**Prediction of Static Modulus and Compressive Strength of Concrete from Dynamic Modulus Associated with Wave Velocity and Resonance Frequency Using Machine Learning Techniques**

#### **Jong Yil Park 1, Sung-Han Sim 2, Young Geun Yoon 3,\* and Tae Keun Oh 3,4,\***


Received: 27 May 2020; Accepted: 24 June 2020; Published: 27 June 2020

**Abstract:** The static elastic modulus (*Ec*) and compressive strength (*fc*) are critical properties of concrete. When determining *Ec* and *fc*, concrete cores are collected and subjected to destructive tests. However, destructive tests require certain test permissions and large sample sizes. Hence, it is preferable to predict *Ec* using the dynamic elastic modulus (*Ed*), through nondestructive evaluations. A resonance frequency test performed according to ASTM C215-14 and a pressure wave (P-wave) measurement conducted according to ASTM C597M-16 are typically used to determine *Ed*. Recently, developments in transducers have enabled the measurement of a shear wave (S-wave) velocities in concrete. Although various equations have been proposed for estimating *Ec* and *fc* from *Ed*, their results deviate from experimental values. Thus, it is necessary to obtain a reliable *Ed* value for accurately predicting *Ec* and *fc*. In this study, *Ed* values were experimentally obtained from P-wave and S-wave velocities in the longitudinal and transverse modes; *Ec* and *fc* values were predicted using these *Ed* values through four machine learning (ML) methods: support vector machine, artificial neural networks, ensembles, and linear regression. Using ML, the prediction accuracy of *Ec* and *fc* was improved by 2.5–5% and 7–9%, respectively, compared with the accuracy obtained using classical or normal-regression equations. By combining ML methods, the accuracy of the predicted *Ec* and *fc* was improved by 0.5% and 1.5%, respectively, compared with the optimal single variable results.

**Keywords:** concrete; static elastic modulus; dynamic elastic modulus; compressive strength; machine learning; P-wave; S-wave; resonance frequency test; nondestructive method
