applied system identification for constructed civil structures lecture
TRANSCRIPT
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AppliedSystem
Identification
or ons ruc e v ruc ures
DionysiusSiringoringo,Ph.D
u u
,
v.
yJuly22,2010
SeriesoflectureonAsiaPacificSummerSchool onSmartStructuresandControl
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Outline
n ro uc on
Definition
Objectives
ExperimentalMethods Classification
TypeofExcitation TypeofResponse
Classification:Parametricvs Nonparametric TypeofModel:Structuralvs Modalvs NonPhysical NumericalModel Domain:Timevs Frequencyvs CrossTimeFrequency
Uncertainties
Exam lesofA lication
Discussions
and
Closure 2
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1.Introduction:Definition
Aprocesstodeveloporimprovemathematicalrepresentationofastructuralsystemusingexperimentallyobtainedstructuralresponse(s).
Mathematicalre resentationofastructurals stem:Mass,
Stiffness,Damping,Flexibility,Connectivity
response/deflection,strainresponse etc.
,
structuralsystem,thetermstructuralidentificationiscommonlyused.
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1.Introduction:Objectives
WhySystemIdentificationforconstructedstructures?
1. Mo e Va at ono new yconstructe structures
verifyassumptionsindesignmodel(e.g.boundarycondition,nonlinear
behavior,energydissipationmechanism/damping)
verifyperformanceofcontrolsystem(e.g.baseisolation,TunedMass
Damper,etc)
2. ModelUpdating
obtainFEMcalibratedstructuralmodel
a just
structura
parameters
a ter
retro it
or
mo i ication
detectstructuralchangespossiblyduetodefectordamage
recognize
environment/loading
influence
or
pattern
on
the
structure
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1.Introduction:Objectives
WhySystemIdentificationforconstructedstructures?
4. Earth uakeEn ineerin
performance
of
structure
during
earthquake postearthquakestructuralassessment
5. Wind Engineering verification/comparison withwindtunnelresults
aerodynamic
performance
(e.g.
aerodynamic
damping
of
long
span
bridges)
6. SoilStructureInteraction
characterizeandquantifyparameterofsurroundingsoilmedium
7. TrafficstructureInteraction
characterizestructuralresponseduetocertaintypeofvehicle/train
detectchangesinstructurevehicleinteractionmedium(e.g.pavementeffectonbridgeresponse,railwaytrackeffectontraincomfortmeasure)
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1.Introduction:Scopes GlobalandLocal
ofinstrumentedbridgesforglobalassessmentofthe
structure
YokohamaBayBridge
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1.Introduction:Scopes GlobalandLocal
Examp eo
Loca
Structura
I ent cat on
:Eva uat on
o
amp ng
onstaycableofcablestayedbridgetoassestheeffectivenessof
cabledampersystem.
CableHydraulicdamperStonecuttersBridge
Singlemodedecayresponse
ofthecable:f=0.49Hz
-3
-2.5
-2
-1.5
=0.055487
)log(m/s2/s)
peak
valley
average
Freevibrationtestofstaycablebypulland
releasetest.
80 100 120 140 160 180 200 220-5
-4.5
-4
-3.5
Time (s)
Log(PeakAcc
Cabledamping
(logarithmicdecrement
:
d=0.055)
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2.ExpMethods:TypeofExcitation
Theexcitationcanbeclassifiedas:
1. Dynamicorstatic(i.e.accordingtowhetherornottheyengage
ner a e ec s
2. Accordingtocontrollability,and
.
1. Controllable(measurableandunmeasurable) staticloads
2. Uncontrollable(measurableandunmeasurable) staticloads
3. Controllable(measurable
and
un
measurable)
dynamic
loads
4. Uncontrollablemeasurable dynamicloads
5. Uncontrollableunmeasurabledynamicinput(ambient
dynamicexcitation)
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2.ExpMethods:StaticLoads
Controllable(measurableandunmeasurable) staticloads
Relativel rareforfullscaleex erimentsonrealstructuresbecauseofthe
scaleoftheloadrequiredtogenerateameasurableeffect.
vehicles,eitherstationaryormoving
Uncontrollable(measurableandunmeasurable) staticloads
Genera yinc u e
e ements
o
ynamic
oa
an
response
monitoring,
particularlyinthecaseoftraffic andwindwhichgeneratequasistatic and
dynamicresponse.
