# HFDF-EffNetV2: A Lightweight, Noise-Robust Model for Fault Diagnosis in Rolling Bearings
## 3 Results
### Determination of the Channel Expansion Factors at Different Stages of HFDF-EffNetV2  
In the design of the CNN model architecture, the channel dimension, as a key adjustment parameter of model capacity, has an expansion ratio that is positively correlated with the model's representational ability and directly affects the degree of overparameterization. Therefore, selecting an appropriate expansion factor is crucial in model design. Rolling bearings in actual operation are subject to interference from factors such as vibrations between equipment and environmental noise. To validate the diagnostic performance of HFDF-EffNetV2 using various expansion factors at different stages, this study simulated real working conditions by adding Gaussian white noise (GWN) with signal-to-noise ratios (SNR) of 2 dB, 4 dB, 6 dB, and 8 dB to the signal samples from the test set in Table 2. The SNR is calculated as in Equation (13), as follows:  
\[\text{SNR}_{\text{dB}}=10\log_{10}\frac{P_{\text{signal}}}{P_{\text{noise}}} \tag{13}\]  
where \(\text{SNR}_{\text{dB}}\) is the ratio of signal to noise (the lower the ratio, the higher the noise intensity); \(P_{\text{signal}}\) is the power spectral density of the original signal; and \(P_{\text{noise}}\) is the power spectral density of the noise signal.  
The experimental results are shown in Figure 7. When the noise intensity is low, the accuracy gap is not significant; therefore, the 2 dB experimental results under strong noise interference were selected as the basis for choosing the channel expansion factors. Under 2 dB of noise interference, the model achieves an accuracy of 92.60% when the channel expansion factors for different stages are (1, 2, 4, 6). The model reaches a maximum accuracy of 95.88% when the expansion factors are (2, 4, 4, 6), and this value decreases to 95.03% when the expansion factors are increased to (4, 4, 6, 8). The results indicate that an increase in the channel expansion factors helps the model fuse information from different channels, enabling it to extract diverse features more effectively. However, an excessively high expansion factor can cause the model to converge to a local optimum. Therefore, proper control of the channel expansion factors can help avoid interference from redundant information. In this study, the channel expansion factors(2, 4, 4, 6), which yielded the best diagnostic performance, were selected, and the specific architectural parameters of HFD-EffNetV2 are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Fault Sizes** & **Fault Type** & **Code** & **Fault Label 1** & **Train** & **Test** \\ \hline None & Normal & N & 0 & 130 & 70 \\ \hline \multirow{3}{*}{0.1778 mm} & Inner Ring & IR1 & 1 & 130 & 70 \\  & Rolling Ball & RB1 & 2 & 130 & 70 \\  & Outer Ring & OR1 & 3 & 130 & 70 \\ \hline \multirow{3}{*}{0.3556 mm} & Inner Ring & IR2 & 4 & 130 & 70 \\  & Rolling Ball & RB2 & 5 & 130 & 70 \\  & Outer Ring & OR2 & 6 & 130 & 70 \\ \hline \multirow{3}{*}{0.5334 mm} & Inner Ring & IR3 & 7 & 130 & 70 \\  & Rolling Ball & RB3 & 8 & 130 & 70 \\ \cline{1-1}  & Outer Ring & OR3 & 9 & 130 & 70 \\ \hline \end{tabular} 1  
The fault labels are utilized to categorize samples based on various fault types, with each label representing a specific type of fault.  
\end{table}
Table 2: Case Western Reserve University (CWRU) bearing dataset composition.  
Figure 7: Comparison of the numbers of parameters and diagnostic accuracies of HFD-EffNetV2 at different expansion factors and at different SNRs on the CWRU bearing dataset.