TREE-BASED AIRSPACE CAPACITY ESTIMATIONKai Zhang, Yongxin Liu, Jian Wang, Houbing Song, and Dahai Liu

Embry-Riddle Aeronautical University, Daytona Beach, FL

AbstractAccurate estimation of airspace capacity is

essential to a safe, efficient and predictable air transportation system. Conventional approaches focus on controller workload using airspace complexity measurements that only consider operational conditions of controllers. However, such model-driven methods don’t completely demonstrate airspace capacity in the real world because of lack of consideration for other critical factors such as weather. To address this challenge, we propose a new airspace capacity estimation model based on decision tree ensembles. Our model combines multi-source data to quantify the maximum transportation capacity of en route sector under different circumstances.

This paper makes the following contributions: (a) we present an interpretable data-driven model that estimates the capacities of the National Airspace System (NAS), and highlight factor importance for airspace capacities; (b) the airspace capacity estimated by our proposed model is dynamically adjusted based on the real-time environment that has the potential to be a guide for temporary flight path changes or air traffic selections for an emergency landing; and (c) we promote the role of machine learning-based methods in future ATM and airspace optimization.

IntroductionA smoother and more robust mechanism to

avoid the overloads and maximize the use of airspace is necessary because of increasing customer demand and number of aircrafts that have brought higher complexity to air traffic management nowadays. Airspace capacity estimation is vital for decision-making of route

design and flight dispatches. However, traditional airspace capacity model is either based solely on handoff workload and fixed procedural constrains using queueing principle such as Monitor Alert Parameter (MAP) [1] or a weighted combination of air traffic density and task-based controller workload like Dynamic Density [2]. However, it can’t reflect the real-world situation because of limitations on the underlying assumption of mathematical model [3] and a limited number of parameters.

With the development of communication, database and Internet of Things (IoT) [4-7], a great quantity of data is captured and stored so that machine learning and data mining techniques have the potential to boost the next generation air transportation system to make flying even safer, more efficient, and more predictable1. In this paper, we present the design and demonstration of generalized en route airspace capacity estimation, where multi-source data is integrated and fed into regression model, where it’s easy to know what features contribute a lot in making the prediction by looking at the generated tree. In addition, some ensemble methods such as bagging and boosting are employed to improve the stability and accuracy of our regression model.

Recent work aims to fill gaps in conventional airspace capacity models. Welch [1] proposed a new model considers conflict workload and recurring workload to amend erroneous conclusions caused by Monitor Alert’s concentration on a single workload type. To coordinate high-density traffic flow of Unmanned Aerial Systems (UAS), capacity for low-altitude airspace was defined as throughput-based metric based on fundamental diagram [8]. However, such mathematical models still don’t take 1https://www.faa.gov/nextgen/

a changing environment into consideration. In addition, the correlation between the controlling actions and air space capacity was not revealed. Regarding this problem, Liu [9] analyzed controller’s attention paid to each route under changing weather topological structure of the route network. The result illustrated that various scales and location of weather have different impacts on capacity. To the best of our knowledge, this paper firstly applies machine learning algorithms to evaluate airspace capacity. Moreover, human factors and climate information are all considered to build a tree-based model which provides importance score for each variable.

The remainder of this paper is structured as follows: Section 2 discusses the background information of procedure of air traffic control and principles of tree-based algorithms that we employed to build air space capacity predictors. In Section 3, we present the detailed construction of our proposed models covering feature engineering, which is followed by the comparison and evaluation of models in Section 4. We summarize results and discuss future scope in Section 5.

Background

Air Traffic ControlThe United States airspace is separated into 22

zones managed by air route traffic control centers (ARTCC) whose control begins at 1,200’ Above Ground Level on airways. Also, within each zone are portions of airspace named Terminal radar approach control (TRACON) and local-airport airspace that are not regulated by the ARTCC2 as shown in Fig. 1 and Fig. 2. There are human air traffic controllers in each air traffic control facility monitoring and conducting aircrafts flying through the designated airspace.

