## 3 Results and Discussion
### Localization of AE Events  
In this study, five AE sensors were used to obtain the location of AE events. The five AE sensors have their own independent coordinates. When an AE signal occurs, the time at which the AE signal reaches the five sensors is different. After obtaining the coordinates of the five sensors and the difference between the time when the AE signal reaches the five sensors, the coordinates of this AE event can be determined, and the locations of AE signals for each specimen can be inferred. In order to determine whether the localization results of AE events are consistent with the locations of real cracks, the locations of cracks (namely, cracks map) after beam failure are also obtained. According to the previous studies done by our team [33; 34], image recognition technology can be used for depicting the cracks map. Since this work is not the focus of this study, it is briefly described here. Step 1, collect the digital images of the side of each of the cracked RC beams and erase the sensor positions markers using the Photoshop Software. Step 2, convert the color image into a grey scale image; Step 3, denoise the grey scale image using Wiener filtering and Median filtering methods. Step 4, use the piecewise linear gray level transformation method to enhance the contrast of the cracks. Step 5, use the Sobel edge detection operator to identify and depict the locations of cracks. Step 2 to Step 5 are processed in the Matlab software. Since concrete on the side of the 40% corroded RC beam had extensive spalling after loading, see Figure 7, crack maps of this sample can't be depicted. Thus, both the locations of AE events and cracks of RC beams with the corrosion ratios of 0% to 30% are shown in Figure 10.  
From cracks maps in Figure 11, there are several main cracks generated on the side surface of RC beams. Cracks in Figure 11a,c mainly belong to shear cracks. From a macro point of view, the location points of AE events mainly exist near the region of the crack, namely. The AE events location points are densely distributed near the cracks. While the AE events location points are sparsely and irregularly distributed away from the cracks. From Figure 11a, it can be clearly observed that there are many AE event location points distributed near the midpoint on the upper surface of the RC beam; these must be generated by the crushed concrete at the load point during the early load stage. This finding from experimental observations is verified by the AE events localization results. From Figure 11b,d, it can be concluded that the extension form of cracks is diverse and the AE events location points are distributed disorderly. Interestingly, the AE event location points also densely distributed near the cracks while they are sparsely distributed away from the cracks. Therefore, it is believed that the region where the crack is located can be roughly judged by the region where the relatively dense distribution of the AE events is. In other words, the denser distribution of the AE events is, the higher the probability that cracks form in this region. In addition, the reason that the many localization points of AE events exist away from cracks may be as follows:  
1. The sensors are placed only on the side surface of RC beams, so AE events can only be located in a two-dimensional way. However, AE events occur in a three-dimensional space in the RC beams, so the localization results of AE events are the projection of its spatial position on the plane where sensors are placed. 2. The diffraction of AE signals due to the existence of cracks caused by steel corrosion hinders the propagation of signals, which makes an inaccurate AE signal transmission time and localization results. 3. The AE signal is reflected during the propagation from the cracking position of the beam to the position of the sensor to cause attenuation of the wave. This process causes the signal from the actual cracking position to differ from the signal received by the sensor which could interfere with the judgment.