and SSA simulates swarming behaviors. 682 CD data sets from published literature were collected and used to develop machine learning models for carbonation prediction for RA concrete. It should be noted that new input parameter combinations, i.e., RA water absorption, water-to-binder ratio (WBR), fine aggregate content (FAC), gravel content (GC), RAC, SP, carbon concentration (CC), and exposure time (T) were considered as potential influencing factors in the model. A total of nine prediction models are provided in this work, so as to provide a comprehensive comparison of different regression techniques and optimization algorithms as well as a better understanding of the relationships between different variables and the CD. The established prediction models were evaluated by eight mathematical indicators and Taylor Diagram. Finally, the most competitive prediction model was validated by parametric analysis from the perspective of physics.

2 Data description

As outlined in the introduction, a plethora of factors can impact the carbonation properties of recycled concrete. This study specifically examined eight key parameters that are commonly considered by researchers in this field. The authors compiled and extracted a database from by Moghaddas et al. [27]. This data set consists of 682 experimental samples gathered from 21 different papers and 11 different countries, as shown in Fig.1. The study of carbonation performance of RA concrete has been conducted by a diverse range of countries worldwide, with a significant proportion of data coming from Portugal, China, and the UK. The data set includes variables such as RA water absorption (RAWA), WBR, FAC, GC, RAC, SP, CC, T, and CD. Tab.1 and Fig.2 present a statistical analysis and distribution of all variables. In the violin plot, the width of “violin” represents the density of data. It can be seen that the T ranges from 177 to 3650 d which indicates a broad database. Notably, T in the data reaches up to ten years, making it possible to consider the effect of long-term exposure on RA concrete carbonization, an aspect that has been previously understudied in models [28]. Potential relationships between different variables were also examined. Pearson correlation coefficient (R) was used to quantify the correlation between pairs of variables, with values ranging from −1 to 1 [29]. A value of 0 indicates no correlation, positive values indicate a positive correlation, and negative values indicate a negative correlation. The greater the absolute number, the stronger the correlation. As seen in Fig.3, WBR and RAC show a higher positive correlation with CD, suggesting that these factors should be given particular attention. T, CC, FAC, and RAWA present a slight correlation with CD. GC and SP show a negative correlation. However, according to the review report from Silva et al. [15], T, CC, FAC, RAWA, and SP showed a significant effect on CD of RA concrete. It is important to note that R is restricted to measuring only linear relationships between two variables, is sensitive to outliers, assumes normality, does not account for causality, and is limited to bivariate analysis. Considering these limitations and the intricate relationship between these factors and CD of RA concrete, alternative correlation approaches were also employed, for comparison.

Mutual information (MI) correlation is a measure of the statistical dependence between two variables [30]. It quantifies the amount of information that is shared by two variables. From the analysis of MI shown in Fig.4, it can be found that WBR has the lowest interactivity with CD and FAC has the highest MI with CD. Other factors have some MI with CD. These findings are different from the analysis of Pearson correlation between potential factors and CD. Therefore, the implementation of machine learning techniques seems to be a desirable approach to integrating these factors and CD.

3 Methodology

In this study, three kinds of machine learning techniques were employed, i.e., SVR, KELM and XGB. The main role of SVR is to optimize the hyper-plane with the largest interval defined in the feature space. The KELM is modified based on classical extreme learning machine (ELM), while the main advantage of KELM over ELM is better generalization performance [31]. KELM achieves this by introducing a regularization term in the objective function (OF), which helps to prevent overfitting to the training data. XGB is a powerful tree-based ensemble machine learning algorithm that has gained popularity in recent years [32,33]. Compared to traditional tree-based models, XGB has higher generalization and prediction accuracy. Therefore, aforementioned representative machine learning techniques were used to implement regression tasks in this study. Meanwhile, three types of optimization algorithms were utilized to optimize the hyper-parameters in SVR, KELM and XGB. In some previous studies, only one kind of regression technique was optimized by optimization algorithms [32,34–37]. However, no obvious predictive performance difference could be observed between different optimization algorithms. In addition, most studies only focused on the same type optimization algorithm which hardly presented the superiority and inferiority of different regression techniques [38,39]. Regarding this, this study proposed to use three kind of different mechanism regression techniques combined with three different mechanism optimization algorithms to predict CD of RA concrete and their prediction abilities were evaluated by various evaluation indicators so as to conclude a competitive CD prediction model. Finally, the superior CD prediction model was used for reflecting the impact of influencing factors on CD.

