## 12 Conclusions  
The concatenation of MFCC and their derivatives is a 2D feature representation of the vibration signal that can be used as input of high-performance deep learning algorithms for classifying faults in a multi-stage centrifugal pump and a reciprocating compressor with high accuracy. All classification models compared in this application allow classification accuracies close to 100% for the 13 faulty conditions in the pump impellers related to several severity levels according to the stage. Similarly, the accuracy is also close to 100% for the 17 valve faults of the reciprocating compressor. The main results state that:  
1. MFCC-based features show a higher classification accuracy than the accuracy attained using 2D spectrogram features when used as inputs to CNN, LSTM, and BiLSTM-based classification models. 2. All compared models are highly accurate when the DL models are trained with a specific vibration channel. There are no significant statistical differences concerning the accuracy attained during cross-validation. 3. The 10-fold cross-validation showed that all compared models have low accuracy variability when trained with the ten data groups. The recall and specificity for each class considered are close to 100% for all models. 4. Visualization of the cluster structure of the activation in the different layers of the DL models shows that the model can attain an almost perfect classification in the experiments under study. The proposed approach was able to classify large MFCC feature arrays using MFCC, LSTM, and BiLSTM-based classification models by subdividing the features array into small 2D pieces and exploiting the pseudo-periodic nature of faults in rotating machines. The patch-wise classification method exploits methodologies successfully applied in random forest classifiers. Further research is still necessary to assess the method's robustness to noise or failure in the sensors. The combination of the investigated models, another type of combination \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Equipment** & **Authors** & **Model** & **Signal** & **No. of Conditions** & **Accuracy (\%)** & **Limitations** \\ \hline \multirow{3}{*}{Centrifugal Pump} & [PERSON] et al. [19] & DBN & Vibration & 6 & 97.40 & NFC \\  & [PERSON] et al. [20] & MFCC- ELM & Sound & 4 & 100 & NFC\&Require denoising \\  & [PERSON] and [PERSON] [67] & AWT-CNN & Sound & 5 & 100.00 & Noise\&NFC \\  & [PERSON] et al. [23] & CNN & Vibration & 4 & 98.23 & Require several signal\&NFC \\ \hline \multirow{3}{*}{Reciprocating Compressor} & [PERSON] et al. [7] & LSTM & Vibration & 17 & 93.00 & Low Resolution Rep. \\  & [PERSON] et al. [12] & CNN & Vibration & 7 & 91.65 & Require Many sensors \\  & [PERSON] et al. [31] & LMD\&GDAE & Vibration & 4 & 92.72 & NFC \\  & [PERSON] et al. [24] & CNN & Vibration & 4 & 100 & NFC\&Complex Architecture \\  & [PERSON] et al. [29] & CNN & Vibration & 4 & 100.00 & NFC\&Complex Architecture \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Deep Learning models applied to fault classification in Pumps and Compressors. of features, or even a model fusion approach by combining different DL models treating separated inputs, i.e., MFCC array, first derivatives, and second derivatives arrays, are also the subject of future research. Conceptualization, D.C., R.M., M.C., R.-V.S. and C.L. ; Data curation, D.C., M.C. and R.-V.S. ; Formal analysis, D.C., E.E. and C.L. ; Funding acquisition, R.-V.S. and C.L. ; Investigation, D.C., M.C. and E.E. ; Methodology, D.C., R.M., M.C., R.-V.S. and C.L. ; Project administration, R.-V.S. ; Resources, D.C., R.-V.S. and C.L. ; Software, D.C., R.M., E.E. and C.L. ; Supervision, C.L. ; Validation, D.C., R.M., R.-V.S. and E.E. ; Visualization, D.C., R.M. and R.-V.S. ; Writing - original draft, D.C.; Writing -review & editing, D.C., R.M., M.C., R.-V.S. and E.E. All authors have read and agreed to the published version of the manuscript. This work is supported in part by the National Natural Science Foundation of China (No.