Prediction of Compressive Strength and Elastic Modulus for Recycled Aggregate Concrete Based on AutoGluon

Abstract

While the civil construction industry brings great convenience to life, the large amount of waste concrete also poses a significant problem of construction waste disposal. As one of the effective ways to utilize waste concrete, recycled aggregate concrete (RAC) can improve the environment while reducing the consumption of construction materials. This study aims to use AutoGluon (AG), an automated machine learning platform, to predict both the compressive strength and elastic modulus of RAC. Then the performance of AG is compared with traditional empirical formulas and multiple linear regression models. The determination coefficient (R²) is chosen as one of the evaluation standards for predicting values. The results demonstrate that the WeightedEnsemble model of AG performed best in predicting both the compressive strength and elastic modulus, which provides a new method for the rapid and accurate prediction of the properties of RAC in engineering construction.

1. Introduction

With the continuous progress of urbanization, civil construction-related industries continue to develop. Numerous construction projects have produced much construction waste while improving people’s lives. The statistical results illustrate that the average annual production of construction waste in China has reached 90 million tons, and there is a trend of year-on-year growth [1]. It is worth noting that concrete waste is the most significant component of construction waste, accounting for about 35% [1]. Currently, construction waste materials are mainly dealt with by landfill and accumulation, which not only causes a large amount of resource waste but also results in severe environmental pollution [2,3]. The current disposal method is a serious departure from sustainable development goals [4]. The current disposal force, increasing the recycling of wasted concrete, plays a significant role in improving our ecological environment.

In order to improve the reuse of construction waste, many countries have carried out in-depth research on the mechanical properties of recycled aggregate concrete (RAC). RAC is a sort of environment-friendly concrete which can be obtained by mixing the waste concrete with a certain amount of natural aggregate after crushing, processing, and sorting [5]. Recycling discarded concrete can effectively solve the problem of harmless treatment and alleviate the ecological pollution brought by the civil construction industry [6]. Kazmi et al. [7] illustrated that the mechanical characteristics of RAC significantly differ from ordinary concrete under the same mix ratio condition. Compared with ordinary concrete, the compressive strength and elastic modulus of RAC can be reduced by about 26% and 35% [7]. Therefore, the existing prediction models for the compressive strength and elastic modulus calculation of ordinary concrete cannot accurately predict the related properties of RAC.

Previous research on the mechanical properties prediction of RAC is usually based on several groups of data measured in experiments or a large number of databases established to fit linear or nonlinear regression prediction formulas [8,9]. It is evident that the equation fitted from the experimental results requires a tedious experimental process and is often restricted by limited data. In addition, the mathematical theoretical derivation of the database is subject to inherent errors due to the simplified approximation of the correlation among complex parameters. Therefore, with the rapid development of modern computer technology, various machine learning techniques with higher prediction accuracy are widely used to analyze and predict the properties of RAC.

Hou and Zhou [10] used machine learning algorithms, such as Gaussian process regression and Radia Basis Function (RBF) neural network, to establish a prediction model for rectangular concrete-filled steel tubular columns’ bias-bearing capacity. They verified that the results from the machine learning are more accurate than the norm and original formula [10]. Liu [11] predicted the properties of ordinary homemade concrete in tunnel engineering through five kinds of machine learning, including the decision tree and integrated learning. The maximum relative error of the outcomes is controlled within 10% [11]. In addition, various artificial neural network algorithm models, including random forest, correlation vector machine, reference model, BP neural network, and multi-layer neural network, have also been applied to predict the performance on compressive strength of the RAC [12,13,14,15]. It provides a reliable basis for allocating RAC according to the requirements of actual projects. However, since the realization of machine learning depends on the continuous debugging of hyperparameters in machine learning models and algorithm pre-processing by professionals, the period of model training and deployment is forced to be prolonged with the high professional requirements for users. The existing machine learning framework needs to carry out many algorithm combination selections and hyperparameter optimization to determine the model used and its corresponding hyperparameters from a mass of models. Due to the high workload and resource requirements for machine learning model training, it is difficult for non-professional users to apply this technology [9,16]. In this case, the invention of automatic machine learning (AutoML) realizes the complete automation of the machine learning process, which can not only effectively reduce the requirement for professional knowledge, but also significantly improve the availability and convenience of machine learning methods.

