## 4 AE Signal Analysis and Application
### AE Energy Parameters for Pipeline Damage Identification  
Many studies have shown that the number of shear rupture activities will increase significantly when the specimen approaches the destabilization stage in the experimental processes of the rock triaxial compression test, cubic compression test with cracks, strain-type rock explosion, and the specimen damage process [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. However, tensile fracture is the main failure mode in concrete bending and barite direct tensile tests. AE parameter analysis is a basic method to identify the type of structural damage, and its basic parameters are shown in Figure 10. Moreover, many researchers have found that the relationship between RA and AF can effectively characterize the type of concrete structural damage [30; 31; 32; 33]. The RA value (rise angle) and AF value (average frequency) can be calculated by the following formulas:  
\[\text{RA}=\text{RT}/\text{A} \tag{1}\]  
\[\text{AF}=\text{C}/\text{D} \tag{2}\]  
where RT is the rise time, A is the maximum amplitude, D is the duration of an AE waveform, and C is the total number of threshold crossings for an AE waveform. When the ratio AF/RA is small, shear damage mainly occurs in the material; when the ratio AF/RA is large, tensile-type damage mainly occurs, and the difference in the damage mechanism is the fundamental reason for the significant difference between the AF and RA ratios. During the pipe loading process, the expansion and development process of the pipe cracks on the side walls were marked according to the time series at the same time, as shown in Figure 11. The cracks on both sides of the pipe gradually sprouted, expanded, and developed in the plastic damage stage, and the crack form was mainly transverse cracks at this stage. As the loading proceeds, longitudinal cracks begin to appear, but the overall the number of longitudinal cracks is significantly lower than that of transverse cracks. When the load reaches the pipe's damaged load, many transverse cracks expand and connect. After calculating and analyzing the AF and RA parameters of the AE signal during the loading process of the pipe, the evolution characteristics of  
Figure 9: Thermal diagram of the correlation coefficient of AE parameters during the stress change. RA and AF parameters during the loading process of the pipe were plotted as shown in Figure 12. In the pipeline linear elastic compression loading stage, the AE signal is sparse due to there being less damage and damage behavior of the concrete material at this stage; the RA and AF fluctuate in two intervals of 0-0.5 and 0-3, respectively, and overall, the RA and AF values of the AE signal are generally low. After entering the plastic damage stage, the two indices show the pulse characteristics of the \"growth period-quiet period\" alternately, which stays synchronized with the changes in the specimen load. The levels of the two indicators increased significantly compared with the previous stage, indicating that frequent structural damage occurred in the pipe during this stage. As the load level increase, the extreme values of the two parameters increase, the AE signal is abundant, and the dense distribution of the two index points increases, indicating that the number and degree of damage activities occurring in the pipeline are increasing. Figure 11: Crack distribution map of pipeline damage under load. Figure 10: AE waveform parameters. To further study the damage form of the pipe specimen during the loading process, the characteristic evolutionary curve of the AF to RA ratio was plotted, as shown in Figure 13. The red curve in the figure is the envelope of AF/RA data, and it can be found from the figure that the overall AF/RA shows \"bimodal\" characteristics during the whole process of pipe loading.