# Automatic Crack Classification by Exploiting Statistical Event Descriptors for Deep Learning
## 3 Framework for the Real-Time Classification of Acoustic Emission Data
### Characterization of Different Crack Events  
It is well known that the waveform of an AE signal is intrinsically representative of the nature of the underlying fracture modes, which generate tensile, shear or mixed-mode deformations. Therefore, the timely characterization of these cracking events can act as a safe measure against the final collapse [6]. As demonstrated in [46], we rely upon the versatility of HHT to analyze AE signals for denoising as well as extracting their intrinsic  
Figure 2: Block diagram of the framework for damage classification implemented in this work.  
mode functions (IMFs). Due to the IMFs, we can highlight the main characteristics of such different types of solicitations. In Figure 3a-c, we illustrate a comparison among tensile, shear and mixed-mode events \(\hat{s}_{q}(t)\) by focusing on their distinctive IMF components.  
Figure 3a represents an AE time trace as emitted during a tensile event (Mode I). When a tensile event takes place, the moving sides of the crack lead to a transient volumetric change in the material. Consequently, most of the energy is released in the form of \(P\)-waves, which are faster [60], whereas only a limited amount is transferred into \(S\)-waves, which are slower. We use HHT to extract the relevant components of the solicitation. As expected, the AE wave (black line) is constituted by a large \(P\)-wave (IMF3, red line) [61], followed by a \(S\)-wave (IMF 4, green line) having a smaller amplitude [62]. For tensile events, the RT is short [63], and then a high RA is observed.  
Figure 3b displays an AE time trace as emitted during a shear event (Mode II). In this case, the shape (and not the volume) of the material changes once in proximity of the crack. On this occasion, the shear crack (black line) emits most of the energy in the form of \(S\)-waves (IMF3, green line) and only a small amount in the form of \(P\)-waves (IMF4, red line). In terms of AE parameters, this cracking event is described by a long RT and a short RA [18].  
Figure 3c displays an example of time trace for a mixed mode (Mode III) which is typically observed during the transition from a tensile dominant regime to a shear dominant one. Mixed modes are originated from a combination of tensile and shear cracks [64; 65; 66] and are important for a wide range of civil engineering [67; 68; 13; 66]. Such events can be described by a balanced combination of \(P\)-wave (IMF3, green line) and \(S\)-waves (IMF4, red line) [64]. Nonetheless, the mixed-modes cannot be properly identified by calculating  
Figure 3: Examples of the time domain trace (black line), \(P\)-wave (red line) and \(S\)-wave (green line) waves as extracted with the HHT from AE waveforms related to different failure events: (**a**) tensile, (**b**) shear and (**c**) mixed-mode, respectively.  
AE parameters, such as RT or RA [10]. Therefore, a more flexible approach is required to discriminate among different classes of failures. The proposed classification of the main fracture modes is based on the approach as described in [46] and confirmed in [69; 70; 71; 72]. Our experimental measurements show AE data as characterized by the generation of tensile, shear as well as mixed-mode events.