Among various machine learning platforms, AG, an open-source automatic machine learning framework developed by Amazon, is selected as the technical basis in this study to establish a high-precision performance prediction model for RAC. This paper first introduces the AG framework and its corresponding model training process. Then, based on the existing literature collection, the experimental data set of RAC is established, and the model training is carried out. After comparing the results of the traditional empirical formula and classical multivariate linear regression with that of AG, the practicability and superiority of the AG model are verified and analyzed.

2. AutoGluon Technology

2.1. Introduction and Advantages of AutoGluon

AutoML is a subfield in machine learning. It effectively combines the advantages of automation and machine learning. Users can deploy machine learning programs and then effectively verify and test the performance of the deployed program [17]. Based on this platform, users only need to develop their data set, and there is no need to learn deeply about the detail of machine learning models. An automatic machine learning platform can deal with whole steps, including data pre-processing, automatic feature selection (data normalization), auto algorithm choice, hyperparameter optimization (e.g., grid search, random searching, Bayesian optimization), auto pipeline development, neural architecture search, auto model choice, and ensemble learning to decide on the best model.

AG is an open-source AutoML frame developed by Erickson et al. in 2020 [9]. As a machine learning platform, compared with the traditional AutoML platform or artificial intelligence, the most outstanding advantage of AG is to avoid vast works for model choice and hyperparameter optimization process of the existing AutoML platform. It also shows a high prediction accuracy based on an original unpretreated database [18]. During the usage of AG, there is no need to learn about the running principle, even the content of the data set; users can use the data set directly and easily. Meanwhile, AG can deal with various kinds of structural data. If the preset training model does not match the original data set, AG has enough ability to solve the problems by itself, without intervention and choice from humans. In addition, it can not only take a high-level data treatment, deep learning, and multi-layer model integration but also automatically identify the data category in each column to measure those data, including the particular measurement of the text field. AG can also automatically optimize the AutoML processes like model network intelligence. Stopping or renewing the training process is another function of AG. Users can determine the training time required for the learning process and return the training results in time to provide the adjustment convenience based on the demand from users [9]. In short, this new AutoGluon AutoML platform simplifies the complex working process of AutoML, which means it decreases the professional requirement of the users to make more researchers could use the AutoML method to help with the studies. Those users could run the AutoML process without those difficult coding processes; the AutoML algorithm functions could be implemented within several lines of code, which is almost no impede to use the modern algorithm tools [19].

2.2. AutoGluon-Based Model Training

The regression and classification problem of table data is the essence of the prediction of RAC compressive strength and elastic modulus. This study uses AutoGluon Tabular, a framework for the prediction of tabular data in AG, to automatically classify the problem types and data regression based on the structural data in the comma-separated values format files [20]. There are various algorithms provided by AG frames, including the Neural Networks algorithm, the Machine Learning algorithm, which contains the Random Forest algorithm and Extreme Random Trees algorithm, the K-nearest Neighbors algorithm, and two types of Boosting Tree algorithm which are CatBoost and LightGBM. AG also covers integrated learning algorithms to improve prediction accuracy [20]. AG users can specify specific machine learning models for model training and model optimization [21].

Different from traditional machine learning, which only selects a single model for training, the output result of AG is integrated by combining multiple models. The results of the data prediction project show that AG performs better than any single training model in its training process [9]. As shown in Figure 1, the single model in the base firstly trains the input parameters. Then the prediction results are concentrated together and delivered to the next training level with several stacks to retrain. In the final layer, the model integrates the predictions of each model in the stack based on the weights [9]. AG combines the pre-built machine learning models through a multi-layer stack (typically 1 to 3 layers) and outputs them as a new fusion model. Meanwhile, AG reduces the prediction error with the help of the k-rule bootstrap aggregation algorithm (the value of k is usually 5 to 10), which optimizes the prediction model [18]. During model fusion and optimization, users can also set the value of stacking levels and the value of ‘k’. AG will automatically choose the suitable value if there is no specialized setting value [18]. The advantages of multi-layer stack and k-rule guided aggregation algorithms are not only in model fusion and model enhancement but also in avoiding the overfitting problem caused by the original data or the model itself during the machine learning process. Therefore, AG effectively improves the superior performance of the fusion models obtained from AutoML training in prediction scenarios in many ways.