3.1 Optimization algorithms

3.1.1 Genetic algorithm

The GA mimics the natural selection process and the genetic mechanism of biological evolution [40,41]. The algorithm begins by randomly generating an initial population of chromosomes, each of which comprises multiple genes that represent specific characteristics of data. These chromosomes are considered potential solutions to a given problem. The population is then updated through a series of iterations, utilizing three primary operators-selection, crossover, and mutation-to preserve the optimal chromosomes for the next generation. The crossover operator involves the exchange of segments of genetic code between two chosen individuals, leading to the creation of new individuals with a combination of their genes. The mutation operator, on the other hand, randomly alters the value of specific genes in an individual, maintaining genetic diversity within the population. The GA continually evaluates the generated solutions, comparing them to a fitness function, until a predetermined number of iterations or a predefined threshold is reached, resulting in the identification of the optimal solution. Fig.5 presents the flowchart of the GA.

3.1.2 Multi-universe optimizer algorithm

Mirjalili et al. [42] proposed the MVO algorithm, which is inspired by the interaction between universes through black holes, white holes, and wormholes. The algorithm is based on the multiverse theory, which posits that objects from parallel universes can be moved from one universe to another through white and black holes, and objects in each universe can travel through wormholes within it. In the MVO algorithm, each set of variables is considered a universe, and each variable within the universe is an object. The corresponding inflation rates, or fitness function values, are then calculated. The universe’s inflation rate is a defining characteristic, and its higher values reflect a greater capability for expansion. A white hole with a high inflation rate tends to send its objects to a black hole with a low inflation rate. This sudden change in universes raises the average population expansion rate and ensures the MVO’s exploration capacity. By utilizing this approach, poor solutions and their mean objective values can be upgraded.

3.1.3 Sparrow search algorithm

In 2020, Xue and Shen [43] introduced the SSA as a novel optimization method that employs swarm intelligence. The algorithm is inspired by the feeding behavior of sparrows and their ability to avoid natural predators. The sparrow population is first divided into producers and scroungers during the foraging phase. The producer is responsible for locating food and directing the entire sparrow population; the scrounger uses an efficient optimization approach for designing machine learning models based on the knowledge provided by the producer to acquire food. Additionally, SSA incorporates a producer-scrounger model to detect early warning systems that represent sparrow anti-predation behavior.

3.2 ML methodology

3.2.1 Support vector regression

Cortes and Vapnik [44] advanced the field of machine learning by introducing SVMs for dichotomous techniques. The SVM model was predicated on the concept of a hyperplane that separates the data set into distinct classes. A variation of this model, SVR, was later developed specifically for regression tasks. It aims to identify an optimal hyperplane that minimizes the overall deviation of all data points from the hyperplane, and endeavors to fit the data as closely as possible while still preserving a desirable margin, as opposed to a hyperplane that simply splits two or more categories of data points.

3.2.2 Kernel extreme learning machine

KELM is a variation of the traditional ELM algorithm, with the key difference being that it utilizes kernel functions to transform the input data into a higher dimensional feature space, allowing for nonlinear decision boundaries [31]. The approach involves randomly initializing the weights of the hidden layer and utilizing the kernel trick to map the input data into a higher dimensional feature space, followed by determination of the weights of the output layer through the least squares method. KELM is computationally efficient as the training process only requires determination of the weights of the output layers, unlike traditional ELM. Additionally, it can handle nonlinear decision similar to SVMs through the use of the kernel trick. The output function of ELM is described in Eq. (1):

(1)f_L\left(x\right)={\sum }_{i=1}^L{\beta }_i{h}_i\left(x\right)=h\left(x\right) \beta ,

where \beta = [{\beta }_1,{\beta }_2,...,{\beta }_L] represents the output weights vector between the hidden layer of L nodes and the output node. h\left(x\right)=[h_1\left(x\right),\dots ,h_L\left(x\right)] defines the hidden layer output matrix. h(x) is a mapping feature because it maps data from the d-dimensional input space to the L-dimensional hidden layer feature space H.

