# A Fault Detection Framework for Rotating Machinery with a Spectrogram and Convolutional Autoencoder
## 2 Related Works  
### Feature Extraction for Analyzing the Signals  
The vibration signals often directly reveal information on the operating state of the rotating machinery [9; 10]. Hence, most of the existing works on the FDD of the rotating machinery are based on vibration signals obtained from the accelerometer sensors. To analyze the vibration signals, several informative features summarizing intrinsic properties of the raw signals should be drawn beforehand. For this reason, various feature extraction techniques for the FDD have been developed during the last decades. Table 1 summarizes previous works on vibration signal-based FDD for rotating machinery. In most of the previous studies on FDD for rotating machinery, the feature extraction is applied to only single domain-represented signals (i.e., time-domain signal or frequency-domain signal). However, in many real situations where the vibration signals are generated with noisy and nonstationary patterns, informative features of signals may not be drawn from these single-domain representation schemes. Under the stationary assumption that the operating environments or settings of rotating machinery are constant, FFT techniques can \begin{table}
\begin{tabular}{c c c c} \hline
**Signal Representation** & **Feature Extraction Schemes** & **Description of Feature Extraction Schemes** & **References** \\ \hline Time-domain representation & Manually defined features & Simple statistics of signals & [12; 23] \\ \hline Frequency-domain representation & Manually defined features & Simple statistics of signals & [24; 25] \\ \hline Time-domain representation & & Unsupervised linear dimensionality reduction & [27; 28] \\ \hline Frequency-domain representation & Principal component analysis (PCA; [26]) & Unsupervised linear dimensionality reduction & [29; 30] \\ \hline Time-domain representation & & Supervised deep neural network model & [32] \\ \hline Frequency-domain representation & Convolutional neural network (CNN; [31]) & Supervised deep neural network model & [33] \\ \hline \multirow{3}{*}{Time-domain representation} & Residual neural networks & Supervised deep neural network model & [35; 36] \\  & (ResNet; [34]) & Supervised deep neural network model & [35; 36] \\ \cline{2-4}  & Gated recurrent unit & & \\ \cline{2-4}  & (GRU; [37]) & Supervised deep neural network model & [14] \\ \hline Frequency-domain representation & Graph convolutional network (GCN; [38]) & Supervised deep neural network model & [39] \\ \cline{2-4}  & Denoising stacked autoencoder (SAE; [40]) & Unsupervised deep neural network model & [41] \\ \hline Time-domain representation & One-dimensional convolutional autoencoder (ID-CAE; [42]) & Unsupervised deep neural network model & [43; 44] \\ \hline Time-domain representation & Deep belief network (DBN) [45] & Unsupervised deep neural network model & [46; 47] \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of previous works on vibration signal-based FDD for rotating machinery. properly work for the vibration signal in that the periodical characteristics of the signal are also rarely varied [48]. However, those operating conditions of the rotating machinery are dynamically shifted. Thus, the stationary assumption is often violated, and time-varying patterns of frequency components cannot be precisely captured by simple FFT [49]. To overcome this limitation, time-frequency analysis can be used before the feature extraction procedure. This technique attempts to represent the signals as two-dimensional image-formatted data whose horizontal axis is time and vertical axis is frequency components. To this end, the short-time Fourier transform (STFT) transforms the time-domain signal into the two-dimensional matrix, referred to as a spectrogram, representing the frequency component of a certain time point. For this reason, this study proposes to use the STFT method before feature extraction in order to better reflect the characteristics of nonstationary signals as time-frequency domain representation.