Figure 1. AG’s multi-layer stacking strategy [14].

3. Data Collection and Evaluation Indicators

3.1. Data Collection

In construction engineering, compressive strength and elastic modulus are critical mechanical properties of concrete, which are usually used to evaluate and control the performance and quality of all kinds of mixed concrete [22]. Currently, the compressive strength and elastic modulus of RAC worldwide are primarily obtained through experiments. The experimental data show that the compressive strength, elastic modulus, and various engineering characteristics of RAC are mainly related to various factors, including the consumption of water, cement, natural aggregate, recycled aggregate, water-reducing agent, additional water, and ultra-fine additives, such as silica fume and fly ash [23]. In order to use AG to train and evaluate the compressive strength and the elastic modulus of RAC, an extensive literature survey was first conducted. We collected 842 groups of mix design and its corresponding compressive strength data and 430 groups of mix design and its corresponding elastic modulus data of RAC concrete from experimental data of 84 literatures, then the impact parameters common to different literatures were extracted and then established into two relevant databases, the specific literatures and corresponding data are listed in Appendix A and Appendix B. Among them, the contents of water, cement, natural coarse aggregate, fine natural aggregate, recycled coarse aggregate, fly ash, silica fume, and water-reducing agent per cubic meter of RAC are selected as the input parameters during the prediction process in the AutoML. The corresponding compressive strength and elastic modulus are selected as output parameters. For the experimental data of compressive strength of RAC, the experimental water content ranges from 116 kg to 271 kg, the amount of cement ranges from 190 kg to 667 kg, the amount of natural coarse aggregate and natural fine aggregate ranges from 0 kg to 1376 kg and 0 kg to 1020 kg, respectively. The amount of recycled coarse aggregate is between 0 kg and 1292 kg. Fly ash, water reducing agent dosage range of 0–234 kg, 0–9.9 kg. The output parameter compressive strength ranges from 17.29 MPa to 80.4 MPa. The statistical information of all features in the database is shown in Table 1. For the experimental data of elastic modulus of RAC, the experimental water content is between 94 kg and 246 kg, and the amount of cement is between 184.5 kg and 546 kg. The amounts of natural coarse aggregate and natural fine aggregate range from 0 kg to 1278 kg and 465 kg to 1073.43 kg, respectively. The amount of recycled coarse aggregate ranges from 0 kg to 1278 kg. Fly ash, silica fume, water reducing agent dosage range of 0–225.5 kg, 0 kg to 38 kg, 0–7.1 kg. The output parameter elastic modulus ranges from 3.67 GPa to 44.9 GPa. The statistics of all features in the database are shown in Table 2.

Table 1. Characteristic of RAC compressive strength parameter.

Type	Variable	Max	Min	Median	Mean	Standard Deviation
Input Value	water [kg]	271.00	116.00	185.49	189.90	23.25
	cement [kg]	667.00	190.00	386.50	393.36	74.48
	natural fine aggregate [kg]	1020.00	0.00	648.00	647.35	126.76
	natural coarse aggregate [kg]	1376.00	0.00	787.50	679.37	363.74
	recycled coarse aggregate [kg]	1292.00	0.00	313.00	417.09	354.19
	water reducer [kg]	9.90	0.00	0.00	0.40	1.41
	silicon ash [kg]	0.00	0.00	0.00	0.00	0.00
	fly ash [kg]	234.00	0.00	0.00	6.66	27.96
Output value	compressive strength [MPa]	80.40	17.29	40.80	41.19	10.56

Table 2. Characteristic of RAC elastic modulus parameter.

