# KACFormer: A Novel Domain Generalization Model for Cross-Individual Bearing Fault Diagnosis
## 3 Experiments
### Learning Dynamics  
To obtain a deeper understanding of the learning dynamics of KACFormer in cross-individual learning tasks, the following experiments are conducted: the model is tested on the testing set to observe phenomena such as convergence and potential overfitting after each epoch. The number of epochs is set to be 100.  
As illustrated in Figure 17, on Task 1, the KACFormer network achieves its best accuracy on the target domain when it begins to converge on the source domain, typically around 5 to 20 epochs. After the 20 th epoch, as training continues, the model's performance on the target domain begins to degrade. Such a phenomenon is not as pronounced on Task 2. As illustrated in Figure 18, the model converges quickly and demonstrates relatively strong stability on the target dataset. However, the rising validation loss may indicate a potential over-fitting risk. Such a difference may be due to the volume of data and the inherent differences between the individuals in target and training datasets. Moreover, as shown in the confusion matrixes listed in Figures 12-16, the features of healthy bearings in the PU and CWRU dataset are more distinct compared to the other two categories, and models participating in the experiment demonstrate strong cross-domain performance. However, there is a significant degree of confusion between Inner Race (IR) and Outer Race (OR) faults.  
Why SiLU  
In the model, the SiLU activation function is employed in the encoder based on experimental validation. This implementation is consistent with the original KAN authors' use of SiLU activation in their work [16], further validating our design choice. As demonstrated in Table 8, using ReLU activation resulted in accuracy degradation in both tasks compared to SiLU. This performance gap may be attributed to SiLU's superior properties: smoothness, non-monotonicity, and boundedness below (unbounded above), which make it particularly suitable for approximating smooth functions, and this may be a latent characteristic exhibited in vibration signal processing.  
Working condition variability is a widely discussed challenge in fault diagnosis, with numerous scholars dedicated to cross-condition diagnosis [34; 35; 36]. Since model performance may vary under different operating conditions, considering data availability, experiments are conducted on Task 1 based on the PU dataset--evaluating the same bearing samples under different conditions. Table 9 presents KACFormer's accuracy for Task 1 across these three distinct working conditions.  
From the experimental data, it can be concluded that when the source domain and target domain individuals work under the same working conditions, the robustness of the algorithm will not be affected.  
Figure 18: Training process on CWRU dataset.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **SiLU** & **ReLU** \\ \hline
**Task 1 on PU** & 95.73\% & 88.74\% \\
**Task 2 on CWRU** & 91.58\% & 89.98\% \\ \hline \hline \end{tabular}
\end{table}
Table 8: Model accuracy with different activation functions on different tasks.