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2.ExpMethods:DynamicLoads ControllableMeasurable
Forcedvibrationtest(FVT)
Transferfunctionsorfrequencyresponsefunctions(FRFs)scale
input(forcing)tooutput(response)viaeithermassorstiffness
,
aboutdissipativeeffects(mathematicallyrealisedasviscous
damping)
Examples: massexciters,Electrodynamicshakers,
u
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2.ExpMethods:DynamicLoads ControllableUnMeasurable
Manualexcitation
Impulseresponsefunctions(IRF)orfreevibrationresponse.
Neither
mass
nor
stiffness
can
be
identified.
Modal
frequency
anddampingcanbeestimatedquiteaccurately.
Examples:Impacthammer,peoplejump,dropweighttest,
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2.ExpMethods:DynamicLoads ControllableUnMeasurableExcitation
Controllablebut
unmeasurable
dynamic
loads
Manualexcitation:ImpactHammerTest
Givin excitation to a short
spanbridge
by
impact
hammer
Free
vibration
response
of
the
bridge
subjected
toimpacthammer
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2.ExpMethods:DynamicLoads ControllableUnMeasurableExcitation
Manualexcitation
:Drop
Weight
Test
bridgebydroppingsandbagweight
Note:whiledropweighttestiseffective
ExampleofFreevibrationresponseofthebridge
excitedbydroppedweight
inexciting
the
free
vibration
response
ofthestructure,additionaldampingis
expectedasthedroppedweighttends
.
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2.ExpMethods:DynamicLoads ControllableUnMeasurableExcitation
1
1.5
anua
exc a on:
uan
re ease
es
o
s ay
ca e
Exampleoffreevibration
res onse of a sta cable
-1
-0.5
0
0.5
Accelera
tion(m/s2)
80 100 120 140 160 180 200 220-1.5
Time (s)
Flowcharttoobtaindampingvalueofastaycable
FreeVi rationResponse
RawDataFrequencyResponse
Filteringmodeofinterest
Singlemodefreevibration
response
Givingexcitationtoastaycablebypulland
releasedtest
usingenvelopeofdecayresponse
Singlemodedampingvalue
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2.ExpMethods:DynamicLoads ControllableUnMeasurable Excitation
e c eexc a on
on ro e
ra c
Exampleofstrainresponse
w ena ruc pass nga r ge
Vehicleexcitation:
1. Responselargerthanambient
vibrationresponse.
2. Stressand
acceleration
responses
can
beconductedsimultaneously
3. Effectofvehiclebridgeinteraction
.
Exampleofaccelerationresponsewhenatruck
passinga
bridge
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Seismic excitation
2.ExpMethods:DynamicLoads UncontrollableMeasurableExcitation
Transferfunctionsorfrequencyresponsefunctions(FRFs)between seismic
input(baseexcitation)tooutput(structureresponse).Structuralproperties,modal ro ertiesandmodal artici ationfactorcanbeestimated.
Example:instrumentedbridgesandbuildingsinJapanandCaliforniaUS.
Example:Yokohama
Bay
Bridge,
instrumented
cable
stayed
bridge
near
Tokyo
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2.ExpMethods:DynamicLoads UncontrollableunmeasurableExcitation
Ambientexcitation:wind,traffic,andunmeasured
microtremor.
Correlationsbetween
response
are
used
to
estimate
modal
ro erties.Modesha esunscaled.Treatedasstochastic
systemidentification.
Example:periodicambientvibrationmeasurementand
instrumentedbridgesandbuildings.
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2.ExpMethods:DynamicLoads UncontrollableunmeasurableExcitation
xamp eo
am en
exc a on
:w n
n uce
v ra on
o
suspensionbridge.Toweraccelerationresponse
Treatedasstationaryrandomprocess.
