Aircraft Wake Recognition and Strength Classification Based on Deep Learning

Aircraft wake is a pair of counter-rotating vortices generated behind the aircraft, which can greatly impact the safety of fast takeoff and landing of aircraft and limit the improvement of airport capacity. The current wake parameter retrieval methods cannot locate the wake vortex's position and estimate its strength level in real time. To deal with this issue, a novel algorithm based on the YOLOv5s deep learning network is proposed. The new algorithm establishes a single vortex locating concept to adapt the wake vortex's evolution at complicate background wind field conditions, and proposes strength-based classification standard which can represent the real-time hazard of wake vortex to shorten the takeoff and landing intervals. Meanwhile, the EIOU loss function is introduced to improve the precision of YOLOv5s network. Compared with the state-of-the-art object detection approaches, such as Cascade R-CNN, FCOS, and YOLOv5l, the superiority of new method is demonstrated in terms of accuracy and robustness by using the field detection data from Hong Kong International Airport.


I. INTRODUCTION
W HEN the aircraft flying in the air, its wing will disturb the atmosphere and generate a pair of counter-rotating vortices, which are caused by the pressure difference between the top and bottom surface of the wings. Wake vortex is regarded as a sort of severe hazard in air traffic management (ATM) because it may cause the follower aircraft to pitch, yaw and roll, even out of control [1] (see Fig. 1). In order to keep safe flight operations, the International Civil Aviation Organization (ICAO) classifies aircraft types into three categories based on their maximum takeoff weight (MTOW), and established a set of fixed separation standards accordingly [2] (as shown in Table I  With the improvement of detection sensors, modifying the aircraft's categorization and its corresponding separation minima become possible. The objective of the international project Re-Categorization (RECAT) is to minimize the existing aircraft takeoff and landing separation standards and safely increase the capacity of the airport. ICAO tasked the Federal Aviation Administration (FAA) [3] and European Organisation for the Safety of Air Navigation (EUROCONTROL) [4] to lead this effort.
RECAT is divided into three phases. In Phase I, the current aircraft categories are optimized and subdivided into six categories. Take the EUROCONTROL's work "RECAT-EU" [5] (see Table II) as an example, the RECAT-EU scheme compares the wake generation and wake resistance between aircraft types, splits ICAO's HEAVY category into "Super," "Upper" and "Lower," and splits MEDIUM category into "Upper" and This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0 /  TABLE II  RECAT-EU WT DISTANCE-BASED SEPARATION MINIMA ON APPROACH  AND DEPARTURE "Lower." The objective of Phase II is to form an optimized airport-specific static pair-wise spacing, which defines separations for all potential aircraft pairs and is valid for all atmospheric conditions. After that, Phase III will provide dynamic pair-wise spacing supported by trajectory-based operations, which will vary with atmospheric conditions and aircraft performances. In Phase II and III, the recognition and strength classification of aircraft wake vortex in real time are needed. Respectively, there are two parameters correspond to it, saying vortex-core positions and velocity circulations. The vortex-core positions indicate where the vortices are, and the velocity circulations well describe the strength of a wake.
Accordingly, there are two categories of wake vortex parameter-retrieval algorithms based on Lidar detection have been proposed.
1) Velocity Envelope Extraction Algorithm: It locates vortex cores by velocity envelopes and obtain the circulations from a given wake velocity model. Holzäpfel et al. [6] used tangential velocities around the vortex-core to locate the core position and estimate its circulation, which is called TV method. Rahm et al. [7] estimated the vortex parameters using velocity envelopes obtained from Doppler spectra by setting a fixed threshold. Furthermore, Wassaf et al. [8] proposed to use a threshold that adapts to signal-to-noise ratio (SNR) instead. Basically, these methods have fast calculation speed, but are sensitive to the complicate background wind field, which would cause estimation bias of vortex-core positions.
2) Template Matching Algorithm: Mathematical model about the wake vortex parameters were established and fitted with the Lidar detection data to estimate the wake vortex-cores and circulations. Frehlich et al. [9] used two maximum likelihood (ML) estimators to estimate the wake parameters by comparing the vortex model and the Lidar spectrum data. Jacob et al. [10], [11] estimated the wake vortex parameters based on spectral-space processing with ML estimation. Hallermeyer et al. [12] estimated the vortex-core positions based on velocity envelopes, and used the ML estimator to estimate the circulations. Smalikho et al. [13], [14] proposed a new parameterretrieval method (radial velocity method, RV method), which used the radial velocities to locate the vortex-cores and estimated the circulations by fitting the measured Doppler velocities with theoretical velocity model. Yoshikawa et al. [15] established a single formulation about the wake parameters and the measured Doppler spectra, and the optimization of wake parameters is made by iteration process. Gao et al. [16] proposed to retrieve the wake vortex parameters with an optimization method (Opt method), but it has a relatively high computation load. Li et al. [17] proposed a new method (path integration method, PI method), the integration of Doppler velocity along a line-of-sight (LOS) is derived as a linear expression about the circulations, this method can solve the circulations in terms of both accuracy and efficiency, but it depends on the locating precision of wake vortex.
The existing parameter-retrieval algorithms mainly concentrate on stable state of the two wake vortices, which have relatively strong strength. Following problems need to be solved.
1) The above methods cannot identify whether there is wake vortex in the RHI image. 2) The left and right wake vortices would evolve far away from each other for the complicate background wind and ground rebound effect, even there is only one vortex left, which have not been considered in the traditional methods mentioned above.
3) The existing aircraft type based RECAT classification rule is not suitable for all airports, where the wake evolution trend would change at different terrain and weather conditions. This article proposed a new method based on deep learning to solve the problems listed above and realize the real-time recognition and strength classification of aircraft wake vortex to reduce the takeoff and landing safe separation distance between flights. The contributions of this article include the following. 1) We presented a new wake vortex recognition concept, single vortex locating, which consider complicated situations, e.g., the two wake vortices move far away from each other, or the wake vortex rebound under the impact of ground mirror effect, or there is only one wake vortex left in one RHI image. 2) A new strength-based classification standard is proposed to characterize the real-time hazard of wake vortex to the following aircraft, which can help to reduce the takeoff and landing interval between flights. 3) An effective YOLOv5s neural network with EIOU loss function is introduced to recognize and classify the wake vortices in terms of both accuracy and robustness. Compared with the traditional IOU loss function structure, the proposed method can obtain about 2% precision improvement and 3% recognition rate improvement. The rest of this article is organized as follows. Related work about detection scene setup and deep learning algorithm selection is shown in Section II. A recognition and strength classification deep learning approach is presented in Section III, details about Lidar data processing, strength classification rule, label and dataset construction, network structure, loss function are introduced. In Sections IV, recognition and strength classification precision are experimentally validated.