3.2.3 Extreme gradient boosting

The XGB model is an implementation of gradient boosting to reduce the training loss function [33]. The XGB consists of a set of decision trees. The model expression can be represented as follows:

(2)\widetilde{y_i}={\sum }_{k=1}^K{f}_k\left(x_i\right),

where \widetilde{y_i} represents the predicted value for input x_i, f_k\left(x_i\right) is the kth tree.

Finally, the expression for OF is as follows:

(3)OF={\sum }_{i-1}^{n}L\left(\widetilde{y_i},y_i\right)+{\sum }_{k=1}^K\mathrm{\Omega }\left(f_k\right),

where OF includes the regularization item Ω and the loss function L which denotes the gap between the predicted result \widetilde{y_i} and the actual result y_i.

The basic structure of XGB is shown in Fig.6 and Ref. [33] provides a more comprehensive description and characterization of XGB.

4 Development of models

Fig.7 depicts the general framework of CD of RA concrete prediction model development. The precision of machine learning algorithms heavily depends on their intrinsic hyper-parameters.

Determining the appropriate combination of hyper-parameters for a given situation can be challenging, so optimization algorithms play a vital role in finding the best hyperparameters. Regarding this, GA, MVO, and SSA were used to identify the optimal hyper-parameters of KELM, SVM, and XGB models to construct accurate prediction models and determine the CD of RA concrete.

To save computation time, the inputs (8 factors) and output (CD) are normalized to [0,1] by the equation below:

(4)\mathit{\text{z}}=\frac{x-\mu }{\sigma } ,

where z is transformed value; μ is the mean; σ is the standard deviation; x is the output value.

To create and evaluate models effectively, 80% of the data (550 data sets) was randomly selected as a training set and 20% (132 data sets) as a testing set. Fig.8 illustrates the distribution of data between the training and test sets. The results evince their comparability, attesting to the homogeneity of the training and test sets. 10-fold cross validation was then adopted in this study to increase the robustness of proposed prediction models where the training set was divided into ten equal sub-sets, with nine sub-sets being used as sub-training sets and the other being used as a validation set. Some initial model parameters were given to these sub-training sets and then a sub-model could be established and the prediction performance of a sub-model could be tested by a validation set. This process was repeated ten times and the average MSE of the ten validation sets was used as fitness value. By optimization from proposed meta-heuristic algorithms, the fitness value was updated until the iteration finished. Tab.2 provides a detailed explanation of the hyper-parameters to be optimized and their search ranges for each model.

5 Evaluation indicators

To measure the overall performance of developed CD prediction models, a total of eight evaluation indicators were used in this study. These indicators include seven classical mathematical indicators, i.e., R², Variance Accounted For (VAF), MAE, Mean bias error (MBE), RMSE, Mean Absolute Percentage Error (MAPE) and R as well as a pre-defined indicator, A10. They can be calculated as follows:

(5)R^2= 1-\frac{\sum _{i=1}^N{\left(y-y^{\prime }\right)}^2}{\sum _{i=1}^N{\left(y-\tilde{y}\right)}^2},

(6)VAF=\left[1-\frac{var(y-y^{\prime })}{var\left(y\right)}\right]\times 100\mathrm{\%},

(7)MAE=\frac{1}{N}{\sum }_{i=1}^N\left|y^{\prime }-y\right|,

(8)MBE=\frac{1}{N}{\sum }_{i=1}^N(y^{\prime }-y),

(9)RMSE= \sqrt{\frac{1}{N}{\sum }_{i=1}^N{(y-y^{\prime })}^2},

(10)MAPE= \frac{100\mathrm{\%}}{N} {\sum }_{i=1}^N\left|\frac{y^{\prime }-y}{y}\right|,

(11)R=\frac{N\sum y{y}^{\prime }-{\displaystyle \sum y\sum y^{\prime }}}{\sqrt{N{\displaystyle \sum y^2-{\left(\sum y\right)}^2}}\sqrt{N{\displaystyle \sum {y^{\prime }}^2-{\left({\displaystyle \sum y^{\prime }}\right)}^2}}} ,

(12)

where y represents the measured CD, y′ and y represent the predicted and average value of measured CD, respectively. NN denotes the total number of samples, while i is the number in the present sample. The proposed comprehensive ranking system by Zorlu et al. [45] is used to give the overall performance of the model by considering all indicators. In this system, higher performing indicators receive higher ranking scores and the model’s overall score is calculated by summing up each score. The model with the highest overall score is considered the most robust prediction model of CD of RA concrete.

