Research Article Intelligent Platform for Model Updating in a Structural Health Monitoring System

12 Pages·2015·2.92 MB·English

Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2014, Article ID 628619, 11 pages
http://dx.doi.org/10.1155/2014/628619
Research Article
Intelligent Platform for Model Updating in
a Structural Health Monitoring System
DanhuiDan,1TongYang,2andJiongxinGong1
1DepartmentofBridgeEngineering,TongjiUniversity,Room711,BridgeBuilding,1239SipingRoad,
Shanghai200092,China
2LinTung-Yen&LiGuo-HaoConsultantsShanghaiLtd.,Shanghai200092,China
CorrespondenceshouldbeaddressedtoDanhuiDan;[email protected]
Received10October2013;Accepted12December2013;Published20January2014
AcademicEditor:Ting-HuaYi
Copyright©2014DanhuiDanetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Themainaimofthisstudyistodevelopanautomatedsmartsoftwareplatformtoimprovethetime-consumingandlaborious
processofmodelupdating.Weinvestigatethekeytechniquesofmodelupdatingbasedonintelligentoptimizationalgorithms,that
is,accuracyjudgmentmethodsforbasicfiniteelementmodel,parameterchoicetheorybasedonsensitivityanalysis,commonly
used objective functions and their construction methods, particle swarm optimization, and other intelligent optimization
algorithms.An intelligent modelupdating prototype softwareframework isdeveloped usingthecommercial softwaresystems
ANSYSandMATLAB.Aparameterizedfiniteelementmodelingtechniqueisproposedtosuitdifferentbridgetypesanddifferent
modelupdatingrequirements.Anobjectivefunctionlibraryisbuilttofitdifferentupdatingtargets.Finally,twocasestudiesare
conductedtoverifythefeasibilityofthetechniquesusedbytheproposedsoftwareplatform.
1.Introduction In recent years, the theory and technology of model
updating have continued to progress, especially in compu-
The use of monitoring information from structural health tational model updating (CMU) and model validation [7,
monitoringsystemsfacilitatestheupdatingoffiniteelement 8] research, some of the techniques used when updating
modelswithreal-timeandonlinestructures.Bydoingso,we parameter selection [9, 10], uncertainty processing tech-
cannotonlyupdatethestructuralbenchmarkanalysesmodel niques for updating results from continuous monitoring
butalsocontinuouslytrackthechangesinthetargetphysical information[11,12],andalternativetechnologiesthatemploy
parameters and the characteristic index in any location [1– small numbers of calculations of complex finite element
3]. The automation and intelligence of the model updating calculation during a modified iteration step [13–16]. Model
process is the key problem that hinders the achievement updatingsoftwarehasalsomaderapidprogress,whilesome
of these goals in structural health monitoring system [4, commercial finite element software systems have expanded
5]. After 20 years of research, existing structural health their functions to model updating, such as DDS’s FEM-
monitoring systems at home and abroad have entered the tools[17],theBalmes’structuraldynamicstoolboxSDTools
third stage, where the emphasis is on the processing and [18], and Schedlinski’s SysVal [19]. All of these software
utilization of data to implement data-based online early systems have model updating functions, but these software
warningsandassessments ofindividualhealthstatus[5, 6]. updating methods are isolated, with poor universality and
During this stage, the model-based assessment method is weak poor optimization abilities. It is difficult to ensure
simplyregardedasasupplementaryapproachthatisusedin the optimization of the updated results, which need to be
an offline manner and it has not become the main focus of programmed completely and automated to reduce human
theonlinealgorithm.Modelupdatinghasbeenstudiedonly intervention. However, technological progress constantly
toprovideabenchmarkmodelforthismethod[1,6]. stimulates structural health monitoring system researchers
2 MathematicalProblemsinEngineering
to include model updating in the development of the next The system matrix of the structure (global stiffness matrix,
generationofstructuralhealthmonitoringsystems,thereby mass matrix, and damping matrix) can be expressed as a
making the systems more intelligent with online and real- functionofthedesignparameters:
time updating processes. This will allow the use of physical K=𝑓𝐾(p),
andmechanicalfieldinformationtoaddressthemonitoring
target, thereby expanding theevaluationof sources andthe M=𝑓𝑀(p), (2)
scopeofinformation,aswellasovercomingtheshortcomings C=𝑓𝐶(p).
causedbylimitedmeasurementpoints[19].
