machine learning applied to airspeed ... - atm seminar · usa/europe air traﬃc management r&d...

Machine Learning Applied to Airspeed Prediction DuringClimb

R. Alligier D. Gianazza N. Durand

ENAC/MAIAA - IRIT/APO

USA/Europe Air Traffic Management R&D Seminar, 2015

R. Alligier, D. Gianazza, N. Durand (ENAC) Airspeed Prediction During Climb ATM 2015 1/35

In this work

ObjectiveImprove ground-based trajectory prediction with a 10 min horizonImprove the prediction in climb phase

IdeasUnavailable parameters: mass and speed intentPredict these parametersUse a physical model with predicted parameters


Ground-based Trajectory Prediction Problem

Aircraft state at t0:

Aircraft intent:

Physical model

(Position,Speed)

Speed Profile: ?

Mass: ?

Thrust setting law: ?

Futuretrajectory

Pastpoints


Baseline


Aircraft intent:

Physical model

(Position,Speed)

Speed Profile: (casref,Mref)

Mass: massref

Thrust setting law: max,climb

Futuretrajectory

BADA files BADA: Base of Aircraft Data

max,climb(casref,Mref)

massref

Pastpoints


Our approach


Aircraft intent:

Physical model

(Position,Speed)

Speed Profile: (hcas(x), hM(x))

Mass: hmass(x)


Futuretrajectory

Predictive models h

x

Set of examples

︸︷︷︸y=(mass,cas,M)

x︷︸︸︷Machine Learning

Pastpoints


Our approach

Previous work [Alligier et al., 2015]Assumes a max climb thrustWe have built a model hmass predicting the massFar more accurate than previously investigated mass estimation methods

This workAssumes the speed follows a CAS/Mach profileWe build models hcas and hM predicting the Cas and Mach parameters

With these two works, we can predict all the missing parameters


1 Data Used in this Study

2 Building the Set of Examples

3 Applying Machine Learning

4 Results


Data Used in this Study




4 Results



The Data

Raw DataRadar Mode-C from Paris Air Traffic Control CenterWeather data from Meteo France

Filtering/SamplingVariables are smoothedKeep only climbing segments with duration > 750 sOne point each 15 seconds

VariablesWe have the altitude Hp, the true airspeed Va, the temperature T , etc.We DO NOT have the mass nor the speed intent (cas,M)



Considered Aircraft Types

type # of flights massref [kg]A319 1863 60000A320 5729 64000A321 1866 72000A332 1475 190000B737 344 60000B744 350 285700B772 910 208700E145 851 38000F100 660 18500

4 Airbus, 3 Boeing, 1 Embraer, 1 Fokker2 light , 4 medium, 3 heavy


Building the Set of Examples




4 Results



Our approach


Aircraft intent:

Physical model

(Position,Speed)


Mass: hmass(x)


Futuretrajectory

Predictive models h

x

Set of examples

︸︷︷︸y=(cas,M)


Pastpoints



Why Do We Have to Build a Set of Examples ?

Predictive models h

Set of examples

︸︷︷︸y=(cas,M)


From {(xi , yi)}, Machine Learningbuilds h such that �y = h(x)�

The Set of Examples is the input of Machine Learning⇒ First step: Build {(xi , yi)}

In what follows:One climbing segment → One example (xi , yi)



What are x and y ?

�y = h(x)�

Explained variables y : What we wantThe speed intent parameters: (cas,M)

Explanatory variables x : What we haveSmoothed radar data:Va1, . . . ,Va11; Hp1, . . . ,Hp10; dHp

dt 1, . . . ,dHpdt 11, etc.

Weather model:temperature and wind at different altitudesFlight plan data:airline operator, RFL, departure airport, arrival airport, etc.Additional Variables:distance(Departure,Arrival), etc.

⇒ 295 explanatory variables



One Climbing Segment → One Example (xi , yi)

xi : information when the prediction is computedyi : speed intent (cas,M)

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past





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cas=314.9 kts

M=0.846

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20000 25000 30000 35000Hp [ft]

Va

[kts

] points●

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future

past



What is a CAS/Mach Speed profile ?Impact of (cas,M) on the speed profile

cas=320 kts

M=0.78

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450

10000 20000 30000 40000Hp [ft]

Va

[kts

]



What is a CAS/Mach Speed profile ?Impact of (cas,M) on the speed profile

cas=310 ktscas=320 ktscas=330 kts

M=0.77

M=0.78

M=0.79

350

400

450

10000 20000 30000 40000Hp [ft]

Va

[kts

]



Extracting Speed Intent (cas, M) from trajectory points(cas,M) is not available, but at each point we know Va, Hp and T

