A Case Study of Non-linear Dynamics of Human-Flow Behavior in Terminal Airspace

Transcription

1 A Case Study of Non-linear Dynamics of Human-Flow Behavior in Terminal Airspace Lei Yang a,b, Suwan Yin a,b, Minghua Hu a,b, Yan Xu c a Nanjing University of Aeronautics and Astronautics b National Lab of Air Traffic Flow Management c Technical University of Catalonia The 12th USA/Europe ATM R&D Seminar June, 2017, Seattle

2 Air Traffic Operations Humanin-theloop Nonlinear Complex technosocial system Dynamic

3 Emergence in air traffic Emergence - through interactions of elements in complex system - Unpredictability ATCO-traffic flow interactions - tactical emergence Traffic flow situation Perception Control command Comprehension Prediction

4 ATCO-flow dynamics (1) Temporal-spatial phase transitions -- Analytical metrics for measuring ATCO-flow performance; -- Uncovering the representative co-evolution pattern of ATCO and traffic flow performance. (2) High-level system dynamics -- Chaotic dynamics identification in ATCO-flow system; -- Correlation between chaos and phase transition; -- Predictability of ATCO-flow behavior.

5 1 Empirical data 2 Phase transition of ATCO-flow at sector level 3 High-level Chaotic Dynamics in ATCO-flow system 4 Conclusions

6 Empirical data Updated flight plan Radar trajectory data Communication Data YIN ATAGA NOLON Sector1 IGONO P268 P4 GYA Sector2 N1 TAN N2 CON P5 P6 Sector5 FO CEN 佛山 POU P3 Sector4 P7 P8 Sector3 SHL P9 龙溪 LMN Duration of communication (second) P1 P2 N3 SAREX IDUMA 樟木头 Start time of communication (second) VIBOS P269 双水 P275 Conversion & Fusion & Synchronization Guangzhou terminal airspace operation on 15/05/2014, 11/09/2014 and 18/12/2014

7 Phase transition of ATCO-flow at sector level The phase is a property of an entire physical system, rather than of any of its particular components. Co-evolution of human-flow performance Metrics

8 Phase transition of ATCO-flow at sector level Modelling Flow-based metrics Flow rate ---The number of aircraft fly out of the sector during a time period. Average density --- Average number of aircraft in the sector during a time period. Average equivalent velocity = 1 ( ) Number of aircraft in sector S at Total snapshots in one time period --- Average effective speed of aircraft travelling inside the sector during a time period. Velocity Gain Coefficient (VGC) = 1 1 ( ) ( ) ( ) I Velocity scalar

9 Phase transition of ATCO-flow at sector level Modelling Flow-based metrics Velocity Gain Coefficient (VGC) VGC is the ratio of standard route length ı to actual travel distance in the sector. Standard route Flight trajectory I = ı (,

10 Phase transition of ATCO-flow at sector level Modelling ATCO-based metrics External (Communication) activities Internal (Cognition) complexity

11 Phase transition of ATCO-flow at sector level Modelling ATCO-based metrics Internal (Cognition) complexity Picture of traffic flow Picture of conflict situation Cognition complexity Difficulty of searching solution for potential conflicts Solution space of potential conflict is defined as the 2D area of continuous heading and speed combination space for conflict resolution.

12 Phase transition of ATCO-flow at sector level Modelling ATCO-based metrics Internal (Cognition) complexity Solution space adapted from (Pallottino et al., 2002; Hermes, et al., 2009) S / 2 A v A max v A min v A S / 2 A v A max v A min v A v B v AB L SS A B ( t) v AB v A v B F SS A B ( t) v B = +

13 Phase transition of ATCO-flow at sector level Modelling ATCO-based metrics Internal (Cognition) complexity = Λ( ( ) ( ) = 1 _ 1 min v A max v A σ=0.5 σ is a co-efficient to model the non-linear impact of solution space on cognition complexity and can be nicely calibrated by human-in-the-loop experiment.

