Prediction Model for the Chloride Ion Permeability Resistance of Recycled Aggregate Concrete Based on Machine Learning

Abstract

The chloride ion permeability resistance of recycled aggregate concrete (RAC) is influenced by multiple factors, and the prediction model for this resistance based on machine learning is still limited. In the paper, six impact factors (IFs), including the carbonation of recycled coarse aggregates (YN), the replacement ratio of recycled coarse aggregates (r), the bending load level (L), the carbonation time (t) and temperature (T) of RAC, and the replacement ratio of carbonated recycled fine aggregates (f), were considered to conduct a chloride penetration test on RAC. Based on the experimental data, four algorithms, including artificial neural network (ANN), support vector machine (SVM), random forest (RF) and extreme gradient boosting (XGBoost), were adopted to establish the machine learning prediction models and study the relationships between the electric flux of RAC and the IFs. The results showed that the predicted values of all four models were in good agreement with the experimental values, and the XGBoost model had the best prediction performance on the testing set. Based on the XGBoost model, the LIME method was adopted to solve the interpretability problem in the prediction process. The importance ranking of IFs on the electric flux was r > t > f > T > L > YN. A graphical user interface (GUI) was developed based on Python 3.8 software to facilitate the use of machine learning models for the chloride ion permeability resistance of RAC. The research results can provide an accurate prediction of the electric flux of RAC.

1. Introduction

The rapid development of the global construction industry has caused enormous resource and environmental problems [1,2]. In order to comply with the trend towards a resource-conserving and environment-friendly society, the construction industry urgently needs to embark on the path of low-carbon development. The application of recycled aggregate concrete (RAC) plays a positive role in the development of the construction industry [3,4,5,6,7], which helps to reduce the consumption of natural resources, alleviates the pollution of the environment caused by construction waste, reduces the emission of CO₂, and promotes the sustainable development of human society. However, due to the presence of more defects in recycled aggregates (RAs) compared to natural aggregates (NAs), RAC has poorer mechanical and durability properties [8,9,10,11,12]. Therefore, it is necessary to strengthen RAs to improve the mechanical and durability properties of RAC. Using the method of carbonation strengthening treatment to improve the performance of RA is currently one of the hotspots in the research of RAC. CO₂ can react with hydration products in the attached old mortar of RA to generate solid calcium carbonate and other substances, which fill the micro-pores and micro-cracks inside RA, thereby reducing its porosity and water absorption levels, improving its crushing index, and improving the interfacial transition zones between the RA and the old mortar [13,14,15]. Moreover, this process can also consume CO₂, which has good environmental benefits.

The chloride ion permeability resistance of concrete is an important evaluation indicator of durability. Many researchers have conducted research on the prediction of the chloride ion permeability resistance of concrete. Wang et al. [16] comprehensively analyzed the experimental data of eight researchers and explored the relationship between the stress ratio of concrete and the stress influence coefficient; based on this relationship, a new formula for the stress influence coefficient was constructed, and a modified chloride ion diffusion model was proposed. Xu and Li [17] proposed a prediction model for the chloride ion diffusion coefficient based on elastic theory, with parameters including the elastic modulus, Poisson’s ratio, initial porosity, and external equivalent stress. Wang et al. [18] conducted regression analysis on the chloride ion permeation curves and proposed an empirical model to quantify the time-dependent and stress-dependent characteristics of the chloride ion diffusion coefficient and the surface chloride concentration of concrete. Xu et al. [19] studied the permeation laws of chloride ions in concrete under sustained axial compression through experiments and established a prediction model for chloride ion concentration considering the characteristics of the chloride ion diffusion coefficient as they change with time and stress. Thus, it can be seen that the traditional prediction models for the chloride ion permeability resistance of concrete are mostly empirical models obtained by fitting and regression analyses of experimental data or by combining experimental data with relevant theories of concrete, which are relatively simple, intuitive, and easy to understand.