6 Result and discussion

6.1 Development of hybrid carbonation depth of recycled aggregate concrete prediction models

For meta-heuristic algorithms, there are two parameters that influence the optimization performance, i.e., swarm size and iteration number where a swarm size and iteration that are too large increase the calculation cost while those that are too small induce under-fitting. After testing and comparison, the swarm size was equal to 30 and the iteration number was set to be 60 which was sufficient to complete the optimization process and these two significant values would be constant in each CD prediction model. The optimized parameters optimization algorithms are listed in Tab.3. In the initialization stage, 30 combinations of hyper-parameters were generated and each combination of hyper-parameters generated a corresponding fitness value. By sorting, the best fitness values and corresponding hyper-parameters can be obtained. In the next step, the iteration progress was initially based on the best combination of hyper-parameters according to different optimization algorithms, until the iteration ends. The change of fitness values (MSE) by different optimization algorithms are shown in Fig.9. It can be seen that XGB-based CD prediction models have lower initial and final fitness values compared with KELM-based and SVR-based CD prediction models. SSA-XGB has the lowest initial and final fitness values among all CD prediction models. For KELM-based prediction models, it can be found that SSA-KELM has the lowest fitness value when the optimization process ends. The same phenomenon can be observed from the SVR-based CD prediction models. Aforementioned facts suggest that the SSA optimization has stronger optimization abilities than GA and MVO.

6.2 Discussion and results

As mentioned above, the SSA produced smaller fitness value than GA and MVO for three regression techniques. However, it can hardly be concluded that SSA-based CD prediction models would bring the best overall prediction performance, because the model parameters obtained from 10-fold cross validation must still be checked by the original training set and testing set. Regarding this, the optimized model parameters were used to predict CD in the training set and testing set. The predicted results for training set and testing set, with prediction errors, are demonstrated in Fig.10 and Fig.11, respectively. In each figure, five fitting lines are depicted to illustrate the general distribution of measured CD and predicted CD. Meanwhile, the predicted error for each sample is also shown in Fig.10 and Fig.11. The performance of the training set is here discussed first in Fig.10. For SVR-based CD prediction models, when the measured CD is lower than 30mm, most predicted errors are lower, between −5 and +5 mm, where one sample has more than 10mm error for MVO-SVR. For GA-SVR and SSA-SVR, the predicted errors for all measured samples, that are lower than 30 mm, are in the range of −8 to 5 mm. With the increase of CD, a few predicted errors are larger than 10mm but smaller than 15 mm for all SVR-based CD prediction models. For KELM-based approaches, it can be seen that when the measured CD is lower than 30 mm, all predicted errors are in the range of −10 to 5 mm. When the measured CD is larger than 30 mm, GA-KELM and MVO-KELM bring an error larger than 10 mm but for SSA-KELM approach, all errors are in the range of −10 and 5 mm. For XGB-based prediction scenarios, it can be seen that only one sample has error than 5 mm. Most samples presented minor prediction errors. Therefore, it can be concluded that XGB-based and SSA-based models seem to have stronger fitting abilities for the training data. In the next step, the performance from the testing set is discussed.

Unlike the performance of the training set, larger prediction errors are produced by the proposed nine prediction models as shown in Fig.11. For SVR-based models, the prediction errors are lower than 10 mm when the measured CD is lower than 35 mm; however, when the measured CD is bigger than 35 mm, the prediction errors are much larger and even equal to 20 mm. For KELM-based models, a similar phenomenon occurs. In other words, the predictive ability for SVR-based and KELM-based models is limited when the measured CD is larger than 35 mm. For XGB-based approaches, better predictive performance can be obtained, as seen in Fig.11. For GA-XGB, all prediction errors are in the range of −6 to 10 mm. And for MVO-XGB and SSA-XGB, there is one sample that has more than 10mm error. However, compared with GA-XGB, the range of errors from MVO-XGB and SSA-XGB are more centralized. For quantifying the prediction performance, eight mathematical indictors as mentioned before are used to provide an overall prediction evaluation as shown in Tab.4 and Tab.5. To intuitively compare these evaluation indicators, the ranking scores of each indicator and model are reflected by bar charts in Fig.12 and Fig.13.