A. Detection Scene Setup
The effective sensors for aircraft wake vortex detecting are Lidar and Radar. Under clear air condition, Lidar can effectively sense the scattering of aerosols and retrieval the wind field that contains the wake vortex [18], [19], [20]. But under wet conditions, the Lidar range dramatically reduced due to the heavy attenuation and the effective sensor is radar [21], [22], [23]. The takeoff and landing process of aircraft mainly occurs in clear air, therefore this article mainly focuses on the Lidar detection of wake vortices in clear air.
The range height indicator (RHI) scan mode is proved to be a good way to detect the fine structure of aircraft wake [17]. The coordinate setting is shown in Fig. 2, the origin is the Lidar, the x-axis is originated from the Lidar and orthogonal to the runway, the y-axis is originated from the Lidar and perpendicular to the ground, the z-axis is originated from the Lidar and parallel to the runway. The RHI scan mode scans the x − y plane up and down alternately at a scan rate ±ω between the minimum elevation angle α min and the maximum elevation angle α max by using the Lidar beam, which would output a series of Doppler radial velocity distributions. More details about the detection setting can be found in [24] and [25].
An example of the Doppler velocity distribution of Lidar RHI scan is shown in Fig. 3. The positive and negative components are toward and away from the Lidar, respectively. There are left and right vortices in one RHI, the two vortices would move by the effect of background wind and interaction with each other. The RHI Doppler velocity distribution images are remotely sensed images which can be used for deep learning.