Type	Variable	Max	Min	Median	Mean	Standard Deviation
Input Value	water [kg]	246.00	94.00	200.00	190.79	30.61
	cement [kg]	546.00	184.50	373.00	378.62	83.71
	natural fine aggregate [kg]	1073.43	465.00	644.00	663.06	110.08
	natural coarse aggregate [kg]	1278.00	0.00	588.00	572.92	411.40
	recycled coarse aggregate [kg]	1278.00	0.00	469.41	501.23	419.42
	water reducer [kg]	7.10	0.00	0.00	1.10	2.08
	silicon ash [kg]	38.00	0.00	0.00	0.27	3.16
	fly ash [kg]	225.50	0.00	0.00	26.11	47.47
Output value	elastic modulus [GPa]	44.90	3.67	28.11	27.92	7.30

The original data are randomly divided into training and test sets. The training set is used to train the model, and the test set is used to evaluate the effectiveness of the trained model but does not change the model parameters and effects. If the training set is too large or too small, the accuracy of the training model will be affected. Besides, when the order of magnitudes of data is within ten thousand, the corresponding data sets are divided into 7:3, and there is no interaction between the training set and the test set. For the subdatabase of compressive strength, the training set includes 603 groups, and the test set includes 239 groups. For the subdatabase of elastic modulus, the training set includes 353 groups, and the test set includes 77 groups. The AutoGluon Tabular function based on tabular data prediction in AG is used to predict RAC’s compressive strength and elastic modulus.

3.2. Evaluation Criteria

This study uses the following statistical parameters to evaluate the predictive performance of automatic machine-learning techniques for compressive strength and elastic modulus of RAC. These include mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination ($R^2$), where m represents the total number of related parameter samples of RAC, $\overline{X}$ represents the average value of the compressive strength or elastic modulus of recycled aggregate concrete, X represents the experimental value of the compressive strength or elastic modulus of RAC, Y represents the predicted compressive strength or elastic modulus of RAC.

Mean absolute error (MAE) is the average of the absolute value difference between a single physical quantity and the arithmetic mean, which can represent the error well. The expression is as follows.

$$MAE=\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\left|Y-X\right|$$

(1)

Root mean square error (RMSE) is a statistical index to measure the accuracy of the forecast. The smaller the value, the higher the accuracy. The expression is as follows.

$$RMSE=\sqrt{\frac{1}{m}{\displaystyle \sum }_{i=1}^m{\left(Y-X\right)}^2}$$

(2)

Mean absolute percentage error (MAPE) measures the relative size of deviation between the actual value of the sample and the predicted value, which is expressed by percentage. A small value indicates a slight deviation. The expression is as follows.

$$MAPE\left(\%\right)=\frac{1}{m}{{\displaystyle \sum }}_{i=1}^m\left|\frac{Y-X}{X}\right|\ast 100$$

(3)

The determination coefficient ($R^2$) unifies the data dimension and can describe the overall regression trend. The closer the value is to 1, the better the regression performance of the model is. It can be expressed as:

$$R^2=1-\frac{{{\displaystyle \sum }}_{i=1}^m{\left(Y-X\right)}^2}{{\left(X-\overline{X}\right)}^2}$$

(4)

This study uses $R^2$ as an evaluation standard to intuitively show the prediction accuracy of compressive strength and elastic modulus of RAC.

4. Results and Discussion

4.1. Predictions Based on AutoML Models of AG

Figure 2 shows the prediction results of the compressive strength of RAC by using nine machine-learning models and one integrated model. Table 3 lists the evaluation indicators $R^2$, MAE, RMSE, and MAPE for each model on the training and test data sets. Among these, 70 percent of the compressive strength data of RAC are used to train ten models, and the corresponding evaluation parameters and the best model with the highest accuracy are automatically presented. The remaining 30 percent of the data are used to verify the accuracy of trained models and present the evaluation parameters compared with real experimental data. In the test sets of the nine machine learning models, the models CatBoost, LightGBMXT, LightGBM, and ExtreTreeMSE exhibit high prediction accuracy with $R^2$ of 0.847, 0.829, 0.822, 0.821, MAE of 2.064, 2.417, 2.428, 2.148, RMSE of 3.738, 3.951, 4.008, 4.043, and MAPE of 6.291, 7.174, 7.289, 6.372, respectively. In comparison, the best-trained model, WeightedEnsemble, integrates the results of several models and, thus, has the highest prediction accuracy in testing results with evaluation parameters of 0.845, 2.100, 3.757, and 6.402, respectively. The results demonstrate that the compressive strength of RAC predicted by the model WeightedEnsemble is closest to the actual experimental values, and the prediction results show a higher evaluation index.

