## 1 Introduction
Additionally, they do not incorporate derivatives as features for fault classification. The research concerning fault detection in centrifugal pumps and reciprocating compressors using DL techniques has shown the feasibility and advantages of such techniques. However, even when the accuracy reported in most of the research using vibration signals is high, their application is limited to classifying a few faults. Moreover, several reported methods need to include formal cross-validation of the classification. In addition, several of the reported DL methods used more complex architectures than the simple architectures we are reporting. This type of machine could have many faults and severity levels in real industrial cases. Consequently, high-performance technologies are developed to classify a large set of possible faults with high accuracy. In this paper, we propose to use the MFCC concatenated with their first and second derivatives as informative and sensitive features. Such features enable the classification of a large set of faults in a multi-stage centrifugal pump and a reciprocating compressor. Specifically, we propose subdividing the features array into small 2D pieces fed to the DL models to classify 13 fault conditions in a multi-stage centrifugal pump and 17 valve faults in a reciprocating compressor. In the classification stage, three DL models such as LSTM [32], Bidirectional LSTM [34], and CNN [35] are used for evaluating their classification ability. The faulty conditions under study involve combined faults in the impellers of a ten-stage centrifugal pump with eight levels of severity. The faults are located in the discharge and input valves of the reciprocating compressor. Then, our paper is focused on signal processing by presenting a new feature extraction approach that is validated on three different and well-known DL architectures for processing 2D images. Specifically, the main contributions of this paper can be considered as follows:  
* A proposal to use MFCC concatenated with their first two time derivatives as a feature space, which can be directly fed into DL classification algorithms. Combined features from MFCC have been proven to be efficient in different application fields of machine learning and DL [36]. * The methodology enables the classification of multi-faults in complex rotating machines by using only small-time windows of 65 ms for vibration signals sampled at 50 kHz. Novelty in the approach consists of subdividing the features array into small 2D pieces by exploiting the pseudo-periodic nature of faults in rotating machines [37]. This patch-wise method allows highly accurate classification of a large MFCC array. * We are proposing an accurate methodology for classifying many combined faults in a multi-stage centrifugal pump and valve faults in a reciprocating compressor. * An evaluation, using 10-fold cross-validation, of multi-fault classification based on three DL techniques, such as LSTM, BiLSTM, and CNN. A simple architecture is proposed to classify 2D feature pieces and the vibration signal in each case. * We are also reporting a comparison between the concatenation of MFCC and their derivatives to the spectrogram as features for classifying faults using DL techniques in the centrifugal pump and the reciprocating compressor. Additionally, our approach is tested on a relatively small balanced data set of vibration signals, proper for conducting supervised fault classification, which can be used in DL applications by adjusting the DL architecture properly and by applying a proper data size augmentation technique [38]. In our case, using features from MFCC faces this challenge, as our approach is, indeed, a data size augmentation procedure. The rest of the paper is organized as follows: in Section 2, the background concerning the spectrogram and the MFCC time-frequency representation is presented. In Section 3, a description of the experimental test bed is detailed. The vibration signal acquisition in both rotating machines is discussed in Section 4.