2https://science.howstuffworks.com/transport/flight/modern/air- traffic-control.htm

Figure 1. Process of Air Traffic Control in US

Figure 2. Air Route Traffic Control Centers3

Automatic dependent surveillance broadcast (ADS-B)

ADS-B is latest technological leap in airspace surveillance, which provides higher accurate positional information of an aircraft than conventional radar to ground controller and other pilots directly. ADS-B is seen as being a replacement for secondary surveillance radar because of significantly cheaper installation of ADS-B ground stations and its wide coverage. This gives air traffic controllers the potential to reduce the required separation distance between aircraft that are ADS-B equipped4.

3https://www.trig-avionics.com/ 4https://www.cfinotebook.net/notebook/air-traffic-control/

4

MethodologyClassification and Regression Tree (CART) is

a classical supervised learning method. For regression problems, we stratify the predictor space into multiple distinct and no-overlapping regions and then the predicted value in a specific region are represented by mean or mode of the corresponding training observation. To split predictor space, we need to find the regions R1 , R2 ,⋯ ,RM that minimize

J=∑i=1

M

∑jϵ Rm

( y j− yR m)2,

where y Rm denotes average values of the training

observations within the m-th region.

Algorithm 1: Gradient Tree Boosting Algorithm

Initial f 0 ( x )=arg minγ∑i=1

N

L ( y i , γ )

For m = 1 to M:

For i=1,2 , …,N :

Compute rℑ¿[∂ L( y i , f (x i))

∂ f (x i)]

f=f m−1

Fit a regression tree to the targets rℑ giving terminal regions R jm , j=1,2, …, J m.

For j=1,2 ,…, Jm :

Compute γ jm=arg minx i ϵ R jm

L( y i , f m−1 ( x i )+γ )

Update f m (x )=f m−1 ( x )+∑j=1

Jm

γ jm I (xϵ R jm)

Output: f ( x )=f M (x)

Ensemble method such as bagging and boosting helps improve machine learning results by combining a few predictors into an even better one. The aggregation function is typically the average

for regression. Random Forest is one of the bagging methods in which each tree (predictor) uses the same algorithm, but training set is sampled randomly with replacement (bootstrapping).

The general ideal of boosting is to fit a sequence of weak learners in order that the subsequent predictor can correct previous predictor to improve the performance of model. Gradient Boosting Regression Tree (GBRT) tries to fit the new predictor to residual error generated by the previous predictor to reduce the bias as well as variance. XGBoost based on extreme gradient boosting, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges [10]. Both GBRT and XGBoot were used to develop our predictive model of en-route airspace capacity. The algorithms for boosting are enlisted in Algorithm 1 and Algorithm 2.

Tree-based methods have a lot of advantages compared to statistical modeling that is widely used for airspace capacity estimation. The biggest advantage is that we don’t need to make assumptions regarding probability distribution. This also indicates greater generalization of tree-based methods. In addition, its efficiency in computation allows to address large problems [11].

Algorithm 2: Exact Greedy Algorithm for Split Finding

Input: I, instance set of current nodes

Input: d, feature dimension

Initial gain←0 ,G ←∑i∈ I

g i , H ←∑i∈I

hi

For k = 1 to m:

GL ←0 , H L← 0

For j∈sorted ( I ,by x jk ):

Do GL ←GL+g j , H L ← H L+h j

Do GR← G+GL , H R ←H +H L

Do

score←max (score ,GL

2

H L+θ+

GR2

H R+θ− G2

H +θ)

Output: Split with max score

Figure 3. Heat Map Indicating Flight Density

Data Analysis

Dataset Description and Feature SelectionThe processing was done on ADS-B data from

the Next-Generation Advanced Research (NEAR) Lab at Embry-Riddle Aeronautical University (ERAU), Quality Controlled Local Climatological Data (QCLCD) from National Climatic Data Center (NCDC) and ATC facilities from 123ATC.com for the period July-December in 2016. Fig. 3 shows flight density heat map of American Southeast in July 2016 via ADS-B records. The required characteristics of the model are defined as follows:

Definition 1

Flight information CF contains aircrafts’ location (latitude, longitude, altitude), state and timestamp.

