A quantitative approach to density–based clustering of flight trajectories for e ffi cient air tra ffi c noise simulations

Shreyas M. Guruprasad 1 , Gil Felix Greco 2 , Tobias P. Ring 3 and Sabine C. Langer 4

Institute for Acoustics (InA), Technische Universität Braunschweig Langer Kamp 19, D-38106 Braunschweig, Germany

ABSTRACT The increased availability of air tra ffi c data has enabled the application of data–driven approaches to support the simulation of noise contours around airports. Aiming at e ffi cient aircraft noise simulations, this contribution proposes a framework for the probabilistic description of the air tra ffi c around an airport. The methodology is based on flight trajectory clustering using the density–based algorithm OPTICS. The clustered trajectories serve as a basis for the creation of backbone and dispersion tracks, which, together with a prescribed number of flight operations per aircraft type, provide a probabilistic description of the air tra ffi c to the noise simulations. A major focus is given to quantitatively assess the sensitivity of the OPTICS algorithm to di ff erent hyper–parameters to reduce the dimensionality of the problem. This framework is demonstrated utilizing a dataset of ADS–B flight trajectories associated with flights approaching the Hannover airport. Noise simulations based on the ECAC Doc. 29 best–practice method are conducted using the software SoundPLAN. A good agreement between noise contours is obtained when comparing simulations performed using the proposed framework and the full dataset while the computational time required is decreased. Furthermore, this approach identifies most of the trajectory patterns with the least amount of outliers.

inter.noise % 2022

1. INTRODUCTION

The expansion of Automatic Dependent Surveillance-Broadcast (ADS–B) technology has enabled open–source flight tracking data to become publicly available, supporting the analyses of aircraft operations at a large scale. This technology helps to track the position of an aircraft, along with other relevant parameters, by sending periodic messages to ground receivers and other aircraft. Recently, ADS–B data has been used in the context of many data–driven applications, such as the identification of air tra ffi c flows [1], to improve time of arrival estimations [2], and for the prediction of aircraft emissions [3], to name a few. Flight trajectory data provided by ADS–B sensors can be used for the study of aircraft noise in many di ff erent ways. Concerning aircraft noise simulations based on best–practice methods, such

1 s.guruprasad@tu-braunschweig.de

2 g.felix-greco@tu-braunschweig.de

3 t.ring@tu-braunschweig.de

4 s.langer@tu-braunschweig.de

as the Doc. 29 from the European Civil Aviation Conference (ECAC) [4], ADS–B data is suitable to provide input information describing the aircraft’s trajectory in terms of geographical position, altitude and velocity. Moreover, the ADS–B data can be used indirectly for best–practice aircraft noise simulations based on a probabilistic representation of the air tra ffi c. This is achieved by identifying air tra ffi c flows around an airport, which are then individually described in the noise simulations as flight corridors by so–called backbone– and side–tracks along with its corresponding number of flight movements. Therefore, in this case the noise simulations are performed based on the probabilistic description of flight movements along a flight route instead of considering all individual flight movements occurring at the same route. The probabilistic approach is specially useful for the noise forecast of future air tra ffi c scenarios, when data concerning single flight trajectories explicitly is not yet available. Moreover, this approach has been previously demonstrated to be more e ffi cient in terms of computational cost when compared to the use of a full dataset of flight trajectories for the noise simulation of large air tra ffi c scenarios [5]. The identification of air tra ffi c routes around an airport requires a large dataset of flight trajectories and is typically performed using density–based clustering algorithms [6, 7] to automatically extract main air tra ffi c flows from a sample of flight track data in the region of interest. In this context, a flow can be defined as a pattern in which 1) entities move along the similar paths / routes in a spatial dimension and 2) the movements starts / ends within the same time interval. Moreover, the identification of air tra ffi c flows from aircraft tracking data can be framed as a problem of discovering spatial and temporal trends in the collective movement of aircraft through space and time [8]. Aiming at e ffi cient noise simulations, this contribution proposes a framework for the probabilistic description of the air tra ffi c around a medium–size airport based on density–based flight trajectory clustering. Traditional clustering algorithms are very sensitive to values of input parameters, often producing very di ff erent partitioning of the data set even for slightly di ff erent parameter settings [9]. Therefore, we quantify the influence of the input hyper–parameters on the clustering performance using local and global sensitivity analysis. Thereafter, an optimal input parameter setting for trajectory clustering is used for deriving a probabilistic description of the air tra ffi c. Finally, aircraft noise simulations are performed and the results obtained using the probabilistic model are compared to the results obtained using the full flight trajectory dataset, where each flight trajectory is individually simulated. This work is structured as follows: the methodology used for this purpose is introduced in Section 2, which includes the description of the steps involved in the pre–processing of the flight trajectories, evaluation of the performance of the clustering algorithm, and the details of the probabilistic description of air tra ffi c based on the ECAC’s Doc. 29 method. Subsequently, Section 3 presents the results obtained after implementation of the methodology. Finally, the conclusions about the outcomes of this work are presented in Section 4.