With the rapid progress of computer science, artificial intelligence technology is gradually maturing. Machine learning, as an important branch of artificial intelligence, can efficiently filter, organize, and mine patterns in massive amounts of information, thus improving the efficiency of data utilization. In the era of big data, machine learning is an indispensable tool [20,21,22,23,24,25] representing an advanced direction that combines data mining and processing techniques with model predictive computing. Currently, some researchers have adopted machine learning methods to establish prediction models for the chloride ion permeability resistance of concrete. Liu et al. [26] established a prediction model for the chloride ion permeability resistance of concrete using an artificial neural network (ANN) algorithm, with the composition of concrete materials and external environmental factors as input variables, and they found that the model had strong robustness and a high prediction accuracy. Li et al. [27] combined the random forest (RF) algorithm with the support vector machine (SVM) algorithm to construct a machine learning prediction model for the chloride ion permeability resistance of concrete and discovered that the model had certain prediction accuracy and stability. Sun [28] collected 194 sets of experimental data as the training set and used different algorithms, including ANN, SVM, decision tree (DT), RF, gradient boosting decision tree (GBDT), and extreme gradient boosting tree (XGBoost), to establish six machine learning models of chloride ion diffusion coefficients, among which the GBDT algorithm had the highest accuracy in predicting the chloride ion diffusion coefficient. Cui et al. [29] built three prediction models of chloride ion concentration in concrete using the SVM, RF, and GBDT algorithms and found that all three models had high accuracies, but it was recommended to prioritize using SVM and GBDT models for prediction. Liu [30] used six machine learning algorithms, including XGBoost, support vector regression (SVR), RF, neural network (NN), GBDT, and DT, to set up prediction models for the electric flux of concrete and the relative chloride ion diffusion coefficient under a load; they showed that the XGBoost model had the best effect on predicting the electric flux of concrete, while the GBDT model provided the best prediction of the relative chloride ion diffusion coefficient under a load. Based on the current research above, it can be seen that models such as ANN, RF, SVM, and XGBoost, have been applied in the field of machine learning prediction for the resistance of concrete to chloride ion penetration and have shown good performance. Most of the prediction models for the chloride ion permeability resistance have been established based on Fick’s second law and experimental results regarding the chloride ion diffusion coefficient as the research object, while a number of models have also been built using machine learning methods. Compared to traditional methods, the prediction models established through machine learning have higher prediction accuracies.

However, the prediction model for the chloride ion permeability resistance of RAC based on machine learning is still limited. There are many factors that affect the chloride ion permeability resistance of RAC, such as the replacement ratio of recycled coarse aggregates (RCA), bending load level, and carbonation temperature of RAC. The combined effects of different factors on the chloride ion permeability resistance of RAC still need to be studied. To promote the low-carbon development of the construction industry, it is urgent to establish an accurate and reliable prediction model for the chloride ion permeability resistance of RAC that considers the effects of multiple factors. However, there is currently no machine learning prediction model for the chloride ion permeability resistance of RAC that considers the effects of the carbonation of RCA, RCA replacement ratio, bending load level, carbonation time and temperature of RAC, and replacement ratio of carbonated recycled fine aggregates (CRFAs).

To fill this research gap, in this study, the electric flux was used as an indicator to evaluate the chloride ion permeability resistance of RAC, and six impact factors (IFs) were considered, including the carbonation of RCA, RCA replacement ratio, bending load level, carbonation time and temperature of RCA, and CRFA replacement ratio. The chloride penetration test was designed to measure the electric flux of RAC, and based on the experimental data, four algorithms, including ANN, SVM, RF, and XGBoost, were used to study the relationships between the electric flux and its IFs. Then, based on the optimal XGBoost algorithm, the LIME method was adopted to solve the interpretability issue in the prediction process. Finally, a graphical user interface (GUI) based on the Python 3.8 software was developed to facilitate the use of a machine learning model for the chloride ion permeability resistance of RAC.

2. Experimental Database

2.1. Experimental Programme

2.1.1. Raw Materials

The cement used was sulphoaluminate cement with a strength grade of 42.5. Natural sand with a fineness modulus of 2.7 was used as the fine aggregate, and continuous-graded macadam with a particle size of 5–20 mm was adopted as the coarse aggregate. Huiba superplasticizer was chosen as the water-reducing admixture, while tap water was used as the mixing water.

The RAs, including RCA and the recycled fine aggregates (RFAs), were made from abandoned concrete with a strength grade of C30 from a material laboratory. The same batch of waste concrete specimens with a strength of C30 was selected. Then, the specimens were manually crushed, cleaned, and graded into coarse aggregates with a particle size of 5–20 mm and fine aggregates with a particle size of less than 5 mm. According to the Chinese Standard GB/T 50082 [31], a certain amount of RCA and RFA were placed in the carbonation chamber with a CO₂ concentration of 20 ± 3%, relative humidity of 70 ± 5%, and temperature of 20 ± 2 °C for carbonation. To determine the time required for the complete carbonation of RA, several RCAs were randomly taken from the carbonation chamber every 24 h. After splitting them from the middle, phenolphthalein solution was sprayed onto their cross-section. If there was no color reaction, it indicated that all RAs were completely carbonated. Because the particle sizes of recycled fine aggregates were much smaller than those of recycled coarse aggregates, the time for the complete carbonation of recycled fine aggregates was shorter than that of recycled coarse aggregates. Therefore, the time required for the complete carbonation of the recycled aggregates was based on the time for the recycled coarse aggregates.

2.1.2. Design of Specimens

RAC specimens were designed to study the chloride ion permeability resistance, with independent variables including the carbonation of RCA, RCA replacement ratio (50% and 100%), bending load level (0, 0.2 and 0.4), carbonation time of RAC (0 days, 7 days and 14 days), carbonation temperature of RAC (20 °C, 30 °C and 40 °C), and CRFA replacement ratio (0, 10% and 20%). The specific design of the specimens is listed in

Table 1. Design of specimens.