Figure 2. Compressive strength prediction model for RAC based on AG.

Table 3. Evaluation parameters for compressive strength of RAC.

Model	Evaluation Parameter
	R²		MAE		RMSE		MAPE
	Training Results	Testing Results	Training Results	Testing Results	Training Results	Testing Results	Training Results	Testing Results
CatBoost	0.875	0.847	2.104	2.064	3.768	3.738	5.800	6.291
XGBoost	0.844	0.802	2.440	2.425	4.222	4.253	6.572	7.210
WeightedEnsemble	0.877	0.845	2.090	2.100	3.736	3.757	5.748	6.402
LightGBMLarge	0.845	0.786	2.374	2.463	4.193	4.420	6.365	7.511
RandomForestMSE	0.799	0.735	2.715	2.795	4.782	4.921	7.400	8.181
LightGBM	0.855	0.822	2.403	2.428	4.040	4.008	6.568	7.290
ExtraTreeMSE	0.815	0.821	2.576	2.148	4.597	4.043	7.283	6.372
LightGBMXT	0.835	0.829	2.590	2.417	4.329	3.951	7.348	7.174
NeuralNetTorch	0.574	0.661	4.262	3.253	6.970	5.572	11.903	8.956
NeuralNetFastAI	0.560	0.631	4.677	3.736	7.083	5.816	14.216	11.266

Figure 3 shows the elastic modulus prediction results of nine machine learning models and one integrated model about RAC. As same as the compressive strength of RAC, 70 percent of the elastic modulus data are used to train ten models, and the remaining 30 percent of data are used to verify the accuracy of trained models and present the evaluation parameters compared with real experimental data. Its corresponding evaluation indicators $R^2$, MAE, RMSE, and MAPE are listed in Table 4, where $R^2$ is 0.962, 0.958, 0.947, 0.912, MAE is 0.889, 0.967, 1.082, 1.381, RMSE is 1.454, 1.523, 1.716, 2.219, MAPE is 1.454, 1.523, 1.716, 2.219. Similarly, the evaluation indicators of the model WeightedEnsemble are 0.957, 0.900, 1.546, and 5.073, which best predict the elastic modulus of RAC with the higher prediction accuracy.

Figure 3. Elastic modulus prediction model for RAC based on AG.

Table 4. Evaluation parameters for elastic modulus of RAC.

Model	Evaluation Parameter
	R²		MAE		RMSE		MAPE
	Training Results	Testing Results	Training Results	Testing results	Training Results	Testing Results	Training Results	Testing Results
CatBoost	0.816	0.962	2.153	0.889	3.114	1.454	9.833	4.958
XGBoost	0.768	0.958	2.276	0.967	3.496	1.533	11.964	5.618
WeightedEnsemble	0.818	0.957	2.150	0.900	3.101	1.546	9.817	5.073
LightGBMLarge	0.765	0.947	2.417	1.082	3.509	1.716	11.210	6.759
RandomForestMSE	0.706	0.912	2.685	1.381	3.935	2.219	14.173	9.184
LightGBM	0.771	0.911	2.397	1.156	3.467	2.270	10.959	6.846
ExtraTreeMSE	0.634	0.910	2.940	1.420	4.395	2.247	17.016	9.316
LightGBMXT	0.740	0.858	2.533	1.556	3.631	2.359	12.614	9.402
NeuralNetTorch	0.506	0.540	3.191	2.576	5.107	5.070	20.875	20.106
NeuralNetFastAI	0.204	0.507	3.682	3.315	5.407	5.210	21.691	21.181

