## 1 Introduction
In recent years, studies have been conducted to overcome the nonlinearity and improve the prediction accuracy of the mechanical properties (such as the _Ec_ and _fc_) of concrete by considering various variables such as the water/binder ratio, type of binders/aggregates and corresponding ratios by machine learning (ML), rather than by general regression analysis. These studies focused on predicting the concrete strength and integrity more accurately with general ML algorithms, such as the support vector machine (SVM), ensemble and artificial neural network (ANN), and provided predictions with relatively improved accuracy [17, 18, 19, 20]. For example, [PERSON] et al. used ensemble and ANN methods with cement, blast-furnace slag, water, and aggregate, and compared the accuracies of _fc_ prediction for high-performance concrete; they found that the ensemble method was slightly better [21]. [PERSON] et al. predicted the _Ec_ and fc using four _Eds_ with SVM, ensemble, ANN, and multiple linear regression (MLR) methods, and announced that the ensemble and ANN were suitable [8]. [PERSON] and [PERSON] predicted the _Ec_ by the fc using an ANN, SVM, linear regression, and four theoretical equations, and reported that the ML methods were more suitable than linear regression and theoretical equations [22]. [PERSON] et al. used an ANN, SVM, and linear regression to predict a 28-day intensity from data with varying mixing ratios and reported that ML methods were more accurate than linear regression [23]. [PERSON] used ANN, ensemble, and SVM methods to estimate the _fc_ and slump values of concrete and reported that the ANN and ensemble approaches were superior to the SVM [24]. Among the ML methods, the ANN and ensemble methods overcome the nonlinear behavior of concrete and provide suitable contributions to quality prediction. However, although some studies have been conducted on the prediction of _Ec_ and _fc_ with _Ed_, few studies have been conducted with _Ei_. Therefore, it is necessary to analyze the relationships among _Ed_, _Ec_, and fc for the application of _Ei_, and to predict the correct _Ei_. In this study, the difference between the dynamic elastic modulus (_Ed_) and initial chord elastic modulus (_Ei_) values obtained with the ASTM theoretical equation was analyzed based on the results of the resonance frequency test, and the relationship between the _Ec_ and fc was analyzed through accurate prediction of the _Ei_. Three _Ed_ values were obtained using the theoretical equations suggested by ASTM C215-14 and [PERSON], as the frequencies of the LT and TR modes of the resonance frequency test. In addition, the exact _Ei_ value at the origin was extracted through curve fitting to the stress-strain curve, and was compared with the _Eds_. The _Ei_ was predicted using ML (ensemble, ANN) for the frequency, and the _Ed_ was obtained by the resonance frequency test. In addition, the contributions of the variables were analyzed. The ML method was trained on several combinations, and a five-fold cross validation was performed to prevent the overfitting of the predicted results. The mean squared error (MSE) and mean absolute percentage error (MAPE) were used to analyze the errors between the predicted and actual _Ei_ values. In addition, the relationships with the _Ec_ and _fc_ were analyzed to confirm the predicted possibility of using the _Ei_.