## 1 Introduction
### Ultrasonic Test  
In linear ultrasonic test, the received waveform is not significantly different from the transmitted waveform. One application of this is ultrasonic pulse velocity test wherein distance of transmitter to receiver and time of the wave traveling that distance are the parameters as shown in Equation (1). \[\text{Ultrasonic pulse velocity (UPV) = distance of transmitter to receiver/time to travel} \tag{1}\]  
The time to travel of the longitudinal wave from transmitter to receiver is shown in Figure 1 and is used to compute the ultrasonic pulse velocity. It is observed that sizes of cracks greater than 100 mm are the only ones detected by longitudinal ultrasonic pulses [6]. Additional study claims that cracks are not detected with accuracy especially if it is filled up with fluids. Another parameter used in linear ultrasonic test in time-domain wave form is peak to peak amplitude (PPA) of the received waveform. It is used as a measurement in damage detection. It is the vertical distance from the highest point to the lowest point of the time-domain waveform. It shows that PPA has also been one of the significant parameters in estimating the residual strength of concrete where reduction of PPA is experienced when the load is increased [7; 8]. On the other hand, nonlinear ultrasonic test method focuses on spectral frequency analysis. This is a phenomenon resulting from interaction between ultrasonic wave and concrete [9]. During the interaction of the load and material, a part of the fundamental frequency is converted to higher harmonics shown in Figure 2 where A1 is the fundamental harmonic amplitude, A2 is the second harmonic amplitude and A3 is the third harmonic amplitude. Harmonic generation will not occur without attenuation. Attenuation is the reduction in intensity during the wave's travel through a material. Moreover, internal friction between surfaces contributes to the attenuation. Occurrence of higher harmonic generation is due to contact of crack interfaces called Contact Acoustic Nonlinearity [10; 11; 12; 13]. The concrete, when loaded, experiences opening and closing of cracks and/orfrictional forces acting on the interfaces between cement paste and the aggregates. The higher harmonics generated depend on the cracks forming inside when compressive load is applied [14] and interact with the defects, causing the opening/closing of the cracks formed when loading and unloading occurs [15; 16]. On the material aspect, unreinforced concrete is sensitive to micro-cracking in the interfacial transition zone [17]. Variation of water-cement ratio proves to be a significant factor. It is found out that third harmonic ratio is sensitive compared to the second harmonic ratio [18]. In addition, second higher harmonic amplitude becomes large when crack opening displacement is small [19]. The sensitivity of the A2 and A3 depends on the type of loading introduced. For single loading pattern, A3 is sensitive compared to A2. On the other hand, in multiple step loading pattern A2 is sensitive to all water-cement ratio introduced [20]. It is also suggested that the amplifier is at high power level during experiments to produce better sensitivity in the generation of higher harmonics [21]. The amplitudes A1, A2, and A3 behaved similarly with PPA, where it is decreasing with respect to increasing load. A previous study shows that in concrete cubes, different loading patterns greatly influence the higher harmonics generation [20]. Complexity in its damage level is recognized when different sizes of aggregates inside the concrete are present [22]. Figure 1: Linear ultrasonic test using ultrasonic pulse velocity (UPV) and peak to peak amplitude (PPA) in time-domain recorded from the transmitter and receiver. Figure 2: Nonlinear ultrasonic test using higher harmonic generations A1, A2, and A3 in frequency-domain recorded from the receiver ([PERSON] et al., 2016 [20]). There are limited papers investigating sensitivity of ultrasonic parameters in reinforced concrete beams.