Specimen Label	RAC Type	RCA Replacement Ratio (%)	Carbonation Time of RAC (Days)	Bending Load Level	CRFA Replacement Ratio (%)	Carbonation Temperature of RAC (°C)
R50–0–0–F0–T20	NCRAC	50	0	0	0	20
R50–7–0–F0–T20		50	7	0	0	20
R50–14–0–F0–T20		50	14	0	0	20
R50–0–0.2–F0–T20		50	0	0.2	0	20
R50–7–0.2–F0–T20		50	7	0.2	0	20
R50–14–0.2–F0–T20		50	14	0.2	0	20
R50–0–0.4–F0–T20		50	0	0.4	0	20
R50–7–0.4–F0–T20		50	7	0.4	0	20
R50–14–0.4–F0–T20		50	14	0.4	0	20
CR50–0–0–F0–T20	CRAC	50	0	0	0	20
CR50–7–0–F0–T20		50	7	0	0	20
CR50–14–0–F0–T20		50	14	0	0	20
CR50–0–0.2–F0–T20		50	0	0.2	0	20
CR50–7–0.2–F0–T20		50	7	0.2	0	20
CR50–14–0.2–F0–T20		50	14	0.2	0	20
CR50–0–0.4–F0–T20		50	0	0.4	0	20
CR50–7–0.4–F0–T20		50	7	0.4	0	20
CR50–14–0.4–F0–T20		50	14	0.4	0	20
R100–0–0–F0–T20	NCRAC	100	0	0	0	20
R100–7–0–F0–T20		100	7	0	0	20
R100–14–0–F0–T20		100	14	0	0	20
R100–0–0.2–F0–T20		100	0	0.2	0	20
R100–7–0.2–F0–T20		100	7	0.2	0	20
R100–14–0.2–F0–T20		100	14	0.2	0	20
R100–0–0.4–F0–T20		100	0	0.4	0	20
R100–7–0.4–F0–T20		100	7	0.4	0	20
R100–14–0.4–F0–T20		100	14	0.4	0	20
CR100–0–0–F0–T20	CRAC	100	0	0	0	20
CR100–7–0–F0–T20		100	7	0	0	20
CR100–14–0–F0–T20		100	14	0	0	20
CR100–0–0.2–F0–T20		100	0	0.2	0	20
CR100–7–0.2–F0–T20		100	7	0.2	0	20
CR100–14–0.2–F0–T20		100	14	0.2	0	20
CR100–0–0.4–F0–T20		100	0	0.4	0	20
CR100–7–0.4–F0–T20		100	7	0.4	0	20
CR100–14–0.4–F0–T20		100	14	0.4	0	20
CR50–0–0–F10–T20		50	0	0	10	20
CR50–0–0–F20–T20		50	0	0	20	20
CR50–7–0–F0–T30		50	7	0	0	30
CR50–7–0–F0–T40		50	7	0	0	40

. For the numbering rules of the specimens in Table 1, the letter “R” represents the RAC mixed with non-carbonated RCA (NCRAC), while the letter “CR” represents the RAC mixed with carbonated RCA (CRAC), and the remaining parts of the specimen label from left to right represent the RCA replacement ratio, carbonation time of RAC, bending load level, CRFA replacement rate, and carbonation temperature of RAC. For example, CR100-14-0.4-F0-T20 refers to the CRAC with an RCA replacement ratio of 100%, a carbonation time of 14 days, a bending load level of 0.4, a CRFA replacement ratio of 0, and a carbonation temperature of 20 °C.

Based on the mix proportion of ordinary concrete with a strength grade of C40, six different mix proportions of the specimens were designed, as detailed in

Table 2. Mix proportions of RAC specimens (unit: kg/m³).

Group Label	Water	Cement	Coarse Aggregate			Fine Aggregate		Water-Reducing Admixture
			NA	Non-Carbonated RCA	Carbonated RCA	Natural Sand	CRFA
R50–F0	200	400	615.2	615.2	0	612	0	4
CR50–F0	200	400	615.2	0	615.2	613	0	4
R100–F0	200	400	0	1230.4	0	614	0	4
CR100–F0	200	400	0	0	1230.4	615	0	4
CR50–F10	200	400	615.2	0	615.2	549.9	61.1	4
CR50–F20	200	400	615.2	0	615.2	488.8	122.2	4

, where the letter “R” also means NCRAC, while the letter “CR” represents CRAC, and the remaining parts of the group label refer to the RCA replacement ratio and CRFA replacement ratio in sequence. For example, R50-F0 refers to the NCRAC specimens with an RCA replacement ratio of 50% and a CRFA replacement ratio of 0.

