## 4 Experiments
### Comparisons with Variable Taining Sample Sizes
The corresponding results are illustrated in Figure 12 and Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Preprocessing** & **Type of Layer** & **Hidden Size** & **Layer Num** \\ \hline MLP & Fast Fourier transform (FFT) & Fully connection layer & 512-128; 128-64; 64-5 & 3 \\ \hline \multirow{4}{*}{SAE} & \multirow{4}{*}{FFT} & Encoder layer & 512-128; 128-64 & 2 \\ \cline{3-5}  & & Decoder layer & 64-128; 128-512 & 2 \\ \cline{3-5}  & & Fully connection layer & 64-16; 16-5 & 2 \\ \hline \multirow{4}{*}{CNN} & \multirow{4}{*}{STFT} & Conv layer & 1-2-5; 2-3-5; 3-3-5 & 3 \\ \cline{3-5}  & & Max pool layer & 2-2 & 1 \\ \cline{3-5}  & & Fully connection layer & 1980-32; 32-5 & 2 \\ \hline
**Dropout** & **Optimizer** & **Training Epochs** & **Learning Rate** & **Batch Size** \\ \hline
0.5 & Adam & 100 & 0.02 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The details of hyper-parameters and model architectures in the deep neural network (DNN) methods. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **SvdEn** & **SampleEn** & **ApEn** & **SpectEn** & **TfEn(Proposed)** \\ \hline Running time(s) per 50 samples & 0.24 & 2862.31 & 2740.10 & 0.14 & 1.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Running time of the above-mentioned entropy-based feature extraction methods. According to the comparative results, we can obtain the following conclusions of the proposed TfEn-RFE method. 1. Stability for variable sizes of training samples As shown in Figure 12 and Table 5, with variable sizes of training samples (4/6/8/10/12/14): For the three DNN methods (FFT-MLP, FFT-SAE and STFT-CNN), the ranges between the maximum accuracy and minimum accuracy are 20.37%, 39.29% and 30.00%, respectively. The DNN-based methods do have extraordinary performance when the training samples are relatively sufficient, with the help of their powerful capability in feature mining. However, their accuracy presents the obvious degradation with the extremely few training samples (size of 4 per fault mode), which results by their worst stability for variable training sizes among all the methods. For the four existing entropy methods (SvdEn-RFE, SampleEn-RFE, ApEn-RFE and SpectEn-RFE), their accuracy ranges are 14.11%, 3.79%, 3.44% and 16.49%, respectively. These entropy-based methods achieve the better stability than the DNN-based ones. However, their performance does not achieve significant improvements like the DNN-based ones with increasing training sizes, because they can  
Figure 12: Comparisons among entropy and DNN-based methods with various training samples. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Training Size/Methods** & **4** & **6** & **8** & **10** & **12** & **14** \\ \hline SvdEn-RFE & 78.93\% & 87.69\% & 82.31\% & 87.20\% & 83.78\% & 93.04\% \\ \hline SampleEn-RFE & 91.43\% & 92.22\% & 92.69\% & 94.80\% & 93.75\% & 95.22\% \\ \hline ApEn-RFE & 93.57\% & 93.71\% & 93.08\% & 94.40\% & 96.25\% & 96.52\% \\ \hline SpectEn-RFE & 81.43\% & 94.07\% & 93.85\% & 93.60\% & 97.92\% & 96.09\% \\ \hline FFT-MLP & 70.36\% & 70.00\% & 74.40\% & 75.00\% & 80.00\% & 90.37\% \\ \hline FFT-SAE & 60.71\% & 80.00\% & 80.00\% & 85.20\% & 100.00\% & 100.00\% \\ \hline STFT-CNN & 70.00\% & 74.82\% & 80.00\% & 100.00\% & 100.00\% & 100.00\% \\ \hline TfEn-RFE (proposed) & 99.29\% & 99.26\% & 100.00\% & 100.00\% & 100.00\% & 100.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Detailed classification accuracy of each method with various training samples. only extract the features from a single domain (time or frequency), and thus lose useful information of those non-stationary Imfs. For the proposed TfEn-RFE method, its accuracy range is only 0.74%. To sum up, the proposed TfEn-RFE method always maintains the best classification accuracy, and shows no obvious degradations, even with extremely few training samples, which exhibits the best stability for the variable training samples among all the methods.