Prediction of unsteady nonlinear aerodynamic loads using deep convolutional neural networks

125 Pages·2017·14.58 MB·English

by  Dávid Papp

Prediction of unsteady nonlinear aerodynamic
loads using deep convolutional neural networks
Investigatingthedynamicresponseofagilecombataircraft
Dávid Papp
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P
REDICTION OF UNSTEADY NONLINEAR
AERODYNAMIC LOADS USING DEEP
CONVOLUTIONAL NEURAL NETWORKS
INVESTIGATING THE DYNAMIC RESPONSE OF AGILE COMBAT
AIRCRAFT
by
DávidPapp
inpartialfulfillmentoftherequirementsforthedegreeof
MasterofScience
inAerospaceEngineering
attheDelftUniversityofTechnology,
tobedefendedpubliclyonTuesday,July31,2018at13:00
Supervisors: Dr.ir.M.Voskuijl, TUDelft
Dr.ir.M.vanRooij, NLR
Thesiscommittee: Prof.dr.L.L.M.Veldhuis, TUDelft
Dr.M.Voskuijl, TUDelft
Dr.ir.M.vanRooij, NLR
Dr.ir.D.M.Pool, TUDelft
Anelectronicversionofthisthesisisavailableathttp://repository.tudelft.nl/.
A
CKNOWLEDGEMENTS
Iwouldliketofirstexpressmygratitudetomysupervisors,Dr.ir.MichelvanRooijandDr.ir.MarkVoskuijl,
withoutwhomthisthesiswouldnothavebeenpossible.Icouldnotsucceedwithouttheirutmosttrust,sup-
portandguidance. Theirhighstandardsandexcellencekeptmeonmytoesduringthepastyearandmade
mepursueasuccessfuloutcome. IhopethatIdidnotletthemdownandthatmyworkliveduptotheir
expectations.IamalsothankfulformyformercolleaguesattheNetherlandsAerospaceCentre.Theyhelped
mecopewithmanyofmyproblems,plustheymadeNLRtheworkplacewhereIgladlycycledtoeachmorn-
ing.
Iamunspeakablygratefulformyfamily. Youalwaysstoodbehindmeregardlessthecircumstances. Youall
aretheabsolutereasonofmyachievements.Yourloveandsupporthelpedmeovercomeallthedifficultiesin
life.IcanonlywishthatonedayIcanreturnyouallthegoodIreceived.
At last but not least, I would also like to thank my friends from all around the world for giving me great
companyoutsideofwork.Icouldnothavemadeitthisfarwithoutyourpleasantmemories.
i
S
UMMARY
Newgenerationcombataircraftareexpectedtooperateoverextendedflightenvelopes, includingflightat
highflowanglesandrapidmaneuvers.Conditionsbeyondtraditionallimitsaregivingrisetononlinearphe-
nomena, such as flow separation, large scale energetic vortices, fluctuations etc. These phenomena have
significantimpactonaircraftperformanceandifnotresolvedaccuratelydesignuncertaintiesareincreased
riskinglackofperformanceorevencostlyredesigns. Thus,accuratemodellingofunsteadynonlinearaero-
dynamicsisessentialformodernandfuturecombataircraft.
Unfortunately, conventionalmodellingtoolseitherlacktherequiredfidelityortheyaretooexpensive.
Traditional,highly-efficientapproachesarenotsuitableformodellingnonlinearflowphenomena. Concur-
rently,highfidelityComputationalFluidDynamics(CFD)simulationsarecomputationallydemandingand
thereforeimpracticalinmanycases. Toenhanceaircraftdesign,itisdesirabletoobtainmodelsjoiningthe
bestofthesetwoworlds. AcommonapproachistodistillhighfidelitymethodsintoReduced-OrderMod-
els(ROMs)thatcanaccuratelyapproximateunsteadyaerodynamicsatordersofmagnitudeslowercoststhan
CFD.RelevantliteratureoffersmanydifferentROMtechniquesforvaryingpurposes.Nonetheless,construct-
ingsuchmodelsisstillchallengingandcurrentlythereisnogenerallyagreedmethod.
InthecurrentthesisaROMtechniquethatmaybeapplicabletowiderrangesofproblemsandsimpler
toconstructissought. Theobjectiveistoobtainamodelthatcanpromoteaircraftcontroldesign,perfor-
manceassessmentandstructuralanalysisthroughoutdynamicmaneuversovercompleteflightenvelopes.