For the ranking scores of the training set, it can be found that for SVR-based methods, GA-SVR has the highest-ranking score. For KELM-based models, SSA-KELM has the highest-ranking score as shown in Fig.12. For XGB-based scenarios, XGB-MVO has the highest-ranking score. For the performance of testing set, GA-SVR is still the best among three SVR models. Similarly, SSA-KELM has better performance than the two other KELM-based models. For XGB-based approaches, GA-XGB brings the best prediction performance for the testing set. It is interesting that the optimization abilities for a certain optimization algorithm are not always the best for different regression techniques. However, XGB-based models present more robust CD prediction performance than the two other regression techniques. The final ranking scores of different models can be seen in Fig.14. The ranking scores from high to low are: XGB-MVO, XGB-GA, XGB-SSA, SVR-GA, KELM-SSA, SVR-MVO(KELM-GA), KELM-MVO and SVR-SSA. The best overall prediction performance from XGB-MVO is R² of (0.9949 and 0.9398), R of (0.9949 and 0.9423), RMSE of (0.5764 and 1.7565), VAF of (99.4877 and 94.0487), MAPE of (0.0300 and 0.1863), MAE of (0.2241 and 1.0688), MBE of (0.0000 and −0.1915) and A10 of (0.9873 and 0.8258), for training and testing stages.

To further reflect the overall performance of proposed CD prediction models, a Taylor diagram is employed in this section, as shown in Fig.15. The Taylor diagram employs three statistical indicators, namely RMSE, R, and standard deviation, to present a comprehensive evaluation. A smaller distance between the predicted point and the reference point (black dot) indicates better predictive performance. The analysis also shows that hybrid XGB models outperformed hybrid SVR and KELM models. Overall, the results suggest that SSA-XGB should be the recommended model for predicting CD due to its excellent performance on both the training and testing sets.

6.3 Model validation by parametric analysis

To verify the feasibility of the proposed CD of RA concrete predictive models, the most competitive prediction model is selected, i.e., XGB-MVO, to conduct parametric analysis. One influencing factor is selected to be variable and the other influencing factors is set to be constant. Moreover, the constant influencing factors were set at their average values, and the variable influencing factor changed from its lowest to highest value, with a defined interval where the former is determined by the original data distribution as shown in Tab.1. The results presented in Fig.16 provide important insights into the effect of various factors on the depth of carbonation in RA concrete by using XGB-MVO model. The following observations can be made from the data presented.

a) The RAWA of RA had a significant impact on the CD in RA concrete. When the RAWA exceeded 6%, the CD increased rapidly due to the increased porosity of the RA, which created more voids in the concrete matrix and reduced its compactness [46].

b) The WBR in concrete is another important factor affecting the CD. A higher WBR leads to a more porous concrete matrix, allowing carbon dioxide to penetrate more easily and increasing the CD [47].

c) The CD initially increased with increase of FAC, but after a certain point (around 600–700 kg/m³), it started to decrease.

d) Increasing the GC in RA concrete had a slight effect on the CD at lower content levels (0–1200 kg/m³), but the increase of CD was not significant. However, when GC was greater than 1200 kg/m³, the CD increased significantly.

e) The increase of RAC significantly increased the CD due to its higher porosity and roughness. The CD increased rapidly from 10 to 14 mm when RAC was between 0 and 1100 kg/m³, and then further increased to 18 mm after RAC reached 1250 kg/m³.

f) The addition of SP to RA concrete significantly decreased the CD, especially when the increase was greater than 1 kg/m³. This is because the higher content of SP improved the flowability and denseness of the RA concrete matrix, reducing its permeability [48].

g) The CC had a significant impact on the CD of RA concrete. The CD increased significantly with the increase in CC up to 12%, after which further increases had little effect on the CD. This can be attributed to the formation of a dense carbonation layer on the surface of the concrete, which increased its resistance to carbonation [49].

h) The CD of RA concrete increased rapidly in the early stages, but after one year of exposure, the change in CD was not significant. The increased T causes the carbonation layer and the layer decreases the adsorption rate on the concrete surface [50].

