A Link Transmission Model for Air Traffic Flow Prediction and Optimization

Transcription

1 School of Aeronautcs and Astronautcs A Ln Transmsson Model for Ar Traffc Flow Predcton and Optmzaton Y Cao and Dengfeng Sun School of Aeronautcs and Astronautcs Purdue Unversty cao20@purdue.edu Aerospace Systems Day, Aug 28, 2010

2 School of Aeronautcs and Astronautcs Research: Ar Traffc Flow Management Deal wth ar traffc congeston Where? -Traffc flow predcton How? -Traffc flow optmzaton A snapshot of ar traffc n U.S. Arspace 2

3 School of Aeronautcs and Astronautcs outlne I. Bacground II. Ln Transmsson Model Model development Formulaton TFM optmzaton III. Dual decomposton method IV. Model valdaton Ar traffc predcton Ar traffc optmzaton 3

4 School of Aeronautcs and Astronautcs Bacground Sector count: Number of arcraft n a sector If Sector count > Sector capacty, congeston! 4

5 School of Aeronautcs and Astronautcs Research objectve Objectve Predct the sector count for traffc broadcast Control the flow to avod congeston Method Ln Transmsson Model (large-scale) Dual decomposton method for optmzaton 5

6 School of Aeronautcs and Astronautcs Ln transmsson model Assumptons: Fxed arway sector level constant ar speed ln level 6

7 School of Aeronautcs and Astronautcs Developed by Metron Avaton & UC Bereley Prototype of ln networ n Future ATM Concept Evaluaton Tool (FACET, NASA Ames) 7

8 Dynamcs: School of Aeronautcs and Astronautcs Ln Transmsson Model x ( t 1) ( t ) x ( t ) (1 ( t ) ) x ( t ) 1 1 where: x ( t 1) f ( t ) (1 ( t ) ) x ( t ) 0 x ( t ) : a g g r e g a t e a r c r a f t c o u n t n l n f ( t ) : d e p a r t u r e n t o t h e p a t h, f x e d f l g h t s c h e d u le ( t ) : t r a n s m s s o n p r o b a b l t y n l n Predcton: nown param extracted from hstorcal data defned as x, 1 x ( t ) ( t) Optmzaton: varables to be optmzed 8

9 School of Aeronautcs and Astronautcs Ln transmsson model Ar traffc predcton Ar traffc optmzaton Wth ( t ) extracted from hstorcal flght data Optmze ( t ) to control the flow TFM optmzaton formulaton: s.t. Mnmum total flght tme = X ( 0 ) B f ( 0 ) T K n x ( t 1) ( t ) x ( t ) (1 ( t ) ) x ( t ) 0 ( t ) 1 m n c x ( t ) t Intal condton 2. System dynamcs (, ) Q s x x C ( t ) ( t ) s 3. Sector capacty constrant 4. Integer constrant 9

10 School of Aeronautcs and Astronautcs Decomposed nto a collecton of ndependent subproblems path by path Subproblem 1 obj = mn f(x 1 ) s.t. g 11 (x 1 ) 0 g n1 (x 1 ) 0 Path varables on average Master problem Obj = mn f(x) s.t. g 1 (X) 0 g 2 (X) 0 g n (X) 0 Subproblem 1 obj = mn f(x 1 ) s.t. g 12 (x 2 ) 0 g n2 (x 2 ) 0 Path 2 11,520,000 varables n total Subproblem obj = mn f(x ) s.t. g 1 (x ) 0 Path g n (x 1 ) 0 10

11 School of Aeronautcs and Astronautcs Dual decomposton algorthm based on LTM Subproblem: T n * d ( ) m n [ c ( t ) ] x ( t ) t 0 1 s. t. x ( 0 ) B f ( 0 ) s x ( t 1) A ( t ) x ( t ) B f ( t ) 0 x ( t ) C ( t ), 0 ( t ) 1 s T T T 0 0 n n t 0 t 0 t 0 T T T t 0 j ( t ) x ( t ) ( t ) x ( t ) f ( t ) ( t ) x ( t ) 0 t T T T t T T T j T ( t ) x ( t ) ( t ) x ( t ) 1 1 Master problem: T S K * * d ( ) m a x ( t ) C ( t ) d ( ) s s 0 t 0 s 1 1 Parameters Update: K g ( t ) ( ) ( ) s x t C t s s 1 ( t ) : ( t ) g ( t ) s s j s 1 w h e r e, j s th e te r a to n n d e x j j 1 j { T T T,, T }

12 School of Aeronautcs and Astronautcs Intal param s 0 0 ( t ), g ( t ), s 1 m a x d ( ) Master problem Converge? no * yes Decomposed path by path Optmal soluton x*(t), β*(t) u*(t) terate Subproblem 1 Subproblem 2 Subproblem 1* m n d ( ) 2* m n d ( ) * m n d ( ) Solve subproblems one by one Parameter update ( t ), g ( t ), s s j 12

13 School of Aeronautcs and Astronautcs Model valdaton NAS-wde Ar traffc predcton NAS-wde Ar traffc flow optmzaton Hardware: Software: Data: 2.8GHz CPU, 16G RAM, DELL worstaton Lnux, Integer Program, C++, CPLEX11.0 A full day (09/01/2005) hstorcal flght record from ASDI data 13

14 School of Aeronautcs and Astronautcs Ar traffc predcton Arcraft count 21:00 24:00 0:00 3:00 6:00 9:00 12:00 15:00 18:00 Statstcs of relatve error ( 20%) Ln model Cell model ZDC % 86.81% ZDC % 85.32% Arcraft count 21:00 24:00 0:00 3:00 6:00 9:00 12:00 15:00 18:00 14

15 School of Aeronautcs and Astronautcs Predcton accuracy statstcs 15

16 School of Aeronautcs and Astronautcs Ar traffc flow optmzaton 2-hour traffc flow optmzaton 2336 paths 2796 flghts Arcraft count 1.Sector capactes are respected 2.Sector worload s balanced 3.Delay s ncurred Arcraft count 16

17 School of Aeronautcs and Astronautcs x ( m n ) ( t ) Objectves are qute close Convergence of the algorthm Lagrangan multplers n dual decomposton method s ( t ) 17

18 School of Aeronautcs and Astronautcs Concluson: Ln Transmsson Model Provde a prototype for ar traffc flow predcton and optmzaton hgh fdelty predcton accuracy Tae nto account of control strategy 18