## 5 Conclusions  
Predicting the static elastic modulus (_Ec_) is important for concrete structures. The ASTM resonance frequency test is commonly used in predicting a consistent dynamic elastic modulus (_Ed_) using a nondestructive method. The resonance frequency test calculates the Ed for a very small stress in the stress-strain curve and assumes that the _Ed_ is equal to the initial chord elastic modulus (_Ei_). However, the calculated _Ed_ derives a large error for utilizing the _Ec_ and fc, owing to the nonlinearity of the concrete. Therefore, the correct _Ei_ as extracted through the curve fitting of the stress-strain curve showed a better correlation between the _Ec_ and fc than the _Ed_. These results indicate that it is desirable to measure and utilize accurate _Ei_ values. In this study, it was possible to predict the actual _Ei_ quite accurately by applying the ensemble, ANN, MLR, and correction factor methods to the _f1_ to _f4_ frequencies of longitudinal (LT) and transverse (TR) modes collected by the ASTM resonance frequency test. If several frequency variables were used, the contributions of the variables were extracted, and the relationships with the _Ec_ and _fc_ were analyzed using the predicted _Ei_. The following conclusions were drawn. * The Ed values calculated by three theoretical equations (ASTM, Rayleigh Ritz) of the resonance frequency test were in the order of _f1_f2_LT \(>\)_ASTM.LT \(>\)_ASTM.TR_, and had nearly the same values. The size of the elastic modulus as measured by static and dynamic tests was _Ed \(>\)_Ei \(>\)Ec_. In addition, it is determined that it is desirable to utilize the _Ei_, as the correlation with _Ec_ is analyzed as _Ei_ \(>\)_Ed_. * The Popovis equation for the relationship between _Ec_ and Ed gives results similar to the _Eds_ of the ASTM, and the Lydon and Balendran equations are similar to _Ei_ values. BS8110 Part 2 is not suitable, as because it has a large error from the _Ed_ and _Ei_ in the resonance frequency test. * As a result of comparing an E-modulus based on _ASTM.LT, f1_f2_LT_, and _ASTM.TR_ had a clear linear relationship, and they were close in the line of equality. They were identified as having a nonlinear relationship with the _Ei_ and _Ec_. As the theoretical equations assumed the concrete as a perfectly elastic body for microscopic stress, it was difficult to overcome the nonlinear behavior of the actual _Ei_ and _Ec_, owing to challenges in considering inhomogeneity and inelasticity of concrete. Thus, it is more appropriate to accurately predict and utilize the _Ei_, which has a similar nonlinear behavior with the _Ec_. * As a result of applying _ASTM.LT, f1_f2_LT_, and _ASTM.TR_ to the correction factors, the MAPE in the _Ei_ could be lowered to 6.40%, 6.50%, and 6.43%, respectively. In addition, the _Ed_ in the three equations and _Ei_ of the MAPE decreased in order in days 4, 7, 14, and 28. The theoretical equation is suitable for concrete after 28 days but is considered difficult to use to accurately predict lower ages. * In the relationship between \(Ei\) and frequency, the correlation of \(Ei\)-\(f1\) was the largest, the nonlinearity increased as the mode appeared later, and the density and consistency of the data gradually decreased. In addition, the \(Ei\) and \(Ec\) values and first frequency of the resonance frequency test tended to be similar to an exponential function, indicating that prediction of the \(Ei\) and \(Ec\) based on frequency was possible. * As a result of predicting the \(Ei\) using only frequencies through the ensemble and ANN methods, the MAPE decreased by 3.90% in the case of using only \(f1\), and by 3.51% in the case of using \(f1\)-\(f4\). Accordingly, the nonlinear behavior could be overcome by using ML. * As a result of analyzing the contributions of variables in predicting the \(Ei,f1\) and \(f2\) were dominant, the RI of the size factor was 0, and 0.3% of the day variables contributed to the \(Ei\) prediction.