Broadband planar nearfield acoustic holography

161 Pages·2016·17.71 MB·English

by  Hefeng Zhou

Broadband planar nearfield acoustic holography
Citation for published version (APA):
Zhou, H. (2016). Broadband planar nearfield acoustic holography. [Phd Thesis 1 (Research TU/e / Graduation
TU/e), Mechanical Engineering]. Technische Universiteit Eindhoven.
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Published: 12/09/2016
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Broadband planar nearfield acoustic holography
Hefeng Zhou
A catalogue record is available from the Eindhoven University of Technology Li-
brary.
ISBN:978-90-386-4121-8
TypesetwithLATEX.
Coverdesign: MengdieChen,Anhui,China.
Reproduction: CPIKoninklijkeWöhrmann,Zutphen,theNetherlands.
(cid:13)c2016byHefengZhou. Allrightsreserved.
Broadband planar nearfield acoustic holography
PROEFSCHRIFT
terverkrijgingvandegraadvandoctoraande
TechnischeUniversiteitEindhoven,opgezagvande
rectormagnificus,prof.dr.ir.F.P.T. Baaijens,vooreen
commissieaangewezendoorhetCollegevoor
Promoties,inhetopenbaarteverdedigen
opmaandag12september2016om16.00uur
door
HefengZhou
geborenteAnhui,China
Ditproefschriftisgoedgekeurddoordepromotorenendesamenstellingvan
depromotiecommissieisalsvolgt:
voorzitter: prof.dr. L.P.H.deGoey
1e promotor: prof.dr. I.LopezArteaga
2e promotor: prof.dr. H.Nijmeijer
leden: prof.dr. A.G.Kohlrausch
prof.dr. H.Bodén (KTHRoyalInstituteofTechnology)
prof.dr. H.J.Ouyang (UniversityofLiverpool)
dr.ir. A.P.Berkhoff (UniversityofTwente)
Het onderzoek dat in dit proefschrift wordt beschreven is uitgevoerd in overeen-
stemmingmetdeTU/eGedragscodeWetenschapsbeoefening.
Contents
Nomenclature v
Summary ix
1 Introduction 1
1.1 HistoryofNAH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Stateoftheart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 ChallengesofNAHapplication . . . . . . . . . . . . . . . . . . . . . 4
1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.7 Outlineofthethesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 TheoryandimplementationofplanarNAH 11
2.1 Planaracousticradiationtheory . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Helmholtzequation . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Planewaveexpansionandangularspectrum . . . . . . . . . 15
2.2 PNAHformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Stationarysources . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Discretesolution . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Finiteapertureeffectsandwraparounderror . . . . . . . . . 25
2.2.4 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.5 Nonstationarysources . . . . . . . . . . . . . . . . . . . . . . 31
2.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Supportvectormachine-basedsoundpressureextrapolation 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 PNAHtheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
i
Contents
3.2.1 ContinuoussolutionforFourier-basedPNAH . . . . . . . . 40
3.2.2 SourcesofPNAHreconstructionerrors . . . . . . . . . . . . 41
3.3 SVM-basedsoundpressureextrapolation . . . . . . . . . . . . . . . 42
3.3.1 Principleofsupportvectormachine . . . . . . . . . . . . . . 42
3.3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Numericalsimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Modalsource . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.2 Pointsources . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Experimentalinvestigation . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 FrequencydomainbroadbandplanarNAH 55
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.1 Fourier-basedPNAH. . . . . . . . . . . . . . . . . . . . . . . 57
4.2.2 PrincipleofFD-BPNAH . . . . . . . . . . . . . . . . . . . . . 58
4.2.3 Determinationofthephase . . . . . . . . . . . . . . . . . . . 59
4.3 Numericalsimulations . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Flowdiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.2 Correlatedpointsources . . . . . . . . . . . . . . . . . . . . . 64
4.3.3 Independentpointsources . . . . . . . . . . . . . . . . . . . 65
4.4 Practicalsourceexperiments . . . . . . . . . . . . . . . . . . . . . . . 67
4.4.1 Measurementset-up . . . . . . . . . . . . . . . . . . . . . . . 67
4.4.2 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5 TimedomainbroadbandplanarNAH 73
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 PrincipleofPNAHfornonstationarysoundsources . . . . . . . . . 76
5.2.1 Thetransientmethodforonefrequency . . . . . . . . . . . . 76
5.2.2 Thebroadbandtransientmethodforafrequencyband . . . 79
5.2.3 TheStockwelltransformanditsdiscreteorthonormalversion 80
5.2.4 DOST-basedTD-BPNAH . . . . . . . . . . . . . . . . . . . . 83
5.3 Numericalsimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.1 Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 Nonstationarymonopolesource . . . . . . . . . . . . . . . . 88
5.3.3 Twomonopolesources. . . . . . . . . . . . . . . . . . . . . . 89
5.3.4 Baffledplanarpiston . . . . . . . . . . . . . . . . . . . . . . . 94
ii
Contents
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6 ExperimentalapplicationofTD-BPNAH 99
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Outlineoftheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2.1 Thebroadbandtransientmethod . . . . . . . . . . . . . . . . 102
6.2.2 DOST-basedtimedomainbroadbandPNAH . . . . . . . . . 104
6.3 Experimentalvalidation . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.3.1 Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.3.2 Enginetest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.3.3 Tyretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 Conclusionsandfuturework 119
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2 Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
A Correlatedpointsources 125
B Independentpointsources 127
C DemonstrationoftheDOST 129
Bibliography 131
Societalsummary 141
Acknowledgements 143
Curriculumvitae 145
iii

Nomenclature
Symbol Description Units
a pistonradius m
A measurementaperture
A(cid:48) projectionofAonthesourceplane
A+ extrapolatedmeasurementaperture
A− hologramplanewithoutthemeasurementaperture
b offset
B 1/3-octavebandproperty
c speedofsound m/s
C penaltyparameter
C(k ) weightingcoefficientoftheplanewaveofk
x x
D Dirichletboundarycondition
D discreteorthonormalStockwelltransformoperator
D−1 inversediscreteorthonormalStockwelltransformoperator
D discreteFouriertransforminthex-direction
x
D−1 inversediscreteFouriertransforminthex-direction
x
D discreteFouriertransforminthey-direction
y
D−1 inversediscreteFouriertransforminthey-direction
y
E reconstructionerror
f frequency Hz
f samplingfrequency Hz
s
f lowerfrequencyofa1/3-octaveband Hz
l
f centerfrequencyofa1/3-octaveband Hz
0
f upperfrequencyofa1/3-octaveband Hz
u
f (x ) realregressionfunction
Re i
f (x ) imaginaryregressionfunction
Im i
∆f samplingfrequencydistance Hz
v