Thethesisproposesanovelapproachutilizingmodern, deepconvolutionalneuralnetworks(CNNs). The
devisedmodelconsistsofthreemaincomponents. Firstitincorporatesageometrydescriptionconstituted
bycoordinatesofanaircraftCFDsurfacegrid.Second,aprimaryencoding-decodingCNNpredictspressure
distributionatthegridpointsofthegeometry.Thefinalandthirdpartofthemodelisanauxiliaryencoding
CNNderivingintegralaerodynamicloadscorrespondingtothepressurefieldpredictionsoftheprimarynet-
work.Themodelevaluatesandproducesinstantaneousvalues.Givenamaneuver,itproceedsintimesteps.
Thepredictionsoftheseparateinstancesarecomputeddirectlywithouttheneedofsubiterations(asitwould
bethecaseforCFDsimulations).
Asaproofofconcept,themodelisappliedtosymmetricmotionsintheverticalplaneatfixedMachnum-
berandaltitude.ThesubjectoftheinvestigationsistheMULDICONconfigurationofthe251thScienceand
TechnologyOrganizationwork-groupofNATO.Tofullyexploittheadvantagesofreduced-ordermodelling,
flowcharacteristicsareinferredfromasingleexcitationfollowinganefficientsystemidentificationtechnique
usingSchroedersweepsasinputsignals. Theperformanceofthemodelisassessedbynumeroustestcases
performedinCFD.First,steadyconditionsofvaryingincidenceanglesareinvestigated. Second,harmonic
pitchandplungeoscillationsarounddifferentanglesofattackatdifferentamplitudesandfrequenciesare
considered.Third,additionaltestcasesofalinearpitchup-down–andaclimbingmaneuverarestudied.
Considering computational efficiency, the results show robust model performance. GPU-accelerated
CNNcalculationsareconductedroughly5000timesfasterthanCFDsimulations. Theprimarynetworkcan
accuratelyresolvethepressuredistributionsoverlargeportionsofthegeometry. Lowersurfacepredictions
areveryaccurate.However,amongcertainconditionsdiscrepanciesareobservableontheuppersurfaceto-
wardsthewingtips. Still,thesecondarynetworkcanpredictcorrespondingaerodynamicforcesaccurately.
Incontrast,itsmomentpredictionsaresensitivetoerrorsinpressuredistributions. Consequently,moment
predictionscanlargelydeviatefromreferencedata,especiallywhennonlinearphenomenaareprominent.
However,inmanycaseserrorsareattributedtoinsufficientregressorspacecoverage,i.e.certaininputcom-
binationsareexploredpoorlybytheSchroedersweeps.Reconsideringsystemidentificationpracticesmight
mitigatethoseissues.Nevertheless,thethesisprovestheapplicabilityofdeepCNNstotheproblemsathand.
Additionally,theresultsencouragefurtherinvestigations.
ii
C
ONTENTS
Summary ii
Nomenclature v
1 Introduction 1
1.1 Projectmotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 TherelevanceofReduced-ordermodellingandtheroleofneuralnetworks . . . . . . . . . . . 1
1.3 Researchobjectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Reportoutline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literaturereview 4
2.1 Introductiontoneuralnetworks:Understandingthecomputationalbasics. . . . . . . . . . . . 4
2.1.1 Generalnetworktopologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Training:Optimizingnetworkparameters . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 Back-propagation:Computingtheparameterupdates. . . . . . . . . . . . . . . . . . . 7
2.1.4 Generalization:Applyingnetworkstounexploreddata . . . . . . . . . . . . . . . . . . 9
2.1.5 Validation:Adjustingthehyperparameters . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.6 Gradientdescentinback-propagation:Optimizingnetworksfornon-convexproblems. . 11
2.1.7 Batch,stochasticandmini-batchgradientdescent:Optimizinglargedatasets. . . . . . . 13
2.2 Convolutionalneuralnetworks:Processingspatiallyrelateddata. . . . . . . . . . . . . . . . . 14
2.2.1 Theconvolutionoperation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Thepoolingstage:down-samplingconvolutionallayers. . . . . . . . . . . . . . . . . . 19
2.2.3 Up-sampling:invertingtheconvolutionalandpoolingstages . . . . . . . . . . . . . . . 20
2.2.4 Thedetectorstage:nonlinearactivationsinmodernconvolutionalneuralnetworks . . . 21
2.3 Summaryofliteraturereview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Stateoftheart:moderndeepconvolutionalneuralnetworks 26
3.1 Candidatenetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 U-netarchitecture:theframeofthenetwork . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.2 Gatedresidualblocks:enhancingtheperformanceoftheconvolutionallayers . . . . . . 29
3.1.3 Networkoptimization:theADAMalgorithm. . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.4 Candidatenetworkend-to-endarchitectureandhyperparameters . . . . . . . . . . . . 32
