Modeling and detection of limit cycle oscillations in thin-wing aircraft using adaptable linear models

231 Pages·2003·8.8 MB·English

by  Johnson, Michael Ray

MODELINGANDDETECTIONOFLIMITCYCLEOSCILLATIONSINTHIN-
WINGAIRCRAFTUSINGADAPTABLELINEARMODELS
By
MICHAELRAYJOHNSON
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2003
ACKNOWLEDGMENTS
Iwouldliketoacknowledgethecontributionsofseveralindividualsinmypursuit
ofeducation. FirstandforemostIacknowledgemyfather,Dr.M.RayJohnson,who
taughtmethattheprimarypurposeofaformaleducationistolearnhowtolearn,that
learningisaprocessuniquetoeachindividual,andthatlearningisalife-longendeavor
thatmoreoftenthannotdoesn’tinvolveaclassroom. Hisexampleasafather,astudent,
ateacherandafriendhasbeenaguideinmylife.
NextIacknowledgeProfessorJosePrincipewho,bymeansofhistalentasa
teacherandadvisor(andperhapsatouchofthesupernatural)understandsmylearning
processbetterthanIdo. Healwaysseemsonestepaheadofme. Forhisguidance,
patienceandfriendshipIamverygrateful.
IwouldberemissifIdidn’tacknowledgethesupportoftheAirForceSEEK
EAGLEOffice. Dr.BillDyessencouragedandsupportedmyeffortsandmadeit
possibleformetoconcentratefulltimeonthisresearch. Dr.ChuckDenegri,myfriend
andmentor,wasareadyandwillingsoundingboard,withoutwhosehelpthiswork
wouldnothavebeenpossible.
Finallyacknowledgmentstomywifeandkids. Wordscannotdescribethesupport
andencouragementtheygave. Sufficeittosaythattheword‘quit’wasnevertolerated,a
— —
closeddoor anall-too-oftenoccurrence wasalwaysrespected,andhugswerewell-
timedandreadilyavailable. Everyguyshouldbesolucky.
n
TABLEOFCONTENTS
page
ACKNOWLEDGMENTS ii
LISTOFTABLES vi
LISTOFFIGURES vii
CHAPTER
1 INTRODUCTION 1
ProblemDescriptionandProposedSolution 3
Motivation 9
DissertationOrganization 10
2 BACKGROUND 12
TheFlutterPhenomenon 12
LinearFlutterAnalysis 14
ABriefFlightTestOverview 21
FlightTestDataSetsandConfigurationLinearFlutterAnalysis 23
AircraftAccelerometerLocations 23
MissionParticulars 24
LinearAnalysisofFlightTestConfiguration 25
FlightTestSignals 27
TestLine17TestSignal 27
TestLine3TestSignal 31
AlternativeApproaches 36
EngineeringApproaches 36
Volterraseries 36
Nonlinearempiricalmethods 37
NASAsolutions 38
SimilarANNwork 38
PhysicalModelingApproaches 39
Computationalfluiddynamics 39
Locallinearmodels 42
3 MODELINGAPPROACH 44
T.I.MApproach:Quasi-FixedHR/AdaptiveFIRModularApproximationofanIIR
System 44
iii
1
ModelImplementation 49
Kuo’sTwo-PEOscillatorasaFoundation 49
Spring-MassLinearOscillator 51
ConversiontoSingle-WeightAdaptation 53
NetworkTransferFunctionAnalysis 56
LinearDamping 60
LocalLinearModels 61
GeneralizedLikelihoodRatioTestBasisforDetectingSignalChanges 63
AProposedModificationtotheGLRT 68
GLRTPracticalConsiderations 73
ChapterSummary:TheInitialModel 75
4 MODELTUNINGANDREFINEMENTS 77
ChapterOrganization 78
LinearOscillatorExperiments 79
NetworkTraining 79
FrequencyTraining 83
PhaseandGainTraining 86
SampleFrequencyTrainingResults 90
DualSinusoidPhaseandGainTrainingExample 91
DualSinusoidPhaseandGainTrainingExampleResults 93
PostAnalysisOscillatorDesignModifications 98
LinearOscillatorSummary 99
ModifiedGeneralizedLikelihoodRatioTestforDetectingSignalChanges 100
PreliminaryExperiments 102
Experiment1 104
Experiment2 109