Definition 2

Meteorological data CM reflects the characteristics of weather for each airspace including visibility, temperature, wind speed and so on at some point.

Definition 3

Attributes of FAA-operated air traffic control facilities CS in its corresponding airspace.

We firstly delete some unnecessary attributes in datasets according to our task and domain knowledge. Further data cleansing progress is introduced in next section.

Data PreprocessingIn this paper, the en-route airspace of

continental United States areas (latitude: 20 ~ 50, longitude: -125 ~ -65) is roughly divided into 100 proportionally cubed and be labeled with corresponding indices (from 1 to 100) as depicted in Fig. 4. The data fusion process is described below:

1. Remove attributes with missing values exceeding a given threshold (0.8). A part of attributes in CM have high percentage of missing values are presented in Table 1;

2. Remove attributes with zero variance or optionally low variance, and pairwise correlations beyond threshold (0.9). Fig. 5 depicts correlation matrix of some highly correlated attributes;

3. Convert the local time in CM to Greenwich Mean Time (GMT) to ensure chronological consistency;

4. Calculate the minimum distance between each center in areas and ARTCCs to determine which areas an ARTCC controls;

Table 1. Parts of Attributes with High Number of Missing Data

Feature Name Missing Rate

SkyConditionFlag 99.80%VisibilityFlag 99.90%WeatherType 92.81%WetBulbFarenheitFlag 1000%ValueForWindCharacter 94.18%PressureTendency 100%PressureChange 100%SeaLevelPressure 80.64%HourlyPrecip 95.71%ValueForWindCharacter 94.18%

Figure 4. Airspace Division

Figure 5. Correlation Matrix of Temperature Features

5. Employees in an ARTCC are evenly distributed for corresponding controlled areas;

6. Map CF, CM to a certain area and merge all instances from these three datasets by taking area index and timestamp as primary keys;

7. Encode categorical features as an integer array using Ordinal Encoder;

8. Count the number of aircrafts for each area with time windows.

Then the features can be obtained after data preprocessing as demonstrated in Table 2.

Table 2. Feature Description

Feature Name Feature DescriptionHour TimestampMin_x Timestampcount_mil Number of aircrafts operated

by militarySkyCondition Cloud amount, height and

typeVisibility A measure of the distance at

which an object can be clearly discerned

DryBulbCelsius Air temperatureWetBulbCelsius Adiabatic saturation

temperatureDewPointCelsius The temperature at which air

becomes completely saturatedRelativeHumidity The amount of water vapor in

the airWindSpeed The unit is knotsFacility Level Represent the amount and

complexity of traffic that facilities manage

Avg. Training Time (Years)

Average time for a new trainee takes to be fully

certified (CPC)Training Success Rate

The percent of trainees who successfully become CPCs

Workload It is defined by the ratio of

number of aircrafts and number of air traffic controllers in an area

Experiments

Model ConstructionCART, Random Forest, GBRT and XGBoost

were chosen to predict the Workload where the remaining 13 features shown in Table 1 are selected to train our machine learning model. We chose mean squared error to measure the quality of a split.

Regression tree was built with following hyperparameters:

The maximum depth of the tree was 37.

The minimum number of samples required to split an internal node was 10.

The minimum number of samples required to be at a leaf node was 2.

Random Forest was built to fit a number of regression trees above. The number of trees in the forest was set as 56.

Figure 6. Deviance vs. Boosting Iterations

Fig. 6 shows that deviance or loss decreases along with the increasing of iteration times and it starts to level off at iteration 60 when we applied boosting methods to train the model. It is the reason we took 60 as the number of boosting stages to perform of GBDT and XGBoost with the learning rate of 0.1.

