A DYNAMIC BAYESIAN BELIEF NETWORK APPROACH FOR MODELING THE ATM - PowerPoint PPT Presentation

A DYNAMIC BAYESIAN BELIEF NETWORK APPROACH FOR MODELING THE ATM NETWORK DELAYS Yi ğ it Bekir Kaya Data Science Researcher at CAL, Aeronautics Graduate Student Prof. Gökhan İ nalhan Director of CAL Istanbul Technical University Controls and Avionics Laboratory Aeronautics Research Center

INTRODUCTION

Problem Statement ¨ Modeling of ATM Network Delays ¨ Identifying Patterns and Best Practices for Resilience against System Upsets (Resilience2050.eu) ¨ Creating a stochastic model that can be used as the basis for ¤ Dynamic Slot Management (SecureDataCloud SESAR WP-E) ¤ A-Collaborative Decision Making

Real Goals ¨ Giovanni Bisignani (CEO of IATA) claims: “Shaving one minute off each commercial flight would save 5.0 million tons of CO2 emissions and $3.8 billion in fuel costs each year” ¨ For airlines having about 2% of market share (e.g. THY), the saving is $76 Million per year

Causes of Delays ¨ Weather ¤ Capacity Decrease n Runway Change n Change in movements per hour ¨ ATC Capacity ¨ Aerodrome Capacity ¨ Environmental Issues ¤ Volcano eruption ¨ Special Events ¤ Airspace closure n Military ¤ Airline strikes ¨ ATC Staffing ¨ Accident/Incident ¨ Airspace Management

Network Flow Model

Air Traffic Connectivity Graph

Network Delay Propagation and Flow Model • Each node of the network is a sector in any demanded level and may include set of aerodromes (airports) • Flights that start and end in the same sector is represented with a loop • Airports of the network system are represented with sources and sinks in each sector block. In this regard, whole sector block can be deemed as delay (and traffic) generator/consumer which consists of mini generators.

Delay Propagation

Main Delay Focus • By comparing flown profile (CPF of CTFM) with filed profile (FTFM), generated delays due to sector capacity/restriction/ traffic overflow is obtained for each Flight • Delays are investigated in FIR segments • Major delays are generated at aerodromes (or at TMAs)

Delay time behavior [Pyrgiotis, Malone, Odoni] ¨ ρ is utilization rate ¨ If ρ < 1 the system is at steady state and ¤ proportional to ¨ Otherwise the system is chaotic

Effect of Demand on Expected Delay

Effect of Annual Operations on Delays

FRA Airport

EWR Airport

Capacity Effects on Delay – 50 move/hr

Capacity Effects on Delay – 40 move/hr

Capacity Effects on Delay – 30 move/hr

Capacity Envelopes (Pareto Optimality)

Weather Effect on Capacity Envelope

Weather Effect on Capacity Envelope (ATL) [FAA]

Weather Effect on Capacity Envelope (BOS) [FAA]

Queue Model

DELAY PERCEPTION

Phases of Flight

Delay Schema

Perception of Delays ¨ Initial Delay Perception ¤ AOBT – EOBT (delay based on estimation; EOBT = IOBT 96% in data) ¨ Strict Definition Delay (Pushback, Gate-out delay) ¤ AOBT – SOBT ¨ Passenger Perceived Delay ¤ ATOT – STOT ¨ Taxi-out Delay ¤ (ATOT - AOBT) – (STOT - SOBT) ¨ Taxi to TMA Exit Delay (ADTET = Actual Departure TMA Exit Time) ¤ (ADTET – ATOT) – (SDTET – STOT) ¨ Departure Delay ¤ Pushback Delay + Taxi Delay + Taxi to TMA Delay ¤ ADTET – SDTET

Perception of Delays ¨ En-route Delay (AATET = Actual Arrival TMA Enter Time) ¤ (AATET – ADTET) – (SATET – SDTET) ¨ TMA Entry to Taxi Delay ¤ (ATOA – AATET) – (STOA – SATET) ¨ Taxi-in Delay ¤ (AIBT – ATOA) – (SIBT – STOA) ¨ Gate-in Delay ¤ AIBT – SIBT ¨ Arrival Delay ¤ TMA Entry to Taxi Delay + Taxi-in Delay + Gate-in Delay ¤ 2*(AIBT – SIBT) – (AATET – SATET) ¨ Passenger perception (*) ¤ STOT as departure time ¤ SIBT as arrival time

Data Source ¨ The ALLFT+ data set is managed by the PRISME (Pan-European Repository of Information Supporting the Management of European Air Traffic Management Master Plan) ¨ Every entry is a single flight information ¤ Flight Plan ¤ Tactical Flight Model n FTFM n RTFM n CTFM ¤ Routes n CPF-GEN n CPF-REF