B. Deep Learning Algorithm Selection
A large amount of Lidar observation data is available on a fine scale, and the wake vortex target in the RHI image can be found by image recognition, therefore it is possible to apply deep learning technology [26], [27] with image dataset [28], [29] to realize the recognition and classification of aircraft wake vortex. The current target detection deep learning algorithms are mainly divided into two types.
1) Region-Based Algorithm: It is a two-stage target detection algorithm. The operation process is divided into two steps. The first step is to extract the target features and generate a region proposal network (RPN) that may contains the target. In the second step, the samples are classified through the classification network. Representative algorithms include region-based CNN (R-CNN) [30], faster region-based CNN (Faster R-CNN) [31], and spatial pyramid pooling net (SPP-net) [32].
2) Regression-Based Algorithm: It is a single-stage target detection algorithm, which does not generate preselected regions, but directly extracts target features through the model to output the target category and location. Representative algorithms are YOLO (You Only Look Once) series algorithms [33].
The two-stage target detection algorithm has a relatively calculation amount at the training and detection process. For the demand of aircraft wake real-time detection, this article adopts YOLO series algorithms. YOLO series algorithms have been updated from YOLOv1 to YOLOv6. Compared with the previous version, each version has improved the network structure, and its detection accuracy and speed have also been continuously optimized. The YOLOv6 algorithm has not been widely verified, so we use YOLOv5 algorithm, which not only inherits the advantages of YOLOv4 [34] algorithm, but also optimizes the trunk network to improve the accuracy of small target detection.
There are four versions of YOLOv5 network, which are YOLOv5s, YOLOv5m, YOLOv5l, and YOLOv5x models. These four network models mainly differ in network depth and width of feature graph. YOLOv5s is the network with the smallest depth and width of feature graph. The following three networks are constantly deepened and widened on this basis. For the detection and identification of aircraft wake vortex, the other three models have little improvement in accuracy, but greatly increase the training time. Therefore, the YOLOv5s network model with the smallest feature width and the fastest speed is selected as the detection model.

III. METHODOLOGY
Estimate the position and strength level of wake vortex instantly can well characterize the behavior of it and evaluate its hazard for dynamic safe distance of two neighboring aircraft. In this section, we introduce the new single-vortex detection concept and strength-based classification standard, and how to use the deep learning network to estimate the position and strength of the vortex core precisely.

A. Lidar Data Processing
The Lidar detection data need to be processed to form the dataset that is available for YOLOv5s neural network training. Based on the statistical analysis of wind velocity information at Hong Kong International Airport, the Lidar Doppler velocity distribution image is transformed to grayscale image by the following: where "10" and "20" are the maximum velocity value and the range of the Lidar Doppler velocities, respectively; V D is the Doppler velocities in a full RHI scan.
As the YOLO network is designed for nature images with RGB channels, so we apply a pseudocolor lookup table to grayscale values, mapping each grayscale value to a color to form an RGB image.
Take the data of Hong Kong International Airport for an example, the pixel size of an RHI image is 768*160, which is consistent to the real detection distance (1 horizontal pixel corresponds to 1 m) and elevation range (1 vertical pixel corresponds to 1 scan interval).

