# Multi-Patch Time Series Transformer for Robust Bearing Fault Detection with Varying Noise
## 5 Experiments
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Noise Type** & **Model** & **Accuracy** & **Precision** & **Recall** & **F1** \\ \hline \multirow{8}{*}{Gaussian noise} & LSTM & 0.9826 & 0.9842 & 0.9839 & 0.984 \\ \cline{2-6}  & GRU & 0.9841 & 0.9852 & 0.9853 & 0.9854 \\ \cline{2-6}  & FCN & 0.9836 & 0.9853 & 0.9845 & 0.9848 \\ \cline{2-6}  & ResNet & 0.9826 & 0.9841 & 0.9836 & 0.9838 \\ \cline{2-6}  & InceptionTime & 0.984 & 0.9849 & 0.9851 & 0.9849 \\ \cline{2-6}  & XceptionTime & 0.9819 & 0.9835 & 0.9834 & 0.9834 \\ \cline{2-6}  & XCM & 0.9836 & 0.9854 & 0.9845 & 0.9849 \\ \cline{2-6}  & LSTMAttention & 0.984 & 0.9854 & 0.9852 & 0.9852 \\ \cline{2-6}  & GRUAttention & 0.9827 & 0.9841 & 0.9835 & 0.9837 \\ \cline{2-6}  & TSSequencer & 0.9825 & 0.9841 & 0.9835 & 0.9837 \\ \cline{2-6}  & PatchTST & 0.9838 & 0.9853 & 0.9847 & 0.9849 \\ \cline{2-6}  & **MultiPatchTST** & **0.9845** & **0.9863** & **0.9856** & **0.9857** \\ \hline \multirow{8}{*}{Electrical interference noise} & LSTM & 0.7596 & 0.8292 & 0.7672 & 0.7695 \\ \cline{2-6}  & GRU & 0.7607 & 0.8292 & 0.7678 & 0.7704 \\ \cline{2-6}  & FCN & 0.7587 & 0.83 & 0.7659 & 0.7687 \\ \cline{2-6}  & ResNet & 0.7628 & 0.8317 & 0.7688 & 0.7718 \\ \cline{2-6}  & InceptionTime & 0.7611 & 0.831 & 0.7685 & 0.7711 \\ \cline{2-6}  & XceptionTime & 0.7619 & 0.8316 & **0.7703** & 0.7724 \\ \cline{2-6}  & XCM & 0.7595 & 0.8273 & 0.7674 & 0.7694 \\ \cline{2-6}  & LSTMAttention & 0.7529 & 0.8268 & 0.7609 & 0.7622 \\ \cline{2-6}  & GRUAttention & 0.7611 & 0.8316 & 0.7673 & 0.7701 \\ \cline{2-6}  & TSSequencer & 0.7581 & 0.8289 & 0.7652 & 0.7686 \\ \cline{2-6}  & PatchTST & 0.7613 & 0.8303 & 0.7691 & 0.7715 \\ \cline{2-6}  & **MultiPatchTST** & **0.7631** & **0.8327** & 0.7697 & **0.7734** \\ \hline \multirow{8}{*}{Harmonic noise} & LSTM & 0.8084 & 0.8576 & 0.8141 & 0.8192 \\ \cline{2-6}  & GRU & 0.8056 & 0.8559 & 0.8102 & 0.815 \\ \cline{2-6}  & FCN & 0.806 & 0.8556 & 0.8118 & 0.8153 \\ \cline{2-6}  & ResNet & 0.804 & 0.8544 & 0.8106 & 0.8142 \\ \cline{2-6}  & InceptionTime & 0.8001 & 0.8539 & 0.8061 & 0.8112 \\ \cline{2-6}  & XceptionTime & 0.8058 & 0.8587 & 0.8119 & 0.8176 \\ \cline{2-6}  & XCM & 0.8044 & 0.8544 & 0.8111 & 0.8156 \\ \cline{2-6}  & LSTMAttention & 0.81 & 0.857 & 0.8153 & 0.8216 \\ \cline{2-6}  & GRUAttention & 0.8057 & 0.8562 & 0.8109 & 0.8155 \\ \cline{2-6}  & TSSequencer & 0.8082 & 0.8587 & 0.8147 & 0.8197 \\ \cline{2-6}  & PatchTST & 0.8086 & 0.8612 & 0.8138 & 0.8199 \\ \cline{2-6}  & **MultiPatchTST** & **0.8112** & **0.8613** & **0.8169** & **0.8216** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._The experiments on the original noiseless datasets demonstrated that all models achieved high performance on the CWRU and MFPT datasets, with accuracy, precision, recall, and F1 metrics exceeding 0.98. These results indicate no significant performance differences between the models under noiseless conditions. Notably, the TSequencer model showed the best performance on the CWRU dataset, whereas the MultiPatchTST model achieved the highest scores on both the MFPT and PU datasets. When a Gaussian noise of amplitude 0.5 was applied, the performance degradation across all datasets was minimal. The top-performing models achieved metrics above 97%, indicating that the impact of Gaussian noise on classification performance was negligible. However, the minimal effect of Gaussian noise highlights its limitations as a method for evaluating the noise robustness of models. Among the models, PatchTST and MultiPatchTST, which utilize patch-based learning, consistently exhibited superior performance, reinforcing their robustness. To evaluate the validity of the models under more realistic industrial noise conditions, the original datasets were combined with noise reflecting electrical interference, harmonic, and random shock noise at four intensity levels. The CWRU dataset consistently maintained strong performance across all noise conditions. Similarly, the MFPT dataset demonstrated high performance, sustaining metrics above 95% in most scenarios.