2. METHODOLOGY

A schematic flow–chart of the methodology employed in this work is presented in Figure 1. Firstly, the ADS–B dataset of flight trajectories associated with flights approaching the Hannover– Langenhagen Airport (IATA code: HAJ), in Germany, is downloaded from the OpenSky Network [10]. Thereafter, the dataset is pre–processed to filter faulty data and enriched to include relevant information necessary for the aircraft noise simulations, as described in Section 2.1. Secondly, the processed dataset is later used for deriving a probabilistic model of the air tra ffi c around the HAJ airport. This involves the representation of air tra ffi c routes in the form of backbone– and side–tracks, which represents the mean flight path adopted by a swathe of flight movements and its corresponding lateral dispersion, respectively. The identification of flight routes from the ADS–B dataset of flight trajectories is done with the aid of a density–based clustering algorithm, which is introduced in Section 2.2. Further, the performance of the cluster algorithm is assessed by a sensitivity analysis, which is presented in Section 2.2. The knowledge about the sensitivity of the

parameters allows for an e ffi cient optimization of the hyper–parameters, which consequently leads to the least amount of outlier flight trajectories on the obtained clusters. A recursively optimized cluster algorithm is used to identify the most representative flight routes present in the ADS–B dataset and derive the probabilistic air tra ffi c model used for the noise simulations. This procedure is presented in Section 2.3. Finally, aircraft noise simulations based on the ECAC’s Doc. 29 best–practice method [4] are performed in the commercial software SoundPLAN 8.2. using 1) the full flight trajectory dataset, and 2) the probabilistic description of the air tra ffi c. Further description of the aircraft noise simulations setup and comparison of results are provided in Section 3.

Flight-trajectory dataset

Air traffic noise simulation

• LAT/LON projection to UTM x,y coordinates • Assignment of runway • Data export to FANOMOS format • Deletion of unwanted/insufficient data

• SoundPLAN 8.2 • ECAC Doc.29 - 3rd Ed.

Data-enrichment & processing

Radar approach

Probabilistic approach

Flight trajectory (discrete waypoints) • Aircraft type • Geo-location (LAT/LON) • Altitude • Ground speed • Operation timestamp

Noise contour maps

Flight-trajectory clustering

Probabilistic air traffic modelling

• Density based algorithm: OPTICS

• Creation of backbone and sub-tracks • Generation of traffic data per A/C

Figure 1. Schematic of the methodology employed in this work for 1) obtain and pre–process an ADS–B dataset of flight trajectories from the Opensky Network, 2) derive a probabilistic model of the air tra ffi c, and 3) conduct the aircraft noise simulations. The results obtained using the probabilistic model of the air tra ffi c are verified with respect to the noise contours obtained by the full–dataset.

2.1. Flight trajectory dataset acquisition and pre–processing The ADS–B trajectory data used in this work was extracted from the OpenSky Network’s [10] historical database using the traffic Python library [11]. The ADS–B data is provided in a tabular form with each row describing the discrete temporal points of a particular flight trajectory throughout the course of the flight. The parameters in each column refer to the geographical location of the aircraft (latitude, longitude, altitude), its motion (ground speed, true track angle and vertical rate) as well as some meta data such as the aircraft type, flight–id, call–sign, origin and destination airport. After collecting the ADS–B data, the next step involves pre–processing the dataset and enriching it by assigning a runway to the respective flight operations, which is an information required for the noise simulations. The data pre–process includes the following steps:

– filtering: to ensure that the flight trajectories intersect and operate to / from the HAJ airport;

– cleaning: identifying and removing duplicate, erroneous or incomplete data (e.g. insu ffi cient data containing ’NaN’ values);

– projection: each LAT and LON pair is projected onto a Universal Transverse Mercator (UTM) coordinate system to generate Cartesian coordinates for spatial trajectory clustering;

– runway assignment: flight tracks are assigned to respective runways based on intersection with runway bounds;

– unwrapping: track angles and headings are unwrapped to avoid gaps between 359 ◦ and 1 ◦ ; and

– re–sampling: all flight trajectories are re–sampled to a time resolution of 4 seconds.