Data Visualization and EvaluationTo evaluate the performance of predictive

model for regression, mean squared error (MSE), mean absolute error (MAE) and R2 (coefficient of determination) regression score are commonly used.

MAE( y , y )=1n∑i=1

n

|yi− y i|,

MSE ( y , y )=1n∑i=1

n

( y i− y i )2,

R2 ( y , y )=1−∑i=1

n

( y i− y i )2

∑i=1

n

( y i− y )2 ,

where y i is the predicted value of the i-th sample and y i is the corresponding actual value of the sample.

Figure 7. Feature Importance

Fig. 7 presents relative importance scores that measure variable's ability to perform in our tree-based models. Overall, human factors involving training success rate of controllers, average training time and the number of military aircrafts play the most important role for airspace capacity estimation. However, climatological features don’t have much effect on the capacity, especially “Visibility”. It is contrary to our commonsense understanding. From Fig. 8, most of values of visibility variable (approximately 82.31%) is 10 that results in less contribution to prediction. In the same manner, we plotted the distributions of other weather variables, as shown in Fig. 9, Fig. 10 and Fig. 11, to discovery whether the distribution imbalance of variables leads to bad importance score. As we can see, there is no

Figure 8. Distribution of Visibility Variable

Figure 9. Distribution of Dry Bulb Celsius

Figure 10. Distribution of Wet Bulb Celsius

Figure 11. Distribution of Dew Point Celsius

distribution imbalance problem. One of the possible explanations is that QCLCD was collected in ground stations to monitor surface weather that can’t represent weather situation in high altitude environment. On account of weather’s influences on airspace capacity to some extent, they were still chosen to build our estimation model. The results for workload forecasting with an identical testing set using different predictive models are shown in Table 3.

Table 3. Results

Method MAE MSE R2

CART 0.1382 0.0863 0.8165Random Forest 0.1253 0.0610 0.8702GBRT 0.1151 0.0587 0.8751XGBoost 0.1158 0.0602 0.8719

This demonstrates that bagging and boosting methods improve the performance of regression tree algorithm in terms of lower smaller MAE, MSE and larger coefficient of determination.

ConclusionThis paper presents a prototype of en-route

airspace estimation using regression tree and

ensemble methods based on it. Our studies conclude that the model has achieved the highest R2 of 0.8751 for the given features that can be used to predict the control workload for an airspace with relatively accurate results. Finding an optimal decision or regression tree is an NP-complete problem [12], hence we didn’t try to build the best predictor in this paper. There are some limitations of our study: (a) aviation weather information is required to evaluate the airspace capacity instead of ground weather data; (b) airspace is divided simply so that such a segment is not well represent complex air traffic. For instance, we didn’t consider the influence of vertical motion of aircraft on different classes of controlled airspace.

AcknowledgementsThis research was supported by the Center for

Advanced Transportation Mobility (CATM), USDOT Grant #69A3551747125.

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[8] Bulusu, Vishwanath, et al., 2018, “A throughput-based capacity metric for low-altitude airspace,” Aviation Technology, Integration, and Operations Conference.

[9] Liu, Lu, 2018, “Terminal Airspace Capacity Evaluation Model under Weather Condition from Perspective of a Controller,” International Journal of Aerospace Engineering.

[10] Chen, Tianqi, and Carlos Guestrin, 2016, “Xgboost: A scalable tree boosting system,” Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.

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Email AddressesKai Zhang: zhangk3@my.erau.edu

Yongxin Liu: liuy11@my.erau.edu

Jian Wang: wangj14@my.erau.edu

Houbing Song: songh4@erau.edu

Dahai Liu: dahai.liu@erau.edu

2020 Integrated Communications Navigation and Surveillance (ICNS) Conference

April 21-23, 2020