ALLFT+ Temporal Variables ¨ AOBT and EOBT as is ¨ IOBT = STOT ¨ SOBT = STOT – nominal time (e.g. 15 min ~ airport) ¨ SFP (Planned Flight Profile, FTFM), AFP (Actual Flight Profile, CPF/ CTFM) ¨ ATOT= first radar point (AFP[0].entryTime) ¤ 0 stands for first entry and -1 stands for last entry (Circular array notation) ¨ ADTET = AFP[0].exitTime, SDTET = SFP[0].exitTime ¨ AATET = AFP[-1].entryTime, SATET = SFP[-1].entryTime ¨ ATOA = AFP[-1].exitTime, STOA = SFP[-1].exitTime ¨ AIBT , SIBT are not in ALLFT+ data ¤ Taking (AIBT – SIBT) as nominal (gate-in)

DELAY PREDICTION MODELS

Some Methods for Delay Prediction Modeling ¨ Linear/Nonlinear Regression ¨ Graphical Models ¤ (Dynamic) Bayesian Belief Network ¤ Hidden Markov Models ¤ Kalman Filter ¨ Time Series Model ¤ SARIMA, GARCH ¨ Nonparametric Methods ¤ Nonparametric Density Estimation n Kernel estimator, Histogram, k-NN ¤ Smoothing models n Mean, kernel, running line, moving median, smoothing splines ¤ Multilayer Perceptrons ¨ Decision Trees ¤ Random Forest

BAYESIAN BELIEF NETWORK

Bayesian Network Structure

Bayesian Network Model ¨ P(G,S,R)= P(G|S,R)P(S|R)P(R) Belief Propagation: ¨ P(X|E)= α P(X | E + )P(E − | X) = απ (X) λ (X)

Bayesian Network Examples

Departure Delay DBBN (initial)

All Flight Model (initial)

Departure Delay DBBN (TAN optimized)

Previous Approaches ¨ Big Picture Approach ¤ No assumptions about inner models of airports ¤ OD pairs are analyzed independently (Eulerian Approach) ¨ Pure Bayesian Model ¤ No assumption about mathematical structure of delay propagation ¤ Observation (data evidence) based probabilistic model ¨ Time Behavior ¤ There is a stochastic relationship between lags

Previous Results

Previous Conclusions ¨ Departure delay prediction benefits from Belief Propagation more than other phases ¨ There is a ±22.5 min margin of error from Departure Delay Prediction for 95% confidence interval ¨ More data samples are needed for accuracy increase ¨ More information should be provided to the system in order to model underlying system ¨ Weather and Capacity Data should be aggregated along with Delay Data

Time Series SARIMA, GARCH

Time Behavior of Movements

Our Aggregate SARIMA Model ¨ Two timing approach ¤ Seasonal periodicity (s) ¤ Hourly periodicity (t) ¨ Delay = f(s, t) = Φ (s) + Θ (t) + w ¨ f bar (s) = daily mean of f(s, t) ¨ Φ (s) = SARIMA(f bar (s)) + WeatherModel(f bar (s)) ¨ f ’ (t) = hourly mean of {f(s, t) - Φ (s)} (Making levels even) ¨ Θ (t) = SARIMA(f ’ (t)) + QueueModel(f ’ (t)) + WeatherModel(f ’ (t)) ¨ w = f(s, t) - Φ (s) + Θ (t) ¨ w ~ N(0, σ )

Delay Prediction SARIMA (Barcelona-Madrid)

Special Day 1: May 6 2011 (Military)

Special Day 2: 30 May 2011 (Weather)

SARIMA ¨ SARIMA ¤ AR - Auto regressive ¤ MA - Moving Average ¤ I - Integrated ¤ S – Seasonal ¨ Conditions ¤ TS should be linear ¤ TS should be stationary ¤ TS should not have any trends (detrending) ¤ TS should be significantly different than white noise ¤ Residuals should be white noise

AR, MA, ARMA, ARIMA ¨ Condition Analysis ¤ Non-linearity: White Test ¤ Stationary/Explosive: Dicky-Fuller Test ¤ White Noise: Box-Jung Test ¤ Seasonality: Auto Correlation Function ¤ Cross Correlation ¨ AR(p) ¤ x t − µ = φ 1 (x t − 1 − µ) + φ 2 (x t − 2 − µ) + ··· + φ p (x t − p − µ) + w t , ¨ MA(q) ¤ x t = w t + θ 1 w t − 1 + θ 2 w t − 2 + ··· + θ q w t − q , ¨ ARMA(p, q) ¤ x t = α + φ 1 x t − 1 + ··· + φ p x t − p + w t + θ 1 w t − 1 + ··· + θ q w t − q

SARIMA&GARCH ¨ A Sample Equation for ARMA(2,2) Model: ¤ x t = .4x t − 1 + .45x t − 2 + w t + w t − 1 + .25w t − 2 ¤ Where x t denotes dependent time series and w t denotes white noise time series ¤ w t ~N(0, σ w 2 ) ¨ ARIMA(0; 0; 0)x(0; 0; 1) 12 ¨ GARCH: Similar to ARIMA ¤ Generalized Auto Regressive Conditional Heteroskedasticity ¤ Heteroskedasticity: No constant variance assumption ¤ The variance can be estimated ¤ Y t = f(X 1,t ;… ; X p,t ) + σ (X 1,t ; … ; X p,t ) w t ;

COMPARISON OF MODELS