2.2. Density–based clustering performance evaluation The Ordering Points To identify Clustering Structure (OPTICS) [9] is selected as the algorithm to perform flight trajectory clustering in this work due to its versatility, ease of implementation and better memory scaling for large datasets. In the context of flight trajectories, a flight falls into a given cluster if its trajectory points are density–reachable from that cluster’s core points. This implies that within each cluster, the density of points is significantly higher than outside. The OPTICS clustering algorithm provided in the machine–learning library scikit-learn [12] is used by the traffic library. The use of the OPTICS algorithm requires the tuning of the following four hyper–parameters [12]:

– xi : minimum steepness on the reachability plot that constitutes a cluster boundary;

– minS amps : minimum number of points (trajectories) in the neighborhood to be a part of the cluster;

– minClustS ize : minimum number of points (trajectories) to be a part of a cluster; and

– ǫ : maximum search radius (distance) from a core point.

A sensitivity based approach is used to study the influence of these parameters on the clustering performance.

2.2.1. Clustering performance evaluation metric

In order to evaluate the performance of a clustering algorithm, an evaluation metric is required, which checks for the separation of data similar to some ground truth set such that the members belonging to the same class are more similar than members of di ff erent classes [12]. The aim of clustering is to organize the dataset into di ff erent groups where the within–group–data similarity is maximized, and the between–group data similarity is minimized [13]. If the ground truth labels are not known, the Davies–Bouldin (DB) index can be used to evaluate the model. This index signifies the average similarity between clusters, where the similarity is a measure that compares the distance between clusters with the size of the clusters themselves. Zero is the lowest possible score. Values closer to zero indicates a better separation between the clusters [14]. Mathematically, the DB–index is computed as,

n c X

DB = 1

j = 1 R j , (1)

n c

where

 D intra j + D intra k D inter jk

 , D inter jk = C j − C k , and D intra j = 1

X

R j = max k , j

tr i ∈ C j tr i − C j , (2)

C j

being tr i an arbitrary flight trajectory, C j and C k the center of j th and k th cluster, respectively, and the total number of clusters given by n c . D intra j and D inter jk denote the intra–class and inter–class distance respectively [15].

2.2.2. Sensitivity analysis of the input parameters

Sensitivity analysis is commonly used to derive diagnostic insight from models by identifying the input factors controlling the model performance. Most common applications of sensitivity analysis include; factor fixing, in which the values of insensitive inputs are fixed to simplify further analysis; and factor ranking, in which the most sensitive input parameters are identified [16,17]. In this work, we aim to analyze the ranking of sensitive model parameters (i.e. both those that are sensitive and insensitive) as well as to quantitatively compare their sensitivities. This is done by evaluating the clustering performance by sampling in the uncertain parameter space with di ff erent sets of parameter values one–at–a–time (OAT) or together. Sensitivity methods are broadly divided into local methods and global methods. Whereas, local methods provide measures of importance around a single point in the parameter space, global methods aims at reflecting the importance of a parameter throughout the full multivariate space of a model [16]. In order to ascertain the sensitivity of the input parameters of the OPTICS algorithm, we used a local (also referred as OAT) approach called the method of Morris [18] and a global method called as Sobol’ sensitivity analysis [19,20].