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2.ExpMethods:DynamicLoads UncontrollableunmeasurableExcitation
.
Bridgeresponsesubjectedtoopentrafficusuallytreatedasstationaryrandomprocess,
Example
of
vertical
acc
and
the
spectrum
of
a
medium
span
highway
bridge
to
traffic.
sincet einputisun nown.E ecto ve ic emassisusua yneg ecte .However,incase
ofshortspanbridge,theeffectofvehiclemassmaynotbenegligibleandinfluencethe
identifiedbridge
frequency.
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2.ExpMethods:TypeofResponseExcitation
,
D namic:
Acceleration Relativeofabsolutedisplacement
Velocity
Inclination Strain
Stress
a er
ressure Structuralandenvironmentaltemperature
WindDirection
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3.AnalysisMethods:Classification
Parametrican
Non
parametric
Mo e s
Structuralmodel
and
initial
estimate
of
model
parameters
are
knownapriori.Measuredresponsesarefittedtoobtainthe
bestestimateofmodelparameters.
NonParametricModel
Modelstructureisnotspecifiedapriori.Structuralresponses
systemand
quantities
such
as
cross/auto
correlations,
transfer
function/frequencyresponsefunction.
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Exam le
of
Parametric
Model
3.AnalysisMethods:Classification
OutputErrorMinimizationforsystemidentificationusingseismicresponse.
modelisrequired
F=objectivefunction
Example:comparisonbetweenrecordedMinimizethedifferencebetweenthe
measuredmodalparametersandmodel
decksubjectedtoseismicexcitationgeneratedmodalparametersbyupdating
parametersofthemodel iteratively
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3.AnalysisMethods:Classification
StateSpaceSystemidentificationusingseismicresponse.
modelandrealizationofobservability matrix,systemmatricesA,B,RandDcanbe
obtainedand
modal
parameters
are
realized.
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3.AnalysisMethods:TypesofModel
.
Systemismodeledintermsofmass,stiffness,orflexibility,and
dampingmatrices.
Geometric
distribution
of
mass,
stiffness
and
damping
are
known
Structuralconnectivitybetweendegreeoffreedomispreserved
)()()()( tBztKutuCtuM =++ &&&Equationofmotion:
tCMKM
IA
=
11
0exp
SystemmatrixAinstatespaceformfor
discretedata:
[ ] [ ]( 1) ( ) ( )x k A x k B z k + = +
k R x k D z k = +
Equationofmotionindiscretedynamicsystem,wheresystem
matrixAistobeindentified
Goal:ToIndentifysystemmatrixAinitsoriginalform,fromwhichthemass,stiffness
anddamping
matrices
can
be
retrieved.
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3.AnalysisMethods:TypesofModel
.
Systemisdefinedinmodalcoordinatesdescribingthevibratorymotionofstructuresintermsofmodalfrequency,modaldampingandmodeshapes(alsomodephaseangleforcomplexmodes)
Geometricdistributionofmass,stiffnessanddampingand
informationon
structural
connectivity
are
not
preserved.
Describestheresonantspatial(modeshapes)andtemporalofthes ruc ure.
Modalparametersareanalogoustoeigensolutionofstucturalmass
and
stiffness.Equationofmotionindiscretedynamicsystem,
wheresystemmatrixAistobeindentified
x x z+ = +
[ ]( ) ( ) [ ] ( )y k R x k D z k = +
Goal:ToIndentifysystemmatrixA bysolvingthe
Eigenvalue problemand
determine
the
modes.
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3.AnalysisMethods:TypesofModel
.
Doesnothavephysicalrelationshipwiththestructure(i.e.nospatialinformation no eometr distributionofmass stiffness anddam in
Simplyaparametercurvefitofthegivenmathematicalmodeltothemeasured
data.
Examples:AutoRegressiveMovingAverage(ARMA)anditsvariants,RationalPolynomialModeletc.
Somecanbeconvertedtomodalmodelform.
