## 4 Experimental Verification
### Analysis of Model Noise Resistance Results  
This section is designed to validate the noise immunity of the model, especially for additive Gaussian white noise, since this noise is one of the most representative noises and is easy to quantify. In this paper, the strength of the bearings subjected to industrial environmental noise is simulated by adding different signal-to-noise ratios (SNRs) [44]. The \(SNR\) is defined in Equation (7), and the unit is usually decibels (\(dB\)), where a smaller \(SNR\) indicates a more contaminated signal. \[SNR_{dB}=10 Log_{10}\bigg{(}\frac{P_{signal}}{P_{noise}}\bigg{)} \tag{7}\]  
In Equation (7), \(P_{signal}\) is the original signal power and \(P_{noise}\) is the added noise power. As shown in Figure 14, the original vibration signal has been completely distorted compared with the original signal after adding Gaussian white noise with \(SNR\) = 0 dB. White Gaussian noise with a signal-to-noise ratio of \(-10\) dB to \(10\) dB was added to the test set, and then the test set data were input into the saved network model. The diagnostic accuracy of the model is shown in Table 6. The table shows the mean values of ten diagnostic accuracies and the range of standard deviations of ten diagnostic accuracies for different models under three working conditions. Figure 14: Schematic diagram of adding noise signal. Figure 13: Test set results of three working conditions’ confusion matrix: (a) Working condition I; (b) Working condition II; (c) Working condition III. In Working Condition 1, the performance of the Propose + FFT model in the low-noise environment is not much different from that of the Propose + original vibration signal model. As the noise intensity intensifies, the diagnostic accuracy of the Propose + original vibration signal model declines sharply. In contrast, the Propose + FFT model still maintains a high diagnostic accuracy, indicating that the proposed model is also suitable for strong noise environments. The diagnostic accuracy of the ANN + FFT model is low in low-noise environments. In the environment of strong noise \(SNR=-10\) db, although the diagnostic accuracy is higher than the other four models, it is still lower than that of the Propose + FFT model. In Working Condition 2, the average accuracy of the Propose + FFT model is significantly higher than that of the other five models. Different from Working Condition 1 and Working Condition 3, the accuracy of the WDCNN+FFT model, except being lower than the proposed Propose + FFT algorithm, has higher diagnostic accuracy compared to the remaining four models. This indicates that the first layer of the 64 \(\times\) 1 large convolutional kernel is suitable for information feature extraction in the dataset of Working Condition 2, and can extract the sample feature information more adequately. In Working Condition 2, the noise immunity performance of the Propose + original vibration signal model is the same as that in Working Condition 1. The diagnostic accuracy of the model is better in the low-noise environment, while it drops sharply in the high-noise environment. This is because the addition of low noise to the signal changes the vibration signal by a small amount, and the model can still have strong diagnostic ability. However, in a strong noise environment, the vibration signal has completely lost its original characteristics. At this time, the FFT transform is used to convert the time-domain vibration signal to the frequency-domain signal, which can ignore the time information because the frequency-domain signal can retain the original vibration information. Therefore, the FFT-transformed model can still maintain a better diagnostic classification capability in the face of strong noise. This shows the necessity of signal FFT feature extraction. In Working Condition 3, the overall trend of various algorithms is almost the same as that of Working Condition 1.