Local sensitivity analysis: the method of Morris [18] derives measures of sensitivity from a set of local derivatives, or elementary e ff ects sampled on a grid throughout the parameter space. It is based on a local approach, in which each input parameter of interest x i is perturbed along a grid of size δ i to create a trajectory through the parameter space. Each trajectory yields one estimate of the elementary e ff ect for each parameter (i.e. the ratio of the change in model output to the change in that parameter). As it is a local approach, it does not account for the interaction between the parameters. This method can estimate the sensitivity of parameters by considering both the mean and variance of elementary e ff ects. Campolongo et al. [21] proposed an improvement in which an estimate of sensitivity of the i th parameter, µ ∗ i is computed from the mean of the absolute values of the elementary e ff ects over the set of N trajectories. This relationship is given by,

N X

j = 1 | EE j i | , where EE i = f ( x 1 , ...., x i + δ i , ....., x p ) − f ( x )

µ ∗ i = 1

δ i , (3)

N

being EE i the single elementary e ff ect for the i th parameter while f ( x ) represents the prior sample point in the trajectory [16].

Global sensitivity analysis: the Sobol’ sensitivity analysis [19, 20] is a global, variance–based method that attributes variance in the model output to individual parameters and the interactions between parameters. The attribution of the total output variance to individual model parameters and their interactions is given by

D ( h ) = X

i D i + X

i < j D i j + X

i < j < k D i jk + D 12 ... p , (4)

where D ( h ) represents the total variance of the output metric h , D i is the first–order variance contribution of the i th parameter, D i j is the second–order contribution between the parameters i and j , and D 12 ... p contains all interactions higher than third–order up to p total parameters. The first–order and total–order sensitivity indices are defined as,

D , total–order index: S T i = 1 − D i

first–order index: S i = D i

D . (5)

The first–order index measures the fraction of the total output variance caused by the parameter i apart from interactions with other parameters.

2.3. Probabilistic air tra ffi c modelling As defined in the ECAC’s Doc. 29 [4], the probabilistic approach for aircraft noise simulations involves the representation of air tra ffi c routes in the form of backbone–tracks, which forms the center of a swathe of flight movements operating in a particular flight route and several side–tracks. Additionally, the lateral dispersion of the flight movements around a backbone–track is modeled using side–tracks. In this work, we explore the use of the clustering technique for deriving an probabilistic representation of the air tra ffi c based on ADS–B flight trajectory data. The clustered flight trajectories data is used to define the backbone– and side–tracks of a particular flight route and the boundaries of the flight track swathe. The distribution of the movements across the swathe is then described by a symmetric Gaussian distribution function. A backbone–track is a form of simplification of multiple radar tracks in order to keep the data preparation and computational e ff ort within reasonable bounds. Finally, the simulated aircraft noise levels are computed based on the backbone– and side–tracks, which represents the flight movements occurring on a particular flight route in a probabilistic manner. [4].

2.4. Air tra ffi c noise simulation The commercial software SoundPLAN 8.2 [22] is used in this work for the air tra ffi c noise simulations. The software supports di ff erent simulation methods including the ECAC’s 3rd Edition Doc. 29 [4], which is used in this work. Furthermore, SoundPLAN has the capability to import and use radar data as input for the simulations. A template with the setup of the HAJ airport is provided by the SoundPLAN demo kit. It includes the Digital Ground Model (DGM), runway coordinates, elevation points, and the reference environmental data. Two simulations are conducted: one considering full ADS–B dataset of flight trajectories (i.e. each flight trajectory is individually described by the ADS-B data), and another considering a probabilistic description of the air tra ffi c using backbone– and side-tracks obtained from the cluster analysis. For simulations considering the full ADS–B dataset of flight trajectories, the ADS–B flight trajectory dataset is loaded after post–processing and transformed into the FANOMOS data format, which is one of the radar data formats readable by SoundPLAN. In our work, standardized flight profiles and operational conditions from the SoundPLAN database are used for each aircraft type instead of the actual flight profiles on the radar / ADS–B input data. For the simulations considering the probabilistic model, the backbone tracks matching each cluster’s centroid tracks are created by specifying the ground track data, runway information and the corresponding air tra ffi c information data (i.e. number of movements per aircraft type).

