## 6 Discussion  
After obtaining the responses of the system in healthy and damaged conditions, it was observed that specific frequencies, between the range of 0 Hz and 8500 Hz, due to the harmonics considered in this work, shift given the presence of damage [50]. Indeed, the results in terms of signals from the healthy system could be validated with the signals from the experimental test. In view of this, a vector was created to organize the input data for the ANN approach. Since the dimension of the analysis (extracted objects from each simulation) went from 100 Hz to 10,000 Hz, the classification method could identify whether a system has damage or not, and the multi-class classification method could recognize the severity of the damages identified. The characteristics and algorithm performances for each test for the classification and multi-class classification methods can be found below. The classification approach consisted of Tests 1, 2, 3, 4, and 5. The total number of observations (objects) and the percentage are exposed in each cell of the confusion matrixes, whose characteristics are related to the demonstration of the actual value and the predicted value. The confusion matrix rows correspond to the output class (true class), which are 0 (no damage) and 1 (damage), while the columns correspond to the target class (predicted class), which are 0 (no damage) and 1 (damage). The main diagonal elements represent the classified samples (correct observations), while the off-diagonal elements correspond to the misclassified samples (wrong observations) [64]. To better visualize the problem regarding the \"All Confusion Matrix\" of Test 5 (the best performance model for the classification method achieved in this work), as shown in Figure 26, its results characteristics can be seen in Table 4, whose parameters and values are explained [65]. For Tests 1, 2, 3, 4, and 5, the network took 14, 19, 18, 28, and 18 epochs (training state plots) to train and validate the model, respectively. Performance per epoch has indicators of Cross-Entropy (CE) and Errors (%E). CE operation computes the CE loss between network predictions and target values for single-label classification tasks. Its value also shows the efficiency of the network, while the %E shows the fraction of predictions misclassified (Table 3). When the CE of the validation phase reaches the minimum value, this is considered the best mark of the training phase, because overfitting occurs from that point. It is possible to observe this characteristic due to the fact that the training curve continues to decrease, while the validation curve starts to increase. Thus, it is possible to observe when the overfitting starts in this part of the plot. Moreover, the \"nprtool\" takes this value index, whose function shows the best possible result for this ANN architecture. In addition, when the validation sampling of input data reaches the lowest CE of the last six epochs, the network (validation) stops training when the non-training validation subset error rate increases continuously for more than six (default) epochs. This can be seen in the training state plots. Considering this, the performance for Test 5 was better than the performance for Tests 1, 2, 3, and 4. When errors between the target values and predicted values appear after the training of a network, the histogram can be used. Then, the Error Histogram has the capacity to show the differences between predicted values and target values. Moreover, an ANN with histogram features is highly recommended for FD in gearboxes [64]. Therefore, by analyzing the detection performances of the confusion matrix and the plots of the best validation performance, error histogram, and training state, for classification problems (Tests 1, 2, 3, 4, and 5), Test 5 was considered the best model. This performance result can be explained by the greater number of objects used in the network compared to the other models. The first case of the multi-class classification approach consists of Tests 6, 7, and 8.