B. Wake Strength Classification
The RECAT-EU scheme [4] compares the wake evolution of different aircraft by large amounts of experiments, splits ICAO's HEAVY category into "SUPPER," "UPPER," and "LOWER," and splits ICAO's MEDIUM category into "UPPER" and "LOWER" (as shown in Table II). This aircraft-based classification standard is mainly based on wingspan and weight of aircraft and verified at certain airports, which represent the wake vortex's evolution under relatively ideal conditions. However, the above aircraft-based classification method may not be suitable for all airports for the reason that the wake vortex's evolution and influence scope may change at different terrains, background wind field, and weather conditions. This article proposes a new classification standard, taking the wake vortex strength level as classification standard according to the RECAT-EU's aircraft classification standard [5] mentioned in Table II. And then, the range of each strength level can be calculated by using most of the aircraft in the respective aircraft-based categories listed in Fig. 4. More details about the new standard are listed as follows.
The common approach for the strength's calculation of a fully developed single vortex is [35] where M A , g, ρ a , V A are the aircraft mass, gravity acceleration, air density, and aircraft speed, respectively. While landing, the aircraft has a relatively large vertical speed, but its impact load is limited because of the material and structure limitation, so the maximum landing weight is generally smaller than the maximum takeoff weight. Meanwhile, the landing process is more dangerous than the takeoff process. Therefore, this article uses maximum landing weight as aircraft mass to calculate the wake circulation.
The strength calculation results of aircraft listed in RECAT-EU's classification standard are shown in Fig. 5, the blue snow spots represent the aircraft wake circulations, the lateral dotted lines are separation lines of RECAT-EU aircraft-based classification standard, the horizontal solid lines are separation lines of new proposed strength-based classification standard. 3) The same situations will occur in the following RECAT-EU's classification types, e.g., A320, AT72, DH8D, and so on. It means that some aircraft have relatively strong circulations but its wingspan are not very long. Therefore, the RECAT-EU's aircraft-based classification standard may not be suitable, which neglected the actual strength level and evolution of aircraft wake vortex. The classification based on aircraft type (wingspan and weight) may cause short takeoff and landing intervals in the neighboring aircraft, which would impact the safety of the following aircraft.
According to the classification method and strength calculation results mentioned above, this article proposes a new strength-based wake vortex classification standard, which is shown in Table III. The new standard calculates the wake circulations of all aircraft in the six categories of the REACT-EU's classification standard and reclassifies six categories according to the circulation values, which are from level A to F. The new strength-based classification standard shows the real hazard to the following aircraft according to the heading aircraft's wake vortex strength, and can be used to form the dataset for deep learning.

C. Label Dataset Construction
Dataset is the basis of deep learning. In the task of object detection and recognition, dataset usually needs to be labeled and then sent to the grid for learning. The dataset of aircraft wake vortex is a set of labeled RHI images. Labeled RHI image in the dataset contains features, which are vortex location range, vortex type and strength level. After labeling, deep learning is used to analyze this features in data training and form a judging rule using in new image recognition and classification.
The traditional parameter-retrieval methods, such as tangential velocity (TV) method, consider to locate the wake vortex by using the symmetry property and distances of the two vortices. But as time go, the left and right wake vortices may move far away from each other, or the vortex may rebound by the ground mirror effect, or there is only one vortex left (as shown in Fig. 6). Therefore, the traditional methods may fail to retrieve the parameters of wake vortex correctly.
In order to recognize the wake vortex correctly, this article proposes a new method, which labels the dataset on single vortex by using the property of vortex type and strength level.
The strength of each labeled vortex is estimated by path integration (PI) method, which estimates the strength (that is circulation) by using the Doppler velocity unit around the vortex core. It locates the vortex-cores according to the Doppler velocity profiles and uses the path integration of the measurement  bins along the line-of-sight above and below the vortex-cores to obtain circulations of the two vortices. Also, an iteration process is proposed to mitigate the impact of compressing and expanding effects of wake vortex caused by the scanning of Lidar beam in an RHI. More details about the PI method can be found in [17].
When preparing the training dataset, the wake vortex targets in the RHI Doppler velocity images are marked using the Sprite marker assistant annotation tool manually. According to the wake strength classification standard introduced in Section III-B, the labels of wake vortex in RHI image are set to 12 categories, which are LA, LB, LC, LD, LE, LF, RA, RB, RC, RD, RE, and RF. Take the letters LE for an example, the first letter L means the wake vortex is an left vortex and the second letter E means its strength level is E.