6.4 Comparison of the developed optimal model with literature models

In this section, the optimized model developed in this study is compared with other models from literature for predicting RA concrete CD [22,23,27,28]. Fig.17(a) shows a comparison of the RMSE and MAE values obtained by each model. It was observed that the RILEM 130-CSL model had the highest RMSE (11.95) and MAE (11.07), which probably can be attributed to the limited data size of 72, as shown in Fig.17(b). The optimal model XGB-MVO predicted in this study had an RMSE of 1.76 and MAE of 1.07, which was the second-best after the GBRT model, with an RMSE of 1.51 and MAE of 0.91. However, it is important to note that the GBRT model only used 217 data points (Fig.17(b)), which may limit its generalizability. The prediction ability for CD of RA concrete by XGB-MVO has been validated by more data (682 data).

7 Conclusions

The monitoring of carbonation of concrete has always been a tough task because it is influenced by various factors. In this study, in order to further develop a model to accurately predict the CD of recycled concrete, a data set of the CD of RA concrete was obtained, based on the literature, and the effect of new combinations of influential factors on CD was simulated: RAWA, WBR, FAC, GC, RAC, SP, CC, and T. CD was the output. Meanwhile, three types of regression techniques and three types of meta-heuristic algorithms were combined and a total of nine CD prediction models were developed. It was found that the best competitive predictive performance was produced by XGB-MVO with R² of (0.9949 and 0.9398), R of (0.9949 and 0.9423), RMSE of (0.5764 and 1.7565), VAF of (99.4877 and 94.0487), MAPE of (0.0300 and 0.1863), MAE of (0.2241 and 1.0688), MBE of (0.0000 and −0.1915) and A10 of (0.9873 and 0.8258) for training and testing set, respectively. The results demonstrate that the proposed predictive model effectively forecasts the CD of RA concrete. The predicted outcomes of the model align with previous research, attesting to its robustness. In addition, XGB-MVO also shows optimal predictive and generalization capabilities when compared with different models in the literature. The model’s ability to estimate CD for unknown RA concrete samples highlights its potential in advancing the development and application of RA s in concrete, and furthering sustainable economic growth.

References

[1] Li E, Xi B, Zhang N, Shi X, Zhou J, Segarra P, Wang H. Circular use of fine-grained tailings to underground mine wind walls. Circular Economy, 2023, 2(3): 100053

[2] Khajuria A, Atienza V A, Chavanich S, Henning W, Islam I, Kral U, Liu M, Liu X, Murthy I K, Oyedotun T D T, Verma P, Xu G, Zeng X, Li J. Accelerating circular economy solutions to achieve the 2030 agenda for sustainable development goals. Circular Economy, 2022, 1(1): 100001

[3] Xi B, Zhou Y, Yu K, Hu B, Huang X, Sui L, Xing F. Use of nano-SiO₂ to develop a high performance green lightweight engineered cementitious composites containing fly ash cenospheres. Journal of Cleaner Production, 2020, 262: 121274

[4] Zeng X, Ogunseitan O A, Nakamura S, Suh S, Kral U, Li J, Geng Y. Reshaping global policies for circular economy. Circular Economy, 2022, 1(1): 100003

[5] Zhang N, Xi B, Li J, Liu L, Song G. Utilization of CO₂ into recycled construction materials: A systematic literature review. Journal of Material Cycles and Waste Management, 2022, 24(6): 2108–2125

[6] Zhang N, Zhang D, Zuo J, Miller T R, Duan H, Schiller G. Potential for CO₂ mitigation and economic benefits from accelerated carbonation of construction and demolition waste. Renewable & Sustainable Energy Reviews, 2022, 169(9): 112920

[7] Zhang N, Duan H, Miller T R, Tam V W Y, Liu G, Zuo J. Mitigation of carbon dioxide by accelerated sequestration in concrete debris. Renewable & Sustainable Energy Reviews, 2020, 117: 109495