Inthecorrespondingfiniteelementmodel,theexperimental
Thus, we studied online intelligent model update tech-
modelalsohasthefollowingrelationshipbetweenthesystem
niques based on monitoring to develop a model updating
matrixanddesignparametervalues:
prototype software framework based on the commercial
finite element software system, ANSYS, and the scientific K∗ =𝑓𝐾∗(p∗),
computingsoftwaresystem,MATLAB.Wealsodevelopedan M∗ =𝑓∗ (p∗), (3)
𝑀
intelligentalgorithmslibrary,whichincludesparticleswarm
C∗ =𝑓∗(p∗).
optimization(PSO),todrivemostoftheupdatingtasks.The 𝐶
use of this platform to combine updating tasks, objective The aim of updating is to ensure that the finite ele-
functions,and intelligent algorithms facilitates efficient and mentmodel(K,M,C)approximatestheexperimentalmodel
flexible automatic model updating without manual inter- (K∗,M∗,C∗), so it can take advantage of the former to
vention, thereby bridging the functions of the structural perform inversions or predictions of the mechanical field,
finiteelementmodelingandupdatingbothinthestructure or to perform system identification, as well as other tasks.
and in component level with the present structural health The sources of updating are the differences between the
monitoringsystem.Finally,weconsiderthekeycomponents two models, where the magnitude of the differences can be
of the technique developed in this study by discussing the describedcomprehensivelybyanobjectivefunction
resultsofavibrationtestwithacontinuousbeamandamoni- 𝑓=𝐹(K,M,C,K∗,M∗,C∗)
toringsystemimplementationofacable-stayedbridge,which
demonstratedthefeasibilityoftheproposedtechnique. =𝐹(𝑓𝐾(p),𝑓𝑀(p),𝑓𝐶(p),𝑓𝐾∗(p∗),𝑓𝑀∗ (p∗),𝑓𝐶∗(p∗))
2.DescriptionsoftheGeneralityof =𝐹𝑓,𝑝(𝑓𝐾,𝑓𝑀,𝑓𝐶,𝑓𝐾∗,𝑓𝑀∗,𝑓𝐶∗,p,p∗).
ParametricModel Updates (4)
Therefore,modelupdatingcanbeconsideredtobeanoptimi-
Basedonthedifferencesbetweentheobjectsupdated,model
zationproblem:
updatingmethodscanbedividedintotwocategories:matrix
updatingandparametricupdating,theessenceofwhichisan (𝑓𝐾,𝑓𝑀,𝑓𝐶,p)opt
optimizationalgorithmthatminimizestheresiduals.Matrix
updatingmethodsmodifythesystemmatrixofstructureor = arg min (𝐹𝑓,𝑝(𝑓𝐾,𝑓𝑀,𝑓𝐶,𝑓𝐾∗,𝑓𝑀∗,𝑓𝐶∗,p,p∗)).
submatricesdirectly.However,therelationsamongelements 𝑓𝐾,𝑓𝑀,𝑓𝐶→𝑓𝐾∗,𝑓𝑀∗,𝑓𝐶∗
p→p∗
may disappear because of the massive volumes of data in
(5)
the matrix elements that need updating and the drastic
manipulations required before and after matrix updating. As mentioned above, the precondition of design parameter
There may be imaginary elements and negative stiffness model updating is ensuring the rationality of the finite
values, which means that the elements lose their definite elementanalysesmodel,thatis,ensuringasuitableapprox-
physicalmeaning,sothesemethodsarenotsuitableforlarge imation of (𝑓𝐾,𝑓𝑀,𝑓𝐶) using (𝑓𝐾∗,𝑓𝑀∗,𝑓𝐶∗). Otherwise, the
structures.Startinginthelate1980s,theresearchfocusshifted results cannot be correct if a wrong finite element model
gradually to parametric updating methods, which regard is used for parameter updating. When modeling a finite
the structural design parameters (such as the boundary element, the assumptions and approximations of structural
conditions,physicalproperties,andgeometricfeatures)that geometry,materials,andboundaryconditionshavethemain
constitute system matrixes or the abstract parameters as effects on rationality and the model structural error. The
updating objects, thereby ensuring that the model has a structural rationality of the finite element model can be
definitephysicalmeaningafterupdating.Althoughthereare guaranteedbyensuringthereasonablemodelingofstiffness,
many parametric model updating methods with different mass,anddampingandtherationalprocessingofboundary
characteristics, the core process can be described using the conditions, rational modeling of loads, structural damage,
samemodel. anddeteriorationofperformance.Thus,theobjectivefunc-
The number of design parameters in structure finite tions and the optimization updating problem, respectively,
element models is 𝑛, where the first 𝑚 is the parameters canbesimplifiedas
that need to be updated, so the design parameters can be 𝑓=𝐹𝑝(p,p∗),
expressedas
p=[𝑝1,𝑝2,𝑝3,...,𝑝𝑚,...,𝑝𝑛]. (1) (𝑓𝐾,𝑓𝑀,𝑓𝐶,p)opt =arpg→mp∗in(𝐹𝑝(p,p∗)). (6)
MathematicalProblemsinEngineering 3
Asaresult,theproblemofdesignparametricmodelupdating withinthedefinitiondomain,whichisonlymathematically
canbedescribedby(6).Thegeneralprocesscanbesumma- reasonable;otherwisethevaluemaybeunreasonablefroma
rizedasfollows. physicalperspectiveandabnormalintheusualsenseofthe
structure.