The compressive and flexural strength tests were conducted on the cubic specimens with dimensions of 100 mm × 100 mm × 100 mm and the prismatic specimens with dimensions of 100 mm × 100 mm × 400 mm, respectively. The same prismatic specimens were adopted in both the carbonation test and the electric flux test. The carbonation test was conducted first, followed by the electric flux test. Following the requirements given in the Chinese Standard GB/T 50081 [32], the specimens were poured and cured. After curing for 28 days, the cubic compressive strengths and flexural strengths of RAC were measured, as listed in

Table 3. Cubic compressive strengths and flexural strengths of RAC at 28 days.

Group Label	R50–F0	R100–F0	CR50–F0	CR100–F0	CR50–F10	CR50–F20
Cubic compressive strength (MPa)	42.53	41.46	46.81	46.39	46.64	46.17
Flexural strength (MPa)	3.96	3.78	4.01	3.96	3.99	3.95

.

2.1.3. Carbonation Test of RAC

According to the Chinese Standard GB/T 50082 [31], the carbonation test was carried out when the specimens reached 28 days of age. Two days before the carbonation test, the specimens were taken out from the standard curing room and placed in an oven for 48 h at 60 °C. To ensure the one-dimensional carbonation of the specimens, one prism specimen surface after drying was treated as the erosion surface of CO₂, and the other five sides were coated with epoxy resin for sealing. The carbonation test began after the epoxy resin on the surfaces of the specimens hardened.

Specimens with a bending load level of 0 were directly placed in the carbonation chamber for rapid carbonation. The carbonation chamber was set to a temperature of 20 ± 5 °C, a relative humidity of 70 ± 5%, and a CO₂ content of 20 ± 3%. After carbonating to the corresponding age (0 days, 7 days, and 14 days), the specimens were removed.

The specimens with a bending load level greater than 0 needed to be loaded during the process of carbonation. The bending load was applied by the method of four-point bending. As shown in Figure 1, the loading device consisted of 4 screws, 8 washers, 8 nuts, 2 steel plates, 2 steel column supports, and 1 bottom plate. During loading, a torque wrench was used to tighten the free nuts on the screws so that the load could be transmitted to the steel plates through the nuts and then to the specimen, causing the upper side of the specimen to be pulled and the lower side to be compressed, thereby achieving the purpose of applying a bending load.

Based on the bending load level to be applied, as listed in Table 1, and the flexural strength measured, as listed in Table 3, the total load applied to each specimen was calculated and divided into four parts to gain the actual load required for each screw. Subsequently, the required torque was obtained using the conversion formula between the load and the torque, as written in Equation (1). The torque required for each screw is listed in

Table 4. Torque required for each screw.

Specimen Label	Flexural Failure Load (N)	Bending Load Level	Applied Load (N)	Applied Torque (N·M)
R50–0–0.2–F0–T20	15,518.39	0.2	775.9195	2.72
R50–0–0.4–F0–T20		0.4	1551.839	5.43
R50–7–0.2–F0–T20	15,518.39	0.2	775.9195	2.72
R50–7–0.4–F0–T20		0.4	1551.839	5.43
R50–14–0.2–F0–T20	15,518.39	0.2	775.9195	2.72
R50–14–0.4–F0–T20		0.4	1551.839	5.43
R100–0–0.2–F0–T20	14,832.50	0.2	741.625	2.60
R100–0–0.4–F0–T20		0.4	1483.25	5.19
R100–7–0.2–F0–T20	14,832.50	0.2	741.625	2.60
R100–7–0.4–F0–T20		0.4	1483.25	5.19
R100–14–0.2–F0–T20	14,832.50	0.2	741.625	2.60
R100–14–0.4–F0–T20		0.4	1483.25	5.19
CR50–0–0.2–F0–T20	15,719.00	0.2	785.95	2.75
CR50–0–0.4–F0–T20		0.4	1571.9	5.50
CR50–7–0.2–F0–T20	15,719.00	0.2	785.95	2.75
CR50–7–0.4–F0–T20		0.4	1571.9	5.50
CR50–14–0.2–F0–T20	15,719.00	0.2	785.95	2.75
CR50–14–0.4–F0–T20		0.4	1571.9	5.50
CR100–0–0.2–F0–T20	15,545	0.2	777.25	2.72
CR100–0–0.4–F0–T20		0.4	1554.5	5.44
CR100–7–0.2–F0–T20	15,545	0.2	777.25	2.72
CR100–7–0.4–F0–T20		0.4	1554.5	5.44
CR100–14–0.2–F0–T20	15,545	0.2	777.25	2.72
CR100–14–0.4–F0–T20		0.4	1554.5	5.44

. In order to make the applied bending load more accurate, a new digital torque wrench was used, which could determine whether the applied load met the requirements by observing the digital values. After loading, the specimens were put into the carbonation chamber to start carbonation, as displayed in Figure 2. To avoid stress relaxation in the screws, stress compensation should be performed every 24 h.

$$T=K{F}_{0}d$$

(1)

where T is the tightening torque; K is the tightening torque coefficient, which is taken as 0.25; F₀ is the preload; and d is the nominal diameter of the nuts.

