Applied System Identification for Constructed Civil Structures Lecture

8/3/2019 Applied System Identification for Constructed Civil Structures Lecture

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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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Manualexcitation

:Drop

Weight

Test

bridgebydroppingsandbagweight

Note:whiledropweighttestiseffective

ExampleofFreevibrationresponseofthebridge

excitedbydroppedweight

inexciting

the

free

vibration

response

ofthestructure,additionaldampingis

expectedasthedroppedweighttends

.


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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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xamp eo

am en

exc a on

:w n

n uce

v ra on

o

suspensionbridge.Toweraccelerationresponse

Treatedasstationaryrandomprocess.


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.

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


OutputErrorMinimizationforsystemidentificationusingseismicresponse.

modelisrequired

F=objectivefunction

Example:comparisonbetweenrecordedMinimizethedifferencebetweenthe

measuredmodalparametersandmodel

decksubjectedtoseismicexcitationgeneratedmodalparametersbyupdating

parametersofthemodel iteratively


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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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.

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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.

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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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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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

37


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s ng

o a

arame ers

38


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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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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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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


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

Applied System Identification for Constructed Civil Structures Lecture

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