Experiment3 11
Experiment4 113
NetworkParametricEvaluation 116
Reduced-ModelSimplifiedGLRTExperimentConclusions 119
Fixed-LengthFlightTestSignalTrainingExperiments 121
PreliminaryWork: ConstantMach,AltitudeandNormalAccelerationLCO
Evaluation(Test8c) 121
EvaluationofthePracticalValueofMSEforTraining 125
Increased-TimeExperimentResults 126
ConsecutiveFixedLengthExperiments(Test8c) 132
ConsecutiveFixedLengthExperiments(TestLine17) 145
ChapterSummary 152
5 FLIGHTTESTEXPERIMENTS 155
TestLine17LLMExperiments 157
ParametricPredictions 160
Reduced-OrderNetworks 163
Reduced-OrderModelResults 173
Reduced-ModeResults 175
IV
Linearly-FitLLMParameterResults 177
TestLine3LLMExperiments 179
Third-OrderParametricFitPredictionResults 181
ParametricPredictionResults 187
Reduced-ModeResults 187
FrequencyAdaptationAnalysis 189
ModelGeneralizationEvaluation 192
ChapterSummary 194
6 DISCUSSIONANDCONCLUSIONS 197
ModelingConclusions 199
LinearOscillator 199
Fixed-lengthSignalModeling 200
Reduced-ModelSimplifiedGLRT 201
FlightTestDataExperiments 202
Furtheranalyses 206
Confirmationofexistingmethods 210
LISTOFREFERENCES 212
BIOGRAPHICALSKETCH 217
v
LISTOFTABLES
Table Eige
2-1 Flight8951freevibrationanalysisfrequenciesbymode 26
4-1 Oscillatortrainabilitywithin1%desiredfrequency 85
44--2 Oscillatortrainabilitywithin1%desiredfrequency,plasticinputweight 86
5-
4-3 Dualsinusoidalfrequencyphase/gaintestphasevalues 93
4-4 Experiment1desiredandANNmodels 106
4-5 Experiment1Results 108
4-6 InitialModalFrequencies(freevibrationvalues) 122
7 InitialModalAmplitudes(fluttersolutionresults) 132
1 Testline17modes1to8adaptedfrequencies(Hz) 190
5-2 Testline17modes9to16adaptedfrequencies(Hz) 191
5-3 Testline3adaptedfrequencies(Hz) 192
vi
LISTOFFIGURES
Figure P.4ge
1-1 LLMconceptualdiagram 6
2-1 DMMpointsonawing 20
2-2 Aircraftconfigurationandsensorlocations 24
2-3 Linearflutteranalysisoftestconfiguration,Damping 26
2-4 Linearflutteranalysisoftestconfiguration.Frequency 26
22--5 KCAS,Mach,andaltituderelationship 27
23--6 Testline17sensortraces:altitude,Machandnormalacceleration 30
2-7 Testline17forwardwingtipsignalandpowerspectraldensity 30
2-8 Testline17aftwingtipsignalandpowerspectraldensity 31
2-9 Testline3flightteststatesandsignals 32
2-10 Test8forwardwing-tipaccelerometer 33
2-11 Testline3analysispoints,flightteststatesandsignals 35
12 Testline3PSD,forwardandaftsensors 35
1 ConceptualdiagramofoscillatordrivenFIRfiltersystem 48
3-2 Kuotwo-PEoscillatornetwork 50
3-3 Originalfour-weightspring-massoscillatornetwork 52
3-4 Spring-massoscillatoroutput 53
3-5 Singleweightoscillatornetwork 56
3-6 Singleweightspring-massoscillatoroutput 56
3-7 Impulseresponseoftotalsystemandtwopartsystem 57
3-8 Multi-modalimpulseresponse 58
vii
1
3-
4-
9 ThreemodelGLRT 64
1 Single-weightoscillatornetwork 81
4-2 Single-weightoscillatorarchitecture 81
4-3 Initialsignaltraceoflinearoscillatoranddesiredresponse 82
4-4Trainedsignaltraceoflinearoscillatoranddesiredresponse 82
4-5 Oscillatorfrequencyweightcurves 84
4-6 Completesinglefrequencyoscillatorarchitecture 87
4-7 Gradientsurfacefor7Hzinitialfrequency 88
4-8 Gradientsurfacefor14Hzinitialfrequency 89
4-9 Freq.trainingtest,twocycles. Trainedinputweight,7to9Hz 91
4-10 Freq.trainingtest,one-second. Trainedinputweight,14.0to14.5Hz 92
