# Traffic Network Identification Using Trajectory Intersection Clustering

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Status Quo

## 3. Materials and Methods

#### 3.1. Clustering Algorithm DBSCAN

#### 3.2. Pathfinding Algorithm ${A}^{*}$

#### 3.3. General Approach

#### 3.3.1. Pre-Processing

#### 3.3.2. Main-Flow Processing

#### 3.3.3. Calculation of Flight Parameters

## 4. Experimental Setup

#### 4.1. Assumptions and Limitations

#### 4.2. Assessment Metrics

#### 4.2.1. Trajectory Distance

#### 4.2.2. Structural Complexity of the Network

- Dominant flows intersected by less frequented other flows.
- Traffic from various directions with similar intensity.
- Broad variability in usage of intersection points.

#### 4.2.3. ${A}^{*}$ Algorithm with Structural Complexity

#### 4.3. Scenario Description and Simulation Parameters

#### 4.4. Simulation Parameters

## 5. Results

#### 5.1. Computational Efficiency

_{adv}. Step D includes the point-balancing functionality which as well works on each identified cluster element.

^{®}Xeon

^{®}E5-2186G 3.8 GHz processor (6 cores), 64 GB Ram, and Windows 10 as operating system was used. The algorithms were implemented in Java.

#### 5.2. Main-Flow Network

#### 5.3. Flight Parameters

#### 5.4. Adapted Cost Function ${A}_{adv}^{*}$

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Schultz, M.; Olive, X.; Rosenow, J.; Fricke, H.; Alam, S. Analysis of airport ground operations based on ADS-B data. In Proceedings of the 2020 International Conference on Artificial Intelligence and Data Analytics for Air Transportation (AIDA-AT), Singapore, 3–4 February 2020. [Google Scholar] [CrossRef]
- Gariel, M.; Srivastava, A.N.; Feron, E. Trajectory Clustering and an Application to Airspace Monitoring. IEEE Trans. Intell. Transp. Syst.
**2011**, 12, 1511–1524. [Google Scholar] [CrossRef] [Green Version] - Gerdes, I.; Temme, A.; Schultz, M. From free-route air traffic to an adapted dynamic main-flow system. Transp. Res. Part C Emerg. Technol.
**2020**, 115, 102633. [Google Scholar] [CrossRef] - Yuan, G.; Sun, P.; Zhao, J.; Li, D.; Wang, C. A review of moving object trajectory clustering algorithms. Artif. Intell. Rev.
**2016**, 47, 123–144. [Google Scholar] [CrossRef] - Basora, L.; Morio, J.; Mailhot, C. A Trajectory Clustering Framework to Analyse Air Traffic Flows. In Proceedings of the 7th Sesar Innovation Days, Belgrade, Serbia, 28–30 November 2017. [Google Scholar]
- Delahaye, D.; Puechmorel, S.; Alam, S.; Feron, E. Trajectory Mathematical Distance Applied to Airspace Major Flows Extraction. In Lecture Notes in Electrical Engineering, Air Traffic Management and Systems III; Springer: Cham, Switzerland, 2018; pp. 51–66. [Google Scholar]
- Marzuoli, A.; Gariel, M.; Vela, A.; Feron, E. Data-Based Modeling and Optimization of En Route Traffic. J. Guid. Control. Dyn.
**2014**, 37, 1930–1945. [Google Scholar] [CrossRef] - Olive, X.; Morio, J. Trajectory clustering of air traffic flows around airports. Aerosp. Sci. Technol.
**2018**, 84, 776–781. [Google Scholar] [CrossRef] [Green Version] - Lee, J.-G.; Han, J.; Whang, K.-Y. Trajectory clustering: A partition-and-group framework. In Proceedings of the SIGMOD’07, Beijing, China, 11–14 June 2007. [Google Scholar] [CrossRef]
- Besse, P.C.; Guillouet, B.; Loubes, J.-M.; Royer, F. Review and Perspective for Distance-Based Clustering of Vehicle Trajectories. IEEE Trans. Intell. Transp. Syst.
**2016**, 17, 3306–3317. [Google Scholar] [CrossRef] [Green Version] - Vlachos, M.; Kollios, G.; Gunopulos, D. Discovering Similar Multidimensional Trajectories. In Proceedings of the 18th International Conference on Data Engineering, San Jose, CA, USA, 26 February–1 March 2002. [Google Scholar] [CrossRef]
- Aggarwal, C.C.; Reddy, C.K. (Eds.) Data Clustering: Algorithms and Applications. In Data Mining and Knowledge Discovery; CRC Press: Boca Raton, FL, USA; Taylor & Francis Inc.: Oxfordshire, UK, 2014; Volume 31, ISBN 978-1466558212. [Google Scholar]
- Mc Innes, L.; Healy, J. Accelerated Hierarchical Density Clustering. In Proceedings of the IEEE International Conference on Data Mining Workshops (ICDMW), New Orleans, LA, USA, 18–21 November 2017. [Google Scholar] [CrossRef] [Green Version]
- Mirkin, B. Mathematical Classification and Clustering; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; ISBN 978-1-4613-0457-9. [Google Scholar]
- Ester, M.; Kriegel, H.-P.; Sander, J.; Xu, X. A Density-Based Algorithm for Discovering Clusters. In Proceedings of the KDD-96, Portland, OR, USA, 2–4 August 1996. [Google Scholar]
- Von Luxburg, U. A tutorial on spectral clustering. Stat. Comput.
**2007**, 17, 395–416. [Google Scholar] [CrossRef] - Ankerst, M.; Breunig, M.; Kriegel, H.-P.; Sander, J. OPTICS: Ordering points to identify the clustering structure. In Proceedings of the ACM SIGMOD International Conference on Management of Data, Philadelphia, PA, USA, 1–3 June 1999. [Google Scholar] [CrossRef]
- Hart, P.E.; Nilsson, N.J.; Raphael, B. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Trans. Syst. Sci. Cybern.
**1968**, 4, 100–107. [Google Scholar] [CrossRef] - Sheridan, K.; Puranik, T.; Mangortey, E.; Pinon, O.; Kirby, M.; Mavris, D. An Application of DBSCAN Clustering for Flight Anomaly Detection during the Approach Phase. In Proceedings of the AIAA Scitech 2020 Forum, Orlando, FL, USA, 6–10 January 2020. [Google Scholar] [CrossRef]
- ICAO. Annex 2 to the Convention on International Civil Aviation. Rules of the Air. ICAO, 10th ed.; ICAO: Montreal, QC, Canada, 2005. [Google Scholar]
- Athènes, S.; Averty, P.; Puechmorel, S.; Delahaye, D.; Collet, C. ATC complexity and controller workload: Trying to bridge the gap. In Proceedings of the International Conference on HCI in Aeronautics, Cambridge, MA, USA, 23–25 October 2002. [Google Scholar]
- Prandini, M.; Piroddi, L.; Puechmorel, S.; Brazdilova, S.L. Toward Air Traffic Complexity Assessment in New Generation Air Traffic Management Systems. IEEE Trans. Intell. Transp. Syst.
**2011**, 12, 809–818. [Google Scholar] [CrossRef] - EUROCONTROL. Complexity Metrics for ANSP Benchmarking Analysis; ACE Working Group on Complexity: EUROCONTROL: Brussels, Belgium, 2006. [Google Scholar]
- Gianazza, D. Airspace configuration using air traffic complexity metrics. In Proceedings of the 7th USA/Europe Air Traffic Management R&D Seminar, Barcelona, Spain, 2–5 July 2007. [Google Scholar]
- EUROCONTROL. DDR2 Reference Manual 2.9.5; EUROCONTROL: Brussels, Belgium, 2018. [Google Scholar]

