# Automatic Crack Classification by Exploiting Statistical Event Descriptors for Deep Learning
## 4 Results and Discussions
### Performance Optimization of Model-Parameters  
We have used a training dataset containing \(Q\) = 15,000, mini-batch sample size \(m=1500\), \(N_{\text{ED}}\) = 67, initial learning rate \(r_{l}=0.001\) using SGDM optimizer. We evaluated a different number of hidden units of the network \(d_{\text{LSTM}}\) = 200, 500 and 800, for various configurations of EDs as input data \(\lambda_{1}\)-\(\lambda_{5}\) (see Table 2). For all the applications, we considered a maximum number of epochs \(\epsilon\) = 220, to avoid overfitting the learning process stops when the loss function does not decrease after 30 epochs [98]. We conducted several numerical tests to determine the optimal configuration. Figure 8a-c summarizes the effect of the number of \(d_{\text{LSTM}}\) (or hidden units) on classification accuracy (i.e., ratio between the number of correctly classified events and the total number of events in the considered dataset, in percentage) for the training, validation and test dataset (testing) of the proposed model (\(d_{\text{LSTM}}\) = 200 in Figure 8a, \(d_{\text{LSTM}}\) = 500 in Figure 8b, and \(d_{\text{LSTM}}\) = 800 in Figure 8c). Here, we can observe that the performance of this model is better as the number \(d_{\text{LSTM}}\) increases under the defined range (\(d_{\text{LSTM}}\) = [200-800]), while it does not undergo saturation or degradation as the scale becomes larger. A value of \(d_{\text{LSTM}}\) = 500 provides the best testing performance with an accuracy of 92% (by combining IF, SE and SK). The reason is that the Bi-LSTM model with fewer LSTM cells suffers from lack of capability of long-term memory, which will result in under-fitting, whereas a model too large (i.e., higher number of hidden cells) will always lead to increasing difficulty due to over-fitting. In Figure 8d, we show the validation performance of Bi-LSTM models in terms of epochs (required to complete the training) for different numbers of cells and inputs \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Available** & **Signal** & **IF** & **SE** & **SK** & **Size of Input** \\
**Inputs** & & & & & **DATASET T\({}_{q}\)** \\ \hline \(\lambda_{1}\) & yes & no & no & no & \(Q\times 1\times N_{\text{ED}}\) \\ \hline \(\lambda_{2}\) & no & yes & no & no & \(Q\times 1\times N_{\text{ED}}\) \\ \hline \(\lambda_{3}\) & no & yes & yes & no & \(Q\times 2\times N_{\text{ED}}\) \\ \hline \(\lambda_{4}\) & no & yes & no & yes & \(Q\times 2\times N_{\text{ED}}\) \\ \hline \(\lambda_{5}\) & no & yes & yes & yes & \(Q\times 3\times N_{\text{ED}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of the components of each combination of inputs \(\lambda_{1}\)-\(\lambda_{5}\) used to train the DL-network. (\(\lambda_{1}\)-\(\lambda_{5}\)). After the training is completed, the model has learned the patterns necessary for the classification of the input events. As expected, the epoch number \(\epsilon\) of each model is different, depending on the choice of \(d_{\text{LSTM}}\), and the input configuration \(\lambda_{\text{r}}\). We also observed that varying \(\lambda_{\text{r}}\) does not significantly impact on the computing time. This is because the training job is mainly affected by both the size \(Q\) of the training dataset, and the complexity of the network \(d_{\text{LSTM}}\) during weights updating and gradient propagation. We only adopted the parameter matrix \(\Theta\) that generates the lowest \(J(\Theta)\) on the input dataset and collected the value of \(J\) for both training, \(J_{\text{TRAIN}}(\Theta)\), and validation \(J_{\text{VAL}}(\Theta)\). The training, validation and testing accuracies increase with \(\lambda_{\text{r}}\) when \(d_{\text{LSTM}}\) is higher than 200 LSTM cells. For \(d_{\text{LSTM}}\) = 200, a local minimum in validation loss is observed with \(\lambda_{\text{r}}=\lambda_{3}\) (which implies using a combination of IF and SE for each acoustic signal). Epoch number \(\epsilon\) tends to decrease with \(d_{\text{LSTM}}\).