3. IMPLEMENTATION AND RESULTS

3.1. Description of the dataset and pre–processing For this work, all flight movements landing at the HAJ airport between 1 May 2019 and 31 October 2019 were requested via the traffic Python library. For this purpose, a bounding box with a latitude and longitude within 32 nautical miles (60 km) of the HAJ airport reference coordinate point was used. It is crucial to pre–process the data downloaded from OpenSky network, as it often contains faulty / incomplete data. Therefore, after filtering out the erroneous flight trajectories with invalid information and selecting only the flights landing in Hannover airport, a dataset with 640 flight trajectories out of a total of 11500 downloaded flight movements were used for the trajectory clustering study (see Figure 2a). The final dataset used in this work for the spatial trajectory cluster is described in Figure 2b in terms of numbers of movements per aircraft type. Furthermore, this dataset contains 472 flights occurring during the day–time period and 168 flights landing at the night–time period.

200 193

150

122 115

Count

100

68

51

50

37 31 12 11

0

A320 B738 A319 A321 E190 E75L C560 E195 others

(a)

(b)

Figure 2. Description of the ADS–B flight trajectory dataset considered in this work for the spatial cluster trajectory: (a) flight trajectory dataset visualization, and (b) number of flight movements per aircraft type.

3.2. Flight trajectory clustering and performance evaluation The OPTICS algorithm [9] is used to extract clusters using the calculated reachability and ordering technique called as the “xi–method”. In this case, ǫ assumes a default value of infinity, which means that it will identify clusters across all scales. In the first step, the influence of three selected input parameters of the OPTICS clustering algorithm, namely minSamps , xi and minClustSize on the DB– index are studied by the method of Morris. The input parameters are perturbed ± 10% from the default value based on previous experience and preliminary tests. The parameter bounds for minSamps , xi and minClustSize are [0 . 03 , 0 . 15] , [0 . 05 , 0 . 1] , [0 . 01 , 0 . 25] respectively. The mean and standard deviation of the elementary e ff ects for each parameter is computed over N = 25 trajectories. The result of the Morris test is presented in Figure 3. The absolute of the mean elementary e ff ect µ ∗ i on the x–axis is plotted against the standard deviation of elementary e ff ect on the y–axis for each parameter. From the plot, it is observed that the minClustSize and minSamps parameters have the greatest influence on the output, as it lies farther away from the origin. As the method of Morris calculates only the local e ff ects of the input parameters on the output, a global approach of sensitivity is required to quantify the global e ff ects of parameters and higher order interaction e ff ects.

4

3 . 5

std(EE)

3

minS amps

xi minClustS ize

2 . 5

1 2 3 4

mean( | EE | )

Figure 3. Local sensitivity analysis of the OPTICS algorithm input parameters using the Morris test.

The variance–based global approach is applied to the selected input parameters of the clustering algorithm. The parameter bounds for minSamps , xi and minClustSize are kept the same as the ones used in the local sensitivity analysis. In order to achieve an accurate approximation of the variances, the parameter space is explored using the Saltelli sampler [20]. The Saltelli sampler generates N × (2p + 2) samples, where N is 256 (the argument defined) and p is 3 (number of selected input parameters) resulting in a total of 2048 samples. The results of the Sobol’ sensitivity analysis with the first–order and second–order sensitivity indices are presented in Figure 4. It is observed that the first– order of the sensitivity indices of the minClustSize and minSamps parameters are 0 . 434 and 0 . 174, respectively. Moreover, it is possible to verify in the heatmap for second-order sensitivity indices shown in Figure 4b, that the minSamps and xi parameters have the highest interaction e ff ects.

minS amps xi minClustS ize

0 . 4

0 . 15

0.17 0.095

0 . 1

0.17 0.0079

S1

0 . 2

5 · 10 − 2

0.095 0.0079

minS amps xi minClustS ize 0

minS amps xi minClustS ize

(a)

(b)

Figure 4. Quantitative sensitivity assessment of the OPTICS algorithm input parameters using a Sobol sensitivity analysis: (a) first–order Sobol indices and (b) second–order sobol indices.