2.1.4. Chloride Penetration Test

After finishing the carbonation test, the central portions of the prismatic specimens were cut into 3 cubic specimens with sizes of 100 mm × 100 mm × 100 mm by using a rock-cutting machine, and the cubic specimens were used for the electric flux test. According to the Chinese Standard GB/T 50082 [31], the electric flux test was carried out using cylindrical specimens with a diameter of 100 mm and a height of 50 mm, so it was necessary to cut the cubic specimens into cylindrical specimens. Firstly, the cubic specimens were cut into rectangular specimens with dimensions of 100 mm × 100 mm × 50 mm, whose upper surface was a CO₂ erosion surface (100 mm × 100 mm). Then, the cylindrical specimens with a diameter of 100 mm and a height of 50 mm were cut from the rectangular specimens.

Epoxy resin was used to seal the sides of the cylindrical specimens obtained. After the epoxy resin solidified, the cylindrical specimens were placed in a vacuum saturation machine, the internal pressure of which was reduced to below 5 kPa within 5 min and maintained for 3 h. Then, deionized water was injected until the upper surfaces of the cylindrical specimens were submerged. After soaking the cylindrical specimens for 1 h, the wastegate was opened to restore normal pressure and soaking was continued for 18 h. After vacuum saturation was completed, the cylindrical specimens were placed in the test chamber, and the chamber was injected with distilled water. The test chamber was left to stand for 10 min to check for any water leakage around it. If there was no water leakage, it indicated that the seal between the cylindrical specimen and the test chamber was good. The test chamber connected to the negative pole of the power supply was injected with a 3.0% NaCl solution, while the test chamber connected to the other pole was injected with a 0.3 mol/L NaOH solution. Subsequently, the wire was connected to an electric flux meter. After being powered on for 6 h, the electric flux of the cylindrical specimens was recorded. Finally, the average electric flux of 3 specimens was taken as the measurement value of the electric flux for each group.

2.2. Database Construction

A new machine learning model database was established by summarizing the experimental data in Section 2.1, with a total of 40 experimental data samples. Figure 3 and

Table 5. Information statistics of input and output variables in the database.

Classification	Variable	Data
		Min.	Max.	Mean	Std.
Input	YN	0	1	0.55	0.50
	r (%)	50	100	72.5	25.19
	L	0	0.4	0.18	0.17
	t (day)	0	14	6.65	5.71
	T (°C)	20	40	20.75	3.50
	f (%)	0	20	0.75	3.50
Output	E (C)	2324.21	5561.99	3459.68	814.65

show the distributions of input and output variables. In Figure 3, the purple shaded area represents the Gaussian probability density distribution of the IFs, while the blue solid line indicates the median of the distribution of electric flux when each IF was at a specific value. The purple dashed line shows the quarter and three-quarters percentiles of the distribution of electric flux when each IF was at a specific value. Six IFs were considered as input variables, including the carbonation of RCA (YN), RCA replacement ratio (r), bending load level (L), carbonation time of RAC (t), carbonation temperature of RAC (T), and CRFA replacement ratio (f), with ranges of 0 or 1, 50–100%, 0–0.4, 0–14 days, 20–40 °C, and 0–20%, respectively. The output variable was the electric flux (E), which ranged from 2324.21 C to 5561.99 C.

2.3. Parametric Sensitivity Analysis

In the process of building machine learning models, if there is a significant interdependence among the input variables, that is, if there is redundancy in the input data, it will lead to a decrease in model performance or even the inability to train, causing the multicollinearity problem [33]. Smith [34] showed that the correlation coefficients of the input variables involved in constructing the model should be kept below 0.80, which would help maintain low collinearity between the input variables and improve the stability and accuracy of the model. The correlation coefficients between all input variables selected in Section 2.2 were computed, and the results are shown in Figure 4. It can be seen from Figure 4 that the absolute values of the correlation coefficients between different input variables were far less than 0.80, with a maximum of only 0.500. This indicated that the multicollinearity between the selected variables was not significant and met the prerequisite for modeling. Moreover, to ensure the generality of the machine learning model, the minimum ratio between the database size and the number of input variables should be between 3 and 5 [35]. In this section, the ratio between database size and the number of input variables was 7, which met this requirement. Considering that processing results were affected by different dimensions, it was not feasible to directly import input variables into the constructed machine learning model. Therefore, in the early stage of modeling, it was necessary to standardize the raw data to a normal distribution. This not only helped to eliminate the impacts caused by different dimensions of input variables but also reduced the sizes of the input data, thereby accelerating the training process of some models (such as ANN) and improving the training efficiency [35].

