## 3 Results and Discussion
### Damage Pattern Recognition
#### 3.1.3 Damage Pattern Recognition of crumb Rubber Concrete by the Density Peak Clustering Method  
According to previous studies, it can be shown that the peak frequency of AE signals generated by the structural failure of concrete changes with the change of the concrete damage mode. Thus, various damage patterns of concrete can be identified and characterized through the peak frequency. The statistical analysis and comparison of the peak  
Figure 8: Density peak clustering results. Figure 7: Peak density of sample points. frequencies of different events in two kinds of concrete (ordinary concrete and crumb rubber concrete) were carried out (Figures 9 and 10). For ordinary concrete, the peak frequency distribution is mainly concentrated in one band, about 35-50 kHz. Hence, Figure 9 shows that the peak frequency of the main frequency band corresponding to the destruction of the concrete matrix, which is about 35-50 kHz. For crumb rubber concrete, due to the incorporation of rubber, another frequency band with a peak frequency of 85-125 kHz is added to Figure 10, which also represents another new failure mode in addition to the failure of the concrete matrix. Based on the results of density peak clustering, the optimal clustering number of crumb rubber concrete is three. Therefore, the acoustic emission signals of crumb rubber concrete were classified into three clusters. According to Figure 11, for the peak frequency of the crumb rubber concrete AE signals, the distribution range of cluster 1 is 10 to 66 kHz, and its main frequency band is 35 to 50 kHz. According to the previous analysis, the damage pattern represented by the cluster 1 signal is the cracking of the concrete matrix. The peak frequency of cluster 2 ranges from 5 to 170 kHz, of which the two main frequency bands are 35 to 50 kHz and 85 to 125 kHz, respectively, which shows that the signal of cluster 2 represents two failure modes: concrete matrix cracking accompanied by rubber particle fracture. The peak frequency distribution of cluster 3 ranges from 20 to 150 kHz, and it has only a main frequency band of 85 to 125 kHz, indicating that the signal of cluster 3 represents a new damage mode after rubber incorporation. Figure 10: Peak frequency distribution of crumb rubber concrete. Figure 9: Peak frequency distribution of ordinary concrete. In addition, the cumulative energy of AE parameters and the length of the propagating cracks generated when concrete is destroyed have also been studied, and scholars have proved that there is a certain correlation between the two. According to Figure 12, the cumulative energy of the signal of cluster 2 over time is much higher than that of the signals of cluster 1 and cluster 3, which indicates that the signal of cluster 2 corresponds to the larger damage inside the concrete matrix, also proving that the signal of cluster 2 includes not only the cracking of the concrete matrix, but also the new failure mode caused by rubber. At the same time, it should be noted that for concrete structures, the acoustic waves generated when the internal fractures are continuously attenuated during the propagation process, and considering that the distance between each acoustic emission sensor and the damage location is different, there is a certain error between the peak frequency received by sensors and the peak frequency at the original location of the concrete damage, which cannot be ignored. Thus, for different failure modes, it is crucial to find another method to more finely determine their corresponding peak frequencies. Figure 11: Peak frequency distribution of three clusters: (**a**) cluster 1; (**b**) cluster 2; (**c**) cluster 3. Fast Fourier transform (FFT) is a calculation method that transforms the time domain into the frequency domain. Due to its high efficiency and speed, this method is commonly used to process acoustic emission waveform signals. For crumb rubber concrete, the peak frequencies of the cluster 1 and the cluster 3 signals have two identical main peaks: 40 and 100 kHz.