3.3. Optimized clustering results The final dataset used for clustering is composed by 640 landing flight–trajectories. The HAJ airport is composed of two main parallel runways with east-west bearing. From visual analysis of the flight trajectories (see Figure 2a), it is ascertained that, for the considered dataset, most of the flights approach the HAJ airport from the east and land on the runways 27L and 27R. Most of the flight–trajectories follow the standard instrument arrivals (STAR) with the aid of navigational beacons, which are represented by black triangular markers. The knowledge about the sensitivity of the input parameters of the OPTICS algorithm (see Section 3.2) enables us to reduce the dimensionality of the problem and focus on optimally tuning the hyper– parameters which have the greatest influence on the clustering performance of the OPTICS algorithm. The hyper–parameters are selected such that the algorithm can bundle similar trajectories together but still is specific enough to separate distinct trajectories [23]. From the results of the sensitivity studies, the value of xi = 0 . 072 is fixed and the best clustering model is selected by recursively varying the values of minClustSize and minSamps until a pre–defined threshold for the outlier coe ffi cient is reached. An optimum solution was reached with minS amps = 0 . 056 and minClustS ize = 0 . 089 with a DB–Index = 5 . 786 and lowest outlier coe ffi cient of 0 . 092. The outliers represent the trajectories which are anomalous or pattern flights. This may happen when a landing attempt has been aborted (also called as “go–around”) due to unstable approach or adverse weather conditions. Hence, the clustering algorithm is also able to identify such trajectory patterns and filter them out of the landing dataset. Using this approach, a total of four trajectory clusters were obtained from the prevailing inbound flights, as shown in Figure 5a. The distribution of flight trajectories among the clusters is summarized in Table 1. The centroid trajectory in each cluster which is the closest to all other trajectories are

indicated in red colored tracks. A qualitative assessment of the clustering solution shows that the main tra ffi c flows around the airport have been properly identified and it can be used for modelling backbone– and side– tracks. For this purpose, a centroid track from each of clustered flight tracks (see Figure 5b) is used to model a backbone–track. Moreover, the lateral–track dispersion for each cluster is modelled by considering the boundaries of the radar track swathe (99 percentile tracks), on the assumption that the spread of tracks perpendicular to the backbone track follows a Gaussian normal distribution according to the modelling approach defined in the Doc. 29. The final probabilistic description of the air tra ffi c routes used for the aircraft noise simulations is shown in Figure 5b.

(a)

(b)

Figure 5. Cluster–based probabilistic air tra ffi c modelling: (a) results of trajectory clustering using the OPTICS algorithm where the cluster centroids are shown in red and the remaining colours represent distinct clusters, and (b) corresponding probabilistic description of the air tra ffi c routes used for aircraft noise simulations (not to scale with Figure 5b).

Table 1. Summary of the obtained clusters and their respective distribution of flight trajectories.

Year=2019, Landing clusters, N=4 Total flight paths = 640, clustered = 581 52.7°N 52.6°N 52.5°N 52.4°N 52.3°N 52.2°N

# Trajectories Runway Proportion of data

Cluster 1 (green) 168 27L 26.3%

Cluster 2 (blue) 63 27L 9.8%

Cluster 3 (yellow) 228 27L 35%

Cluster 4 (black) 122 27R 19%

Outliers 59 – 9.2%

3.4. Comparison of full radar track and backbone track approaches A calculation area of 32 . 5 km × 8 . 8 km is defined around the HAJ airport and the simulations are computed considering a receiver grid with spatial resolution of 50 m and at 4 m above the ground level. In this work, we focus on the A–weighted equivalent sound pressure level, L p , A , eq , Day , which quantifies the averaged sound pressure level caused by multiple fight operations over the time–period

between 06 AM and 10 PM of each day in consideration. Therefore, the measurement time–period for both radar and backbone simulations is set to be 118 days as the number of days with zero flight operations on our dataset are not considered. The noise contour results obtained from both full radar tracks and backbone tracks simulation are hereafter evaluated in terms of accuracy and computational time. Concerning the latter, the simulation time for full radar track approach is around 28 minutes, whereas, for the probabilistic backbone approach is about 9 minutes. There is an overall reduction in simulation time of 67% using the probabilistic backbone approach. As of accuracy, Figure 6 presents a comparison between the results of the noise simulation from both approaches in the form of noise contours (see Figure 6a) and isocontour area di ff erence (see Figure 6b). The results of the noise contours are presented in terms of absolute L p , A , eq , Day levels ranging between 30 dBA – 60 dBA with 10 dBA intervals. Furthermore, in order to compare the results obtained from the backbone approach with the full radar approach, the results in Figure 6a are expressed in terms ∆ L p , A , eq , Day , which is defined as

∆ L p , A , eq , Day = L p , A , eq , Day , Backbone − L p , A , eq , Radar . (6)

