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Advanced Aircraft Performance Modeling for ATM: Enhancements to the BADA Model
Presented at 24th Digital Avionics System Conference
Washington D.C. October 30 – November 3, 2005
Angela Nuic, Chantal Poinsot, Mihai-George IagaruEUROCONTROL Experimental Centre, France
Eduardo Gallo, Francisco A. Navarro, Carlos Querejeta Boeing Research & Technology Europe, Spain
European Organisation for the Safety of Air Navigation
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Introduction
Accurate prediction of aircraft trajectory is a cornerstone for the development and evaluation of the future Air Traffic Management (ATM) system
Aircraft Performance Model (APM) is the core of trajectory prediction
BADA - Base of Aircraft Data – is a kinetic, mass-varying APM developed and managed by the Eurocontrol Experimental Center
BADA provides aircraft performance data and operations models suitable for
trajectory prediction and simulation
Current BADA 3.6 version provides aircraft performance data for 88 aircraft types
An initiative (AMEBA Advanced Model Engineering for BADA) is undergoing in
collaboration with Boeing Research & Technology Europe to develop BADA 4.0
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BADA model structure and main features
<<model>>Aircraft Characteristics
<<model>>APM
<<model>>Actions
<<model>>Motion <<model>>
Operations <<model>>Limitations
B772SMTOW{a1, a2, …}{o1, o2, …}{l1, l2, …}
A340
{a1, a2, …}{o1, o2, …}
{l1, l2, …}
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B777-200
Model Identification
…………….
32362082208.770001.6
33102083077.060001.3
33842083955.350001.0
165.7
3.7
2.2
0.7
0
r [NM]
2722049474200023.9
346220848240000.7
354920856930000.4
362620865620000.1
363120870015000.0
ROC [fpm]m [Kg]Hp [ft]t [min]
ESF mg
,...)a,D(a,...)a,T(a v
dt
dh 111021 −=
Model Identification
,...)a,F(a dt
dm2120−=
Observed values from reference data
Predicted values based on BADA model for T, D & F
Reference data
( )∑=
−−=
n
ii
i
iii
i
ih
ESFgm
vDThSSE
1
2
.
n
SSERMS =
∑=
+=
n
iii
mFmSSE
1
2.
.
Optimization objectives (metrics)
B772
{a1, a2, …}
RMS1=72.3RMS2=45.2RMS3=81.5…
Model Instance
Accuracy figures
310/ .84ISA+0
208700
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Aircraft reference data sources
Aircraft Operation Manuals (AOM’s) – low granularity and precision, normal aircraft operation data coverage
Output of Aircraft Performance Engineering Programs – high granularity and precision, entire flight envelope data coverage
Aircraft performance reference data pointsmin to max a/c mass, ISA-20 to ISA+30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 5000 10000 15000 20000 25000 30000 35000 40000
Hp [ft]
Mac
h
Aircraft Performance Programs Aircraft Operation Manual
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Current BADA model - 3.X family
Focuses on modelling of aircraft normal operation envelope
Ensures high coverage of aircraft types
Coverage of European air traffic with BADA a/c modelsin relation to the quality of aircraft reference data
Synonym models 17% coverage
Original models55% coverageOriginal models
27% coverage
Aircraft manufacturers programs Aircraft Operation Manual
204 aircraft types
32 aircraft types56 aircraft types
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Current BADA model - 3.X family accuracy level
Aircraft normal operationsMean RMS error in vertical speed: 100 fpm
Fuel flow error: 5%
Complete aircraft flight envelopeMean RMS error in vertical speed: 300 fpm
B744: Absolute error in vertical speed for 195 climb and descent profiles under ISA conditions
B744: Absolute error in vertical speed for 18 nominal climb and descent profiles under ISA conditions
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Enhancements to the BADA model
Advanced Model Engineering for BADA (AMEBA)on-going research that exploits the possibilities for improvements of the kinetic aircraft performance modeling by using today’s:
availability of better quality aircraft reference data
computing capabilities
the work performed in cooperation with Boeing Research & Technology Europe
Why AMEBA?More applications rely on APM
Advanced Decision Support Tools, Analysis and Validation
New requirements for improved accuracy on complete aircraft flight envelope, flight phases and type of operation
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BADA 4.0 objectives
Provide realistic, accurate and complete aircraft performance model:
with reasonable complexity, maintainability and computing requirements
capable of supporting accurate computation of the geometric, kinematicand kinetic aspects of the aircraft behaviour applicable to a wide set of aircraft types, over the entire operation envelope and in all phases of flight
susceptible of being identified from trajectory data
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BADA 4.0 modelling premises
Physical modelinganalysis of the underlying physical laws governing aircraft behavior
identification of the physical variables upon which aircraft performance is to be represented
selection of appropriate mathematical models to relate them
Systemic modelingway of organizing APM architecture as a system so functional requirements are met (e.g. provision of drag, thrust and fuel flow)ensure adequate balance of model performance with respect to non-functional requirements (e.g. realism, accuracy, complexity, completeness, maintainability, etc)
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Approach and steps
In-depth review of Flight Dynamics fundamentals underlying aircraft behavior under no simplifying assumptions other than those reasonable in the ATM context
Dimensional Analysis (DA) to identify the right physical dependencies for the mathematical models created to represent the required aircraft performances (drag, thrust, fuel consumption, etc).