Example:AutoRegressiveMovingAverage(ARMA)Modelwheretheautoregressive
coefficientscanberelatedtomodalparameters
)()()()( 0111
1 tyadt
tdyadt
tydadt
tydn
n
nn
n++
L
)()()()(
0111tub
dt
tdub
du
tudb
du
tudb
mmmm++=
L
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3.AnalysisMethods:Domain
1. FrequencyDomain
TransferFunction
/Frequency
Response
Function/
Impulse
ResponseFunction.
AverageNormalizedPowerSpectrumDensity(ANPSD)
ComplexExponentialFrequencyDomainMethod(Schmerr
Eigensystem RealizationAlgorithminFrequencyDomain(ERAFD)(Juang &Suzuki1988)
Frequency
Doma n
Decompos t on
Br nc er et
a .
2001
28
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3.AnalysisMethods:Domain
2. TimeDomain
IbrahimTimeDomain(ITD)(Ibrahim&Mikulcik 1973)
LeastSquaredComplexExponentialMethod(LSCE)(Brown
Polyreference ComplexExponentialMethod(PRCE)(Vold etal.
1982) Eigensystem RealizationAlgorithm(ERA)(Juang &Pappa 1985)
StochasticSubspaceIdentification(Overschee &DeMoor
29
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3.AnalysisMethods:Domain
Representsfrequencyevolutionastimeprogresses.
Can detect nonlinearit and nonstationar si nals
ShortTimeFourierTransform(STFT)
Waveletbasedsystemidentification
EmpiricalModeDecomposition HilbertHuangTransform
signals)
30
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3.AnalysisMethods:DirectandIndirectMethodTimeDomain
WhentheIRF/FRFisavailable,theycanbeuseasinputdirectlyto
s stemidentificationmethod.
IndirectMethod
When
the
IRF/FRF
is
unavailable
such
as
in
case
of
ambient
v ra onmeasuremen ,ana ona me o snee e o
constructsyntheticIRF,ex.throughcrosscorrelation(Natural
ExcitationTechnique(NEXT)or throughRandomDecrement.
RawData NEXT ERA
Randec ITD
31
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3.AnalysisMethods:Checklist
Typesof
Inputs
and
Outputs
System
Identification
Method
Controllabledynamicloads
MeasuredInput(s)
assexc teran a er rans er unct ons nput utput ys
InstrumentedImpact
Hammer
SingleInput SingleOutput(SISO)orSingleInputMulti
Output(SIMO)
system
Unmeasured In ut s
Manualexcitation(people jumping) ImpulseResponseFunction/FreevibrationResponse
Snapback, or step relaxation ImpulseResponseFunction/FreevibrationResponse
Swingingbelltoexciteacathedraltower ImpulseResponseFunction/FreevibrationResponse
Uncontrollabledynamicloads
MeasuredInput(s)
seismicexcitation(SingleInput) Transferfunction,SISOorSIMO
seismicmultipleexcitation(MultipleInput) Transferfunctionmatrix, MIMO
Uncontrollabledynamic
loads
UnmeasuredInput(s)
ambientvibrationtest(operationalmodal
analysis) Stationarybroadbandassumption
windexcitation OutputCrosscorrelation
trafficexcitation CovarianceDrivenSystemIdentification
microtremorwith
unmeasured
input Data
Driven
Stochastic
Subspace
Identification 32
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4.Uncertainties
Uncertaintyisunavoidableinunderstandingtheresultsofsystemidentification. Modalpropertiesaresusceptibleto
.
Howtoquantifytheconfidenceoftheidentifiedmodalproperties?
.
