## 5 Results and Discussion  
### The Advantages of the Spectrum in Training Neural Networks  
[PERSON] trains 1-D CNN based on temporal signals to identify bearing faults [60]. There are initial phase differences between the temporal samples, which will interfere with the learning process of CNN. Therefore, the spectrum of the signal was utilized as the input of CNN in this paper. In this section, we will conduct an experimental study of the performance of these two methods of training CNN. A 1-D temporal data set and a 1-D spectral data set were respectively created based on the reconstructed temporal signal and spectrum of the frequency band \(\textit{iwp}_{1}^{2}\). Then, a normalized 1-D temporal data set and a normalized 1-D spectral data set were respectively created by normalization processing. The depth of the 1-D CNN model used was the same as the depth of the previously optimized 2-D CNN model. The size and number of convolution kernels in each layer were set with reference to published literature and optimized using the process described above. The optimized model hyperparameters are listed in Table 2, and the specific optimization process will not be described in detail. Figure 16: Illustration of the effect of the learning rate on convergence speed and convergence stability of the model. The data sets were randomly divided to the training set, validation set and test set by a ratio of 3:1:1. The result is shown in Figure 17, where TD means the temporal data set, NTD means the normalized temporal data set, SD means the spectral data set and NSD means the normalized spectral data set. Tra-Acc denotes training accuracy, Val-Acc denotes validation accuracy and Test-Acc denotes test accuracy. Tra-Loss denotes training loss value, Val-Loss denotes validation loss value and Test-Loss denotes test loss value. As the tool wears, the mechanism of the cutting edge removing material gradually changed, and the vibration state of the spindle changed accordingly. The vibration signal records the tool wear process. As can be seen from Figure 17, the 1-D CNN could extract effective features from the spindle vibration signal. The test accuracy of the model trained with the temporal data set was 74.7%. For a 6-class problem, this was far beyond the accuracy of a random decision. Transforming the temporal signal to the frequency domain eliminated the interference of the initial phase of the signal sample on the classification process. The trained model had a test accuracy of 90%, which made it more informative for industrial sites. The normalization process reduced the discrimination of temporal signals, but the test accuracy of the spectral data set was improved, and the test loss value was also significantly reduced. When the neural network was trained with the unnormalized segment spectrum data set, from the 50 th epoch, the training accuracy was significantly higher than the validation accuracy, which means the model began to over fit. At the 100 th epoch, the training accuracy had stabilized at 100%, and the validation accuracy reached a steady state, but not more than 90%. The unnormalized spectrum retained the intensity information of the vibration signal, which was the parameter most directly related to the sharpness of the cutting edge, which was also the parameter most tightly related to the cutting conditions. Therefore, when using it to train a neural network, the model could converge quickly; nevertheless, it was also easier to over fit. Normalization could cancel out the intensity information, forcing the model to mine the variation of the spectrum shape and enhance the generalization of the model. In summary, converting the original signal to the frequency domain and normalizing it was most beneficial to the neural network model. The test accuracy was 92.2%, and the test loss value was 0.246.