3.1.1 One-Dimensional Dual Attention Module

In the task of flight maneuver recognition, the multi-dimensional flight parameter sequence exhibits dependencies over time and correlations among different features. Depending on the situation, features such as normal load factor, heading angle, or altitude become critical. To address this, we propose a strategy that incorporates an attention mechanism within the feature representation, it becomes feasible to focus on important features while suppressing irrelevant ones. Inspired by the Convolution Block Attention Module [23] (CBAM) in computer vision, we introduce a one-dimensional dual attention module (1D-DAM) that highlights meaningful features in both the channel and temporal dimensions. As shown in Figure 2, the 1D-DAM consists of two sub-modules: variable attention (VA) submodule and temporal attention (TA) submodule, which interact to capture long-range dependencies and variable interactions.

Figure 2 The architecture of the proposed 1D-DAM.

The VA submodule is designed to automatically learns the attention allocation weights for features in the variable dimension of the flight maneuver sequences. Assuming the input to the VA submodule corresponds to a feature map $y\in {ℝ}^{C\times N}$, where $C$ and $N$ represent the variable and temporal dimensions, respectively. To efficiently compute variable attention, global max pooling and global average pooling are applied across the temporal dimension for each feature map $y^i\in {ℝ}^N,i=1,2,\dots ,C$, generating two feature vectors: max pooling feature $M^V=[M_1^V,M_2^V,\dots ,M_C^V]$ and average pooling feature $A^V=[A_1^V,A_2^V,\dots ,A_C^V]$. The $i\text{-}th$ element of these two vectors is calculated as follows:

where $\max (\cdot )$ denotes the maximum element in the vector, and $\text{average}(\cdot )$ denotes the average of all elements in the vector.

These two vectors $M^V$ and $A^V$ are then fed into a multi-layer perceptron (MLP) with two fully connected layers: a $C$ dimensional input layer, a $C/r$ dimensional hidden layer, and a $C$ dimensional output layer. The goal of this MLP is to adaptively adjust the weights for each channel by first reducing the feature map channels using a reduction factor $r$ and then re-scaling them to the original size. The MLP produces two new feature vectors ${\hat{M}}^V$ and ${\hat{A}}^V$, which are merged by element-wise summation and then normalized using the sigmoid function to produce the variable attention weight vector $W_V\in {ℝ}^C$, as follows:

where $\sigma$ and $\delta$ denote the GELU and sigmoid activation functions, respectively, $F_1$ and $F_2$ are convolutional mapping functions with kernel size 1.

Finally, the variable attention weight vector $W_V$ is element-wise multiplied with the corresponding feature maps to generate a new feature representation $f\in {ℝ}^{C\times N}$. The calculation formula for the $i\text{-}th$ feature map is as follow:

The TA submodule focuses on the crucial positions in the flight maneuver sequences along the temporal dimension. The output of the VA submodule $f$ serves as the input to this submodule. Similarly, we employ global max pooling and global average pooling operations to compute the maximum and average values across the variable dimension, resulting in two feature vectors: the max-pooled feature $M^T=[M_1^T,M_2^T,\dots ,M_N^T]$ and the average-pooled feature $A^T=[A_1^T,A_2^T,\dots ,A_N^T]$. The calculation formulas for the $i\text{-}th$ element of these two feature vectors are as follows:

Unlike the additive strategy used in the VA submodule, these two pooled vectors are concatenated to aggregate variable dimension information, forming a feature tensor $S^V\in {ℝ}^{2\times N}$. A standard one-dimensional convolution with a kernel size of $k$, followed by a sigmoid activation function, generates the temporal attention weight vector, as follow:

where $\sigma$ denotes the sigmoid activation function, $F_3$ is a convolutional mapping function with kernel size $k$.

Finally, the output feature map $\hat{y}\in {ℝ}^{C\times N}$ is computed by element-wise multiplication of $f$ each channel dimension feature map with the corresponding element of $W_T$. This feature map simultaneously captures more critical information in both the temporal and variable domains. The calculation formula for the $i\text{-}th$ feature map of $\hat{y}$ is as follows:

3.1.2 Improved Classification Layer

The original classification layer in the ResNet18 network consists of a global average pooling layer followed by a fully connected layer. In this paper, we introduce an improved classification layer while retaining the network structure before the global average pooling layer. The modified classification layer includes a $1\times 1$ convolutional layer, a global average pooling layer, another $1\times 1$ convolutional layer, and a final linear transformation layer. The linear transformation layer is designed to map the extracted high-dimensional features to the flight maneuver classification categories. To enhance the generalization capability of the flight maneuver recognition model, a Dropout layer is inserted between the $1\times 1$ convolutional layer and the linear transformation layer following the global average pooling layer. By integrating the attention mechanism and a modified classification layer within the ResNet18 framework, the proposed 1D-DAMResNet structure is shown in Table 1.

