## 3 Results and Discussion
### Comparison between the Proposed Method and Several Artificial Intelligence Algorithms  
This part mainly compares the proposed method with several artificial intelligence algorithms in terms of their performance in the fault diagnosis of rolling bearings. Firstly, the fault prediction performance of the proposed method was compared with deep learning methods, such as 1D CNN and LTSM. The input data of the 1D CNN and LTSM were the raw vibration signal. The optimal number of samples for the 1D-CNN was 24,000, and the shape of its input data was 24,000 \(\times\) 1024. The optimal number of samples for the LTSM was 22,000, and the shape of its input data was 22,000 \(\times\) 1024. The architecture parameters of the 1D CNN and LSTM are shown in Tables 3 and 4, respectively. The influence of number of samples, ranging from 5000 to 30,000, on the algorithm's performance is shown in Figure 14. In terms of the fault diagnosis based on VMD and an ANN, its prediction accuracy reached the maximum value of 99.3% when the sample number was 8000. In addition, the prediction accuracy did not rise with the increase in the number of samples after the peak point. Therefore, the number of samples selected for this paper for the training data was 8000. In comparison, the number of samples for the CNN and LSTM in attaining maximum the prediction accuracy were 24,000 and 22,000, respectively. The increase in the number of samples for the CNN and LSTM led to an increase in the computation time. Then, to further verify the superiority of the proposed method, it was compared with the other five artificial intelligence fault diagnosis methods for rolling bearings with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Layers** & **Kernel Size** & **Kernel No.** & **Activation** & **Output** \\ \hline
1 & LSTM & 1 & 32 & Tanh & 1024 \(\times\) 32 \\
2 & Flattening & - & - & - & 32,768 \\
3 & FC & 32 & 1 & ReLU & 32 \(\times\) 1 \\
4 & Output & 10 & 1 & Soft-max & 10 \\ \hline \hline FC, fully connected. & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The architecture parameters of the LSTM. Figure 14: The influence of the number of samples on the algorithm’s performance: (**a**) influence of the number of samples on the prediction accuracy; (**b**) influence of the number of samples on the computation time. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Layers** & **Kernel Size** & **Kernel No.** & **Stride** & **Padding** & **Activation** & **Output** \\ \hline
1 & Conv1D & 20 \(\times\) 1 & 32 & 8 & 10 & ReLU & 128 \(\times\) 32 \\
2 & Max Pooling & 4 \(\times\) 1 & 32 & 4 & 0 & - & 32 \(\times\) 32 \\
3 & Flattening & - & - & - & - & - & 1024 \\
4 & FC & 100 & 1 & - & - & ReLU & 100 \(\times\) 1 \\
5 & Output & 10 & 1 & - & - & Soft-max & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The architecture parameters of 1D CNN. the same CWRU bearing vibration signal dataset. These five fault diagnosis methods for rolling bearings include the ensemble deep neural network and CNN (CNN-EPDNN) method [29], long short-term memory with multichannel continuous wavelet transform (LSTM-MCCWT) method [30], weighted k-nearest neighbor (WKNN) method [31], medium Gaussian support vector machine (MG-SVM) method [32] and rotation forest with principal component analysis (PCA-RF) method [33]. With the i7-6700 CPU and 32 GB memory, the implementation and training process of these methods were conducted with MATLAB machine learning and deep learning toolboxes for the CWRU bearing vibration dataset with a load of 0 HP and a sampling frequency of 48 kHz. As shown in Figure 15, the proposed method in this paper featured a higher prediction accuracy of 99.3% and a lower computation time of 2.4 s in comparison with the CNN-EPDNN method and LSTM-MCCWT method. Meanwhile, although the computation time of the proposed method was more than the other machine learning methods, such as WKNN, MG-SVM and PCA-RF, its prediction accuracy was obviously higher.