## 8 Results for the Centrifugal Pump  
The performance results during 10-fold cross-validation are shown in Table 7 for each of the deep learning models tested: CNN, LSTM, and BiLSTM. The metrics are calculated during the cross-validation procedure. The CNN models are fed with pieces of size \(96\times M\) extracted from the MFCC-based features array representing each of the  
Figure 10: Accuracy as a function of hyper-parameters for the CNN trained with the centrifugal pump dataset. The accuracy was calculated using the validation dataset. (**a**) Accuracy as a function of M, (**b**) accuracy as a function of the batch size, (**c**) accuracy as a function of the dropout probability, and (**d**) accuracy as a function of the initial learning rate.  
vibration signals denoted A2, A3, and A4 according to the designation of the accelerometer used for recording such a signal. Similarly, the LSTM and BiLSTM models are fed with pieces of MFCC of size \(96\times M\) (The M parameter is set according to Table 6).  
Even when each model is fed with pieces of the MFCC array representing a window of the vibration signal of about 65 ms for a signal sampled at 50 kHz, the accuracy is high. The classification accuracy is very high, independent of the particular vibration signal channel. The standard deviation obtained considering the ten data groups used in cross-validation is low, and the maximum standard deviation attained is 0.248 % for the CNN model. The accuracy attained by the CNN models is 99.76% for A2, 99.64% for A3, and 99.96% for A4. Results for the LSTM and BiLSTM models show standard deviations lower than the standard deviations of the CNN models. The highest standard deviation value is 0.095% for the LSTM model trained with signals from A3. The accuracy attained by the LSTM model is 99.81% for A2, 99.81% for A3, and 99.91% for A4. The BiLSTM models attained an accuracy of 99.89% for A2, 99.89% for A2, and 99.96% for A4.  
The accuracy as a function of the fault class for the MFCC features is shown in Figure 11a-c. The accuracy attained by the models trained with channel A3 is slightly lower than that of those trained with A2 and A4. Generally, higher accuracy is obtained with the vibration signal from channel A4. Classification accuracy attained by all models is higher than 99.5% for all fault classes.  
Figure 12 compares the boxplots of each model trained, considering the accuracy obtained during the 10-fold cross-validation. Such a comparison was determined using the Kruskal-Wallis test [63] method, which provides a set of mean ranks. Each of the boxplots shows the statistical values corresponding to the minimum and the maximum, and the box is the inter-quartile range that represents the 25 % (first quartile), the median (second quartile, shown in red), and 75% (third quartile). Any values outside this range are known as outliers. All accuracy median values for all the models trained are higher than 99.4%. In all vibration signal channels, there are no significant statistical differences between the accuracy results obtained by CNN and the accuracy results obtained by LSTM and BiLSTM. The accuracy attained by the CNN model trained with channel A4 is the highest, and there are significant statistical differences concerning the CNN models trained with A2 and A3 (\(p<0.05\)). There are also statistical differences regarding the accuracy attained by the LSTM models trained with A2 and A3.