# Bearing Fault Diagnosis Method Based on Improved VMD and Parallel Hybrid Neural Network
## 5 Discussion
### Experimental Results and Comparative Analysis  
To test the feasibility and superiority of the proposed method, this paper, respectively, compares the proposed method with the improved and the latest fault diagnosis model. Considering the reliability of the experiment, the following experiments are repeated 10 times, and an average is found. Firstly, ablation experiments were carried out, and the proposed method was compared with the GRU model, GRU-CNN model, BiGRU-CNN model, parallel hybrid neural network full connection model, and parallel hybrid neural network GAP model to verify the feasibility of the method. The GRU model uses two GRU layers, and the number of neurons is 32 and 16 separately. GRU-CNN model adds two 1 DCNN layers based on the GRU model. The output dimension numbers are 32 and 16 separately, and the convolution kernel size is 64 and 16 separately. The BiGRU-CNN model replaces the GRU layer with the BiGRU layer, while the parallel hybrid neural network-FC model fuses the characteristics abstracted from the two networks and uses the flatten layer and the two FC layers to reduce the data dimension. The number of neurons in the FC layer is 64 and 32 separately. The parallel hybrid neural network-GAP model replaces the flatten layer and two FC layers of the above model with a GAP layer. The diagnostic results were evaluated by time index and accuracy index. In terms of time, the training time and testing time of the diagnostic model were mainly observed. The accuracy indicators include the accuracy rate (\(P\)) and harmonic mean (\(F_{1}\)), whose mathematical expression is  
\[P=TP/(TP+FP)\times 100\% \tag{16}\]  
\[F_{1}=\frac{2 TP}{2 TP+FP+FN}\times 100\% \tag{17}\]  
In the formula, \(TP\) is the real class, \(FP\) is the false positive class, and \(FN\) is the false negative class; the ablation results are shown in Table 6.  
In Table 6, the time index and accuracy index are employed to evaluate the results. From the experimental results, the effect of using only the GRU layer is not ideal, and the \(p\) value and \(F_{1}\) average are 93.95% and 93.87%, respectively. After adding the CNN layer, the GRU-CNN model becomes more complex, and the training and testing time increases, but the \(p\) value and \(F_{1}\) average value reach 95.91% and 95.77%, respectively; it reflects the further extraction ability of the CNN layer for deep-seated information in the signal. The BiGRU-CNN model uses a two-way cyclic structure, and its \(p\) value and \(F_{1}\) mean value reach 97.03% and 96.76%, respectively, which reflects the more powerful feature extraction ability of BIGRU. The parallel hybrid network-FC model adds a parallel BiLSTM-CNN \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fault Diagnosis Model** & **Train Time (s)** & **Test Time (s)** & \(P\) **(\%)** & \(F_{1}\) **(\%)** \\ \hline GRU & 674.93 & 3.89 & 93.95 & 93.87 \\ GRU-CNN & 940.97 & 3.95 & 95.91 & 95.77 \\ BiGRU-CNN & 1120.87 & 4.12 & 97.03 & 96.76 \\ The parallel hybrid neural & 1953.28 & 5.17 & 98.47 & 98.42 \\ network-FC & & & & \\ The parallel hybrid neural & 1864.88 & 4.18 & 98.50 & 98.46 \\ network-GAP & 1867.56 & 4.19 & 99.73 & 99.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of ablation results. network for feature extraction, and fuses the features extracted by the two networks, using the complementarity between features to improve the diagnostic accuracy, and its \(p\) value and \(F_{1}\) average is 98.47% and 98. 42%, respectively. Then, the gap layer is used instead of the FC layer to form the parallel hybrid neural network-GAP model. The training time and testing time are reduced by 88.4 s and 0.99 s, respectively, indicating that the GAP layer has unique advantages in reducing model parameters and calculation. Finally, the fault diagnosis method of improved VMD and parallel hybrid neural network is proposed in this paper. The fault signal is handled by the improved VMD algorithm and then input into the parallel hybrid neural network-GAP model.