## 4 Analysis and Verification of Rolling Bearing Fault Diagnosis Tests
### Additional Validation Experiments
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Accuracy of the Model in the Testing Phase/\%**} & & & & & & & & \\ \cline{2-10}
**Model** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
1-VMD-PE-LSTM & 83.33 & 84.11 & 84.90 & 85.68 & 86.20 & 86.98 & 87.50 & 87.67 & 88.02 & 88.28 \\
2-VMD-PE-IGTO-LSTM & 87.50 & 88.02 & 88.54 & 88.80 & 86.20 & 89.06 & 89.32 & 89.58 & 90.99 & 92.45 \\
3-GTO-VMD-PE-LSTM & 89.58 & 90.36 & 91.41 & 92.45 & 92.97 & 93.23 & 91.41 & 90.36 & 94.27 & 93.75 \\
4-IGTO-VMD-PE-LSTM & 91.41 & 95.57 & 94.79 & 93.23 & 95.83 & 94.79 & 93.23 & 94.01 & 92.19 & 95.83 \\
5-IGTO-VMD-PE-GW-LSTM & 97.40 & 96.61 & 96.35 & 96.09 & 97.40 & 92.97 & 96.61 & 95.57 & 97.14 & 93.23 \\
6-IGTO-VMD-PE-PSO-LSTM & 96.61 & 96.35 & 96.09 & 97.14 & 96.61 & 96.88 & 96.09 & 98.70 & 94.79 & 95.05 \\
7-IGTO-VMD-PE-GTO-LSTM & 97.14 & 96.88 & 97.40 & 96.88 & 97.40 & 96.61 & 97.66 & 97.92 & 96.09 & 97.14 \\
8-IGTO-VMD-PE-ICO-LSTM & 98.18 & 98.44 & 97.92 & 97.66 & 97.66 & 98.44 & 98.84 & 96.88 & 96.61 & 98.70 \\
9-GWO-VMD-PE-IGTO-LSTM & 97.4 & 96.61 & 96.35 & 96.09 & 97.4 & 92.97 & 96.61 & 95.57 & 97.14 & 93.23 \\
10-PSO-VMD-PE-IGTO-LSTM & 96.61 & 96.35 & 96.09 & 97.14 & 96.68 & 96.09 & 98.97 & 94.79 & 95.05 \\
11-GTO-VMD-PE-IGTO-LSTM & 97.14 & 96.88 & 97.4 & 96.88 & 97.4 & 96.61 & 97.66 & 97.92 & 96.09 & 97.14 \\
12-CDO-VMD-PE-IGTO-LSTM & 98.18 & 98.44 & 97.92 & 97.66 & 97.66 & 98.44 & 98.44 & 96.88 & 96.61 & 98.78 \\
13-IGTO-VMD-PE-IGTO-LSTM & 99.48 & 98.44 & 98.7 & 98.96 & 92.22 & 97.92 & 99.48 & 98.96 & 99.22 & 98.18 \\ \hline \end{tabular}
\end{table} 
Table 9: Accuracy of the model in the testing phase. The above content verifies the proposed model (IGTO-VMD-PE-IGTO-LSTM) in terms of accuracy, demonstrating its strong fault diagnosis capability. To further analyze the diagnostic efficiency of each model, the diagnostic time for each model on the same dataset was statistically calculated. The results are shown in Table 11 below. After comparing the runtime of the aforementioned models, it is evident that although Model 13 has a relatively longer runtime (with an average runtime of 13.88 s), it achieves the highest fault diagnosis accuracy among all models. This result indicates that Model 13 provides more precise results in diagnostic tasks. Therefore, in practical applications, it is entirely acceptable to sacrifice some computational time in exchange for higher accuracy. From an engineering perspective, when diagnostic accuracy is critical to the task outcome, choosing a model with a longer runtime but higher accuracy can significantly enhance the reliability of the diagnosis. This is especially true in domains that require precise fault detection, where a reasonable trade-off between computational time and accuracy is justified. Therefore, despite Model 13's slightly longer runtime, its superior accuracy makes it a more attractive choice in high-precision scenarios. In such tasks, extending the computation time to achieve higher diagnostic accuracy is a rational and worthwhile decision.