(i)We regard the experimental model as the refer- Therefore, the design parameters should be selected
ence to model the finite element model reasonably, beforetheparametersensitivityanalysesbasedontheactual
therebyensuringtheapproximationof(𝑓𝐾,𝑓𝑀,𝑓𝐶)as conditionsoftheupdatingobject.Asensitivityanalysesthat
(𝑓𝐾∗,𝑓𝑀∗,𝑓𝐶∗). considers the statistical properties of updating parameters
(ii)Dependingontheaimofupdatingandtheupdating can then be performed. Given that the updating target
object’s characteristics, the design objective func- function is 𝑓 and the updating parameter is 𝑝, the initial
tion describe the differences in performance (static valueoftheupdatingparameteris𝑝0and𝛿𝑝isthestatistical
effect, dynamic response, or structural character- variation coefficient of parameter 𝑝, so the sensitivity after
istics) between the finite element model and the consideringparameter’sstatisticalfeaturescanbedefinedas
experimentalmodel. follows:
(iii)fiAnndatphperoopprtiimatealomptoimdeilz.ationalgorithmisselectedto 𝑠=𝛿𝑝⋅ 𝜕𝜕𝑓𝑝󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨 . (7)
𝑝=𝑝
0
Thus,itisclearthatfiniteelementmodel,theobjectivefunc- Aftercomparingandselectingvariousparametersusing(7),
tion,andtheoptimizationalgorithmarethreemainfactors the parameters with high sensitivity but low dispersion can
that affected design parameter model updating. Therefore, berankedattheendoftheoptionalparametersequence,or
these three main factors must be standardized first before evenexcluded,toensurethecorrectphysicalmeaningandthe
automating the updating process to ensure their seamless structuralrationalityoftheresults.TheMonteCarlomethod
integrationanddataexchange,whichisalsothemainfocus orbootstrapmethodcanbeusedtomakethesamechoices.
ofthepresentstudy. Updatingtheboundariesoftheparameterscanbeachieved
usingtheinitialvalueandthecoefficientofvariation,thatis,
3.KeyTechniquesfor IntelligentModel 𝑝0(1±𝛿𝑝).
UpdatinginanOnlineEnvironment
3.2. Hybrid Objective Function. In recent years, research
Finite element model updating research has made great progressinmodelupdatingtechniquesmeansthatdynamic
progressandhasbeenappliedinsomefieldsofengineering, fingerprints have been used increasingly to reflect the
but many problems still need to be solved when model dynamic characteristics of the structure, such as the flexi-
updatingisappliedtolargestructures.Themajorconstraints bility matrix, strain mode, modal curvature, and frequency
on online model updating are as follows: (1) model updat- responsefunction.Thesehavebeenappliedwidelytomodel
ing with large structures entails many degrees of freedom, updating techniques with good results. However, there are
intensiveandcomplexcalculations,andmanyiterativesteps; numerous dynamic fingerprints and many different cases,
(2)thelimitsoftheiterativeoptimizationalgorithmandthe which have created problems when deciding the success or
difficultyofappropriatealgorithmdesign, which meanthat failure of model updating, because it is difficult to choose
theoptimizationprocesshasproblemsconvergingonanideal anappropriatedynamicfingerprintasanobjectivefunction.
solution; (3) the improper selection of the design variables During dynamic model updating, there may be various
ordesignspaceoftenleadstotheoptimizationresultslosing choices of objective functions, such as frequencies, mode
theirphysicalmeaning;(4)singlestepiterationcalculations shapes, modal flexibility, modal strain energy, frequency
are large and difficult to perform online and in real time; response function, and static displacement, which can all
(5)someoptimizationstepsarenotcompletelyprogrammed beusedastheindependentvariablesofobjectivefunctions.
and may need manual intervention. These difficulties form Various objective functions perform differently in diverse
a bottleneck that hinders model updating in an online updatingenvironment,butinhybridobjectivefunctionsgen-
environment.Therefore,weusedthefollowingtechniquesto erallyperformbetter.Inthepresentstudy,thekeyobjective
overcomethesedifficulties. functionswereasfollows.
Atypeofobjectivefunctionthatusuallycombinesnatural
3.1.SelectionofModelUpdatingParametersandDesignofthe frequenciesandmodeshapesis
Space Boundary Value. The selection of model parameters
has a huge effect on model updating, because the number 𝑓=∑𝑛 𝛼(𝜔𝑖−𝜔𝑖∗)2+∑𝑛 𝛽(1−√MAC𝑖)2. (8)
of parameters selected will affect the scale and speed of 𝑖=1 𝑖 𝜔𝑖∗ 𝑖=1 𝑖 MAC𝑖
the optimization calculations directly, while the parameters
selected will affect the physical meaning of the updating In(8),𝜔𝑖 and𝜔𝑖∗ arethe𝑖thorderofthemodalfrequencies
resultsandthepathologicaldegreeoftheequationgoverning and the measured modal frequencies of the finite element,
updating.Afterupdatingtheparameterselection,thechoice respectively, 𝛼𝑖 and 𝛽𝑖 are the weight coefficients of the 𝑖th
of the upper and lower bounds of the design space also order,andMAC𝑖 isthe𝑖thordermodalassurancecriterion
needs to be reasonable. The choice should not vary greatly ofthemeasuredmodelandthefiniteelementmodel.