Object Oriented Modelling (OOM) to identify the right roles and responsibilities of the different components encompassing the APM architecture.
Model selection Model identification Improvement assessment
Theoretical review
Dimensional analysis OOMTheoretical review
Dimensional analysis OOM
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Approach and steps
New dependencies for drag, thrust and fuel consumption modelsCD = f(CL, M)
T / δ = f(M, δT)
δT = f(M,δ) for ∆TISA < ∆TKINK
δT = f(M,θT) for ∆TISA ≥ ∆TKINK
F / δθ½ = f (M, T / δ)
Theoretical review
Model selection Model identification Improvement results
Dimensional analysis OOM
θ
δ
δThrottle
Theoretical review
Dimensional analysis OOM
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Approach and steps
Selection of appropriate mathematical models
Polynomial functionsLeast square techniqueRaw thrust, drag and fuel flow data for 6 Boeing airplane (different size and technology)
Several candidate models analysed
Statistical metrics used to measure fit of model to reference data
Theoretical review
Model selection Model identification Improvement results
Dimensional analysis OOM
1 7
2 2 2T ,flat 1 2 3 4 5 6 7
(7 parameters: d , , d )
δ d d δ d δ d M d δM d M d M δ= + + + + + +
FLAT RATING MODEL K
1 9
2 2 2 2 2 2T ,temp 1 2 t 3 t 4 5 t 6 t 7 8 t 9 t
(9 parameters: e , , e )
δ e e θ e θ e M e Mθ e Mθ e M e M θ e M θ= + + + + + + + +
TEMPERATURE RATING MODEL K
1 6
2 3 2MTOW 1 2 3 4 T 5 T 6 T
(6 parameters: c , , c )
TW (c M c M c M c δ c δ M c δ M )
δ= + + + + +
GENERALIZED THRUST MODEL K
New models selected
Model selection
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Approach and steps
Obtain coefficients for thrust, drag and fuel flow from trajectory information that contains kinematicinformation only
( ) TASvdHT D ESF
dt W= −
Theoretical review
Model selection Model identification Improvement results
Dimensional analysis OOM
IDLE THRUST = 0 DRAG
DESCENTS
Fixed Models Models to Fit
Trajectories
GEN. THRUST MCMB FLAT RTG MCMB TEMP RTG MCRZ FLAT RTG MCRZ TEMP RTG
DRAG
ALL
DRAG GEN. THRUST MCMB FLAT RTG
CLIMBS MCMB Flat
DRAG GEN. THRUST
MCMB FLAT RTG
CLIMBS MCMB Flat
DRAG MCMB FLAT RTG MCMB TEMP RTG MCRZ FLAT RTG MCRZ TEMP RTG IDLE THRUST
GEN. THRUST
ALL CLIMBS DRAG GEN. THRUST
MCMB TEMP RTG
CLIMBS MCMB Temp
DRAG GEN. THRUST
MCRZ FLAT RTG
CLIMBS MCRZ Flat
DRAG GEN. THRUST
MCRZ TEMP RTG
CLIMBS MCRZ Temp
Fixed Models Models to Fit
Trajectories
DRAG IDLE THRUST
DESCENTS
INNER LOOP
OUTERLOOP
OUTERLOOP
IDLE FUEL
DESCENTS
FUEL
CLIMBS
ENTRY
EXIT
Model identification
Process fully automated
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Approach and steps
Assess model improvements in terms of accuracy in: Vertical speed and fuel flow
Underlying aircraft forces
25 aircraft models used for assessment 18 Boeing, 4 Mc Donnell Douglas, other 3 jet commercial aircraft
Theoretical review
Model selection Model identificationDimensional analysis OOM Improvement assessmentImprovement assessment
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Approach and steps
Mean RMS error in vertical speed of 70 fpm over complete aircraft flight envelope
Theoretical review
Model selection Model identification Improvement assessment
Dimensional analysis OOM
B773: absolute error in vertical speed for 195 climb and descent profiles under ISA+15 conditions
Non-Boeing jet: absolute error in vertical speed for 195 climb and descent profiles under ISA+20 conditions
Improvement assessment
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Approach and steps
Over complete aircraft flight envelope: Thrust error well below 10%
Theoretical review
Model selection Model identification Improvement assessment
Dimensional analysis OOM
B773: absolute error in CT for 195 climb and descent profiles under ISA+15 conditions
Improvement assessment
B773: absolute error in CF for 195 climb and descent profiles under ISA+15 conditions
Fuel error well below 5%
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Current and future work
Action modelModel identification for low quality reference data
Turboprops and piston aircraft types
Non clean aerodynamic configuration
Motion and operation modelFlight regimes other than constant CAS/Mach
Lateral motion (roll in/ roll out)
Limitations model
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Conclusions
BADA 3.X accurately models aircraft at typical operational conditions
Substantial room for improvement exists by using today’s available data and computing resources
BADA 4.0 provides significant accuracy improvements over complete flight envelope, including non clean configuration
Thrust and Drag models are susceptible to be identified from trajectory data
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Publication
This paper is going to be published on EUROCONTROL web site
www.eurocontrol.int
©2005 - The European Organisation for the Safety of Air Navigation (EUROCONTROL). All rights reserved. The content represents the Author’s own views which do not necessarily reflect EUROCONTROL’ official position
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Thank you for your attention !
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