## 3 Results and Discussion
### Cluster Analysis and Pattern Recognition  
To conduct a detailed study of the AE source mechanisms, all the AE signals are classified into different types via the K-means cluster algorithm. The K-means is a cluster algorithm that partitions observations into \(k\) clusters, aiming to minimize the sum of Euclidean distances from signals to their clustering centroids. The K-means cluster algorithm has been proved to be efficient and reliable for AE signal analysis [43; 44; 45]. The value of \(k\) is artificially set. To obtain the optimum solution of \(k\), the Davies and Bouldin (DB) index [46] is employed, and it can be expressed as in Equation (6):  
\[DB=\frac{1}{c}\sum_{i=1,j+j}^{c}\max(\frac{d_{i}+d_{j}}{M_{ij}}) \tag{6}\]  
where \(c\) is the number of clusters; \(d_{i}\) and \(d_{j}\) denote the average Euclidean distances of vectors in clusters \(i\) and \(j\) to the centroids of clusters \(i\) and \(j\), respectively; and \(M_{ij}\) is the distance between the two clusters \(i\) and \(j\). A lower value of the DB index indicates greater concentration in the cluster and separability between clusters. To describe the AE signal, we employ five AE characteristics, comprising rise time, duration, ringing count, amplitude, and energy, to represent the waveform features of an AE signal. Some studies have indicated that these five characteristics demonstrate notable diversity against different damage patterns [43; 47; 48]. We simplify each AE signal to the above five characteristics and later introduce all the signals into the K-means cluster algorithm. The number of clusters is set from two to nine. Figure 9a shows the DB index values of for different cluster numbers. For both G20 Mn5 QT and the welds, the optimum cluster number is three. The proportions of the three clusters' AE signals are shown in Figure 9b. The proportion of cluster 1 is more than 70%, and that of cluster 2 is more than 20%. The proportion of cluster 3 is considerably lower than that of clusters 1 and 2. To recognize the AE source pattern, the typical AE signals from each cluster for both G20 Mn5 QT and the weld are analyzed. The AE signals of cluster 1 are of a typical burst type, which has a short rise time and duration and a notable peak amplitude, which is much stronger than that of other peaks (see Figure 10a,b). The AE signals of cluster 2 demonstrate a short rise time but a long duration. Unlike in the burst type, some strong peaks arise repeatedly after the peak amplitude (see Figure 10c,d). Therefore, cluster 2 can be confirmed to pertain to continuous-type signals. The research of [PERSON] et al. [49] indicated that burst-type AE signals in fatigue crack growth are released from metal fractures during tensile crack propagation, while continuous-type AE signals are released  
Figure 8: AE normalized cumulative hit and energy. from the plastic deformation before the crack tip. When a tensile crack fracture occurs, the materials adjacent to the new crack separate, which leads to a transient volumetric change. The fracture generates a shear wave that consumes only a little energy and has a low propagation velocity and a longitudinal wave that consumes most of the energy and has a high propagation velocity. The two types of waves combine and create a wave with a short rise time and duration. In addition, [PERSON] et al. [50] and [PERSON] et al. [51] suggested that continuous-type AE signals should be derived from the cyclic plastic deformation zone because the formation of stress-strain hysteresis loops occurs only in the cyclic plastic deformation zone. [PERSON] et al. [52] clarified the mechanism of the burst-type and continuous-type AE signals using another approach. They collected the AE signals before and after fatigue initiation using a CT specimen and noted that the AE signals before crack initiation were mainly of the continuous type, which can be released only from the cyclic plastic deformation of the material before the crack tip.