4 MathematicalProblemsinEngineering
Another objective function used in previous study [14] The response surface method and the influence matrix
is the cross-model cross-mode (CMCM) model updating methoddeterminetherelationshipbetweenanexplicitfunc-
method: tionformulatedasatransformationofthelinearmatrixand
𝑓=󵄩󵄩󵄩󵄩𝛿𝜆−[C E]󵄩󵄩󵄩󵄩. (9) bbyetswimeeunlatthiengsttrhuectcuarlcaulrlaetsipoonnssienaanddvathneceu,pwdhaitcinhgreppalraacmesettehre,
finiteelementcalculationusingafunctionortheproductofa
In(9),𝛿𝑗isthefluctuationratiooftheeigenvalue: matrix.TheneuralnetworkandSVMmethodssimulatethe
𝜆∗−𝜆 complexfunctionalrelationshipusingintelligentalgorithms.
𝛿𝑗 = 𝑗𝜆 𝑗 (10) A common feature of all of these methods is that a large
𝑗 number of finite element calculation rounds are needed in
advance,andthenanalternativetechniqueofsmallamounts
𝜆∗𝑗 and𝜆arethe𝑖thordereigenvaluesofthemeasuredmode ofcalculationsisinducedintheprocessofupdatingbyself-
andthefiniteelementmode,respectively,andCandEarethe learningalgorithmorfittingmethodsmathematically.
valuesofthecross-correlationcoefficientofstiffness(COK) The model reduced method does not require a large
andcross-correlationcoefficientofmass(COM),whichare numberofcalculationsbecauseitreplacesthefiniteelement
definedasfollows: systemwithmanydegreesoffreedomintheoriginalcalcula-
tionwiththefiniteelementanalysesofareducedmodelwith
𝐶 ⋅⋅⋅ 𝐶
[ 1,1 1,𝑁𝑒 ] fewdegreesoffreedom.Thetransformmatrixofthereduced
C=[ ... 𝐶𝑘,𝑛 ... ], model,𝑇,isafunctionofthecorrectionparameters,which
[𝐶𝑛𝑓×𝑛𝑡,𝑁 ⋅⋅⋅ 𝐶𝑛𝑓×𝑛𝑡,𝑁] is concerned with the iterative calculations. Additionally,
𝑒 𝑒 the process to generate 𝑇 is also a complex calculation
𝐸 ⋅⋅⋅ 𝐸 process which needs large amount of calculations. In the
1,1 1,𝑁
E=[[ ... 𝐸𝑘,𝑛 ... 𝑒 ]], pNreeusemnatnsntudseyr,itehseirsefporroep,aosdeydnatomoicverercdoumceedamboetvheomdebnatsieodnoend
[𝐸𝑛𝑓×𝑛𝑡,𝑁 ⋅⋅⋅ 𝐸𝑛𝑓×𝑛𝑡,𝑁] (11) troublesome.
𝑒 𝑒
𝐶 = COK(𝑖,𝑛𝑗)∗ = (𝜑𝑖)𝑇K𝑛𝜑∗𝑖 , 3.4. Automation of the Optimization Algorithm. After con-
𝑘,𝑛 COK𝑖,𝑗∗ (𝜑𝑖)𝑇K𝜑∗𝑖 structingtheobjectivefunction,themodelupdatingproblem
is transformed into a constrained optimization problem.
𝐸 =(1+𝛿 )COM(𝑖,𝑛𝑗)∗ =(1+𝛿 )(𝜑𝑖)𝑇M𝑛𝜑∗𝑖 . Thmiezraetioarnepthrorebelemmasi:nacnaatleygtoicraielsmoeftmhoedths,odtrsafdoirtiosonlavlinnguompetri--
𝑘,𝑛 𝑗 COM𝑖,𝑗∗ 𝑗 (𝜑𝑖)𝑇M𝜑∗𝑖 ical methods, and intelligent optimization algorithms. In
general, if an analytical method is used to solve complex
Intheequations,𝑘=𝑖×𝑗=1,2,...,𝑛𝑓×𝑛𝑡,𝑛=1,2,...,𝑁𝑒. optimization problems, it is almost impossible to achieve
The two objective functions are the representation of the solution because the conditions of the problems can-
the directly designed parametric updating method and the not meet the requirements of the assumed conditions for
indirectly designed parametric updating method based on the analytical solution. Therefore, numerical methods have
phenomenologicaltheory,respectively. many advantages when dealing with complex optimization
problems. Some traditional numerical iteration algorithms
3.3. Alternative Technique for Complex Finite Element Cal- include Newton’s method, the conjugate gradient method,
culation Using Small Amount of Computation Methods in a linear programming method, and nonlinear programming
Single Updating Iteration Step. The model updating process method. With multiobjective combinatorial optimization
can be transformed into an optimization problem, which problems, however, the traditional numerical optimization
generally requires an iterative technique that calculates an algorithmsalsohavedifficulties.Theintelligentoptimization
objective function many times according to certain rules. algorithms that have emerged since the 1980s, such as
For large complex structures, each iterative step requires geneticalgorithm,simulatedannealingalgorithm,antcolony
one (linear) or more (nonlinear) finite element analyses to algorithm, PSO, artificial immune algorithms, and hybrid
obtain the independent variables of the objective function, optimization strategies, have been developed by simulating
which can include static effects, dynamic responses, the certain natural phenomena or processes to provide feasible
modalparametersandtheirrelevantderivedquantities,and solutions for combinatorial optimization problems that are
frequency response functions. Thus, each calculation has a difficult to solve using traditional optimization techniques.