[8] Visintin P, Xie T, Bennett B. A large-scale life-cycle assessment of recycled aggregate concrete: The influence of functional unit, emissions allocation and carbon dioxide uptake. Journal of Cleaner Production, 2020, 248: 119243

[9] Villoria Sáez P, Osmani M. A diagnosis of construction and demolition waste generation and recovery practice in the European Union. Journal of Cleaner Production, 2019, 241: 118400

[10] Lu W, Webster C, Peng Y, Chen X, Zhang X. Estimating and calibrating the amount of building-related construction and demolition waste in urban China. International Journal of Construction Management, 2017, 17(1): 13–24

[11] Bai G, Zhu C, Liu C, Liu B. An evaluation of the recycled aggregate characteristics and the recycled aggregate concrete mechanical properties. Construction & Building Materials, 2020, 240: 117978

[12] Li X. Recycling and reuse of waste concrete in China. Resources, Conservation and Recycling, 2008, 53(1−2): 36–44

[13] Xiao J, Lei B, Zhang C. On carbonation behavior of recycled aggregate concrete. Science China. Technological Sciences, 2012, 55(9): 2609–2616

[14] Li L, Wu M. An overview of utilizing CO₂ for accelerated carbonation treatment in the concrete industry. Journal of CO₂ Utilization, 2022, 60(3): 102000

[15] Silva R V, Neves R, de Brito J, Dhir R K. Carbonation behaviour of recycled aggregate concrete. Cement and Concrete Composites, 2015, 62: 22–32

[16] Balayssac J P, Détriché C H, Grandet J. Effects of curing upon carbonation of concrete. Construction & Building Materials, 1995, 9(2): 91–95

[17] Atiş C D. Accelerated carbonation and testing of concrete made with fly ash. Construction & Building Materials, 2003, 17(3): 147–152

[18] Leemann A, Loser R. Carbonation resistance of recycled aggregate concrete. Construction & Building Materials, 2019, 204: 335–341

[19] Lovato P S, Possan E, Molin D C C D, Masuero B, Ribeiro J L D. Modeling of mechanical properties and durability of recycled aggregate concretes. Construction & Building Materials, 2012, 26(1): 437–447

[20] Matias D, de Brito J, Rosa A, Pedro D. Durability of concrete with recycled coarse aggregates: Influence of superplasticizers. Journal of Materials in Civil Engineering, 2014, 26(7): 06014011

[21] Zega C J, di Maio Á A. Use of recycled fine aggregate in concretes with durable requirements. Waste Management, 2011, 31(11): 2336–2340

[22] Nunez I, Nehdi M L. Machine learning prediction of carbonation depth in recycled aggregate concrete incorporating SCMs. Construction & Building Materials, 2021, 287: 123027

[23] Liu K, Alam M S, Zhu J, Zheng J, Chi L. Prediction of carbonation depth for recycled aggregate concrete using ANN hybridized with swarm intelligence algorithms. Construction & Building Materials, 2021, 301: 124382

[24] Liu B, Vu-Bac N, Rabczuk T. A stochastic multiscale method for the prediction of the thermal conductivity of Polymer nanocomposites through hybrid machine learning algorithms. Composite Structures, 2021, 273: 114269

[25] Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464

[26] Nariman N, Hamdia K, Ramadan A, Sadaghian H. Optimum design of flexural strength and stiffness for reinforced concrete beams using machine learning. Applied Sciences, 2021, 11(18): 8762

[27] Moghaddas S A, Nekoei M, Mohammadi Golafshani E, Nehdi M, Arashpour M. Modeling carbonation depth of recycled aggregate concrete using novel automatic regression technique. Journal of Cleaner Production, 2022, 371(3): 133522

[28] Zhang K, Xiao J. Prediction model of carbonation depth for recycled aggregate concrete. Cement and Concrete Composites, 2018, 88: 86–99

[29] BenestyJChen JHuangYCohenI. Pearson correlation coefficient. Noise Reduction in Speech Processing, 2009, 1–4

[30] Kraskov A, Stögbauer H, Grassberger P. Estimating mutual information. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2004, 69(6): 066138

