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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 !

Q&A