## 2 Acoustic Emission Test on RC Beams
### Using Computational Geometry and Acoustic Emission Source Location (AESL)  
The AESL can be determined using the time-difference approach. Adaption of the Bancroft algorithm from geodesy to the localization procedure of sources of elastic waves gave good stability, automation, and performance of localization results. A combination of the permutation approach led to reliable results for larger specimens that may show an accurate fracture process in concrete [37]. It was recommended that the use of AE test data from the literature be analyzed using the artificial intelligence method to identify damage modes in concrete [38]. Using AE test results with artificial intelligence such as support vector machine or pattern recognition proved to be a good tool in assessing materials [39; 40; 41].  
The localization of damage in this paper was focused on the middle third span of the beam, where the mode of failure is the crushing of concrete in the compression zone. A multiscale approach was used to determine the damage inside the beam regardless of tensile cracks at the initial stages and shear cracks at the latter stages. These AESL hits were analyzed and simplified regardless of whether they were under tensile (type-I) or shear (type-II) cracks. The objective is to use AESL to visualize damage growth under computational geometry. The AESL results under different loads were employed in MATLAB for solving the volume of the convex hull generated in three dimensions.  
In 1970, computational geometry emerged from the field of algorithm design and analysis. Some successes in the research discipline include robotics, computer graphics, geographic information systems, and others, where geometric algorithms play an important aspect [42]. One category of computational geometry is the convex hull algorithm. The conventional convex hull algorithm uses points in space to form the smallest convex polygon in recognized shapes and sizes. There are numerous algorithms designed to achieve a convex hull [43]. In the field of medicine, convex hull imaging is capable of detecting defects [44]. In material science, the ability to visualize a concentration of points in space can lead researchers to determine growth of points inside. An example of research is the use of convex hulls as one of the techniques in determining minor impact, perforations, and debonding damages in sandwich composites [45].  
Shown in Figure 2 is the illustration of beams under small and large loads. A small load leads to low AESL hits, while a large load leads to high AESLs hits. The convex hull algorithm connects the vertices of points in space to form the CHV. In general, the AESL hits spread out wider when the load is increased, and that can lead to an increase in CHV. However, some AESL hits, such as those marked in red, form at the latter stages of loading and are inside CHV. This red AESL hits may be classified as shear cracks (type-II) or mixed mode inside the damaged zone. Further investigation is recommended to explore the AESL inside CHV and AESL as vertices of the volume formed.  
MATLAB software was used to solve the CHV [43]. It was shown from previous work that convex hull visualization exhibits a good relation to the damage progression inside concrete [4].