3. Machine Learning Algorithms

The machine learning models ANN, SVM, RF, and XGBoost, as the four most commonly used models, were adopted in this paper, and their basic principles are as follows:

ANN is a kind of computational model that mimics the working principles of biological neural networks (such as the human brain), and it is used to simulate complex relationships between inputs and outputs. ANN is composed of a large number of nodes (called neurons) that are connected to each other in the form of “weights”. Each neuron can receive and process the input and then generate the output. These neurons are organized into different layers. For instance, the input layer receives external signals, and one or more hidden layers are located between the input and output layers, which are responsible for actual data processing. The output layer generates processing results. Due to its powerful non-linear and parallel processing capabilities, ANN can be adopted to simulate different kinds of non-linear complex relationships between the data input and output [35].

SVM is a machine learning technique used to solve classification problems; the principle of minimizing structural risk is to achieve the minimum upper limit of expected risk and find an optimal hyperplane to separate two different classifications [36]. The goal is to maximize edges in order to achieve better classification performance of the data, and when the optimal hyperplane is found, the points on the boundary are called support vectors. This non-probabilistic binary linear classifier records data as points in space and maps them to ensure that different categories of data are recorded as clearly as possible. When making new data predictions, the new data will be mapped to the same space, and the category they belong to will be determined based on their location.

RF is an integrated bagging method that utilizes regression trees to improve the accuracy and robustness of the overall model by combining the prediction results of multiple decision trees. Due to its limited parameters and high parallel computing capability, this algorithm has been widely adopted in the field of civil engineering [37,38]. RF consists of multiple decision trees, each of which is trained on a randomly selected dataset and is featured during the training process. The core idea behind it is the bagging algorithm, also known as Bootstrap aggregating. In this method, the original training dataset is randomly resampled to generate multiple subsets, each of which is used to train an independent decision tree. This resampling allows the same data to appear in different subsets, which can increase the diversity of the model and improve data utilization.

XGBoost is a typical machine learning algorithm for newly established boosting ensemble learning models [39], which is a comprehensive enhanced version of GBDT, with the difference being the loss function of the model. It improves learning performance by sequentially adding models (usually decision trees), with each new model adjusted based on the performance of previous models to better predict data. The loss function of XGBoost adds a regularization term on the basis of GBDT to control the complexity of the model and avoid overfitting problems. During the optimization process of XGBoost, the second-order Taylor expansion is applied to the loss function, utilizing both first-order and second-order derivative information. Therefore, its performance has greatly improved compared to GBDT.

4. Model Operation and Result Analysis

4.1. Model Training

The ANN, SVM, RF, and XGBoost algorithms mentioned in Section 3 are adopted to establish corresponding machine learning models. The performance of hyperparameters of various machine learning models on different datasets is evaluated using the 5-fold cross-validation method to select the optimal model, as shown in Figure 5. Firstly, the hyperparameter ranges are determined based on prior experience, and the combination of the optimal parameters is determined through grid search optimization. During the process of optimization, the models are validated by a five-fold cross-validation method with MSE as the objective function. For each model, the above process is repeated five times on five datasets, and the average MSE is taken as the final performance of the model.

This paper primarily addresses model overfitting by applying regularization parameters. Specifically, for ANN, various alpha values are tested, which control L2 regularization, and these values help prevent overfitting by penalizing large weights. For SVM, different C values are explored, with lower C values increasing the regularization strength, thus helping to avoid overfitting. For tree-based models like RF and XGBoost, limiting max_depth and testing a range of ccp_alpha values helps control tree growth and prevent overly complex trees. Additionally, XGBoost uses varying learning_rate values, with lower rates leading to slower but more stable learning. Furthermore, for each model parameter (including those mentioned above), we apply five-fold cross-validation to tune the parameters. The parameter combination that produces the best average performance across the folds is selected as the final model, helping to reduce the model sensitivity to specific data splits. Together, these strategies reduce the risk of overfitting by balancing training accuracy with model generalization. The ranges of hyperparameters are tabulated in

Table 6. Parameters of models.

Model	Parameters and Ranges
ANN	hidden_layer_sizes				alpha
	(8, 8), (16, 16), (16, 16, 16), (16, 16, 16, 16), (32, 32), (64, 64), (128, 128)				0.001, 0.005, 0.01, 0.05, 0.1, 1
SVM	kernel	C	gamma	/	/
	linear, poly, rbf, sigmoid	0.01, 0.03, 0.05, 0.1, 0.3, 0.5, 1, 5, 10, 100	scale, auto	/	/
RF	n_estimators	max_depth	ccp_alpha	/	/
	50, 100, 150, 200, 250, 500	5, 10, 15, 20, None	1, 0.5, 0.1, 0.05, 0.01	/	/
XGBoost	n_estimators	max_depth	learning_rate	/	/
	50, 100, 150, 200, 250, 500	5, 10, 15, 20, none	0.01, 0.05, 0.1, 0.15, 0.2	/	/

.