Remarks: $n$ is the number of flight parameter features; $k$ represents the kernel size; $C$ denotes the number of flight action categories.

4.1.1 Quantification Method for Anomaly Levels

To quantify the abnormality of flight maneuvers, we first calculate the similarity between a test maneuver and all corresponding standard maneuvers using the DTW algorithm. The lowest similarity value among these comparisons is taken as the similarity score for the test sample. This process can be represented as follows:

where $X_{\text{test}}$ is the test flight maneuver sample, $X_{\text{std}}^i$ denotes the $i\text{-}th$ sample from the standard maneuver set, $\text{DTW}(X_{\text{test}},X_{\text{std}}^i)$ is the similarity between $X_{\text{test}}$ and $X_{\text{std}}^i$, and $\text{len}\left({\text{path}}_i\right)$ represents the shortest path distance in the DTW algorithm, while $\min \left({\text{DTW}}_{\text{distance}}^i\right)$ is the minimum similarity value between the test sample and the standard maneuvers, effectively serving as the similarity score for the test sample.

Next, this similarity score is normalized to quantify the anomaly score, as expressed by:

where Score is the normalized similarity score, with a range of $(0,1]$, and $AQS\left(X_{\text{test}}\right)$ is abnormality quantification score for the test maneuver sample, with a range of $[0,1)$. A higher value indicates a greater level of anomaly.

Subsequently, a mapping is established between the abnormality quantification score and anomaly levels. Specifically, according to the flight training guidelines, maneuver quality is categorized as "Poor" for scores in the range $[0,2.5)$, "Good" for $[2.5,4)$, and "Excellent" for $[4,5]$. From each maneuver category, 100 samples are randomly selected along with their instructor-assigned scores. For samples with scores closest to 2.5 and 4, the abnormality quantification scores are calculated. By averaging the abnormality quantification scores of the samples nearest to 2.5 and 4, the threshold values ${\theta }_1$ and ${\theta }_2$ are determined. Based on these thresholds, the mapping between abnormality quantification scores and anomaly levels is defined as follows: a score in $[0,{\theta }_2)$ is classified as "Excellent," a score in $[{\theta }_2,{\theta }_1]$ is classified as "Good," and a score in $(0.79,1]$ is classified as "Poor." Additionally, these mappings can also be defined manually by domain experts.

To facilitate anomaly analysis, we identify the key dimensional features that flight instructors focus on for each type of maneuver. By visualizing the curves of the test maneuver and the corresponding standard maneuver for these key features, we can highlight deviations at critical points. This visualization enables instructors to diagnose the causes of anomalies more effectively.

5.2.1 Experimental Setting

In this experiment, We used Python 3.9 and PyTorch 2.0.1 to train the model on an i9-13900HX CPU and RTX 4090 GPU. Training lasted 50 epochs with a batch size of 64, using Adam [24] optimizer and Label Smoothing Regularization [25] (LSR) loss function.

Figure 3 The average loss and precision of each method: (a) Training loss; (b) Training precision; (c) Validation loss; (d) Validation precision.

5.2.2 Model Training

To evaluate the effectiveness and accuracy of the proposed flight maneuver recognition model, we conducted a comparative study using 1D ResNet18 [22], 1D VGG11 [26], 1D MobileNet [27], and the multi-scale feature extraction deep residual network (MSDRN) proposed in [1]. To accommodate the time-series characteristics of flight parameter data, the ResNet18, VGG11, and MobileNet models were modified by replacing their original 2D convolutional layers with 1D convolutional layers, while keeping the rest of the network architecture unchanged. For a fair comparison, all models were trained on the same dataset from scratch, without using any pre-trained weights, to eliminate the potential influence of prior knowledge on the results. Each experiment was repeated five times to mitigate the effect of randomness, and the loss and accuracy were recorded for both the training and validation sets. The average loss and accuracy from these five experiments are showed in Figure 3.