hugecomputationalload,whichmeansthatmodelupdating Fromthebeginningoftheintelligentoptimizationalgorithms
is not suitable for performing online. To achieve real-time are presented, the applications cover all the field of civil
onlineupdating,alternativetechniquesusesmallamountof engineeringaredonebyresearchers,Yietal.usedgeneralized
calculations approaches to replace complex finite element genetic algorithm and modified monkey algorithm to treat
calculation.Themainmethodsincludetheresponsesurface theproblemofoptimalsensorplacementforstructuralhealth
method, influence matrix method, neural network method, monitoring[20,21].Xuetal.usedneuralnetworksmethod
supportvectormachine(SVM)method,andmodelreduced to treat the real-time computing problem in the semiactive
method. controlofstructures[22,23].ThePSOisalsoinvestigatedand
MathematicalProblemsinEngineering 5
appliedontheautomationFEMmodelupdatingproblemby toensurethecollaborationbetween MATLABandANSYS,
ourteam[24–26]. there needs to be smooth transmissions among three types
We compared most of the optimization algorithms for of information: call instructions, data interactions, and the
modelupdatingandfoundthatmostalgorithmswereuseful interactionsamongrunningstate.
in specific conditions [21–23]. Building an intelligent plat- Thereisnoready-madeinterfacebetweenMATLABand
formformodelupdatingtomakefulluseoftheoptimization ANSYS,butMATLABprovidessomeuniversalmethodsfor
resultscanbehelpfulwhenselectingatraditionaloptimiza- callingexternalprograms,suchas“!,”theDOSfunction,and
tion algorithm (such as sequential quadratic programming thesystemfunction.“!”andtheDOSfunctioncancallashell
method) or a modern intelligent optimization algorithm program to execute a command required by the Windows
(suchasparticleswarmintelligentalgorithmandevolution- system, while the system function can perform operating
aryalgorithm)toaddressdifferentissues,whichcanmakethe systemcommandsandreturntheresults.
modelupdatingprocessmoreflexibleandefficient,soitcan There is also no direct data exchange system between
beappliedtoengineeringapplications. MATLAB and ANSYS, so the exchange of data must occur
viafiles.Weusedtextfilesasthemediumofdataexchange.
Textfilesaresimplebuttheyhaveahighdatastoragecapacity.
4.ComponentsofanIntelligent
Bothsoftwaresystemsprovidesuitablefunctionsforreading
Platformfor StructuralHealthMonitoring
andwritingtextfiles.
SystemModelUpdating Implementingthetransferofstatusinformationbetween
two types of software is the key to process control. We
Atpresent,mostofthelargefiniteelementsoftwaresystems
achieved the mutual notification of status information by
that are used widely in engineering lack support for model
setting up a state variables identification function (flag M).
updating, while some finite element software systems that
ThisfunctionjudgeswhetherANSYSisoperatingbyreading
have been developed specifically for model updating do
the status value in the MATLAB program. Thus, if ANSYS
not performwell with conventionalfinite element analyses,
stopsrunning,theflagwillbezeroanditnotifiesMATLAB
which makes it difficult for them to handle complex engi-
thatthecurrentrunisoversothenextstepofthecalculation
neering structures and they have insufficient optimization
canberun;otherwiseMATLABwillwait.Theformatusesthe
ability. Based on the sensitivity analyses theory of model
systemorDOSfunctionstocallANSYSasfollows:
parameterupdatingandbycombiningthenumericalcalcu-
lation software MATLAB with the finite element modeling [status,result]
ability ANSYS, we developed an intelligent platform for =system ("D:\Ansys\v110\ANSYS\bin\intel
model updating in a structural health monitoring system.
\anss110 −b -i ansys/ansysconcle
Oursystemfacilitatesautomatedmodelupdatingforactual
engineering structures because there is an urgent need -o output.out")
for health monitoring systems at present. By extracting
AftertheANSYSperformsthecalculation,thestatusreturns
the general steps of the dynamic-based parametric bridge
avalueof0.Thus,thereturnedvalueofthestatuscanbeused
model updating process, we developed a common software
towriteaflagfile,asfollows:
architecture and implemented some key techniques, which
should allow the subsequent production of large online function flag(status)
bridgeupdatingsoftware.
if status==0
Thecommonalityofourproposedframeworkismainly
reflected in the following: the optimization algorithm and out=objfunt4;
target functionare modular, so different optimizationalgo-
%objfunt4 is the objective function
rithmsandtargetfunctionscanbeselectedfordifferentprob-
lems;thesystemisextensible,sotheoptimizationalgorithm end
andtargetfunctioncanbeaddedindependentlydepending
onneeds,accordingtocertainstandards.
