Simulated Annealing for Strategic Traffic Deconfliction by Subliminal Speed Control under Wind Uncertainties Manuel Soler 28th-30th Nov. 2017 Co-author: Valentin Courchelle, Daniel González Arribas, Daniel Delahaye Manuel Soler SID’17 28th-30th Nov. 2017 1 / 27
Introduction Introduction Issues of the future Air Traffic Management (ATM) An increase in global air traffic is foreseen in the coming decades. Will airspaces capacities be sufficient ? How to increase them without affecting safety ? Will Air Traffic Controllers’s workload be manageable ? Manuel Soler SID’17 28th-30th Nov. 2017 2 / 27
Introduction Introduction Issues of the future Air Traffic Management (ATM) An increase in global air traffic is foreseen in the coming decades. Will airspaces capacities be sufficient ? How to increase them without affecting safety ? Will Air Traffic Controllers’s workload be manageable ? ATM system needs to be improved Anticipating conflict detection Resolving the most of them Minimizing impact on flight efficiency Through automatic ways thanks to advanced algorithm Taking into account uncertainties is paramount. Manuel Soler SID’17 28th-30th Nov. 2017 2 / 27
Introduction Introduction A large range of possibilities has been developed Consider a micro/mesoscaled or macroscaled airspace ? With uncertainties on aircraft positions ? Through which separation maneuvers ? Heading change Flight level assignment Delays on departure ... Speed control Manuel Soler SID’17 28th-30th Nov. 2017 3 / 27
Introduction Introduction A large range of possibilities has been developed Consider a micro/mesoscaled or macroscaled airspace ? With uncertainties on aircraft positions ? Through which separation maneuvers ? Heading change Flight level assignment Delays on departure ... Speed control A strategy seems to be unexplored What about a deconfliction using speed control on a macroscaled traffic under uncertainties ? Manuel Soler SID’17 28th-30th Nov. 2017 3 / 27
Introduction Table of contents Introduction 1 Mathematical modelling 2 Uncertainty modelling Conflict evaluation Mathematical modelling setting up Simulated Annealing 3 General description of simulated annealing Adaptation of SA for our problem Results 4 Proof of concept 2D Case 3D case Conclusion 5 Manuel Soler SID’17 28th-30th Nov. 2017 4 / 27
Mathematical modelling Uncertainty modelling Uncertainties due to wind forecast errors Wind affects ground speed − V G = − → TAS + − − − → → V W Errors on − V W ⇒ Errors on − → → V G Manuel Soler SID’17 28th-30th Nov. 2017 5 / 27
Mathematical modelling Uncertainty modelling Uncertainties due to wind forecast errors Wind affects ground speed − V G = − → TAS + − − − → → V W Errors on − V W ⇒ Errors on − → → V G t 1 Weather? Mass? + t 2 t Performance? 0 p ( ) x ... t 1 t 2 t 0 = Manuel Soler SID’17 28th-30th Nov. 2017 5 / 27
Mathematical modelling Uncertainty modelling How to model forecast errors ? The MétéoFrance PEARP EPS is used to obtain wind uncertainties by generating: an initial wind forecast 34 other wind scenarios Data can be accessed at the TIGGE dataset by the European Center for Medium-Range Weather Forecasts (ECMWF). Deterministic forecast Initial condition uncertainty Ensemble members Figure: A subset of the PEARP Figure: Uncertainty propagation ensemble forecast at 250 hPa Manuel Soler SID’17 28th-30th Nov. 2017 6 / 27
Mathematical modelling Uncertainty modelling Aircraft position uncertainty modelling For each aircraft a Max arrival time uncertainty range: ∆ T a = max( δT a min , δT a max ) Manuel Soler SID’17 28th-30th Nov. 2017 7 / 27
Mathematical modelling Uncertainty modelling Aircraft position uncertainty modelling For each aircraft a Max arrival time uncertainty range: ∆ T a = max( δT a min , δT a max ) For all t between departure time T a 0 and arrival time T a : ⇒ ∆ T a ( t ) = ∆ T a × t − T a 0 T a − T a 0 Uncertainty area at date t . Manuel Soler SID’17 28th-30th Nov. 2017 7 / 27
Mathematical modelling Conflict evaluation Conflict detection Two types of conflicts Link conflict Node conflict Detection principle Specific time intervals are considered to detect conflicts as follow: A conflict exists if: t in − t out < 0 Manuel Soler SID’17 28th-30th Nov. 2017 8 / 27
Mathematical modelling Conflict evaluation Conflict evaluation Time intervals for link conflicts Time intervals: for a : [ t a − , t a − + 5 NM G ( l ) ] V a for b : [ t b + − 5 NM G ( l ) , t b + ] V b Potential conflict if: φ l ( a, b ) = ( t a − + 5 NM G ( l ) ) − t b + < 0 V a Link conflict evaluation Let L the set of links and A l the set of aircraft couple (a, b) involved into a conflict at the link l ∈ L : � ∀ l ∈ L , φ L ( l ) = − φ l ( a, b ) (1) ( a,b ) ∈ A l Manuel Soler SID’17 28th-30th Nov. 2017 9 / 27