[31] Shamshirband S, Mohammadi K, Chen H L, Narayana Samy G, Petković D, Ma C. Daily global solar radiation prediction from air temperatures using kernel extreme learning machine: A case study for Iran. Journal of Atmospheric and Solar-Terrestrial Physics, 2015, 134: 109–117

[32] LiEZhangN XiBZhouJ GaoX. Compressive strength prediction and optimization design of sustainable concrete based on squirrel search algorithm-extreme gradient boosting technique. Frontiers of Structural and Civil Engineering, 2023, 17(9): 1310−1325

[33] Carmona P, Climent F, Momparler A. Predicting failure in the US banking sector: An extreme gradient boosting approach. International Review of Economics & Finance, 2019, 61: 304–323

[34] Biswas R, Li E, Zhang N, Kumar S, Rai B, Zhou J. Development of hybrid models using metaheuristic optimization techniques to predict the carbonation depth of fly ash concrete. Construction & Building Materials, 2022, 346(7): 128483

[35] Li E, Zhou J, Shi X, Jahed Armaghani D, Yu Z, Chen X, Huang P. Developing a hybrid model of salp swarm algorithm-based support vector machine to predict the strength of fiber-reinforced cemented paste backfill. Engineering with Computers, 2021, 37(4): 3519–3540

[36] Vu-Bac N, Duong T X, Lahmer T, Zhuang X, Sauer R A, Park H S, Rabczuk T. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering, 2018, 331: 427–455

[37] Vu-Bac N, Rabczuk T, Park H S, Fu X, Zhuang X. A NURBS-based inverse analysis of swelling induced morphing of thin stimuli-responsive polymer gels. Computer Methods in Applied Mechanics and Engineering, 2022, 397: 115049

[38] Zhou J, Huang S, Qiu Y. Optimization of random forest through the use of MVO, GWO and MFO in evaluating the stability of underground entry-type excavations. Tunnelling and Underground Space Technology, 2022, 124(4): 104494

[39] Zhou J, Shen X, Qiu Y, Shi X, Khandelwal M. Cross-correlation stacking-based microseismic source location using three metaheuristic optimization algorithms. Tunnelling and Underground Space Technology, 2022, 126(5): 104570

[40] Ding S, Su C, Yu J. An optimizing BP neural network algorithm based on genetic algorithm. Artificial Intelligence Review, 2011, 36(2): 153–162

[41] Hamdia K M, Zhuang X, Rabczuk T. An efficient optimization approach for designing machine learning models based on genetic algorithm. Neural Computing & Applications, 2021, 33(6): 1923–1933

[42] Mirjalili S, Mirjalili S M, Hatamlou A. Multi-Verse Optimizer: A nature-inspired algorithm for global optimization. Neural Computing & Applications, 2016, 27(2): 495–513

[43] Xue J, Shen B. A novel swarm intelligence optimization approach: sparrow search algorithm. Systems Science & Control Engineering, 2020, 8(1): 22–34

[44] Cortes C, Vapnik V. Support-vector networks. Machine Learning, 1995, 20(3): 273–297

[45] Zorlu K, Gokceoglu C, Ocakoglu F, Nefeslioglu H A, Acikalin S. Prediction of uniaxial compressive strength of sandstones using petrography-based models. Engineering Geology, 2008, 96(3–4): 141–158

[46] Eckert M, Oliveira M. Mitigation of the negative effects of recycled aggregate water absorption in concrete technology. Construction & Building Materials, 2017, 133: 416–424

[47] Ho D W S, Lewis R K. Carbonation of concrete and its prediction. Cement and Concrete Research, 1987, 17(3): 489–504

[48] Papayianni I, Tsohos G, Oikonomou N, Mavria P. Influence of superplasticizer type and mix design parameters on the performance of them in concrete mixtures. Cement and Concrete Composites, 2005, 27(2): 217–222

[49] Peter M A, Muntean A, Meier S A, Böhm M. Competition of several carbonation reactions in concrete: A parametric study. Cement and Concrete Research, 2008, 38(12): 1385–1393

[50] Dias W P. Reduction of concrete sorptivity with age through carbonation. Cement and Concrete Research, 2000, 30(8): 1255–1261

RIGHTS & PERMISSIONS

The Author(s) 2024. This article is published with open access at link.springer.com and journal.hep.com.cn