## 3 Results
### Wavelet Residual Network  
For each type of working condition, the sample length is 784, and the sample number of each type is 600. The dataset is divided into a training set, a validation set, and a test set. The ratio is 0.5:0.25:0.25. Two completed experiments are detailed in this paper. Experiment 1 relates to a residual neural network, and Experiment 2 is wavelet transform, which is then input to a residual neural network. The sample signal is normalized, and the Adam optimization algorithm is adopted. The initial learning rate of the model is 0.001, which decreases to one-tenth every five iterations. A total of 10 types of sample signals are input into the model. The ResNets model was used in Experiment 1. The accuracy of the training set was 100%, and that of the test set was 93.80%, as shown in Figure 9. In Experiment 2, the accuracy of the training set and test set was 99.15% and 99.12%, respectively, as shown in Figure 10. The results show that the accuracy of the proposed method was improved by 5.32%. Figure 8: Time–frequency map obtained by improved Morlet wavelet transform, with central frequency \(\omega_{0}=2\pi\). In summation, the model proposed in this paper can identify faults more accurately than ResNet under variable load conditions. The proposed method can be effectively applied to diagnosis. Figure 11 shows the confusion matrix of the residual network training results. As apparent from the graph, prediction errors exist in the categories labeled 0, 1, 2, and 8. Specifically, the prediction accuracy rates were 94.67%, 88.00%, 77.33%, and 98.67%, respectively. Figure 12 shows the confusion matrix of the wavelet residual network's training results. As observed in the figure, only the classification labeled as 1 has errors in the prediction, and the accuracy rate was 96.00%. Classification performance usually varies with the number of training samples in the training set. Table 4 shows the training results for 300, 600, 900, and 1200 samples per class. The results include accuracy and loss rates for the training and validation sets. Meanwhile, Figure 13 shows the training set's accuracy trend, while Figure 13 shows that of the validation set. These trends can be observed to determine whether the model converges during training and how well it generalizes the validation set. Figure 10: Accuracy and loss in Experiment 2. The model is a wavelet residual network. Figure 9: Accuracy and loss in Experiment 1. The model is a residual neural network. Figure 11: Confusion matrix results for Experiment 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Samples** & **Accuracy** & **Loss** & **Val_Accuracy** & **Val_Loss** \\ \hline
300 & 99.00\% & 0.12\% & 98.80\% & 2.05\% \\
600 & 99.15\% & 0.10\% & 99.12\% & 1.72\% \\
900 & 99.50\% & 0.07\% & 99.25\% & 1.84\% \\
1200 & 98.94\% & 0.09\% & 97.40\% & 2.31\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Training results for different sample sizes. Figure 12: Confusion matrix results for Experiment 2. As can be seen from Figures 13 and 14, with increasing training samples, the accuracy of both the training and validation sets is improved, and the model performance is enhanced. However, when the sample size reaches 1200, the accuracy decreases by 0.56% and 1.85%, respectively. From the above, as the number of training samples increases, the classification model can more easily capture the overall characteristics and general rules of the data, thus reducing the risk of overfitting. However, if the number of training samples is too large, it may also cause the model to overfit the training data and perform poorly on unseen data. Therefore, there is a trade-off between overfitting and underfitting. A total of 600 sample points are selected for the following reasons: (1) as seen in Figure 14, 600 sample points for training can provide enough information for learning the characteristics and laws of data. (2) A smaller sample size means shorter training time.