# Small-Sample Bearings Fault Diagnosis Based on ResNet18 with Pre-Trained and Fine-Tuned Method
## 4 Experimental Verification
### Case 1: CWRU Bearing Dataset
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fault Sizes** & **Fault Type** & **Code** & **Label** & **Train** & **Test** \\ \hline \multirow{3}{*}{0.01778 cm} & Inner ring & IR1 & 0 & 20 & 80 \\  & Outer ring & RB1 & 1 & 20 & 80 \\  & Ball & OR1 & 2 & 20 & 80 \\ \hline \multirow{3}{*}{0.03556 cm} & Inner ring & IR2 & 3 & 20 & 80 \\  & Outer ring & RB2 & 4 & 20 & 80 \\  & Ball & OR2 & 5 & 20 & 80 \\ \hline \multirow{3}{*}{0.05334 cm} & Inner ring & IR3 & 6 & 20 & 80 \\  & Outer ring & RB3 & 7 & 20 & 80 \\ \cline{1-1}  & Ball & OR3 & 8 & 20 & 80 \\ \hline None & Normal & N & 9 & 20 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset composition. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(k\) & \multicolumn{6}{c}{**Center Frequency/HZ**} \\ \hline
5 & 0.0496 & 0.1097 & 0.2268 & 0.2877 & 0.3133 & & & \\
6 & 0.0497 & 0.1078 & 0.2103 & 0.2369 & 0.2901 & 0.3146 & & \\
7 & 0.0498 & 0.1052 & 0.1576 & 0.2178 & 0.2818 & 0.3026 & 0.3268 & \\
8 & 0.0037 & 0.0519 & 0.1085 & 0.2129 & 0.2368 & 0.2846 & 0.3048 & 0.3306 & \\
9 & 0.0037 & 0.0518 & 0.1084 & 0.2114 & 0.2358 & 0.2818 & 0.3009 & 0.3205 & 0.3657 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Center frequencies of different \(k\) values. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **IMF1** & **IMF2** & **IMF3** & **IMF4** & **IMF5** & **IMF6** & **IMF7** & **IMF8** \\ \hline Kurtosis & 2.9749 & 2.9262 & 3.1383 & 5.1418 & 5.3571 & 3.7027 & 3.9743 & 4.1558 \\ average & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average kurtosis of 8 IMF components. First, to avoid interference from external factors, the polar axis was eliminated in the SDP image, and a gray-scale transformation was applied, converting it into a two-dimensional numerical matrix. Subsequently, normal samples and random fault samples were selected for quantitative analysis. The average correlation coefficients of \(g\) and \(l\) under various parameter combinations were determined using the Pearson correlation analysis method. Then, the uncorrelation coefficients of \(g\) and \(l\) were obtained, and the specific data are shown in Figure 8.  
The greater the value of the uncorrelation coefficient, the greater the difference between the two parameters, and this implies that the disparity among SDP bearing fault images is the greatest. As shown in Figure 8, when the horizontal label \(l\) is 2, the value of each column \(g\) is generally high and performs well. Particularly, when the vertical column label \(g\) is 35\({}^{\circ}\), the value of the uncorrelation coefficient reaches 0.4696, which is the best in this row. At the same time, it also shows the highest value in all the data, with a vertical column \(g\) of 35\({}^{\circ}\), which is significantly better than other values. When the parameters \(g\) and \(l\) are, respectively, set to 35\({}^{\circ}\) and 2, the bearing fault exhibits the greatest disparity in SDP images. When the parameter \(g\) is 20\({}^{\circ}\) and the parameter \(l\) is 1, the difference in the SDP bearing fault image is the smallest, and the value of the uncorrelation coefficient is 0.2969. A VSDP diagram for maximizing the difference of 10 bearing faults is shown in Figure 9 below. Under the same SDP parameters, the differences in different bearing faults are shown in the thickness of the arm and the density of data points. As can be seen from Figure 9, different bearing fault types show strong discrimination.