# Automatic Crack Classification by Exploiting Statistical Event Descriptors for Deep Learning
## 3 Framework for the Real-Time Classification of Acoustic Emission Data  
Figure 2 shows the schematic block diagram of the processing pipeline. It comprises a number of waveform preprocessing blocks [46] performing: (I) transducer's transfer function removal (TFR), (II) Hilbert-Huang transform (HHT) and (III.1) feature extraction. Once preprocessed, the output data feed the (III.2) DL-based [46; 57] processing block used for the classification of AE signals. From a given input, each block on the pipeline performs different I/O operations and it is numbered according to sequential tasks. In the waveform preprocessing blocks, any raw transducer time-domain measurement \(r_{b,q}(t)\) related to the \(q\)-th AE (q = 1... Q) captured from the \(b\)-th channel (\(b\) = 1... 5 in our system) is processed through blocks from (I) to (III.2). In (I), \(r_{b,q}(t)\) is deconvoluted using TFR [10] with the sensing acquisition system, thus generating a reconstructed signal \(s_{b,q}(t)\). Then in (II), \(s_{b,q}(t)\) is processed by means of the HHT [58], in order to perform denoising and detrending, generating refined signal \(\tilde{s}_{b,q}(t)\). Subsequently, we have evaluated, againstall the available channels, the solicitation having the highest energy E, \(\hat{s}_{q}(t)\), such that \(\hat{s}_{q}(t)=\max_{b}\Bigl{\{}E_{\hat{s}_{b_{d}}}\Bigr{\}}\). \(\hat{s}_{q}(t)\) is then used to feed the next block of the pipeline.  
In block (III.1), for a given \(q\)-th AE, we have extracted different statistical properties (described in Section 3.2 and Table 1), hereinafter named as event descriptors (ED): instantaneous frequency (IF) [59], spectral entropy (SE) [30] and spectral kurtosis (SK) [31], which are arranged into the matrix \(\Gamma_{q}\):  
\[\Gamma_{q}=\bigl{\{}IF\bigl{(}\hat{s}_{q}(t)\bigr{)},SE\bigl{(}\hat{s}_{q}(t) \bigr{)},SK\bigl{(}\hat{s}_{q}(t)\bigr{)}\bigr{\}} \tag{1}\]  
This array of features, \(\Gamma_{q}\), is used to populate the input dataset, \(\boldsymbol{\Gamma}\), such that:  
\[\boldsymbol{\Gamma}=\bigl{[}\Gamma_{q}\bigr{]}_{q=1,\ldots,Q} \tag{2}\]  
In \(\Gamma_{q}\), each ED is represented by a series composed of \(N_{\text{ED}}\) elements that represent the chosen statistical function once it is calculated from the input data \(\bigl{(}\hat{s}_{q}(t)\bigr{)}\). Considering that we have collected \(Q=15000\) AE events, where each event is of 2 ms duration (10.000 samples), we have extracted the properties in order to have a 67 samples discretization (\(N_{\text{ED}}=67\)). Therefore, the available dataset \(\boldsymbol{\Gamma}\) has a size of \(Q\)-x-3-x-\(N_{\text{ED}}=15\),000 \(\times\) 3 \(\times\) 67.  
Finally, the block (III.2) performs DL-based classification of AE events by analyzing \(\boldsymbol{\Gamma}\) through a deeply stacked Bi-LSTM architecture (described in Sections 3.3 and 3.4) and providing the recognized category of such events as output. Here, the input data are used to automatically discriminate among crack solicitations by solving a multi-class classification, which is the problem of categorizing instances into precisely one of more than two classes.