# Aircraft Wake Recognition Based on Improved ParNet Convolutional Neural Network
## 2 Establishment of Dataset
### Establishment of Dataset  
The wind field data obtained by lidar are one-dimensional data. To enable the recognition model to better extract the spatial characteristics of the wake and facilitate its processing, the obtained radial velocity of the wind field was imaged, as shown in Figure 4. First, the data were reconstructed according to the working mode set by the lidar, and the radial velocity matrix of the wind field was obtained. According to the statistical characteristics of the historical wind speed, the radial velocity matrix of the wind field was linearly transformed as follows:  
\[I=f(V)=255\times\frac{V+5}{10}, \tag{1}\]  
where \(V\) stood for the radial velocity matrix of the wind field captured by the lidar. The parameters in the equation were determined by the maximum and minimum of the radial wind velocity. Further, the wind field matrix was expanded by bicubic interpolation, and the greyscale images with 72 \(\times\) 158 pixels were then generated, as shown in Figure 4. In Figure 4, red, orange, and yellow indicate that the radar radial velocity is positive, while blue and green indicate that it is negative. The relative relationship between wind speed and the laser beam's emission direction is expressed as positive or negative.  
A total of 6352 wind speed images were obtained, including 3169 images with a wake and 3083 images without a wake. For these images, ordinary atmosphere phenomena may occur, e.g., calm wind, downwind, and headwind. In the experiment, 1500 images were selected as the training dataset. A total of 320 images were selected in each validation and test set.  
The images with wake were marked as positive, while the images without wake were marked as negative. The positive and negative images are shown in Figure 5. Figure 5a,c,e shows the positive samples under downwind, calm wind, and headwind. It is seen that the wake may shift, affected by the ambient wind. Figure 5b,d,f shows the negative samples under downwind, calm wind, and headwind.  
Figure 3: Lidar maps demonstrating the aircraft wake evolution. **(a–c)** Early stage; **(d–f)** middle stage; **(g–i)** late stage.  
Limited sample quantity may lead to the overfitting of the CNN model. The data augmentation technique was used to overcome the problem [19]. In the experiment data, enhancement was used to expand the training set. The data were enhanced by scaling and rotating the images. The images may be scaled by a random ratio within the range of 0.8-1.2. Similarly, they can be rotated by random degrees within the range of \(-5\)-\(+5^{\circ}\). The consequent images may be cropped or refreshed by adding pixels in order to maintain the size of the images. The data augmentation technique helped to produce images with wakes of different intensities, which enabled the diversity of the data samples. The scaling of the images imitated the wakes produced by different aircraft. The rotation of the images imitated the wakes affected by the ambient wind.  
Figure 4: Lidar image conversion.  
Figure 5: Wind field images with and without a wake. (**a**) Positive downwind; (**b**) negative downwind; (**c**) positive calm wind; (**d**) negative calm wind; (**e**) positive headwind; (**f**) negative headwind.