4.2.ParametricFiniteElementModelingSolution. Thepara-
metricfiniteelementtechniquereferstothedefinitionofthe
4.1.DataExchangeInterfaceandtheProcessControlbetween finiteelementmodelstructureusingagroupofundetermined
MATLAB and ANSYS. The ANSYS parametric design lan- parameters, where the parameters can be the structural
guage (APDL), which is shipped with ANSYS, can be used geometrysizeandphysicalandmechanicalproperties.Dur-
for general process control, but it may be more difficult ing parametric model updating design, the parameters that
andveryslowwhenimplementingspecificcomplexphysical needtobeupdatedconstitutetheundeterminedparameters
models.Intheproposedframework,therefore,MATLABis oftheparameterizedfiniteelementmodel.ANSYSprovides
responsiblefortheoptimizationandcontrolprocess,whereas a parameter design language (APDL), which is used to
ANSYSisresponsibleforfiniteelementcalculation.Thedata complete the finite element analyses automatically. APDL’s
generatedbyMATLAB’soptimizationmodulearepassedto command is a type of script command, which can provide
ANSYS for structure analyses and ANSYS then returns the users with parameters, vectors, cycles, and a series of func-
updatingdatatoMATLAB’soptimizationmodule.Thiscycle tions,whileabatchedanalysestechniqueisalsoprovidedby
is repeated until the results converge. During this process, ANSYS.
6 MathematicalProblemsinEngineering
The basic steps of the parametric finite element anal- anobjectivefunction,andreturningobjectivefunctionvalues
yses method are as follows. First, abstract the character- to the optimization algorithm. The method used to call an
istic parameters of the described model according to the objectivefunctionisshowninFigure2.
geometrical structure of the model and simplify them as
ObjectiveFunctionLibrary.Differentobjectivefunctionsare
appropriate. Second, establish the finite element analyses
calculated depending on the parameters transferred from
process, including entity modeling, analyses, and results
parafinder. Each objective function has its own name and
treatment processes, using the command stream file in
themainfunctionsincludeobtainingtheparameterspassed
ANSYS. Third, replace the parameters in the model with
bythemasterprogram,obtainingthedataproducedbythe
abstracted characteristic parameters by APDL, which con-
optimization algorithm, and calculating the objective func-
stitutes the finite element analyses process with variable
tionvalue.Basedonthecommonlyusedobjectivefunctions
parameters. Finally, depending on the requirements of the
forbridgemodelupdatingtoproduceanobjectivefunction
designandanalyses,providespecificcharacteristicvaluesto
librarywithastandardinterface,wedevelopedtheobjective
the parameters and conduct the finite element analyses to
function library table shown in Table1. The standard input
obtain the results. The main difference between parametric
andoutputofeachobjectivefunctionareshowninTable2.
finiteelementanalysesandgeneralfiniteelementanalysesis In the table, 𝑓𝑎𝑖 and 𝑓𝑡𝑖 represent the calculated frequency
that the preprocessing geometry model, material property, and test frequency, respectively, 𝜙𝑎𝑖 and 𝜙𝑡𝑖 represent the
loading, and boundary conditions are parametric and the
calculatedmodalvectorandtestmodalvector,respectively,
parametersmustbeassignedvaluesbeforethecalculations. and 𝑢𝑎𝑖 and 𝑢𝑡𝑖 represent the calculated static displacement
Dependingonthebasicflowoftheparametricfiniteele-
andthemeasureddisplacement,respectively.
mentanalyses,wedividethegeneralfiniteelementmodelinto
thecorrespondingmodulesshowninFigure1.Ansysconsole
4.4. Intelligent Algorithm Library Design. After establishing
isthemaincontrolmoduleofthemodel,whichisresponsible
theobjectivefunction,themodelupdatingproblemistrans-
for the finite element analyses process control. Text file
formed into a constrained optimization problem with mul-
Inf and Para are the initial parameter files of parametric
tiobjectivefunctions.Inthissection,themainproblemthat
model,whereInfrecordsthemodel’scalculationtype,basic
needstobesolvedisdevelopingamethodthataddressesthe
parameters, and so forth and Para records the trial data
modelupdatingproblem,thatis,theoptimizationalgorithm.
generated by the optimization algorithm. MCF and MCS
MATLABprovidesintelligentalgorithmlibraries,whichcan
aretheresultfilesforthefiniteelementanalyses,wherethe
be used as tools by the model updating software. We used
former records the modal frequency and the latter records
PSO as a possible method for the intelligent optimization
themodalshape.Thesefourfilescomprisethedatamoduleof
algorithmclasslibrary.