**Figure 1.**(

**a**) Intersection points (green circles) of a trajectory (blue line) and its intersecting trajectories (red lines); (

**b**) Resulting CP trajectory (blue line) with aggregated common points (yellow circles).

**Figure 4.**Common points of original trajectory (small circles) of a trajectory (black line) and centers (larger circles) in assigned colors (

**left**), CP trajectory after step B as sequence of cluster centers a-b-d-e-b-c in purple (

**right**).

**Figure 6.**Calculation of Segment-Path distance for points of trajectory $G$ to segments of trajectory $T$. $minDis\left({G}_{i},T\right)$ denotes the minimal distance of point ${G}_{i}$ to trajectory $T$.

**Figure 7.**Definition of similar (green), other (red) and opposite (yellow) direction between flights.

**Figure 8.**Example for the combination of link sequences $\overline{ab}\mathrm{and}\overline{cb}$ with $w\left(\measuredangle \left(c,b\right)\right),w\left(\measuredangle \left(b,b\right)\right)=1$, $w\left(\measuredangle \left(a,b\right)\right),w\left(\measuredangle \left(a,c\right)\right)=10$ and $cf\left(\overline{ab},\overline{cb}\right)=5.5$.

**Figure 9.**German airspace boundary (

**a**) and EDYYDUTA (

**b**) with flown trajectories as turquoise lines. The darker the color the more flights use the corresponding part of the airspace.