4.2. Comparison with Existing Empirical Formulas

In this study, we selected the empirical equations obtained from the study of Gholampour et al. [24] for the prediction of the compressive strength and elastic modulus of RAC. The empirical equations are as follows.

$$f_{c,cube}^{\prime }\left(MPa\right)=\frac{19.1\ast {0.998}^{RCA\%}\ast \left(w_{eff}/c+0.33\right)}{{\left(w_{eff}/c\right)}^{1.5}}$$

(5)

$$E_c\left(GPA\right)=16\ast \left(6.1-0.015r\right)\ast {\left(5.3-\frac{1.7w_{eff}}{c}\right)}^{3.9}$$

(6)

where $f_{c,cube}^{\prime }$ denotes the predicted compressive strength of RAC, $E_c$ denotes the predicted elastic modulus of RAC, RCA% denotes the replacement rate of coarse aggregate in recycled aggregate concrete in percentage, $w_{eff}/c$ denotes the effective water–cement ratio in the design of RAC mix.

The corresponding values from the database in this study are substituted into this formula to calculate the compressive strength and elastic modulus of RAC. The calculated results are compared with the actual experimental data provided in the available database. Figure 4 shows the predicted results of this empirical formula. For the compressive strength of RAC, the evaluation index is about 0.103 for $R^2$, 7.819 for MAE, 9.919 for RMSE, and 21.759 for MAPE, the evaluation index of elastic modulus $R^2$ is about 0.030, MAE is about 6.212, RMSE is about 8.497, and MAPE is about 35.546. Table 5 and Table 6 present the evaluation indicators of the empirical formula on the compressive strength and elastic modulus of RAC, respectively. Compared with the empirical formula, the evaluation indicators of the WeightedEnsemble model for the compressive strength, $R^2$, MAE, RMSE and MAPE, are relatively 88% higher, 73% lower, 62% lower and 71% lower, respectively. The evaluation indicators for the elastic modulus, $R^2$, MAE, RMSE and MAPE are 97% higher, 86% lower, 82% lower and 86% lower, respectively. The results show that the AutoML model based on AG has significant advantages.

Figure 4. Comparison of conventional formulas for predicting compressive strength and elastic modulus of RAC. (a) Compressive strength; (b) Elastic modulus.

Table 5. Comparison of the traditional formula for compressive strength of RAC, multiple linear regression model and WeightedEnsemble model.

Model	Evaluation Indicator
	R²	MAE	RMSE	MAPE
Gholampour et al. (2017) [24]	0.103	7.819	9.919	21.759
Xu et al. (2019) [25]	0.135	7.807	9.689	22.174
Linear regression model	0.209	6.320	8.489	17.809
WeightedEnsemble	0.845	2.100	3.757	6.402

Table 6. Comparison of the traditional formula for the elastic modulus of RAC, multiple linear regression model and WeightedEnsemble model.

Model	Evaluation Indicator
	R²	MAE	RMSE	MAPE
Gholampour et al. (2017) [24]	0.030	6.212	8.497	35.546
Xu et al. (2019) [25]	0.053	5.374	7.597	32.359
Linear regression model	0.311	4.473	6.164	25.843
WeightedEnsemble	0.957	0.899	1.546	5.073

The empirical equations obtained from the study of Xu et al. [25] are selected for the prediction of compressive strength and elastic modulus of RAC. The empirical equations are as follows.

$$f_{c,cube}^{\prime }\left(MPa\right)=\frac{28.97-4.71\ast r^{1.69}}{{\left(w_{eff}/c\right)}^{0.63}}$$

(7)

$$E_c\left(GPa\right)=\frac{26836.23-5477.29\ast r^{1.14}}{{\left(w_{eff}/c\right)}^{0.25}}$$

(8)

where $f_{c,cube}^{\prime }$ denotes the predicted compressive strength of RAC, $E_c$ denotes the predicted elastic modulus of RAC, r indicates the replacement rate of coarse aggregate in RAC in percentage, $w_{eff}/c$ indicates the effective water–cement ratio in the design of RAC mix.

