# Bearing Fault Diagnosis Method Based on Improved VMD and Parallel Hybrid Neural Network
## 4 Results
### Fault Diagnosis Model Based on Parallel Hybrid Neural Network  
During the design of the fault diagnosis model, setting different super parameters will affect the diagnosis results, and elements such as the complicacy of the problem, the size of the data set, and computation need to be considered. In this paper, the number of network layers, neurons, and training times of the diagnostic model are repeatedly adjusted. Specifically, the number of network layers is determined first, then the number of neurons  
Figure 8: Image of reconstructed signal and original signal. Figure 9: Square envelope spectral image of reconstructed signal. is determined, and finally, the training times are determined according to the size of the loss value. The finally established parallel hybrid neural network fault diagnosis model is composed of two parallel neural networks, as shown in Figure 4 above. One neural network is the BiGRU-1 DCNN structure, including two BiGRU layers and two 1 DCNN layers. The number of neurons in BiGRU layer 1-1 and BiGRU layer 1-2 are set to 32 and 16, respectively, the filters of 1D-CNN_1-3 are set to 32, the convolution size is set to 64, the filters of 1D-CNN_1-4 are set to 16, and the convolution size is set to 32. The other neural network is a BiLSTM-1 DCNN structure, which contains two BiLSTM layers and two 1 DCNN layers. The number of neurons in BiLSTM layer 2-1 and BiLSTM layer 2-2 are set to 32 and 16, respectively. The filters of 1 DCNN_2-3 are set to 32, the convolution size is set to 64, the filters of 1 DCNN_2-4 are set to 16, and the convolution size is set to 32. The fault diagnosis model uses two BiLSTM layers and two BiGRU layers to extract the features of the training samples with time series, capture and remember the relevant features in the samples, and use the two-way cyclic structure to better handle the long-term dependence in the sequence data. Then, the extracted memory features are input into two 1 DCNN layers, respectively, for in-depth feature mining, and the small differences between different faults are extracted from the data, thus raising the diagnosis accuracy of the model. Then, the features extracted by the two neural networks are fused using the splicing method to obtain more comprehensive fault features. After the CNN layer, the GAP layer is employed to take the place of the traditional FC layer, which can significantly reduce the parameters of the model while preventing the model from being overfitted and also upgrade the training speed of the model. Finally, fault classification is completed through the SoftMax layer. The super parameters of the model are shown in Table 4.  
At the same time, to improve the training effect of the model, the batch training method and Adam optimizer are used to train the model in the experiment. The batch training method divides the training data set into multiple mini batches, and each iteration uses the data of one batch to calculate the gradient and update the model parameters, which can improve the convergence speed and generalization ability of the model. The Adam optimizer can adapt to the learning rate without manually adjusting the learning rate of each parameter, which is suitable for non-stationary targets. In this paper, Dell g15-5520 with the i7-12650h CPU model, rtx3060 graphics card model, and 6 GB video memory capacity are used for training (Dell, Round Rock, TX, USA). The number of samples put into the model each time batch size is set to 32, and the total number of training times is set to 20. The error curve of model training is shown in Figure 10. The model basically converges and is stable after training 20 times, and there is no fitting problem.