**Figure 10.**Cluster elements (small dots) for Scenario 1 (

**a**) and 2 (

**b**) without noise. Each color marks a cluster.

**Figure 11.**Reduced main-flow system for Scenario 1 (

**a**) and Scenario 2 (

**b**). Line thickness reflects the number of flights using a link.

**Figure 13.**Example with as-flown trajectory (green) and reduced trajectory (blue) for Scenario 1 (

**a**, SSPD 5.7) and Scenario 2 (

**b**, SSPD 4.0).

**Figure 14.**Structural complexity for intersections (

**a**) and reduced main-flow network (

**b**) for Scenario 1.

**Figure 15.**Structural complexity for intersections (

**a**) and reduced main-flow network (

**b**) for Scenario 2.

**Figure 16.**Denominator tests for ${f}_{adv}$ with $infl\left({r}_{part}\right)=0$ (c) and denominator 10, 50, 100 (c10, c50, c100) for formula (9) for both scenarios.

Objects Clustered | Scenario | $\mathit{\epsilon}$ [NM] | $\mathit{m}\mathit{i}\mathit{n}\mathit{P}\mathit{t}\mathit{s}$ [# Points] |
---|---|---|---|

Common Points | 1 | 0.7 | 30 |

2 | 0.6 | 20 | |

Entry/Exit | 1 | 2.0 | 5 |

2 | 2.0 | 3 |

**Table 2.**Computation times in seconds for the process steps A to D (Section 3.3.1 and Section 3.3.2).

Scenario | Step A | Step B | Step C | Step C_{adv} | Step D | |
---|---|---|---|---|---|---|

1 | German Airspace [s] | 45 | 32 | 225 | 1040 | 2 |

2 | EDYYDUTA [s] | 2 | 2 | 7 | 136 | 1 |

Common Points | Cluster Centers | |||||
---|---|---|---|---|---|---|

Scenario | # Flights | Total | Different | Adapted | Reduced | Noise [%] |

1 | 4027 | 4,048,686 | 53,449 | 3698 | 1866 | 2.6 |

2 | 1183 | 310,704 | 23,897 | 1538 | 642 | 11.8 |

Scenario | Entry | Exit | Combined |
---|---|---|---|

1 | 54 | 55 | 25 |

2 | 36 | 45 | 7 |

Scenario | SSPD [NM] | Route Length Relative to Original Routes [%] | SC Intersections | SC Cluster Centers | Trajectories per Cluster Center [#] | |
---|---|---|---|---|---|---|

1 | Median | 0.8 | 100.2 | 7.1 | 2.9 | 48 |

1. Quartile | 0.2 | 99.9 | 5.6 | 1.8 | 25 | |

3. Quartile | 2.6 | 101.2 | 7.5 | 4.4 | 84 | |

2 | Median | 1.4 | 100.5 | 8.8 | 2.80 | 38 |

1. Quartile | 0.5 | 100. | 9.6 | 1.9 | 14 | |

3.Quartile | 2.9 | 101.5 | 11.7 | 4.3 | 58 |

**Table 6.**Average flight levels for each wake vortex class and semicircular cruising level direction.

Flight Level | Track 0–179° | Track 180–359° | ||||
---|---|---|---|---|---|---|

H | M | L | H | M | L | |

Scenario 1 | 356 | 351 | 350 | 364 | 358 | 355 |

Scenario 2 | 330 | 344 | 330 | 345 | 345 | 356 |

Speed | Track 0–179° | Track 180–359° | ||||
---|---|---|---|---|---|---|

H | M | L | H | M | L | |

Scenario 1 | 510 | 493 | 309 | 422 | 412 | 309 |

Scenario 2 | 506 | 483 | 370 | 428 | 418 | 327 |

Scenario | Route Length Relative to Original Routes [%] | SC of Cluster Centers | Number of Links | Length of Main-flow System | SSPD | Node Number per Trajectory |
---|---|---|---|---|---|---|

$1\mathrm{with}{A}^{*}$ | 100.5 | 2.9 | 4942 | 29,159 | 0.78 | 43 |

1 with ${A}_{adv}^{*}$ | 100.6 | 2.7 | 5329 | 31,641 | 0.78 | 43 |

2 with ${A}^{*}$ | 100.3 | 2.8 | 1780 | 10,089 | 1.35 | 36 |

2 with ${A}_{adv}^{*}$ | 101.4 | 2.6 | 2060 | 11,437 | 1.49 | 35 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gerdes, I.; Temme, A.
Traffic Network Identification Using Trajectory Intersection Clustering. *Aerospace* **2020**, *7*, 175.
https://doi.org/10.3390/aerospace7120175

**AMA Style**

Gerdes I, Temme A.
Traffic Network Identification Using Trajectory Intersection Clustering. *Aerospace*. 2020; 7(12):175.
https://doi.org/10.3390/aerospace7120175

**Chicago/Turabian Style**

Gerdes, Ingrid, and Annette Temme.
2020. "Traffic Network Identification Using Trajectory Intersection Clustering" *Aerospace* 7, no. 12: 175.
https://doi.org/10.3390/aerospace7120175