D. YOLOv5s Deep Learning Network Structure
The YOLO network [36] equally divides the input RHI image into S * S grid cells. All grid cells are processed simultaneously with class information that established by the labeled dataset, the detection processing flow is shown in Fig. 7.
Each grid cell predicts B bounding boxes, which contains five variables, x, y, w, h, and confidence. The variables x and y are the horizontal and vertical positions for the center of the bounding box. The variables w and h are the width and height of the bounding box. The confidence is defined as where P r (Object) is 1 or 0, which represents the wake vortex exists in the cell or not, respectively. IOU = A∩B A∪B is the intersection over union between the predicted box and the real box. The schematic diagram of IOU is shown in Fig. 8, where dotted box B represents wake prediction box, solid box A represents the target box of wake vortex.
Each grid cell also predicts C class probabilities, P r (Class i |Object), where C = 12 corresponding to the number of wake vortex's type in the manuscript.
When detecting the wake vortex, the class probability and the bounding box confidence are multiplied as follows: which present specific class confidence that contains both the probability of that class appearing in the box and how confidence the predicted box fits the wake vortex. The YOLOv5s network is shown in Fig. 9, the red boxes are the four main modules of YOLOv5s, which are Input, Backbone, Neck, and Prediction, respectively. The specific structure of small and medium size modules in the network is marked by blue boxes in the figure below. Important improvements of the modules are listed below: 1) Input Module: The input module of YOLOv5s adopts adaptive anchor frame calculation, adaptive image scaling and Mosaic data enhancement to process the input wake data. After the RHI Doppler velocity image enters the network, the input module calculates the optimal anchor frame value adaptively, scales the RHI Doppler velocity image to a uniform size. Then Mosaic data enhancement was used by random scaling, clipping and arrangement to enhance the dataset.
2) Backbone Module: Focus structure is designed in the Backbone module. The key of focus structure is the slicing operation. The wake data is an RHI Doppler velocity distribution image with resolution 768 × 160 × 3. The RHI image is transformed into a feature map of 384 × 80 × 12 by slicing operation first, and then through a convolution operation of 32 convolution kernels, it finally becomes a feature map of 384 × 80 × 32. The slicing operation can reduce the number of parameters and increase the training speed.
3) Neck Module: In order to better extract fusion features, some layers are inserted between Backbone and Prediction modules. This part is called Neck module, which is equivalent to the neck of target detection network. The neck of YOLOv5s adopts FPN+PANet structure to enhance the ability of network feature extraction and fusion. Through bottom-up path enhancement, the path aggregation network (PANet) [37] uses precise location signals at the bottom layer to enhance the entire feature layer, thus, shortening the feature information path between the bottom and the topmost layers.

4) Prediction Module:
In Prediction module, the weighted nonmaximum suppression (NMS) method is adopted for the screening of target prediction boxes, that is, the category prediction boxes with the maximum local score are retained, and the prediction boxes with low scores are discarded, and finally the prediction box closest to the real value is obtained.

E. Loss Function Optimization
Loss function contains bounding box regression loss, confidence loss, and class loss. The bounding box regression loss can measure the difference between the predicted region and the actual region, which can represent the advantages and disadvantages of model and determine the final performance of model training.
During the training, the network model is optimized by the optimization algorithm based on the output value of the loss function to improve the prediction precision, so this manuscript mainly focuses on the optimization of bounding box regression loss function. The current YOLO series network use IOU, GIOU, CIOU loss functions for the optimization of network training.
1) IOU Loss: IOU (intersection over union): Loss is the intersection ratio of target box and prediction box, which is defined as follows: In a large number of RHI Doppler velocity images, there are various wake situations, which should be taken into account in the loss function to optimize the network model during training. IOU loss has two deficiencies: as shown in State 1 [see Fig. 10(a)], when the wake prediction box does not intersect with the target box, IOU = 0, which cannot reflect the distance between the two boxes, and the loss function cannot be derived. In this case, the wake network model cannot be optimized. As shown in Fig. 10(a) and (b), the conditions of the prediction box  and IOU between State 2 and State 3 are the same, but IOU loss cannot distinguish the relative positions between the prediction box and the target box in this two states.
2) GIOU Loss: In order to overcome the disadvantage of IOU loss, generalized IOU (GIOU) loss is proposed (as shown in Fig. 11), which introduces the minimum enclosing rectangle C of target box of wake vortex and its prediction box, and the difference set of union D between the enclosing rectangle C and the two boxes. The calculation formula is shown in follows: Although GIOU loss solves the problem that IOU loss function cannot predict the distance between the target box and its prediction box when they do not intersect, it also has defects. As shown in Fig. 12, when the wake prediction box is inside its target box and the size of the prediction box is the same, the difference sets of the wake prediction box and the target box are the same, and the GIOU values in these three states are also the same. At this time, GIOU degenerates into IOU, and the relative positions of the wake prediction box in the target box cannot be distinguished.