4

20

3000

Isocontour area di ff erence [km 2 ]

∆ L p,A,eq,Day [dBA Ref.: 20 µ Pa]

2000

30 30 30 30

3

30

10

40 40

50

50

40

40

30 30

30

1000

30

y [m]

30

2

0

40 40

40

50 50 50

30

40

50

0

40 40 40

30

30 30

− 10

1

∆ L p,A,eq,Day L p,A,eq,Day -Radar L p,A,eq,Day -Backbone

− 1000

− 20

− 1000 0 1000 2000 3000 4000 5000 − 2000

30 40 50 0

L p,A,eq,Day [dBA Ref.: 20 µ Pa]

x [m]

(a)

(b)

Figure 6. Comparison of noise contour results obtained between the full radar track approach and the probabilistic backbone approach: (a) absolute L p , A , eq , Day values (solid and dashed black lines) and ∆ L p , A , eq , Day values (colour), and (b) isocontour area di ff erence.

A qualitative comparison of the noise contours presented in Figure 6a shows that the results from the backbone approach slightly overestimates the values throughout the grid. The di ff erence between the noise contours is noticeably high towards the end of runway 27L, which could be due to some incorrect assumptions of landing roll distance or spurious flight trajectories. Owing to the relatively small number of flight trajectories in the dataset considered in this work, the overall noise levels observed is relatively low for the considered time–period of 118 days. A maximum noise level of 60 . 3 dBA is predicted in an area which is very small and close to the runway. An improvement in the accuracy of noise prediction is expected by increasing the size of the dataset and also considering departure flight trajectories in the modelling process. Moreover, the di ff erence of isocontour areas are observed to be below 1 km 2 for relevant L p , A , eq , Day levels of 40 dBA and 50 dBA. The isocontour area di ff erence is computed using the same di ff erence relationship adopted by Equation (6).

4. CONCLUSIONS

In this contribution, we propose a cluster–based probabilistic approach to model air tra ffi c flows in the context of best–practice aircraft noise simulations. The approach is demonstrated using an ADS–

B dataset containing flights landing at the HAJ airport between the months of May and October of 2019. The methodology describes the di ff erent steps required to access and post–process the open– source ADS–B flight trajectories for clustering and aircraft noise simulation purposes. Then, the density–based clustering algorithm OPTICS is used to identify and group all major air–tra ffi c flows around the airport in order to provide a probabilistic description of the air tra ffi c to the aircraft noise simulations. The performance of the OPTICS clustering algorithm is quantitatively evaluated and its capabilities to group flight trajectories is e ff ectively demonstrated in this work. For this purpose, a quantitative sensitivity based approach was used to identify and optimally adjust the most important input hyper– parameters of the density–based clustering algorithm rather than selected using a heuristic approach. Finally, the verification of the proposed approach is done by comparison with noise simulations results obtained using the entire full dataset of flight trajectories. A majority of flight trajectories, which were extracted from the database were found to have considerable missing information, in terms of trajectory points, duplicate and erroneous data. As a result, the clustering performance and the accuracy of prediction of noise using backbone tracks were restricted. Nevertheless, the results of the noise simulation presented in this preliminary study showed the plausibility of using a flight trajectory clustering approach to perform best–practice aircraft noise simulations based on a probabilistic description of the air tra ffi c. The accuracy of the noise contours with backbone– and side– tracks is shown to be comparable with the full radar model, along with a substantial reduction in computational time. Future works needs to be conducted using a bigger dataset to enable a more robust implementation of this approach. The choice of the method to use depends on the volume of trajectories to be processed and the desired accuracy.

ACKNOWLEDGEMENTS

We gratefully acknowledge the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2163 / 1—Sustainable and Energy E ffi cient Aviation—Project-ID 390881007. Furthermore, the granted permission to access, download and use ADS–B data from the Opensky’s network for research purposes is highly appreciated.