14 Phase transition of ATCO-flow at sector level Modelling ATCO-based metrics External (Communication) activities Communication load here is defined as the percentage of air-ground communication channel occupancy in certain time period = ℶ Integrated output of human internal complexity and strategies

15 Phase transition of ATCO-flow at sector level Analysis Flow dynamics at sector level Average flow rate (aircraft/min) Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Critical density Average R 2 =0.922 Network congestion Speed reduction Headway increase Capability of controllers Stress status Unprecise command Average density (aircraft)

16 Phase transition of ATCO-flow at sector level Analysis Flow dynamics at sector level Average flow rate (aircraft/min) Sector 1 Sector 2 Sector 3 Sector 4 Sector Average density (aircraft)

17 Phase transition of ATCO-flow at sector level Analysis ATCO-flow phase transition Average communication load Average flow rate(aircraft/min) 1.2 Free Smooth Average density (aircraft) Average cognition complexity Average equivalent velocity (km/h) Average communication load Congested Free Smooth Average flow rate (aircraft/min) 1.2 Semistable Semistable Congested Average density (aircraft) Average cognition complexity Average equivalent velocity (km/h) Average communication load Average flow rate (aircraft/min) Free Smooth Semi-stable Average cognition complexity Average density (aircraft) Average equivalent velocity (km/h) Average communication load Average flow rate (aircraft/min) 1.2 Free Smooth Average cognition complexity Average equivalent velocity (km/h) Average communication load Average flow rate (aircraft/min) Free Smooth Semistable Congested Average cognition complexity Average equivalent velocity (km/h) Significantly correlated Average density (aircraft) Average density (aircraft)

18 Phase transition of ATCO-flow at sector level Analysis Free Phase ATCO-flow phase transition Low density Little conflict Short-cut: Unequal travel length Flow ATCO Average communication load Average flow rate(aircraft/min) Free Smooth Semistable Average density (aircraft) Congested 0.5 Average cognition complexity Average equivalent velocity (km/h) Less tasks Speed up operation Fast increase of Comm. Load Meta-cognition Dynamics-1: Pre-activation Distance to AGVOS (km) Free flow Time (Second)

19 Phase transition of ATCO-flow at sector level Analysis ATCO-flow phase transition Smooth Phase Conflicts emerge Speed reduction Standard procedure: Equal travel length Flow ATCO Average communication load Average flow rate(aircraft/min) Free Smooth Semistable Average density (aircraft) Congested 0.5 Average cognition complexity Average equivalent velocity (km/h) Smooth Complexity rises Mental resource reservation Slower increase of Comm. Load Meta-cognition dynamics-2: Inhibition Distance to AGVOS (km) Time (Second)

20 Phase transition of ATCO-flow at sector level Analysis ATCO-flow phase transition Semi-stable Phase Approach to the capacity More Conflicts Fix-based maneuvering Flow ATCO Average communication load Average flow rate(aircraft/min) Free Smooth Semistable Average density (aircraft) Congested 0.5 Average cognition complexity Average equivalent velocity (km/h) Semi-stable High Complexity Stabilize traffic picture Slow increase of Comm. Load Meta-cognition dynamics-2: Inhibition Distance to AGVOS (km) Time (seconds)

21 Phase transition of ATCO-flow at sector level Analysis ATCO-flow phase transition Congested Phase Severe conflicts Chaos and conditioned reflexes Reduced efficiency Safety priority Meta-cognition dynamics-3: Stressed Vectoring and holding Flow ATCO Sharp increase of Comm. Load Average communication load Distance to AGVOS (km) Average flow rate(aircraft/min) Free Smooth Semistable Average density (aircraft) Congested 0.5 Average cognition complexity Congested Average equivalent velocity (km/h) Time (seconds)

22 Phase transition of ATCO-flow at sector level Analysis Traffic situation Task demand Control strategy Meta-cognition of ATCO Self-evaluation of experienced workload Command Cognition complexity management

23 High-level Chaotic Dynamics in ATCO-flow system ATCO-flow system Chaotic system Complex interactions Non-linear Random factors Feedback loops Topological mixing Sensitive to initial states Hypothesis 1: air traffic system is a chaos system, and the chaotic phenomenon can be observed in both potential conflict ( flow level ) and communication ( ATCO level ) behavior. Hypothesis 2: Chaos is highly related to the phase state of ATCO-flow.