themodelandtheyarethekeycomponentsoftheinteraction
withMATLAB,thatis,Model,Loading,D&D,andBCform The PSO Intelligent Algorithm. The PSO algorithm was
thebasicmodelfile,whereModelistheinitialmodel,Loading inspiredbypopulationbehaviorandhasbeenusedtosolve
simulatestheloadconditions,D&Dcansimulatethedamage optimizationproblems.Inthealgorithm,eachcaserepresents
and performance degradation of the structure, and BC is a potential solution to the problem, where each particle
themodelboundarycondition.Specificmodulescanalsobe has a corresponding fitness value that is determined by s
added to the fixed format. Finally, Cal m is the computing fitness function. The velocity of a particle determines the
coreofthemodelthathandlesthemodelanalyses. direction and distance of the particle’s movement, where
the velocity is adjusted dynamically based on the particle’s
4.3. Objective Function Library Design. An objective func-
experience, thereby allowing individual optimization in the
tion is a metric used to describe the level of difference
solutionspace.ThecallingformatforthePSOalgorithmisas
betweentheoreticalandexperimentalmodelfeatures,which
follows:
comprised the geometrical and mechanical parameters of
the structure. Optimization processes are error-minimizing d shown=[]; %PSO drawing parameters.
processesthatareappliedtotheexperimentalmodelandthe
D=; % The dimension of the input.
theoretical model. The objective functions used for model
updatingincludestatic-basedobjectivefunctions,dynamic- mv=60; % The largest particle velocity.
basedobjectivefunctions,andstaticanddynamiccombined VR=[];% Hunting zone.
objectivefunctions.
PSO = [10 300 20 3 3 0.9 0.9 100 1e-25
Method for Calling an Objective Function. Because the data
2000 1e-5 1 1 1e-5 10 10.0];
generatedbytheintelligentalgorithmsaretheinitialparam-
eters that need to be updated and the data needed by the % Basic parameters of PSO.
objective function are the corresponding responses of the
seed=;%Original value.
structure, an interface function, called parafinder, must be
established between the intelligent algorithm and objective [optOUT,tr,te,bestpos]
function.Itsmainfunctionsarepassingtheparameterspro- =pso Trelea vectorized
vided by master program, passing the parameters provided
("parafinder",D,d shown,mv,VR,0,PSO,
bytheoptimizationalgorithm,preliminaryprocessingofthe
parametersprovidedbytheoptimizationalgorithm,selecting "goplotpso",seed);
MathematicalProblemsinEngineering 7
Damage model and
FEM Load performance degradation Boundary ···
model model condition model
model
Inf.txt MCF.txt
Ansysconsole
Para.txt MCS.txt
Input the parameters for Calm Output the results
algorithm modules and of model updating
Analysis and computing engines
functions
Figure1:SchematicoftheparameterizedFEmodel.
Optimization algorithm
Parafinder Objective function
Objfuncs Objfunc-f1 Objfunc-mac ···
Figure2:Invokingaroutineusingthetargetfunctionslibrary.
Table1:Libraryoftargetfunctions.
Objectivefunctiontype Features Name Functionname
Static-based Staticobjectivefunction Objfuns
Staticanddynamicbased Staticanddynamicobjectivefunction Objfunsd
Objfund-f1
Frequency
Objfund-f2
Objfund-mac1
Transmissioncharacteristics Modeofvibration
Objfund-mac2
Strainmode Objfund-strain
Frequency-responsefunction Objfund-response
Modalcurvature Objfund-mcurvature
Transmissioncurvature
Flexibilitycurvature Objfund-fcurvature
Frequencybandenergyspectrum Objfund-spectrum
Characteristicparameter
Dynamic-based Subbandenergyspectrum Objfund-subspectrum
Jointfrequencyandmodeshape Objfund-fmac
Complexfunction Flexibilitymatrix Objfund-fmatrix
Modalstrainenergy Objfund-starinenergy
Table2:Input-outputtargetfunctionslibrary.
Objectivefunction Remarks Input Output
Objfun-df1 Frequencychangesquareratio 𝑓 ,𝑓 Dependsonitsdefinition[20]
ai ti
Objfun-df2 Frequencychangesquareratio 𝑓 ,𝑓 Ditto
ai ti
Objfun-mac1 Modalassurancecriterion 𝜙 ,𝜙 Ditto
ai ti
Objfun-mac2 Modalassurancecriterion 𝜙 ,𝜙 Ditto
ai ti
Objfun-fmac Jointfrequencyandmodeshape 𝑓 ,𝑓,𝜙 ,𝜙 Ditto
ai ti ai ti
Objfuns Staticobjectivefunction 𝑢 ,𝑢 Ditto
ai ti
Objfunsd Staticanddynamicbased 𝑢 ,𝑢 𝑓 ,𝑓,𝜙 ,𝜙 Ditto
ai ti ai ti ai ti
8 MathematicalProblemsinEngineering
Table3:Libraryofintelligentoptimizationalgorithms.
