## 1 Introduction  
To evaluate the compressive strength of concrete in cast-in-place or existing structures, the standard destructive test is the most reliable method. Typically, standard cylindrical samples are made on site and sent to the laboratory for compressive strength testing. However, the test results may not be representative, because many factors such as the type and size of the aggregate and cement, the fine aggregate modulus, the water to cement ratio, and the interfacial transition zone, etc., are not considered [1]. Furthermore, the drilling of core samples from existing concrete members is not always possible on site and the concrete member might be damaged by the process. In this respect, one suitable alternative is to apply non-destructive evaluation (NDE) methods to estimate the concrete strength when core sampling is not preferable. The most widely used NDE method for the strength evaluation of concrete is the ultrasonic pulse velocity test, which measures the velocity between two transducers on both sides of a specimen. The velocity can be calculated based on the assumption that the wave path is known in advance. Many attempts to apply the pressure wave velocity Vp (km/s) as a measure of the concrete compressive strength have been made, using field convenience and simple equipment. The estimation of concrete strength is typically based on various empirical relations between the concrete strength and nondestructive variables, such as the ultrasonic pulse velocity and rebound number. NDE tests typically have their own empirical relations to connect the test parameter and concrete strength, but these depend strongly on factors such as the water to cement ratio, type and size of the aggregate and cement, and the amount of aggregate. Thus, they cannot be applied universally and require supplemental methods. Furthermore, the typical approach using regression analysis, such as with an exponential function, has not been successful [1]. The proposed equations have not been accurate for strength estimations because the strength may depend on factors other than the P-wave velocity (Vp). There are many factors that affect concrete strength, in addition to the ultrasonic pulse velocity. For example, the type and size of the aggregate affect the relationship between Vp and the concrete strength. Concrete with the largest aggregate content tends to have the highest pulse velocity [2]. Furthermore, a higher water content results in a higher ultrasonic velocity of the concrete [3,4]. However, a higher water content typically corresponds to a lower strength of the concrete [5]. This inconsistency can make the interpretation of the ultrasound results difficult. [PERSON] et al. [6] investigated the effects of many factors, including the type, size, and shape of the aggregate, the concrete cast temperature, and the water to cement ratio, on the ultrasonic velocity. They concluded that the aggregate properties were the most effective factors. For normal-strength concrete, many regression methods, such as linear or nonlinear regressions, have been applied to estimate the concrete strength. However, such regression methods cannot directly predict the concrete strength. Recently, various studies have been performed to obtain more accurate predictions of the concrete strength using machine learning algorithms, such as support vector machine (SVM) and artificial neural network (ANN) methods [7; 8; 9; 10]. [PERSON] et al. analyzed the performance of an ANN to estimate the 28-day concrete strength of normal and high-strength concretes [9]. In their work, factors such as the water to cement ratio, aggregate to cement ratio, and the amount of cement were used as input parameters, and the concrete strength was the output of the network. As an alternative to ANN, an SVM was developed that could effectively classify data and minimize the risk [11].