development and use of operational modal analysis … · 27 may 2008 – development and use of...

DEVELOPMENT AND USE OF

OPERATIONAL MODAL ANALYSISExamples of Civil, Aeronautical and Acoustical Applications

Francesco Marulo – Tiziano [email protected]

27 27 MayMay 20082008StructuralStructural and and GeotechnicalGeotechnicalDynamicDynamic LaboratoryLaboratory STREGASTREGA

EngineeringEngineering FacultyFaculty -- University of MoliseUniversity of MoliseCampobasso Campobasso -- ItalyItaly

UniversitUniversitàà deglidegli StudiStudididi NapoliNapoli Federico IIFederico II

227 May 2008 – Development and Use of Operational Modal Analysis – F. Marulo and T. Polito

OverviewOverview

IntroductionIntroduction

TheoreticalTheoretical BackgroundBackground

NumericalNumerical assessmentassessment

Case Case StudiesStudies

DiscussionDiscussion of of ResultsResults

ConcludingConcluding RemarksRemarks

TypicalTypical ApplicationsApplications


IntroductionIntroduction

•• The operational modal analysis (OMA) is an added tool for the The operational modal analysis (OMA) is an added tool for the continuing improvement of the mancontinuing improvement of the man’’s productss products

•• Real time measurements and analysis represents an invaluable Real time measurements and analysis represents an invaluable process for gaining true experiences on structural dynamic process for gaining true experiences on structural dynamic behaviourbehaviour

OMA OMA advantagesadvantages:: OMA OMA drawbacksdrawbacks::

RealReal structuresstructures exhibitsexhibits truetruedynamicdynamic responseresponse

HypothesisHypothesis on the forcing on the forcing functionsfunctions

No No prepre--studiesstudies –– OnlyOnly retrofitretrofit

ExpertExpert useruser –– heavyheavy mathmath


Theoretical BackgroundTheoretical Background

[ ] ( ){ } [ ] ( ){ } [ ] ( ){ } ( ){ } [ ] ( ){ }tuDtFtxKtxCtxM ==++ &&&

maymay bebe writtenwritten asas::

kkkk

kkkk

vDuCxywBuAxx

++=++=+1

[ ] [ ] [ ][ ] [ ] [ ] [ ]⎟⎟⎠

⎞⎜⎜⎝

⎛−−

= −− CMKMI

Ac 11

0[ ] [ ] [ ]( )[ ] [ ]cc BAIAB 1−−=

[ ] [ ][ ] [ ]⎟⎟⎠

⎞⎜⎜⎝

⎛= − BM

Bc 1

0

( )tkxxk Δ=

( )tAA cΔ= exp

wherewhere

•• OMAOMA’’ss objective is the modal parametersobjective is the modal parameters’’ identification from outputidentification from output--only measurementsonly measurements

•• The classical structural equation of motion:The classical structural equation of motion:

•• DiscreteDiscrete--time stochastic statetime stochastic state--space model under the assumption of space model under the assumption of white noise or time impulse excitationwhite noise or time impulse excitation


HankelHankel matrixmatrix

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

a b c d eb c d e fc d e f gd e f g he f g h i

•• A A HankelHankel matrix is a square matrix that is symmetric and constant matrix is a square matrix that is symmetric and constant across the antiacross the anti--diagonalsdiagonals

•• HankelHankel matrices are formed when given a sequence of output data matrices are formed when given a sequence of output data and a realization of an underlying stateand a realization of an underlying state--space or hidden Markov space or hidden Markov model is desired. model is desired.

•• The Singular Value Decomposition (SVD) of the The Singular Value Decomposition (SVD) of the HankelHankel matrix matrix provides a means of computing the A,B, and C matrices which defiprovides a means of computing the A,B, and C matrices which define ne the statethe state--space realization space realization


•• Data Driven (DD)Data Driven (DD)

This algorithm is based on the following definition of the This algorithm is based on the following definition of the HankelHankelmatrixmatrix

Methods for OMAMethods for OMA

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=−

−

−+−

+++

−++

−+−

−

f

refp

ii

refi

Niii

Niii

Niii

refNi

refi

refi

refN

refref

refN

refref

ref

YY

YY

yyy

yyyyyyyyy

yyyyyy

NH

12|

1|0

22212

21

11

21

21

110

...............