The regularization technique is adopted to prevent model overfitting. The regularization technique restricts the learning ability of the model by introducing penalty terms that increase the complexity of the model, avoiding the phenomenon of overfitting to the training data due to the unlimited increase in model complexity and thereby improving the generalizability and reliability of the model, which can be expressed as:

$$\tilde{J}(w,X,y)=J(w,X,y)+\alpha \Omega (w),$$

(2)

where $\tilde{J}$ is the total loss of the model; w is the model parameter; X is the training sample; y is the corresponding label; J is the objective function; α is the penalty coefficient; and Ω is the penalty term. Different penalty terms have different preferences for the optimal solution of w.

The n-order penalty function is called Ln regularization. In this paper, using L1 regularization, the Lasso regularization, as shown in Equation (3), is introduced into the loss function to limit the size of the model parameters, ensuring the simplicity of the model and facilitating its interpretation. Meanwhile, an excessively large penalty coefficient is not conducive to optimizing the model, so the range of α is 0.1–1.

$$\mathrm{L}1:\Omega (w)= ||w|{|}_1={\displaystyle \sum _i|} w_i|$$

(3)

4.2. Model Evaluation

The coefficient of determination (R-squared, R²), absolute deviation (BIAS), and mean absolute percentage error (MAPE) are used as evaluation indicators, and the calculation formulas are shown in Equations (4)–(6), respectively. Among them, BIAS is adopted to measure the average absolute difference between the predicted values of the model and the experimental values, reflecting the degree of overestimation or underestimation of the predicted values relative to the experimental values, while MAPE is adopted to characterize the relative deviation of the predicted values. If the two indicators are both smaller, it indicates the accuracy of the model is better. The R² is used to measure the goodness of the fitting effect of the model.

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle \sum _{i=1}^n{(y_i-{\overline{y}}_i)}^2}}}$$

(4)

$$BIAS={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\frac{{\widehat{y}}_i-y_i}{y_i}}$$

(5)

$$MAPE={\displaystyle \frac{100\%}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{{\widehat{y}}_i-y_i}{y_i}\right|}$$

(6)

where ${\widehat{y}}_i$ and $y_i$ are the predicted values of the model and the experimental values, respectively; ${\overline{y}}_i$ is the average value of all experimental values; and n is the number of samples.

4.3. Model Results

The best model is obtained based on cross-validation and grid search optimization, and evaluation metrics are calculated on the testing set to examine the performance and the generalizability of the model. The performance indexes of the developed models are summarized in

Table 7. Summary of performance indexes for developed models.

Index	Data	ANN	SVM	RF	XGBoost
R2	training	0.964	0.991	0.950	0.988
	testing	0.929	0.897	0.843	0.959
	all	0.955	0.966	0.923	0.981
BIAS	training	−1.762	−11.712	−0.832	−1.381
	testing	28.649	64.753	66.008	50.021
	all	4.320	3.581	12.536	8.899
MAPE	training	3.431%	2.201%	4.534%	1.864%
	testing	4.818%	3.753%	7.871%	4.339%
	all	3.708%	2.512%	5.202%	2.359%

. It can be seen from Table 7 that all four models have shown good performance in predicting the chloride ion permeability resistance of RAC, with values of R² that are all above 0.80 after training on the testing set. The R² of the XGBoost model trained on the testing set is 0.959, which is 3.23%, 6.91%, and 13.76% higher than the values of the ANN model, SVM model, and RF model, respectively. This indicates that the XGBoost model has the best fitting performance for the samples. Moreover, the BIAS of the four models on the testing set are all greater than 0 and lower than 70, indicating high prediction accuracy, and each model tends to overestimate the actual electric flux. The BIAS of the ANN model on the testing set is 28.649, which decreases by 55.76%, 56.60%, and 42.73% compared to the SVM model, RF model, and XGBoost model, respectively. It shows that the ANN model has the lowest degree of overestimation of the predicted values relative to the experimental values. In addition, the MAPE values of the four models trained on the testing set are all below 8%, demonstrating high prediction accuracy in practical engineering applications, and the MAPE of the SVM model trained on the testing set reaches 3.753%, which is 22.11%, 52.32%, and 13.51% lower than the values of the ANN model, RF model, and XGBoost model, respectively. This reflects that the SVM model has the smallest difference between the predicted and experimental values. Moreover, regarding the XGBoost model trained on the testing set, the R² is significantly greater than the other three models, and the BIAS and MAPE are hardly any different from other models, demonstrating that the XGBoost model can achieve the best fitting effect on the sample with a low degree of relative deviation in the predicted values. Therefore, the XGBoost model is the optimal model for predicting the chloride ion permeability resistance of RAC.

Figure 6 shows the scatter diagrams of regression prediction results for four models. It is not difficult to find that most of the data points of the four models are distributed around the line (y = x), and the predicted values of the electric flux are concentrated within the error limit of ±10%. Moreover, the MAPE medians are all below 9%, illustrating that the prediction accuracy of all four models is relatively high. Among them, the predicted values of the electric flux of the XGBoost model are all within the error limit of ±10%, which is closer to the experimental values. The MAPE median of the XGBoost model is 4.66%, and the MAPE values of all samples are less than 8%. The XGBoost model has good stability and few outliers, and its anti-interference capability is strong. This once again indicates that the prediction accuracy of the prediction model of the electric flux for RAC based on the XGBoost algorithm is the highest.