Plug the corresponding values into the above formula in the same way to obtain the calculated results of compressive strength and elastic modulus of RAC. The results are compared with the experimental data in the database. Figure 4 shows the prediction results of the empirical formula. The evaluation indicators $R^2$, MAE, RMSE and MAPE of compressive strength are about 0.135, 7.807, 9.689 and 22.174, respectively. The evaluation indicators of elastic modulus, MAE, RMSE and MAPE are 5.374, 7.594 and 32.359, respectively, while $R^2$ is only 0.053. Table 6 presents the specific evaluation indicators of this empirical formula. Compared with the prediction results, the evaluation index of the WeightedEnsemble model for compressive strength prediction $R^2$, MAE, RMSE and MAPE are relatively 84% higher, 73% lower, 61% lower and 74% lower, respectively. For the predicted elastic modulus, $R^2$, MAE, RMSE and MAPE are 93% higher, 60% lower, 59% lower and 65% lower, respectively. Therefore, the AG-based AutoML model has an obvious advantage over the above formulas, which7 exhibits higher prediction accuracy.

4.3. Comparison of Multiple Linear Regression Models Based on SPSS Software

In addition to the published empirical formulas of existing studies, this paper also uses the classical linear regression analysis software SPSS to analyze the compressive strength and the elastic modulus of RAC. Through multiple linear regression analysis, we obtain the accuracy of the fit on the original database. Then the results are compared with the experimental compressive strength and elastic modulus of RAC in the database. The regression prediction results of 30 percent of compressive strength and elastic modulus data are shown in Figure 5. In addition, the evaluation indicators of the prediction results on compressive strength and elastic modulus obtained from the multiple linear regression are shown in Table 5 and Table 6, respectively. The evaluation indicators of the compressive strength of RAC $R^2$, MAE, RMSE, and MAPE are about 0.209, 6.320, 8.489 and 17.809, respectively. The evaluation indicators of the elastic modulus $R^2$, MAE, RMSE and MAPE are about 0.311, 4.473, 6.164 and 25.843, respectively. It can be seen that the prediction accuracy of SPSS-based multiple linear regression fitting is significantly improved compared with the existing empirical formulas provided in the previous section. However, it is still at a low accuracy level compared with the prediction accuracy of the WeightedEnsemble model in AG, which may not be effectively used in practical applications.

Figure 5. Multiple linear regression model of compressive strength and elastic modulus of RAC based on SPSS. (a) Compressive strength; (b) Elastic modulus.

4.4. The Compressive Strength and Elastic Modulus of Traditional Conversion Formulas

Compressive strength and elastic modulus are two typical mechanical characteristics when considering the mechanical performance of concretes. While compressive strength is the resistance ability of compression forces of a specimen, the elastic modulus could be defined as the relationship between the strain and stress caused by the load acting on the specimen [26,27]. It could be found that these two factors are both directly related to loading conditions and specimens responding to those loads; it is possible to determine the relationship between compressive strength and elastic modulus to make a conversion between them. In specific, when the acting loading reaches the compressive strength of a specimen, there would be a corresponding strain and stress at this specific condition, and the conversion relationship is possible to be determined. According to the literature review, amounts of researchers have published their regression equation to convert the compressive strength to elastic modulus in their studies. In general, these study results show that while the increment of concrete strength of concrete, the elastic modulus of concrete will also increase [28,29,30]. When only considering the compressive strength as the variable in the conversion equation, there is a group of the equation that has a similar general form shown as $E_c=\alpha f_c^{\beta }+\gamma$, which also fits with Equation (11) in the below discussion [30]. In addition, there are also a lot of variable parameters which is related to the proportion of the concrete mixture design for the content of different materials considered in the conversion equations to make the conversion results could fit the realistic better [28,29,30].

