## 3 Simulation Experiments
### Error Classification Case Analysis  
In the experiments using the TCN-BiLSTM model for fault classification, although the overall performance outperformed other models, there were still some notable instances of misclassification. By conducting an in-depth analysis of specific misclassified cases, we gained further insights into the limitations of the model.  
First, the model misclassified a heat dissipation failure as a random failure. Heat dissipation failure is typically caused by uneven temperature distribution or insufficient heat dissipation characterized by a minimal difference between air temperature and process temperature. It is also closely associated with parameters such as rotational speed and torque. In contrast, a random failure is an extremely rare type of fault (with an occurrence probability of approximately 0.1%) that is completely independent of the operational state of the equipment and occurs randomly. The model may have failed to sufficiently recognize the unique physical characteristics of heat dissipation failure, leading to its misclassification as a random failure. The critical distinction between these two failure types is that heat dissipation failure follows a certain physical mechanism, whereas random failure is entirely stochastic. The model likely struggled to capture the essential differences between these two types of failures.  
Second, the model misclassified an overstrain failure as a tool wear failure. Overstrain failure typically occurs when the product of tool wear and torque exceeds a certain threshold, leading to sudden mechanical strain or a violent response of the equipment. In contrast, tool wear failure is a gradual process that progresses more slowly over time. The model may not have effectively captured the temporal dependencies and abrupt characteristics that distinguish overstrain failure from tool wear failure. Moreover, due to the imbalanced dataset, overstrain failure had relatively fewer samples compared to tool wear failure.  
\begin{table}
\begin{tabular}{c c c c c c} \hline _p_-**Values** & **TCN-BiLSTM** & **A-BiLSTM** & **BiLSTM** & **CNN** & **RNN** \\ \hline TCN- & / & 0.0006 & 0.0004 & 0 & 0.0011 \\ BiLSTM & 0.0006 & / & 0.6273 & 0.0068 & 0.0999 \\ BiLSTM & 0.0004 & 0.6273 & / & 0.0016 & 0.1772 \\ CNN & 0 & 0.0068 & 0.0016 & / & 0.0002 \\ RNN & 0.0011 & 0.0999 & 0.1772 & 0.0002 & / \\ \hline \end{tabular}
\end{table}
Table 6: Results of the paired _t_-test.  
This imbalance may have caused the model to favor predicting tool wear failure, thereby overlooking the distinguishing features of overstrain failure.  
In conclusion, while the comparison of experimental results validated the superior performance of the proposed TCN-BiLSTM model in time-series fault prediction tasks, the analysis of misclassification cases revealed areas for further improvement. The model not only demonstrated higher prediction accuracy but also exhibited faster convergence and stronger adaptability to sequential data. These findings establish the TCN-BiLSTM model as a robust and effective solution for tackling complex time-series prediction challenges, offering a significant advantage over traditional approaches.