3) CIOU Loss:
Considering the defects of the original YOLOv5s loss function (including overlap area, center point distance, aspect ratio, etc.), Complete IOU (CIOU) loss was adopted, the calculation formula is where b and b t are prediction and target box, ρ(b, b t ) is the Euclidean distance between the center points of prediction and target box, c is the diagonal length of the smallest enclosing box covering the two boxes, v measures the consistency of aspect ratio where w t and h t are width and height of the target box respectively, w and h are width and height of the prediction box, respectively. Positive tradeoff parameter α is defined as CIOU loss considers the overlap area, center point distance and aspect ratio of boundary box regression. However, the aspect ratio v is a relative value, which could not reflect the real difference of width and height and its confidence, and sometimes may prevent the model from effectively optimizing similarity.

4) EIOU Loss:
In order to solve the problems mentioned above, this article introduces efficient IOU (EIOU) loss function to optimize the locating precision of the wake vortex, which is defined as where C w and C h are the minimum width and height of the outer box covering the two boxes. The EIOU loss function contains three parts: overlap loss, center distance loss, width and height loss. The first two parts continue the method in CIOU, but width and height loss directly minimizes the difference between the width and height of the target box and the prediction box, making the convergence speed faster.

IV. EXPERIMENT VALIDATION OF THE METHOD
A. Training Process 1) Field Campaigns Setting: Wind Lidar measures the atmospheric wind field by using the Doppler frequency shift, which can be divided into coherent detection and incoherent detection. Coherent detection measures the wind field through the coherence of atmospheric echo signal and local laser, and the incoherent detection measures the Doppler frequency shift of wind field by converting the frequency of laser echo signal into the relative change of energy. Comparatively, coherent Lidar has the advantages of small size, high precision of wind field measurement, and high temporal and spatial resolution.
The all-fiber pulse coherent wind Lidar operating at 1.55 μm wavelength has become mainstream equipment with following advantages: 1) the wavelength is safe for human eyes; 2) the maximum permissible exposure of 1.55 μm laser is about 1 order of magnitude higher than 2.1 μm and about 6 orders of magnitude higher than 1.06 μm; 3) optical communication devices of it are mature, and its fiber loss is less than the others.
According to the analysis above, a Doppler Lidar (WindCube 200 s) is used at Hong Kong International Airport (HKIA) to detect the aircraft wake vortices. The Lidar was set beside the runway (about 7 m above the ground) to observe the south way of HKIA at a distance of 240 m from the south see Fig. 13(a)].
As shown in Fig. 13(b), the Lidar scans up and down alternately at a scan rate 5 • /s on the plane perpendicular to the runway, which would output an RHI Doppler velocity distributions. Its main working parameters are listed in Table IV.  TABLE IV  MAIN PARAMETERS OF THE PULSED LIDAR IN HONG KONG FIELD CAMPAIGNS 2) Dataset Construction: Large amounts of observation data were obtained through a long time of detection to form the RHI velocity distribution images. In this article, 2000 images with wake characteristics were selected manually as the dataset. In addition, 200 images without wake features were randomly selected, and 200 images with wake features were reselected to form the testset.
The strength of each labeled wake vortex is calculated by PI method. Select 1/5 of the labeled dataset to make the validation set, and the rest is the training set for model training. The labeled information of the image dataset is read out and written into the label file, so as to complete the preparation of the dataset required by this training.
3) Model Training: The parameters of the experiment training are set as follows: the batch size is 16, the maximum iteration number is 80, and the EIOU loss function mentioned above is adopted. YOLOv5s uses genetic algorithm (GA) to optimize the hyperparameters, which is called hyperparameter evolution. The hyperparameters used in this experiment are evolved by using hyperparameters on common objects in context (COCO), which performs well in many image detection and recognition tasks.
In COCO object detection experiments, the important initial hyperparameters are set as follows: the initial learning rate is 0.01; the momentum and weight decay are set as 0.937 and 0.0005, respectively; the warmup epochs, initial momentum and initial bias learning rate are 3, 0.8 and 0.1, respectively; class loss gain and object loss gain are set as 0.5 and 1, respectively.