Mathematical modelling Conflict evaluation Conflict evaluation Three configurations of node conflicts n ( a, b ) = ( t b + n − S ( α,θ ) φ 1 G ( n ) ) − t a − n ( a, b ) = t b + + S ( α,θ ) φ 2 n − ( t a − G ( n ) ) V b n n V a where: α = V b G ( n ) /V a G ( n ) √ α 2 − 2 .α. cos ( θ )+1 S ( α, θ ) = 5 NM × | sin ( θ ) | √ α 2 − 2 .α. cos ( θ )+1 n ( a, b ) = ( t b + n − r ( α,θ ) n + r ( α,θ ) r ( α, θ ) = 5 NM × φ 3 G ( n ) ) − ( t a − G ( n ) ) 2 . cos ( θ 2 ) V b V a Manuel Soler SID’17 28th-30th Nov. 2017 10 / 27
Mathematical modelling Conflict evaluation Conflict evaluation Node conflict evaluation Let: A 1 n = { ( a, b ) /φ n, 1 ( a, b ) < 0 } N the set of nodes A 3 n = { ( a, b ) /φ n, 3 ( a, b ) < 0 } � A 2 A 2 n = { ( a, b ) /φ n, 2 ( a, b ) < 0 }\ A 1 \ ( A 1 n n ) n ∀ n ∈ N , � � � φ N ( n ) = − φ n, 1 ( a, b ) − φ n, 2 ( a, b ) − φ n, 3 ( a, b ) (2) ( a,b ) ∈ A 1 ( a,b ) ∈ A 2 ( a,b ) ∈ A 3 n n n Total conflict evaluation � � Φ( X ) = φ N ( n ) + φ L ( l ) n ∈N l ∈L where X is the state vector of the problem. Manuel Soler SID’17 28th-30th Nov. 2017 11 / 27
Mathematical modelling Mathematical modelling setting up Mathematical modelling setting up State vector X = ( x i ) i =1 ..N ∈ Z N where : N = number of flights x i = TAS variation applied to the aircraft i Subliminal control constraint ∀ i ∈ � 1 , N � , − 0 , 06 × v i ≤ x i ≤ 0 , 03 × v i where v i is the initial TAS of the aircraft i . Objective function N � min f = M × N × Φ( X ) + | x i | i =1 Manuel Soler SID’17 28th-30th Nov. 2017 12 / 27
Mathematical modelling Mathematical modelling setting up Problem statement Objective function: N � min f = M × N × Φ( X ) + | x i | i =1 Subject to: ∀ i ∈ � 1 , N � , − 0 , 06 × v i ≤ x i ≤ 0 , 03 × v i ∀ k ∈ � 1 , N � , x k ∈ Z Where: � � Φ( X ) = φ N ( n ) + φ L ( l ) n ∈N l ∈L ∀ l ∈ L , φ L ( l ) ← (1) ∀ n ∈ N , φ N ( n ) ← (2) Manuel Soler SID’17 28th-30th Nov. 2017 13 / 27
Simulated Annealing General description of simulated annealing General description of simulated annealing Main parameters Initial solution X 0 Initial temperature T 0 Neighbourhood function Number of transitions Cooling up law Stop criterion Acceptance probability Let f c = f ( S c ) and f n = f ( S n ) : � e − fn − fc if f n > f c T P ( S n accepted ) = 1 otherwise Manuel Soler SID’17 28th-30th Nov. 2017 14 / 27
Simulated Annealing General description of simulated annealing Neighbourhood function Pseudo code Input: Current solution X c Procedure: new X n ← X c Chose a flight index i ∈ � 1 , N � Generate a random TAS variation δx ensure ( X c [ i ] + δx ) ∈ [ − 0 . 06 × v i ; 0 . 03 × v i ] X n [ i ] ← X c [ i ] + δx Output: Next solution X n Flight index choice function The likelihood of choosing a flight increases with the number of conflicts encountered during this flight. Manuel Soler SID’17 28th-30th Nov. 2017 15 / 27
Simulated Annealing Adaptation of SA for our problem Adaptation of SA for our problem Initial solution No modification of TAS planed into the flight schedule: X 0 = (0) i ∈ � 1 ,N � Initial temperature T 0 is chosen so as to obtain 80% of acceptance rate. Tuneable parameters Number of transitions: 200 Geometric cooling up law: T i +1 = α × T i with α = 0 . 96 with ε = 10 − 4 Stop criterion: T final = ε × T i Manuel Soler SID’17 28th-30th Nov. 2017 16 / 27
Results Table of contents Introduction 1 Mathematical modelling 2 Simulated Annealing 3 Results 4 Proof of concept 2D Case 3D case Conclusion 5 Manuel Soler SID’17 28th-30th Nov. 2017 17 / 27
Results Proof of concept Proof of concept Before resolution After resolution Manuel Soler SID’17 28th-30th Nov. 2017 18 / 27
Results 2D Case Simulation context Flights considered with wind uncertainties 55 9.152 m/s Case study 50 The data set corresponds to air-traffic over Spanish airspace on 45 4.8565 m/s 26th July 2016 between 40 12. am and 4. pm associated with corresponding wind forecast. 35 1060 flights are considered. 30 0.5611 m/s 15 10 5 0 5 10 All aircraft are flying at the same FL It can illustrate the expected increase of air traffic. → but we need to separate flights flying to East and those flying to West. Manuel Soler SID’17 28th-30th Nov. 2017 19 / 27
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