4-11 Completedouble-frequencyoscillatorarchitecture 93
4-12 Dualfrequencyoutputwithtrainedinputweights 94
4-13 Dualfrequencywithtrainedinputweightstrainingresults 95
4-14 Dualfrequencyoutputwithfixedinputweights 97
4-15 DualFrequencyoutputwithnotrainedinputtrainingresults 97
4-16 Modifiedsaturatedlinearactivationfunction 98
4-17 Experiment1testsignal 105
4-18 Experiment1L-values 107
4-19 Experiment2testsignalcomparison 110
4-20 Experiment2L-values 11
4-21 Experiment3testsignalcomparison 112
4-22 Experiment3L-values 113
4-23 Experiment4testsignalcomparison 115
4-24 Experiment4L-values 115
4-25 Experiment3networkparametercomparison 117
viii
4-26 Experiment4networkparametercomparison 118
4-27 Complete16-modeLLMarchitecture 122
4-28 Test8cSpectrogram 125
4-29 One-eightsecondsignaltrainingtest 127
4-30 One-quartersecondsignaltrainingtest 127
4-31 One-halfsecondsignaltrainingtest 128
4-32 Onesecondsignaltrainingtest 128
4-33 Foursecondsignaltrainingtest 129
4-34 Fivesecondsignaltrainingtest(failure) 129
4-35 Test8cquarter-secondbursttrainingresults 137
4-36Test8cquarter-secondburstnetworkparameters 138
4-37 Test8cone-secondbursttrainingresults 140
4-38 Test8cone-secondburstnetworkparameters 141
44--39 Test8cone-secondpredictionplots 142
5-
4-40Test8cfour-secondbursttrainingresults 143
4-41 Test8cfour-secondburstnetworkparameters 144
4-42 Testline17forwardwingtipaccelerometersignalandPSD 146
4-43 Testline17originalarchitecturetrainingresults 147
4-44Testline17originalarchitecturenetworkparameters 148
4-45 Completetwo-delayoscillatorarchitecturewithoutputbias 149
4-46 Testline17two-delay,biasedarchitecturetrainingresults 150
47 Testline17two-delay,biasedarchitecturenetworkparameters 151
1 Complete2-delay,16-modeLLMarchitecture 156
5-2 ResultsofTestline17auto-switchedLLMdatasynthesis 158
5-3 PSDfortestline17auto-switchedLLMdatasynthesis 159
5-4 L-valuesfortestline17auto-switchedLLMdatasynthesis 159
IX
5-5 Testline17zero-orderFIRweight(mode1)vs.Mach. 161
5-6 Testline17zero-ordervs.second-orderFIRweights(mode1) 161
5-7 Testline17firstorderFIRweight(mode1)vs.Mach 162
5-8 Testline17LLMbiasvs.Mach 163
5-9 Testline17reduced-orderLLMFIRmodalvectoranglesbysegments 167
5-10Testline17reduced-orderFIRweightvectoranglesvs.Mach 170
5-11 Testline17reduced-orderFIRzero-ordervs.first-orderweights 171
5-12 Testline17reduced-orderFIRweightvectors 172
5-13 Testline17synthesisusingreduced-orderFIRfilters 174
5-14 PSDoftestline17synthesisusingreduced-orderFIRfilters 174
5-15 Datasynthesisoftestline17usingLLMsformodes1,2,and7 175
5-16PSDcomparisonoftestline17usingLLMsformodes1,2,and7 176
5-17 Datasynthesisoftestline17usinglinear-approximatedLLMs 177
5-18 PSDcomparisonofdatasynthesisusinglinear-approximatedLLMs 179
5-19 Testline3reducedorderresults 181
5-20Testline3reduced-orderLLMFIRmodalvectoranglesbysegments 182
5-21 Testline3reduced-orderFIRweightvectoranglesvs.g-loading 184
5-22 Testline3reduced-orderFIRfirst-ordervs.second-orderweights 185
5-23 Testline3reduced-orderFIRweightvectors 186
5-24 DatasynthesisofTestline3usingThirdorderapproximatedLLMs 188
5-25 DatasynthesisofTestline17usingLLMsformodes1,2,and7 189
5-26 Datasynthesisoftestline3segment1,LLMforTestline17Model1 193
x