B. Case Study of Recognition of Wake Vortex
As shown in Section III-C, the wake vortex would move for the cause of background wind and interaction of the left and right vortices. Meanwhile, the wake vortex would evolve as time elapse, for example, the left and right vortices may rebound for the ground effect, or there is only one vortex left, or there are three or more vortices in one RHI. In this section, the article evaluates the recognition performance of wake vortex at different situations.
1) Stable State: The aircraft wake vortices at stable state have the property of counter rotation with stable speed and existing for quite a long time, which is dangerous for the following aircraft. Fig. 14 shows two examples of wake vortex at stable state, results show that the new proposed method can recognize the left and right vortices correctly.
2) Ground Effect: When the distance of wake vortex-core from the ground is smaller than 1.5b 0 , the ground effect needs   to be considered [38], [39], where b 0 is the aircraft wingspan. The ground effect can be modeled by using two image vortices which rotate inversely to the real vortices [40] (see Fig. 15), and the circulations of the image vortices are Γ img,c1 = −Γ c1 and Γ img,c2 = −Γ c2 . The ground effect would cause the real wake vortex's rebound above the ground. Fig. 16 shows two examples of rebound wake vortices, the two left vortices rebound to a certain degree and far away from the right vortex. Results show that the proposed method can recognize the wake vortex at this situation precisely.
3) Multiple Vortices in One RHI: In order to increase the capacity of airport, the airport management may arrange the aircraft taking off and landing as soon as possible, which may leave multiple vortices in one RHI image.   Fig. 17 shows two examples, there are two left and two right vortices in one RHI. The traditional locating method mainly focuses on stable state wake vortex and would be impacted at complicate background, which make it impossible to locate the wake vortex at this situation. The proposed method locates the vortex core by using the velocity symmetry feature and focuses on one vortex. Results in Fig. 17 show that the method can locate the vortex-core and distinguish the vortex type precisely.

4) Strong Cross Wind and Single Vortex Conditions:
Sometimes the left and right wake vortices would move far away from each other because of the strong cross wind, as shown in Fig. 18(a). Sometimes there would be only one vortex left as time elapse, as shown in Fig. 18(b). Results in Fig. 18 show that the proposed method can locate the vortex-core precisely in the above two conditions.

C. Recognition Rate of Wake Vortex
From the analysis above, we can found that the new proposed method can well recognize the wake vortex at different situations, in this section we analyze the recognition precision rate by using 2000 RHI Doppler velocity images. Table V shows the recognition rate with different loss function. Results show that the YOLOv5s network can recognize the left and right wake vortices at a high recognition rate, and the EIOU loss function used by the new proposed method has the highest recognition rate, which proved the superiority of the proposed method.

D. Strength Classification Precision
This section analyzes the strength classification precision by using 2000 wake vortices. The strength of each wake vortex is calculated by using the PI method. Table VI shows the strength classification results of each type, the second row is the classification number of each type established by using PI method, the third row is the classification number of each type established by using YOLOv5s network structure, the fourth row is precision rate of YOLOv5s.
Results show that the YOLOv5s network can well estimate the strength level of wake vortices at level A, C, and E. One vortex with level B and two vortices with level D are wrongly estimated as level C, and one vortex with level F is wrongly estimated as level E. This is mainly for the reason that the circulations of this three vortices are very close to the neighboring strength scope. Results show that the proposed method can well estimate the strength category.

