## 6 Deep Learning Fault Classification  
In practical situations, fault classification is usually performed by considering the fusion of vibration signals collected from different sensors over a specific time interval in which the machine is assumed under specific working conditions. This context is feasible, and it allows for obtaining good results. However, in this paper, only the collected vibration signals from one sensor are used for fault classification. The reason is to develop an accurate classification method with a minimum number of sensors. As stated in Section 4, the vibration signals dataset includes only 780 signals of 10 s for the centrifugal pump dataset and 255 signals for the reciprocating compressor. Although there is no limitation concerning the quantity of data that can be acquired, it is desirable to require few signals due to the costs of acquisition and processing resources. On the other hand, the length of the signals is enough, as each signal is measured for 10 s, representing 583.3 turns for the pump motor and 64 cycles of the compressor. This signal length enables the extraction of five signal samples from each recorded signal and augments the feature dataset. The proposed fault classification approach based on deep learning techniques is presented in Figure 7. The deep learning model can be the CNN, the LSTM, or BiLSTM models. The approach implicitly assumes that the fault signature is embedded in the vibration signal as a pseudo-periodic process [37]. Consequently, such fault signature is also repeatedly present in the time-frequency representation. The approach includes two stages. The first stage corresponds to vibration signals pre-processing:  
1. Each signal sample is processed for obtaining the MFCC and derivatives. 2. The feature array of size \(96\times 3921\) is obtained by concatenating the MFCC and their derivatives. The second stage corresponds to the classification. 1. The feature dataset is split into a test set (15%) and a train set (85%). This corresponds to a hold-out cross-validation used for assessing the performance of an already trained (and cross-validated model) when used for classifying entire vibration signals. 2. The method has two branches. The branch at the right is the deep learning model training: 1. Each feature array in the training dataset is subdivided into \(N_{B}\) patches (or pieces) of size \(96\times M\) to increase the original size of the dataset. It also permits dealing with the computational cost of training the deep learning model. This subdivision assumes that the feature arrays do not show strong variation along the temporal axis (see Figure 6). Each patch keeps the label and a portion of the feature array. The number of patches \(N_{B}\) can be calculated as \(N_{B}=\frac{3921}{M}\). The pieces are represented as a double-precision array. The value of \(M\) is selected to reach a compromise between accuracy and reduction of the variance, which we have called clean loss convergence. Figure 6: MFCC feature space including the first and second derivatives of MFCC. (**a**) MFCC features space for a vibration signal for the healthy class. (**b**) MFCC feature space for a vibration signal extracted from a faulty condition. * All pieces in the training dataset are put in a bag where the original temporal order is lost by randomization. * The next step in this branch is the deep learning model 10-fold cross-validation using the pieces from the bag. * The 10-fold cross-validated model is evaluated concerning their accuracy for classification of signals pieces (see results sections 8 and 9). * The branch on the left for the test set works differently. In this case, the branch is executed for one feature array from the test set at a time. Then, the difference between the two branches is how to assign the predicted label for one feature array obtained from a signal fragment of the test set.