# A Novel Integrated Fault Diagnosis Method Based on Digital Twins
## 4 Experiments and Results
### Comparative Experiments
#### 4.2.4 Results and Analysis  
Due to the relatively few hyperparameters in the SVM model, we used a grid search algorithm to select the optimal hyperparameter combination for SVM. By employing a grid search, we systematically traversed a range of predefined hyperparameter values to find the combination that performed best on the validation set. Table 2 lists the optimal hyperparameter combination for the SVM model obtained through the grid search algorithm. Figure 8 shows the changes in accuracy (PA) and loss values during the training process for LSTM, ANN, CNN, CNN-BLSTM, Transformer, and the proposed model. In the graph, the abscissa (\(x\)-axis) represents the training epochs, while the ordinate (\(y\)-axis) denotes both the prediction accuracy (PA) and the loss values. As the number of iterations increases, both the training accuracy and validation accuracy gradually improve, while the training loss and validation loss gradually decrease and eventually stabili \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline C & 100 \\ Kernel & Poly \\ Gamma & Auto \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal hyperparameters for SVM model. a certain number of iterations, these values remain relatively constant. Specifically, the proposed model achieves a stable training and validation accuracy of 0.9646. For the LSTM, ANN, CNN, CNN-BLSTM, and Transformer models, their training accuracies are 0.9592, 0.9479, 0.8662, 0.9627, and 0.9632, respectively. From the illustrated data in the table, we can conclude that despite the complexity of the model and the large dataset, the proposed model does not exhibit severe overfitting. Additionally, in terms of convergence speed, the proposed model significantly outperforms the other five models. The proposed model converges within 10 iterations, while the other models require 30, 40, 45, 20, and 15 iterations, respectively. Table 3 shows the performance of different models in terms of PA. As can be seen, the proposed DCBA model outperforms traditional deep learning models and machine learning models both in results and values. This indicates a significant advantage of the DCBA model in terms of PA. The success of the DCBA model may be attributed to its integration of the strengths of CNN, LSTM, and attention modules, enabling it to handle and analyze data more effectively. Figure 8: PA and loss values obtained from training and validation models. Specifically, when using the CNN model, the diagnostic \(PA_{normal}\) and \(PA_{noise}\) score decreased by 9.84% and 23.74%, respectively, compared to the DCBA model. This decline may be attributed to the fact that, while CNN excels in spatial feature extraction, it may not be as effective in analyzing sequential data as other models. Similarly, when using the LSTM model, the diagnostic \(PA_{normal}\) and \(PA_{noise}\) score decreased by 9.84% and 23.74%, respectively, compared to the DCBA model. Although the DCBA model demonstrated slightly better performance in these metrics, the difference is relatively small and may be influenced by random factors such as parameter initialization. Therefore, this difference should not be regarded as a significant advantage of the DCBA model over the LSTM model. However, it is noteworthy that in multiple comparative experiments, the DCBA model consistently achieved superior performance metrics compared to the LSTM model. Additionally, as shown in Table 3, the DCBA model demonstrated stronger noise resistance in factory environments with high noise interference, highlighting its potential advantage in practical applications. This improved robustness contributes to enhanced diagnostic performance in complex fault scenarios. In summary, although the LSTM model exhibits excellent performance in processing sequential data, the DCBA model demonstrates superior overall performance due to its enhanced noise resistance and improved stability.