## 4 Experimental Validation
### Results and Analysis
This contradicts the essence of gradual deterioration caused by a gradual fault over time. Therefore, the addition of residuals assists in fault diagnosis. It can effectively reflect the fault condition as time progresses and the fault severity increases. The t-distributed stochastic neighbor embedding (t-SNE) algorithm is employed to visualize the classification effectiveness of features, which is shown in Figure 13. It can be observed that the result based on the innovation and residual sequences of the UKF, after feature extraction via the Inception V3 network, exhibits a significant improvement in fault discrimination, and only a small number of samples are misclassified. In contrast, the other two show a substantial overlap in the feature regions, indicating the difficulty in distinguishing fault conditions. The fault diagnosis results for the three types of data under the same model are shown in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Innovation and Residual** & **Innovation** & **Filtered Data** \\ \hline Precision & 0.9920 & 0.8057 & 0.8897 \\ Recall & 0.9920 & 0.8057 & 0.8897 \\ F1 Score & 0.9920 & 0.7830 & 0.8898 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Diagnostic results for the innovation and residual sequences, raw signal data, and innovation sequences. Figure 12: Filtered data (**a**), innovation sequence (**b**), and residual sequence (**c**) of the airspeed signal under gradual fault. From the results, it can be seen that, in scenarios with low fault severity and varied experimental settings, relying solely on the fault signal for diagnosis does not yield satisfactory results. As mainstream information used for fault diagnosis, innovations exhibit obvious limitations when it comes to diagnosing small faults and gradual faults. It becomes difficult to distinguish them from normal conditions, and the diagnostic performance is even poorer at times. The combination of innovations and residuals overcomes the aforementioned problems and achieves better diagnostic results. In order to better simulate actual conditions, a certain level of Gaussian noise was added to the collected airspeed, angle of attack, and sideslip angle signals. This was conducted to test the ability of the proposed method to accurately identify faults when they are submerged in noise and to verify its robustness against significant noise interference. According to relevant research, the signal-to-noise ratio (SNR) is typically around tens of decibels (dB), where a lower signal-to-noise ratio indicates a higher level of noise. As an example, an SNR of 40 dB was chosen to conduct further experiments. Furthermore, to validate the superiority of the neural network used in this paper, a comparison was made with other commonly used networks, including the convolutional neural network (CNN), fully convolutional network (FCN) [47], and temporal convolutional network (TCN) [48]. To ensure fairness in the comparison, the inputs for all neural networks are based on the innovations and residuals generated by the same unscented Kalman filter, and the same test dataset was employed to conduct tests and obtain fault diagnosis results, including accuracy, recall, F1 score, and the number of model parameters. In the process of this new experiment, k-fold cross-validation was employed to reduce overfitting and improve generalization ability. Unlike the conventional approach of dividing the dataset into training and testing sets with a certain ratio, k-fold cross-validation divides the entire dataset into k mutually exclusive subsets. In each iteration, k--1 subsets are used for training, while the remaining subset is used for testing. This process is repeated until each subset has been used as the test set. This generates k evaluation metrics, and the final result is obtained by calculating the mean and variance of these metrics. k is set to 5 in this experiment, and the performance metrics of different networks are shown in Table 5, where the results presented are the average values obtained after five iterations.