2. MonteCarloSimulation
3. BootstrapMethod
33
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4.Uncertainties:Errorpropagationanalysisusingperturbation
CorrelationMatrix
Input[Up]
InformationMatrix = Ryy()=Ryy(0)+RyyCorrelationMatrix:
InformationMatrix
[Ryy],[Ryu],
[Ruu]
Output[Yp] SingularValue
Yp()=Yp(0)+Yp Ryu()=Ryu(0)+Ryu = +
Rhh()=Rhh(0)+RhhSingularValue
Decom osition
RealizationofSystem
Matrix[A]
ecompos on RealizationofSystem
Matrix
A()=A(0)+AObjectives:
Realizationof
Modal
Parameters
, ,
RealizationofModal
Parameters
() = (0) + To
define and
quantifythe
error
on
themodalparametersastheeffect
ofinputandoutput noise
34
() = (0) + () = (0) +
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4.Uncertainties:Bootstrap Analysis
boundsofidentifiedmodalparametersbyNEXTERA
Randomlyselected Ensemble1 ERA
CCF1,CCF2,CCF3,CCFN
Randomlyselected
componen
CCF1,CCF5,CCF3,CCFMComputeCCFaverage
Ensemble2 ERA
1,1,1
McomponentCCF7,CCF2,CCF1,CCFMComputeCCFaverage
.
2,2,2
.
Randomlyselected EnsembleP
(Mcomponent)
.
.
ERA
.
.
CCF4,CCF6,CCF2,CCFM
ComputeCCF
average
p,p,p
CCF:CrosscorrelationfunctionEstimatemeanvalueand
95%Confidencebound
35
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4.Uncertainties:Bootstrap Analysis
confidencelevelcanbeobtained
Examp eso ri ge1s requencystatistica istri utionon i erentstructura con itions
usingBootstrap
Method
36
withcertainstatisticalcharacteristics.Thereforedecisionmadeonstructural
condition
involved
statistical
confidence.
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5.Examples:AmbientVibrationMeasurementofSuspensionBridge
BridgeType:
3SpanSuspensionBridge
Simplysupportedatthe
Tower Height : 130m
Tower width :21m atbase
Length:
1,380m
Span: 330720330m
montop
Girdermaterial: Streamlinedsteelbox
Towermaterial: Steelbox(welded)
TotalDeckWidth: 20m Completed : 1998
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5.Examples:AmbientVibrationMeasurementofSuspensionBridge
s ng
o a
arame ers
38
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5.Examples:AmbientVibrationMeasurementofSuspensionBridge
Structuralidentification
:effect
of
friction
force
and
aerodynamic
forces
on
identified
frequencyanddamping(Nagayama et.al2005)
39
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5.Examples:SeismicInducedSystemIdentificationofCableStayedBridge
40
l S i i d d S d ifi i f C bl S d id
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5.Examples:SeismicInducedSystemIdentificationofCableStayedBridge
Adatadrivenidentificationmethodwasappliedconsideringmultipleinputexcitation
andmultiple
responses
(MIMO
System)
41
5 E l S i i I d d S t Id tifi ti f C bl St d B id
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5.Examples:SeismicInducedSystemIdentificationofCableStayedBridge
Withdenseinstrumentationandgoodqualityofseismicrecordsweidentifybridge
modalparameters
until
high
order
42
5 E l S i i I d d S t Id tifi ti f C bl St d B id
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Observationofthe erformanceofseismicisolationdevicesusin 1st lon itudinal
5.Examples:SeismicInducedSystemIdentificationofCableStayedBridge
mode(Siringoringo &Fujino 2008)
(b)TypicalMixedSlipStickMode(Earthquake19950703)(a)TypicalslipslipMode (Earthquake19900220)
FromthefirstlongitudinalmodewecanobservebehaviorofLinkBearingConnection
during
earthquake.
Differentbehaviour ofLinkBearingConnectionattheendpierswasobservedduring
43
.
It
was
found
that
the
expected
slip
slip
mode
only
occurred
during
large
earthquake.
S t d R di M t i l
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SuggestedReadingsMaterials:
,
,
,
.AppliedSystemIdentification byJer NanJuang
MonitoringandAssessmentofStructuresbyGSTArmer
TheStateoftheArtinStructuralIdentificationofConstructedFacilities(ASCEReport1999)
Q
&
SQuestions andSharing? DionysiusSiringoringo
. .u y . .
44