...

...

...............

...

...

1

which projects future outputs into the space of the past outpuwhich projects future outputs into the space of the past outputsts

•• Again the singular value decomposition provides, through the Again the singular value decomposition provides, through the observabilityobservability and controllability matrices, the structural modal and controllability matrices, the structural modal parametersparameters


Methods for OMA Methods for OMA (cont(cont’’dd))

[ ][ ] [ ] [ ][ ] [ ] [ ]

[ ] [ ] [ ]⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

−++

+

11

132

21

,

qppp

q

q

qp

RRR

RRRRRR

H

L

LLLL

L

L

whichwhich, , eventuallyeventually through a through a weightingweighting processprocess, can , can bebe realizedrealizedin the in the observabilityobservability and and controllabilitycontrollability matricesmatrices

ChoiceChoice of the of the weightingweighting matricesmatrices maymay help help forfor ananimprovedimproved system system identificationidentification

[ ] { }{ }∑−−

=+−

=1

0

1 kS

s

Trefsskk yy

kSR

[ ][ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ]

[ ][ ]

[ ][ ][ ]TT

T

qp VSUVVS

UUWHW 1112

11212,1 00

0=⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=

•• Covariance Data Driven (CDD)Covariance Data Driven (CDD)

Based on the Based on the HankelHankel matrix built asmatrix built as


InIn--house Software house Software AMOpAMOp

•• DevelopedDeveloped in the in the MatlabMatlab©© environmentenvironment•• Text format for the input data files (different sources)Text format for the input data files (different sources)•• Useful for both novice and expert userUseful for both novice and expert user

Sta

rtin

gSta

rtin

gsc

reen

scre

en

Sta

biliz

atio

nSta

biliz

atio

ndi

agra

mdi

agra

mGeometryGeometrymodulemodule


Numerical SimulationNumerical Simulation

6 6 dofdof’’s s systemsystem

ResponseResponse toto ImpulseImpulse ExcitationExcitation

ResultsResults

ReferenceValues

17.7227 0.0101

33.2686 0.1191

36.0597 0.1242

46.6333 0.0538

64.5757 0.0001

78.2414 0.3103

nf nξ

ResponseResponse toto RandomRandom ExcitationExcitation

•• The numerical simulation appears to be a viable tool for checkinThe numerical simulation appears to be a viable tool for checking g the algorithms and the developed softwarethe algorithms and the developed software


Numerical ResultsNumerical Results

RobustRobust methodologymethodology

ReferenceValues

17.7227 33.2686 36.0597 46.6333 64.5757 78.2414

0.0101 0.1191 0.1242 0.0538 0.0001 0.3103

Impulse Exc. Random Exc.

AMOpCDD

17.7208 0.0790 16.8556 0.0259

33.2341 0.1161 34.9262 0.1580

36.0521 0.1215 35.6151 0.1212

46.6298 0.0520 48.1198 0.0529

64.5776 0.0001 64.5817 0.0001

78.2288 0.3091 89.0154 0.3489

Impulse Exc. Random Exc.

AMOpDD

17.7227 0.0101 16.8801 0.0266

33.2686 0.1191 35.0807 0.1209

36.0597 0.1242 37.0801 0.0330

46.6333 0.0538 46.8852 0.0541

64.5757 0.0001 66.2111 0.0000

78.2414 0.3103 80.2832 0.3503

nξ

nf

nf nξ nf nξnf nf nξnξ


Simulation of a Real StructureSimulation of a Real Structure

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-8

-6

-4

-2

0

2

4

6x 10-8

Am

plitu

de

time [sec]

Grid Point #3 - Acceleration Time History

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-7

Am

plitu

de

time [sec]

Grid Point #10 - Acceleration Time History

CloseClose toto excitationexcitation Far Far fromfrom excitationexcitation

•• Finite element analysis of a bridgeFinite element analysis of a bridge

•• Modal parameters easily computed numericallyModal parameters easily computed numerically

•• Simulation with impulse forcing functionSimulation with impulse forcing function


Flight TestingFlight Testing

To establish variation of the modal parameters with speed

ObjectiveObjective::

•• In Flight measurement of the vertical fin & rudder vibration behIn Flight measurement of the vertical fin & rudder vibration behaviouraviour

Pilot induced excitation through pedals mixed with air turbulence

Input Force:Input Force:


Flight Test ResultsFlight Test Results

180 km/h

DD 4.25 0.641 11.75 0.028 24.24 0.039 33.20 0.018

CDD 4.74 0.731 11.80 0.043 NI NI 32.81 0.030

200 km/h

DD 3.96 0.280 11.65 0.038 28.96 0.020 NI NI

CDD 3.91 0.440 11.75 0.058 28.51 0.052 NI NI

220 km/h

DD 3.73 0.600 11.81 0.023 25.05 0.163 NI NI

CDD 4.45 0.630 11.83 0.032 25.85 0.320 NI NI

f [Hz] ξ f [Hz] ξ f [Hz] ξ f [Hz] ξ

mode 1 mode 2 mode 3

mode 4

mode 4

Rudder & Fin - Test Case A

mode 1 mode 2 mode 3

mode 1 mode 2 mode 3 mode 4

ResultsResults

V=180 Km/hV=180 Km/h

V=220 Km/hV=220 Km/h

FinFin RudderRudder

InputInput

•• Example of measured acceleration timeExample of measured acceleration time--historieshistories


Testing on Civil StructuresTesting on Civil Structures

Traffic excitationTraffic excitation Step bumper truckStep bumper truck

Freq. [Hz] Damp. [%]

DD CDD DD CDD

0,89 0,91 0,04 0,04

1,15 1,20 0,03 0,04

2,44 2,03 0,05 0,06

3,01 2,95 0,04 0,04

3,75 3,65 0,06 0,06

11stst

33rdrd

•• Bridge deck motorwayBridge deck motorwayIdentification of the first structural modeIdentification of the first structural mode--shapes shapes

(model correlation, structural monitoring, (model correlation, structural monitoring, ……))


Acoustic ApplicationAcoustic Application

FacilityFacility forfor the the measurementmeasurement of the of the

TransmissionTransmission LossLoss (TL) of (TL) of StructuralStructural

PanelsPanels

•• SMallSMall Acoustic Research Facility (SMARF)Acoustic Research Facility (SMARF)


Receiving RoomReceiving Room

RunRun 4 4 –– ModalModal HammerHammerRunRun 5 5 –– ModalModal HammerHammerRunRun 6 6 –– SpeakerSpeaker

RunRun 1 1 –– SpeakerSpeakerRunRun 2 2 –– ModalModal HammerHammerRunRun 3 3 –– ModalModal HammerHammer

MicrophoneMicrophone SetupSetup #1#1 MicrophoneMicrophone SetupSetup #2#2


AMOpAMOp ApplicationApplication

•• Examples of Stabilization DiagramsExamples of Stabilization Diagrams


Num Num –– Exp CorrelationExp Correlation

OMA vs. FEM Comparison OMA vs. FEM Comparison –– Receiving RoomReceiving Room


Soundproofing EffectSoundproofing Effect

RunRun 7 7 –– Speaker (Speaker (withoutwithout soundproofingsoundproofing))RunRun 8 8 –– Speaker (Speaker (withwith soundproofingsoundproofing))

MicrophoneMicrophone SetupSetup #3#3Time history comparison with and without soundproofing treatmentTime history comparison with and without soundproofing treatment


Damping BehaviorDamping Behavior

•• OMA computed damping tendency with and without soundproofing walOMA computed damping tendency with and without soundproofing wall l treatmenttreatment


ConclusionsConclusions

•• Operational Modal Analysis is an important tool, eventually the Operational Modal Analysis is an important tool, eventually the only only one, for the structural identification of real structureone, for the structural identification of real structure

•• Two correlationTwo correlation--driven stochastic subspace techniques have been used driven stochastic subspace techniques have been used on both simulated and real measurementson both simulated and real measurements

•• Efficiency of the methodology even in high modal density environEfficiency of the methodology even in high modal density environmentment

•• Good ability and coherence in identifying the damping behaviourGood ability and coherence in identifying the damping behaviour

•• It may need an expert user, for a correct interpretation of the It may need an expert user, for a correct interpretation of the input input data and identified resultsdata and identified results

•• More reliable results are generally obtained combining all the aMore reliable results are generally obtained combining all the available vailable information on the tested structure, properly information on the tested structure, properly weightedweighted

development and use of operational modal analysis … · 27 may 2008 – development and use of...

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