3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Methodology:Flightdynamics,aerodynamicandsurrogatemodelderivation 35
4.1 TheMULDICONunmannedcombataerialvehicle . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Flightconditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Maneuverdescription:Definingmotiontrajectories . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1 Referenceframes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.2 Motionvariables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Aerodynamicmodels:Aircraftrepresentationsandcomputationaldomains . . . . . . . . . . . 41
4.3.1 Full-ordermodelforcomputationalfluiddynamicssimulations. . . . . . . . . . . . . . 41
4.3.2 Reduced-orderaerodynamicmodelforneuralnetworkcomputations. . . . . . . . . . . 42
4.4 Experimentdesign:trainingmaneuverforsystemidentification . . . . . . . . . . . . . . . . . 44
4.4.1 Multisineinputdesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5 Aerodynamicsurrogatemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5.1 Primarynetwork:Surfacepressureprediction . . . . . . . . . . . . . . . . . . . . . . . 48
4.5.2 Secondarynetwork:Integralloadprediction. . . . . . . . . . . . . . . . . . . . . . . . 52
4.5.3 Modeloptimization:Performancemeasuresandtrainingsettings. . . . . . . . . . . . . 54
4.5.4 Networkhyperparameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
iii
CONTENTS iv
5 Simulationsandresults 57
5.1 Training:inferringsystemdynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1.1 Trainingsetresults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Steadysimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 Harmonicoscillations:Modelperformanceovertheregressorspace . . . . . . . . . . . . . . . 66
5.3.1 Resultsofharmonicexcitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Specialmaneuvers:Applyingthemodeltonewtypesofmotions. . . . . . . . . . . . . . . . . 80
5.5 Modelperformance:Costsofmodelconstructionandapplication . . . . . . . . . . . . . . . . 83
5.6 Summaryofsimulationsandresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6 Conclusion&recommendations 89
6.1 Majorconclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Modellimitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.3 Recommendationsforfuturework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
A Harmonicexcitationresults 91
A.1 Pitchoscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A.2 Plungeoscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
Bibliography 112
N
OMENCLATURE
Romansymbols
ˆt Tensorofpredictedoutputs −
C Convolutionalmatrix −
G Geometrytensor −
h Outputtensorofnetwork(layer) −
I Inputtensor −
K Convolutionkerneltensor −
S Outputtensorofconvolution −
T Transformationmatrix −
t Tensoroftrueoutputs −
A Axialforceinaerodynamicbodyframe,or N
Signalamplitude −
A Normalforceinaerodynamicbodyframe N
a Activationoutput,or −
Speedofsound ms−1
b Bias −
C Cost −
C Axialforcecoefficient −
A
C Pitchingmomentcoefficient −
M
C Normalforcecoefficient −
N
C Pressurecoefficient −
p
d Tensordepth −
e Unitvector −
f Activation −
G Sumofgradients −
h Tensorheight,or −
Altitude m
L Trainingloss −
l Length m
M Pitchingmoment,or Nm−1
Machnumber −
v
NOMENCLATURE vi
p Pressure,or Pa
Signalpower −
q Dynamicpressure Pa
S Surfacearea m2
s Outputofconvolution,or −
Strideofconvolution,or −
Halfspan,or m
Non-dimensionaltime −
T Temperature K
t Time sec
U Axialvelocity ms−1
u Signalinput −
V Velocity ms−1
v Changes −
W Normalvelocity ms−1
w Weights −
X Axialforceinflightdynamicbodyframe N
Z Normalforceinflightdynamicbodyframe N
z Weightedinputofneuron −
Greeksymbols
α Valueofsaturationin(C)ELUactivations,or −
DecayofEMA,or −
Angleofattack deg
β Inertiaofparameterupdate −
δ Partialderivativeofcost −
η Learningrate,or
Ordinateofcomputationalspace − −
γ Flightpathangle deg
µ Airdynamicviscosity kgsm−1
Φ Phaseangle rad
ρ Airdensity kgm−3
σ Sigmoidfunction −
τ Timevariable sec
θ Modelparameter,or −
Pitchangle deg
ξ Abscissaofcomputationalspace −
Superscripts
NOMENCLATURE vii
dec Decodedfeaturesinnetworkoutput
dist Disturbedfeaturesofcontrollerandregressorblocks
enc Encodedfeaturesofinputtensors
ext Extendedfeaturesofcontrollerandregressorblocks
C Integralloadcoefficientsinoutputtensors
p Pressurecoefficientsinoutputtensors
Subscripts
∞ Freestreamproperties
ref Referencevalue
p Tensorsoftheprimarynetwork
s Tensorsofthesecondarynetwork
T Transposeconvolutionmatrix