As shown in Figure 3, during the early training stages, all methods exhibited significant fluctuations in loss and precision due to the random initialization of model parameters. However, after approximately 20 epochs, all models converged, achieving low loss and high precision on both the training and validation sets, demonstrating good stability. Notably, VGG11 showed a slower convergence rate and lower precision on the validation set, both in terms of loss and precision. This is possibly due to the larger number of parameters in VGG11, which may have led to underfitting on small samples. On the other hand, MobileNet showed lower loss and higher precision on the training set but underperformed on the validation set, suggesting overfitting and reduced generalization ability. In contrast, the proposed 1D-DAMResNet model consistently achieved lower average loss and higher average precision on the validation set, with both metrics exhibiting high stability. This excellent performance can be attributed to the model’s ability to extract robust feature representations. Overall, the experimental results validated the accuracy and stability of the proposed method.

5.2.3 Model Test

Table 3 shows the test set recognition performance of various methods, with the 1D-DAMResNet18 model achieving the highest average precision, recall, and F1 score of 99.75%. It outperforms the second-best MSDRN model by 0.25% in these metrics. The excellent performance of 1D-DAMResNet18 is due to its dual attention mechanism (DAM), which enhances feature extraction. ResNet18 and VGG11 also show high accuracy but are limited by traditional convolutional layers in capturing feature correlations. MobileNet has the lowest scores (97.50%) due to its focus on computational efficiency over accuracy. Overall, the 1D-DAMResNet model excels in recognition performance, making it a strong foundation for anomaly level quantification.

5.3.1 Generation of Standard Flight Maneuver Set

Figure 4 Time Normalization Process: (a) the original altitude data; (b) the altitude data after time normalization.

 (a) Loop

 (b) Cloverleaf

 (c) Aileron Roll

 (d) Immelmann turn

 (e) Split-S

 (f) Pull-up

 (g) Push-over

 (h) Circulating

Figure 5 Clustering Results of Flight Maneuver Samples.

First, following the method described in Section 4.1, the duration of different flight maneuvers was normalized. Taking the loop maneuver as an example, the altitude changes before and after time normalization are shown in Figure 4. It is evident from Figure 4 that before normalization, the durations of the flight maneuvers vary significantly, while after normalization, the durations become uniform. This consistency facilitates the subsequent quantification of anomalies and comparative visual analysis. This consistency facilitates subsequent quantitative analysis and visualization of anomaly levels. Next, the K-Means clustering algorithm was applied to the training and validation datasets for each type of flight maneuver, with the number of clusters set to three. The results are shown in Figure 5, where each point represents a flight maneuver sample, different colors indicate different clusters, and the red stars mark the cluster centers. Finally, the sample closest to the center of each cluster was selected to represent the standard flight maneuver for that category. As a result, each flight maneuver category includes three representative samples. This process ensures that the standard flight maneuver set is both representative and accurate, providing a reliable reference for further anomaly quantification and analysis.

5.3.2 Quantitative Evaluation Results of Anomaly Levels

In this section, we randomly selected one sample from the test set of each flight maneuver category. Using the corresponding standard flight maneuver set for each category, we calculated the similarity score based on Equations (9) and (10). The results are shown in Table 4, where the minimum similarity score between the test flight maneuver and the standard maneuver is highlighted in bold. The corresponding standard flight action is used as the reference for that test sample.

Next, based on the similarity scores in Table 4, we applied Equations (11) and (12) to compute the anomaly quantification scores for each category’s test flight maneuver, as shown in Table 6. To establish threshold values for defining different anomaly levels, we selected 10 samples from the training and validation sets with expert ratings closest to 2.5 and 4 points, then calculated their abnormality quantification scores. The mean values of these scores were used to establish the threshold values for each category, denoted as ${\theta }_1$ and ${\theta }_2$, as shown in Table 5.

Figure 6 Comparison Curves of Select Parameters Between the Test Sample and Standard Maneuver for the Loop Maneuver: (a) Pitch Angle; (b) Altitude; (c) Velocity; (d) Normal Load Factor.

Based on these threshold values, we define the mapping between abnormality quantification scores and performance grades as follows: scores in the range $[0,{\theta }_2)$ were classified as "Excellent," scores in the range $[{\theta }_2,{\theta }_1]$ as "Good," and scores in the range $({\theta }_1,1]$ as "Poor". Consequently, the anomaly levels for each category’s test flight maneuver are shown in Table 6. These results indicate that the proposed quantitative evaluation method for anomaly levels of complex flight maneuver is effective in evaluating the anomaly levels of different flight maneuvers.

To provide a more intuitive understanding of the abnormality quantification results, we used the "loop" maneuver as an example. Figure 6 shows the comparison of the test flight maneuver sample and the corresponding standard maneuver sample across four dimensions: pitch angle, altitude, velocity, and normal load factor. From Figure 6, it is clear that deviations between the test maneuver and the standard maneuver in these flight parameters can be easily observed, demonstrating the strong interpretability of the proposed method.