## 5 Results and Discussions
In Figure 6, a visual representation of the new extracted features achieved by means of the LDA technique is shown. From this resulting projection, it can be appreciated that different clusters appear separated between them; each cluster represents each one of the considered conditions evaluated under different operating supply frequencies (5 Hz, 15 Hz, and 50 Hz). Moreover, although the clear separation between all considered conditions is desired, a slight overlapping appears between the conditions S3 and S5; such overlapping may lead to achieving a lower performance of classification performance during the condition assessment. However, on the other hand, it should be highlighted that the HC is well separated from all faulty conditions, and this fact results in avoiding false negatives during the condition assessment, which is an advantage because the proper working condition of rotating electrical machines is assured. From the obtained projection of Figure 6, it must be highlighted that the proposed signal characterization by means of the statistical features estimated from different signals in different domains, and its fusion and compression through the LDA can lead to a wide range of operating frequencies that, in industrial environments, cover the common ranges of rotating speeds for any considered electrical machine. Previous to the application of the automatic diagnosis and severity detection, aiming to emphasize the effectiveness of the proposed method in regards to the consideration of different signals and in regards to their processing in different domains, in Figure 7a,b the qualitative representations are shown, which were achieved by means of a PCA projection over the representative feature matrices estimated from analyzing the vibrations signals in both domains, TD and FD, respectively. In both resulting projections, the data distributions of all considered conditions can be appreciated, and from Figure 7a,b, it can be also seen that the characterization of vibration signals in the TD may contribute to the separation of the S2, S3, S4, and S5 conditions. Conversely, the characterization of the vibrations signals through the FD leads to the separation of S1, S2, S3, and S4 conditions. Therefore, the fusion of the information calculated from different signals and different domains will improve the contribution in the face of the separation of the considered conditions. Figure 6: The resulting 2-dimensional LDA projection achieved over all considered conditions, that is, HC, S1, S2, S3, S4, and S5. Subsequently, the automatic condition assessment and fault severity identification is carried out by means of the proposed NN-based classifier; thereby, the new features extracted by the application of the LDA are evaluated through the proposed classifier. As mentioned previously, the NN-based structure consists of three layers, where the input, hidden, and output layers have a number of neurons defined as 2, 10, and 6, respectively. Additionally, the NN-based classifier is trained and tested under a \(k\)-fold cross-validations scheme with a number of \(k=5\) folds, and the NN is trained and tested during 50 epochs through a probabilistic sigmoid function that is used as the activation function. Hence, each considered condition is represented by a total number of samples equal to 450, from which 360 samples are used for training purposes and the remaining 90 samples are used for validation purposes. As a result, during the training and validations of the proposed NN, global classification ratios around 98.9% and 98.7% are achieved, respectively. In Table 4, the confusion matrix that summarizes the individual classification scores performed by the NN-based classifier is shown. As can be seen, most of the misclassifications are between faulty conditions, which proves that the prediction of false negatives is avoided. Additionally, for the training of the NN-based classifier, the decision regions of all considered conditions are modeled and estimated to be projected over a 2D plane.