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cas=314.9 kts

M=0.846

425

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500

20000 25000 30000 35000Hp [ft]

Va

[kts

] points●

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future

past

(cas,M) = argmin(cas,M)

∑i

(Va(cas,M;Hpi ,Ti)− Va

(obs)i

)2


Applying Machine Learning




4 Results



Supervised Learning

Formalization of the ProblemLet:

(X ,Y ): a joint probabilityh: the learned model, knowing x it predicts y : �y = h(x)�

L: a loss function specified by the user of hFind h minimizing the risk:

Rrisk(h) = EX ,Y [L (h(X ),Y )] (1)

Empirical Risk MinimizationWe have a set T = (xi , yi)16i6n of examples i.i.d. from (X ,Y )We choose h minimizing the empirical risk:

Rempirical(h,T ) =1n

n∑i=1

L (h(xi), yi) (2)



Gradient Boosting Machine (GBM)

Gradient Boosting Machine (GBM) [Friedman, 2000]h(x1, . . . , xp) = µ+

m∑i=1

hi(x1, . . . , xp)

hi are small regression trees

One small tree: h1

CAS11 6 311.12

CAS11 6 295.12

DEST = CYUL

−0.112 −0.038

−0.035

0.018



Summary


Aircraft intent:

Physical model

(Position,Speed)


Mass: hmass(x)

Thrust setting: max,climb

Futuretrajectory

Predictive models h

x

Set of examples

︸︷︷︸y=(cas,M)


Pastpoints


Results




4 Results


Results

Results on the speed profile

Statistics on (Va(cas, M;Hp(obs), T (obs))− Va

(obs))(t > 0) [kts]type speed mean stdev mean abs rmse max abs

A320 ref 2.34 21 15.3 21.2 134A320 mean 1.1 21.2 14.9 21.2 129A320 GBM 0.57 12.6 8 12.6 114A320 adj 0.0262 7.71 4.68 7.71 124E145 ref 69.2 31.7 69.2 76.1 166E145 mean 1.82 29 24.1 29 93.3E145 GBM 1.12 16.2 12.2 16.2 81.2E145 adj -0.0446 8.26 5.85 8.26 65.3

Great improvement: A319, A320, A321, A332, B737, B744, B772Even greater improvement: E145, F100


Results







Results

Results on the altitude

Statistics on (Hp(pred) − Hp

(obs))(t = 600s) [ft]type mass speed mean stdev mean abs rmse max abs

A320 ref ref 290 1420 1165 1449 5753A320 GBM ref 187 715 553 739 6815A320 GBM mean 45.3 718 534 719 6707A320 GBM GBM 23.5 681 490 681 7193A320 GBM adj -0.895 523 389 523 6202E145 ref ref 1623 1801 1909 2425 7428E145 GBM ref 1667 2064 2032 2653 8280E145 GBM mean 548 2115 1741 2185 7289E145 GBM GBM 190 1314 1010 1327 5378E145 GBM adj 68.7 750 562 753 5858

Slight improvement: A319, A320, A321, A332, B737, B744, B772Great improvement: E145, F100


Results







Results

Results on the altitude for the 9 aircraft typesA319 A320 A321

A332 B737 B744

B772 E145 F100

−2000−1000

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(Hp(p

red)

−H

p(obs

) )(t

) [ft

]

method

BADAGBM

BADAref


Results

Conclusion

Concerning the altitudeRMSE on the altitude reduced by 45 % to 87 %Predicting speed intent has limited impact on altitude RMSE, except for twoaircraft types: E145 and F100.

Concerning the speedRMSE on the speed reduced by 36 % to 79 %Should probably also reduce longitudinal (along-track) error

Way to Improve (?)Model different types of aircraft intent:

�(cas1, cas2,Mach)�, �ROCD = constant�, etc.


Results

Thank you, any questions ?


Results

Alligier, R., Gianazza, D., and Durand, N. (2015).Machine learning and mass estimation methods for ground-based aircraft climb prediction.Intelligent Transportation Systems, IEEE Transactions on, (accepted).

Friedman, J. H. (2000).Greedy function approximation: A gradient boosting machine.Annals of Statistics, 29:1189–1232.


Results

Building Examples from a Climbing SegmentPrediction on a 10 minutes horizon ⇒ future contains 40 points11 past points to predict the future ⇒ example contains 51 points

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example 1 example 2

example 3 example 4

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Hp

[ft]

points●

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future

discarded

past

R. Alligier, D. Gianazza, N. Durand (ENAC) Airspeed Prediction During Climb ATM 2015 36

machine learning applied to airspeed ... - atm seminar · usa/europe air traﬃc management r&d...

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