REFERENCES

[1] Samantha J. Corrado, Tejas G. Puranik, Oliva J. Pinon, and Dimitri N. Mavris. Trajectory clustering within the terminal airspace utilizing a weighted distance function. Proceedings , 59(1), 2020. [2] Jorge Silvestre, Miguel de Santiago, Anibal Bregon, Miguel A. Martínez-Prieto, and Pedro C. Álvarez Esteban. On the use of deep neural networks to improve flights estimated time of arrival predictions. Engineering Proceedings , 13(1), 2021. [3] Junzi Sun and Irene Dedoussi. Evaluation of aviation emissions and environmental costs in europe using opensky and openap. Engineering Proceedings , 13(1), 2021. [4] European Civil Aviation Conference (ECAC). Methodology for Computing Noise Contours around Civil Airports . ECAC.CEAC Doc 29, 3rd edition, 2005. [5] Sarah Fauziah Maulydiana. Probabilistic approach in flight trajectory modeling for fast and e ffi cient noise contour generation . PhD thesis, Hong Kong University of Science and Technology, 2019. [6] Xavier Olive and Jérôme Morio. Trajectory clustering of air tra ffi c flows around airports. Aerospace Science and Technology , 84:776–781, 2019. [7] Samantha J. Corrado, Tejas G. Puranik, Olivia Pinon Fischer, and Dimitri N. Mavris. A clustering-based quantitative analysis of the interdependent relationship between spatial and

energy anomalies in ads-b trajectory data. Transportation Research Part C: Emerging Technologies , 131:103331, 2021. [8] Mayara Condé Rocha Murça, R. John Hansman, Lishuai Li, and Pan Ren. Flight trajectory data analytics for characterization of air tra ffi c flows: A comparative analysis of terminal area operations between New York, Hong Kong and Sao Paulo. Transportation Research Part C: Emerging Technologies , 97:324–347, 2018. [9] Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel, and Jörg Sander. OPTICS: Ordering points to identify the clustering structure. SIGMOD Rec. , 28(2):49–60, jun 1999. [10] Matthias Schäfer, Martin Strohmeier, Vincent Lenders, Ivan Martinovic, and Matthias Wilhelm. Bringing Up OpenSky: A Large-scale ADS-B Sensor Network for Research. In Proceedings of the 13th IEEE / ACM International Symposium on Information Processing in Sensor Networks (IPSN), ICRAT, Berlin, Germany , 2014. [11] Xavier Olive and Luis Basora. A python toolbox for processing air tra ffi c data: A use case with trajectory clustering. In Christina Pöpper and Martin Strohmeier, editors, Proceedings of the 7th OpenSky Workshop 2019 , volume 67 of EPiC Series in Computing , pages 73–84. EasyChair, 2019. [12] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research , 12:2825–2830, 2011. [13] T. Warren Liao. Clustering of time series data—a survey. Pattern Recognition , 38(11):1857– 1874, 2005. [14] David L. Davies and Donald W. Bouldin. A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence , PAMI-1(2):224–227, 1979. [15] Zihan Peng, Junfeng Zhang, Xuhao Gui, and Rong Hu. Trajectory clustering of inbound aircraft based on feature representation and selection. In ICRAT , 08 2020. [16] J. D. Herman, J. B. Kollat, P. M. Reed, and T. Wagener. Technical Note: Method of Morris e ff ectively reduces the computational demands of global sensitivity analysis for distributed watershed models. Hydrology and Earth System Sciences , 17(7):2893–2903, 2013. [17] Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, and Tarantola S. Global Sensitivity Analysis: The Primer . Wiley, Chichester (England), 2008. [18] Max D. Morris. Factorial sampling plans for preliminary computational experiments. Technometrics , 33(2):161–174, 1991. [19] I.M Sobol ′ . Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation , 55(1):271–280, 2001. The Second IMACS Seminar on Monte Carlo Methods. [20] Andrea Saltelli. Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications , 145(2):280–297, 2002. [21] Francesca Campolongo, Jessica Cariboni, and Andrea Saltelli. An e ff ective screening design for sensitivity analysis of large models. Environmental Modelling & Software , 22(10):1509–1518, 2007. Modelling, computer-assisted simulations, and mapping of dangerous phenomena for hazard assessment. [22] SoundPLAN GmbH / SoundPLAN International LLC. SoundPLAN User’s manual , soundplan 8.1 edition, 2019. [23] Sasha Madar, Tejas G. Puranik, and Dimitri N. Mavris. Application of Trajectory Clustering for Aircraft Conflict Detection. In 2021 IEEE / AIAA 40th Digital Avionics Systems Conference (DASC) , pages 1–9, 2021.