Figure 7 shows a comparison between the predicted and experimental values of the electric flux of RAC for the four models. From Figure 7, it can be intuitively seen that the predicted values of all four models are in good agreement with the experimental values. Moreover, the prediction accuracies of the XGBoost model and the SVM model are significantly better than the other two models. However, at local extremum points, the XGBoost model has higher prediction accuracy, further confirming that the XGBoost model has the best prediction ability.

According to the above analysis, it can be seen that the methods of machine learning can accurately predict the chloride ion permeability resistance of RAC, but the prediction performance of different models varies. Zhang et al. [40] conducted a study using the prediction models of machine learning on the chloride ion permeability resistance of ordinary concrete and obtained similar conclusions.

4.4. Model Interpretability

Based on the optimal XGBoost model, the LIME method [41] is adopted to explain the predicted results of the models. Figure 8 shows the analysis results of the importance (absolute value) of the IFs of the electric flux, with the mean values of the importance of each IF in parentheses. The impacts of various IFs on the electric flux of RAC show significant differences, among which r has the greatest impact, reaching 1.29, while YN is only 0.38 and has the smallest impact. The importance ranking of IFs on the electric flux is r > t > f > T > L > YN. Overall, L shows a weak negative correlation, while the other variables show a positive correlation. In addition, f displays a significant positive correlation; that is, an increase in f can significantly improve the electric flux of RAC.

Figure 9 provides an explanation of the XGBoost model at the global level. The results indicate that each IF has a significant nonlinear relationship with the electric flux of RAC, and the relationship between each IF and the electric flux is not simply a positive or negative correlation. The four IFs, including r, t, f, and T, are positively correlated with the electric flux when their values are small, but when their values are greater than a certain degree, they show a negative correlation. However, for the remaining two IFs, that is, YN and L, their relationship with the electric flux is opposite.

Figure 10 provides local explanations for each individual sample. The benchmark value is the minimum value predicted by the XGBoost model for the entire database, which is 2324.21 C. The visualization results in Figure 10 suggest that the predicted result of the samples is 3992.3 C. Besides, r, t, f, and T provide positive contributions to the results of the electric flux, while YN and L show negative contributions to the results.

4.5. Development of GUI

A graphical user interface (GUI) for the electric flux of RAC that considers the effects of multiple factors is developed based on the Python 3.8 software to efficiently and accurately predict the chloride ion permeability resistance of RAC, as shown in Figure 11. Users can execute the program through the following steps. Firstly, whether to carry out carbonation strengthening treatment on RCA needs to be selected. Secondly, the values of various variables are input or adjusted. Thirdly, the model used for prediction is specified. Fourthly, the button “Analyze” is clicked, and the results are displayed in the output box. Finally, the prediction results based on the GUI are used to evaluate the chloride ion permeability resistance of RAC.

5. Conclusions

In this study, by considering the influence of the carbonation of RCA, the RCA replacement ratio, the bending load level, the carbonation time and temperature of RCA, and the CRFA replacement ratio, the chloride penetration test was designed to measure the electric flux of RAC. Then, based on the experimental data, a prediction model of the electric flux for RAC based on machine learning was proposed. The main conclusions are as follows:

(1)

Four prediction models of machine learning for the electric flux of RAC were constructed using ANN, SVM, RF, and XGBoost. All four models performed well, with values of R² all above 0.80, BIAS greater than 0 but below 70, and MAPE below 8% when trained on the testing set. They were all able to accurately predict the electric flux of RAC, demonstrating the reliability of using machine learning methods for prediction. The XGBoost model was the optimal model, with an R² of up to 0.959 and BIAS and MAPE as low as 50.021 and 4.339%, respectively, when trained on the testing set.

(2)

The prediction results of the models were explained both globally and locally based on the LIME method. The importance ranking of IFs on the electric flux was r > t > f > T > L > YN. L showed a weak negative correlation with the electric flux, while the other variables showed a positive correlation. Each IF had a significant nonlinear relationship with the electric flux of RAC. For the four IFs, including r, t, f, and T, they were positively correlated with the electric flux when their values were small. However, when their values were greater than a certain degree, they showed a negative correlation. However, for YN and L, their relationships with the electric flux were opposite.

(3)

A GUI for the electric flux of RAC considering the effects of multiple factors was developed based on Python 3.8 software in order to efficiently and accurately predict the chloride ion permeability resistance of RAC.

(4)

The experimental data used to establish the prediction model of the electric flux for RAC based on machine learning was limited in this research. In the future, more IFs (such as axial compression load, water-to-cement ratio, and strength of waste concrete) could be considered to conduct supplementary experiments. More experimental data should be adopted to revise the proposed model.