E. Performance Evaluation of Loss Function
The evaluation of the experimental model mainly uses Precision, Recall and mean Average Precision (mAP). Precision and Recall are calculated by the following formulas: Recall = T P T P + F N (12) where TP represents true prediction, F P represents false alarm, F N represents missing alarm. The Precision represents how many predicted wake targets are real targets and reflects the accuracy of detection results. Recall can reflect the proportion of wake targets that are correctly detected among all wake targets, and can represent the comprehensiveness of detection results. The Precision-Recall (P-R) curve is used to characterize the model recall at different thresholds, and the area enclosed by the curve is obtained by integrating it. The area enclosed by this curve is the average precision (AP) AP = 1 0 p(r)dr (13) mAP is to average the AP values of all kinds of targets. mAP 0.5 is to calculate the average precision value of each target type when IOU is set to 0.5. The YOLOv5s network model is trained for a total of 80 epochs, and the Precision, Recall, and mAP performance of the model were obtained, which is shown in Table VII.
Results show that the performance of YOLOv5s network at wake vortex detection are good at different loss functions, and EIOU loss function is the best option for the network under comparison of Precision, Recall, and MAP 0.5 .

F. Computational Efficiency of the Algorithm
The experiment uses a deep learning framework called Pytorch, and the operating platform is windows 10, more details about the GPU and memory are shown in Table VIII. For wake vortex recognition and strength classification, the efficiency is an important index. First, the YOLOv5s network model is compared with traditional parameter retrieval methods, such as Optimization (Opt) method, PI method, which have relative high strength estimation precision [17]. When constructing the label dataset for training, the strength of each labeled vortex is estimated by PI method. In Section IV-D, the strength classification precision of proposed YOLO method is proved to be close equal to the PI method. The time costs that dealing an RHI image of the traditional Opt method, PI method are serval minutes and 1.2 s, respectively, while the YOLO method is 2.4 ms. The time cost of the YOLO method is much smaller than the traditional parameter retrieval methods.  Table  IX, we can find that the YOLOv5m, YOLOv5l, and YOLOv5x models have little improvement in accuracy, but greatly increase the training time. Therefore, the YOLOv5s network model is the best choice for wake vortex recognition and strength classification.

V. CONCLUSION
In summary, this article proposes a recognition and strength classification method of wake vortex based on deep learning network. The method proposes a deep learning network based on YOLOv5s to identify the wake vortex and estimate its strength level. A new strength classification standard is proposed, which divides the wake strength into six categories according to the aircraft classification of RECAT-EU. Also, the EIOU loss function is introduced to improve the performance of the method.
Field detection campaigns at Hong Kong International Airport show that the proposed method has the benefits of being accurate, efficient, and robust. The main reasons for these good performances are as follows.
1) The dataset uses large number of RHI images which contain different categories of wake vortex. 2) The new detection concept based on single wake vortex is proposed and used to adapt the complicated background wind field.
3) The use of EIOU loss function which estimates the width and height loss by directly minimizing the difference between the width and height of the predict box and the target box, making the converge faster and more precise than other traditional loss functions. In this sense, this method can provide good support for air traffic controller to assess the hazards of wake vortex in real time.
It is noted that the performance of this method depends on the accuracy of dataset construction which may be impacted by the RHI image number and label setting precision. In the near future, following efforts will be made to improve the recognition rate and classification accuracy of the method: 1) obtaining more Lidar field data at different airports and weather conditions to construct a more comprehensive Lidar dataset, and validating the adaptability of proposed method; 2) trying to compare different hyperparameters in the network and making ablation analysis about the network structure to optimize the deep learning network; 3) trying to obtain microwave radar detection data, doing data fusion about Lidar and radar data to form a high spatial and temporal resolution dataset for the training of neural network model so that the network can work in all weather conditions.