## 4 Experimental Validation
### Results and Analysis  
Under normal conditions, the innovation and residual sequences generated by the UKF model are shown in Figure 9. It can be observed that they fluctuate around zero in the absence of faults. However, when a fault occurs, it significantly disrupts this characteristic, which will be further illustrated by examples later on. Figure 9: Innovation and residual sequences under normal conditions. (**a**) Airspeed (Vr). (**b**) Angle of attack (Alfa). (**c**) Sideslip angle (Beta). (**d**) Roll angle (Phi). (**e**) Pitch angle (Theta). (**f**) Yaw angle (Psi). Model-based fault diagnosis methods generally involve constructing test statistics based on the information generated by the model and comparing them to a threshold to judge the occurrence of faults. However, on one hand, constructing evaluation metrics is often challenging. For example, the residual chi-squared test has low sensitivity to gradual faults, and many self-defined metrics are subjective, making it difficult to demonstrate their applicability to various types of faults. On the other hand, these methods often lack the ability to locate faulty sensors and identify the type of fault effectively after fault detection. Typically, setting thresholds for corresponding fault signals of sensors is subjective and difficult to account for variations caused by various uncertainties. Therefore, in addition to establishing the model, a data-driven approach is combined to complement the model-based fault diagnosis strategy. In this regard, the experimental results of the neural network component are presented. Figure 10 illustrates the training process of the neural network model. After 50 epochs of training, the error gradually decreases and stabilizes at around 0.001. Testing was conducted on the testing dataset, and Figure 11 shows the confusion matrix. It can be observed that the Inception V3 network, based on UKF's innovations and residuals as inputs, achieves ideal diagnostic results with diagonal elements in the confusion matrix close to 1. This indicates that it can effectively discriminate among various fault conditions, with only a small number of misclassifications. Figure 11: Confusion matrix of the Inception V3 network based on the UKF’s innovations and residuals. Figure 10: Error curve of the training and validation process. We quantitatively analyzed the diagnostic results through three metrics: precision, recall, and F1 score. The closer these metrics are to 1, the better the diagnostic performance. According to the statistics, the accuracy of this method is 0.9920, the recall is 0.9920, and the F1 score is 0.9920. All metrics are above 99%, and the results can be obtained within 200 ms. It can be seen that the fault diagnosis strategy utilizing data-assisted models has achieved excellent results. In the selection of fault characteristic data, to demonstrate the necessity of utilizing the UKF's innovation and residual sequences, this study compares the results with those using raw data and innovation data only. The raw data refer to the filtered six-dimensional measurement signal sequences. Taking the gradual fault in the airspeed signal as an example, with a fault severity of 0.05 (m/s\({}^{2}\)) and fault injection time of 23.5 s (the 2350 th data point), the filtered airspeed data, innovation sequence, and residual sequence are shown in Figure 12.  
When the fault severity is small, the post-fault data do not exhibit significant changes compared to the original signal, and the data have some inherent fluctuations. It is difficult to judge whether the observed variations are normal or indicative of a fault compared to the pre-fault condition, and fault diagnosis based solely on the fault signal becomes challenging. Although innovations can also reveal some changes, due to the iterative nature of the filtering process, the subsequent innovations continuously track the fault and exhibit minor fluctuations when dealing with small fault severities.