24 High-level Chaotic Dynamics in ATCO-flow system Method for chaos identification H = [ħ 1, ħ 2,, ħ ] ℷ M Time series-1: Length of communication interval Time series-2: Number of potential conflict L 0 L L > 0

25 High-level Chaotic Dynamics in ATCO-flow system Conflict chaos at terminal airspace level Conflict frequency (times/5min) 50 Conflict frequency Time Slice =5min Value of autocorrelation function Proportion of false nearest neighbor Evolutionary distance Delay Time (a) Embedded Dimension (b) The largest Lyapunov exponent λ =0193 > Number of phase point (c)

26 High-level Chaotic Dynamics in ATCO-flow system Conflict chaos at terminal airspace level Peak traffic volume (aircraft) peak traffic volume peak potential conflict the largest Lyapunov exponent Time slice Peak potential conflict (times) The largest Lyapunov exponent Chaos in air traffic might be caused by high-density traffic which result in intensive potential conflicts and create more random factors.

27 High-level Chaotic Dynamics in ATCO-flow system Chaos of ATCO-flow system at sector level Silence Period (second) Evolutionary distance Serial number Evolutionary distance Linear fit (a) Conflict frequency (times/5min) Evolutionary distance Time Slice (b) Average communication load Average flow rate (aircraft/min) 1.2 Free Smooth Semistable Congested Average density (aircraft) Sector Average cognition complexity Average equivalent velocity (km/h) Number of phase point ATCO (c) Number of phase point Flow (d)

28 High-level Chaotic Dynamics in ATCO-flow system Chaos of ATCO-flow system at sector level Average communication load Average flow rate (aircraft/min) Free Smooth Semi-stable Free Smooth Average density (aircraft) Average density (aircraft) Average cognition complexity 600 Sector 3 Sector 4 Average equivalent velocity (km/h) Average communication load Average flow rate (aircraft/min) Average cognition complexity Average equivalent velocity (km/h) Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Flow ATCO Flow ATCO Flow ATCO Flow ATCO Flow ATCO Delay time Embedded dimension The largest Lyapunov exponent

29 High-level Chaotic Dynamics in ATCO-flow system Predictability of chaotic ATCO-flow system The largest Lyapunov exponent based prediction (Wolf et al., 1985) Short term prediction = h( ) h( ) h( + ( 1) ) h( + ( 1) ) ħ = = ( ) ± ( )

30 High-level Chaotic Dynamics in ATCO-flow system Predictability of chaotic ATCO-flow system Prediction for potential conflict Potential conflict (times/5min) Predicted Original Potential conflict (times/5min) Rel. error = 4.3% Rel. error = 15.5% 0 Predicted Original Time Slice Chaotic prediction Time Slice Support vectoring machine (SVM) Training data: 200; prediction period: 15min

31 High-level Chaotic Dynamics in ATCO-flow system Predictability of chaotic ATCO-flow system Prediction for communication interval Communication interval (second) Rel. error = 6.3% Rel. error = 20.9% Serial number Chaotic prediction Original Predicted Communication interval (second) Original Predicted Serial number Support vectoring machine (SVM) Training data: 1000; Prediction period: 10 data point

32 High-level Chaotic Dynamics in ATCO-flow system Predictability of chaotic ATCO-flow system Average relative error of potential conflict prediction Size of training data for communication interval prediction Chaotic prediction for potential conflict SVM based prediction for potential conflict Chaotic prediction for communication interval SVM based prediction for cummunication interval Size of training data for potential conflict prediction Average relative error of communication interval prediction Average relative error of potential conflict prediction Forecast period for communication interval prediction Chaotic prediction for potential conflict SVM based prediction for potential conflict Chaotic prediction for communication interval 0.5 SVM based prediction for cummunication interval Forecast period for potential conflict prediction (min) Average relative error of communication interval prediction The chaotic ATCO-flow behavior can be well predicted using chaos theory.

33 Conclusion and future work The existence of phase transitions in the interacted ATCO-flow operations from free to congestion are initially explored. Chaos is proved as an emergence effect in ATCO-flow operation at system level and is highly depends on the phase of ATCO and traffic flow. Bring new perspective to understand the characteristics of air traffic system and provide references to macroscopic air traffic flow modeling and tactical management. Validation of Universality

34 Thanks & QA The 12th USA/Europe ATM R&D Seminar June, 2017, Seattle