In this study, some conversion equations are selected by a literature review to compare and contrast with the performance of the AutoML model based on AG. The data containing both the compressive strength and elastic modulus of RAC are extracted from the original total database and established as a separate database. A set of elastic modulus data is obtained by AG prediction. The other sets of elastic modulus data are obtained by the traditional conversion formula between compressive strength and elastic modulus. Figure 6 shows the prediction results between the conversion formulas and the predictions of AG. Table 7 lists the corresponding statistical parameters. The conventional conversion equations involved are as follows, where $E_c$ denotes the predicted elastic modulus of RAC, and $f_{c,cube}^{\prime }$ denotes the predicted compressive strength of recycled aggregate concrete.

Figure 6. Prediction results of traditional conversion formula and WeightedEnsemble model in RAC’s compressive strength and elastic modulus.

GB 50010-2010 [31]:

$$E_c=\frac{{10}^5}{2.2+34.7/f_{c,cube}^{\prime }}$$

(9)

Corindalesi (2010) [32]:

$$E_c=\frac{26836.23-5477.29 \ast r^{1.14}}{{\left(w_{eff}/c\right)}^{0.25}}$$

(10)

Ravindrarajah (1978) [33]:

$$E_c=3.02f_{c,cube}^{\prime }{}^{0.50}+10.67$$

(11)

From Table 7, the statistical parameter $R^2$ of the elastic modulus predicted by AG is 0.734, MAE is 3.051, RMSE is 4.420, and MAPE is 27.307. Whereas the statistical parameters of the traditional conversion formula $R^2$ ranges from 0.153–0.330, MAE ranges from 5.563–6.514, RMSE ranges from 8.286–10.420, and MAPE ranges from 48.051–55.527. Through comparison, the WeightedEnsemble model has better evaluation indexes, which are better than the results of any of the conversion formulas. The results show AG still has a higher accuracy in predicting the elastic modulus than using the conversion formulas, which reflects its significant advantage and applicability.

Table 7. Evaluation parameters for prediction results of traditional conversion formula and Weighted Ensemble model in RAC’s compressive strength and elastic modulus.

Experience Formula	Statistical Parameter
	R²	MAE	RMSE	MAPE
GB 50010-2010	0.330	6.514	8.772	53.949
Corindalesi (2010) [32]	0.206	5.563	8.286	48.051
Ravindrarajah (1978) [33]	0.153	6.307	10.074	55.527
WeightedEnsemble	0.734	3.051	4.420	27.307

Table 7. Evaluation parameters for prediction results of traditional conversion formula and Weighted Ensemble model in RAC’s compressive strength and elastic modulus.

Experience Formula	Statistical Parameter
	R²	MAE	RMSE	MAPE
GB 50010-2010	0.330	6.514	8.772	53.949
Corindalesi (2010) [32]	0.206	5.563	8.286	48.051
Ravindrarajah (1978) [33]	0.153	6.307	10.074	55.527
WeightedEnsemble	0.734	3.051	4.420	27.307

5. Conclusions

In conclusion, in order to determine an accurate prediction method for recycled aggregate concrete (RAC) compressive strength and elastic modulus, this study uses the AutoGluon-Tabular framework to do the auto-machine-learning based on two collected databases, which is based on a previous literature review, of compressive strength and elastic modulus, respectively. By considering multiple indexes of RAC, including the content of water, cement, natural coarse aggregate and recycled coarse aggregate, this study compares the prediction results of auto-machine-learning models with the model from the representative empirical formulas and the SPSS-based multiple linear regression model. The comparison results show that the AG models have the best performance among all alternative prediction methods in both fields of compressive strength and elastic modulus prediction. In addition, the study also tests the AG performance in the field of converting the compressive strength of RAC into elastic modulus. AG still has a significantly higher accuracy in the conversion work rather than conventional conversion formulas. Take the accuracy performance evaluation parameter R² as an instance, the R² value could increase by around 90% and 70% when predicting the compressive strength and elastic modulus compared with the traditional empirical formulas and multiple linear regression models, respectively. Although the conversion result is not good as the previous two fields, it still increases the accuracy by 55% under the consideration of evaluation parameter R². In specific, the best prediction model during the AG training and test is considered the WeightedEnsemble model.