Type Name Interface Input Output
Traditionalalgorithm Sequentialquadraticprogramming byfmincon a,b 𝑋𝑁
Particleswarmoptimization Bypso a,b,c,d,e 𝐴𝑀×𝑁
Geneticalgorithm Byga a,c,f,g,h,i 𝐴𝑀×𝑁
Intelligentalgorithm Artificialfish-swarmalgorithm Byaf a,c,j,k,l,m 𝐴𝑀×𝑁
Antcolonyalgorithm Byaca a,s,n,o,p 𝐴𝑀×𝑁
Immunealgorithms Byia a,c,h,i,q,r,s 𝐴𝑀×𝑁
Annealingalgorithm Bysa t,u,v,w 𝐴𝑀×𝑁
Parafinder is an interface function between the PSO algo-
Master control program
rithmandtheobjectivefunctionlibrary.
Intelligent Optimization Algorithm Library. Based on the
callingmethodandthemethodusedtoestablishtheinterface Intelligent optimization Loop iteration
functionwiththePSOalgorithm,thestandardprogramming algorithm
libraryincludingothercommonlyusedintelligentoptimiza-
tionalgorithmsisshowninTable3.
InTable3,theparametersoftheoutput𝑋𝑁,whichisan FEM module Objective functions
𝑁-dimensionaltrialvectorwhere𝑁isthenumberofparam-
eters,areasfollows:𝐴𝑀×𝑁representsan𝑀∗𝑁trialmatrix, Figure 3: Flowchart of the software system for intelligent model
𝑀representsthesizeofthepopulation,and𝑁representsthe updating.
numberofparameters.Theinputparametersareasfollows:
𝑎representsthemaximumnumberofiterations,𝑏represents Table4:Parameterstobeupdated.
theconvergenceerror,𝑐representsthesizeofthepopulation,
𝑑 represents the algorithm type, 𝑒 represents the disturbed Num. Parameter Initialvalue Upperlimit Lowerlimit
value, 𝑓 represents the individual length, 𝑔 represents the 1 (𝐸)Mpa 3.2×104 3.6×104 2×104
generationgap,histhecrossoverprobability,𝑖isthemutation 2 (𝐷)kg/m3 2.5×103 2.6×103 2.2×103
probability, 𝑗 represents the largest feed testing number, 𝑘 3 (𝐾1)N⋅m/rad 1000 1×106 0
rdeepgrreeseenfatsctopre,rc𝑚eprtieopnresdeinsttasntchee, lmroevpirnegsesnttesp,th𝑛ercerporwesdeinntgs 45 ((𝐾𝐾23))NN⋅⋅mm//rraadd 11000000 11××110066 00
the importance factor of a pheromone, o represents the 6 (𝐾4)N⋅m/rad 1000 1×106 0
importancefactorofaninspirationfunction,prepresentsthe
pheromone volatilization factor, 𝑞 represents the volume of
a memory database, 𝑟 represents the evaluation parameters 5.VerificationoftheValidityof
ofdiversity,𝑠representsthenumberofdistributioncenters,
thePrototypeSoftware
𝑡 represents the cooling rate, 𝑢 represents the initial tem-
perature, v represents the termination temperature, and 𝑤
5.1. Offline Verification of the Prototype Software Intelligent
representsthechainlength.
UpdatingPlatform:ContinuousBeamExperiments. Thetest
model was a three-span reinforced concrete continuous
4.5.TechnicalProposalandPrototypeSoftwarefortheModel beamstructure,wherethethreespanswere1000,1700,and
Updating Platform. After choosing appropriate updating 1700mm,respectively,asshowninFigure4.Atthebottomof
parameters, it is necessary to enter the updating module, thecontinuousbeam,therewerefivepositions,thatis,A,B,C,
where the parameters produced by the optimization algo- D,andE,whichwereinstalledwithaccelerationsensors.The
rithm are subjected to finite element analyses to determine test was a single-point excitation method and the sampling
the physical quantities that correspond to the measured frequencywas512Hz.
values.Theobjectivefunctionvalueiscalculatedtodetermine Before model updating, the parameters with greater
whetherthemodelerrorhasbeenminimizedandtodeter- sensitivityshouldbeselectedastheparametersforupdating.
minewhethertheiterationsshouldcontinue;otherwisethe Basedonthestructure,theparametersselectedareshownin
updatingprocessisover.Thebasicflowchartofthisprocess Table4.
isshowninFigure3. InTable4,𝐸istheelasticmodulus,𝐷isthedensity,and
Basedonprocesses,theprototypeoftheoverallsoftware 𝐾𝑖istherotationalstiffnessofthe𝑖thbearing.
frameworkwasimplementedusingMATLABinaprototype Based on a model test where the physical quantities
program.ANSYSwasreadilyimplementedintheMATLAB were measured, the objective function given in (8) was
environmenttocombinethemodel,objectivefunction,and selectedasthe𝑚function,Objfund-fmac,fromtheobjective
optimization algorithm, thereby implementing the overall functionlibrary.AfterselectingthePSOalgorithmfromthe
processofautomatedmodelupdating. intelligent optimization algorithms library and configuring
MathematicalProblemsinEngineering 9
3800
50 1000 1700 1000 50
0
3 1 2 3 4
3800
00 A B C D E
2
Figure4:Three-spancontinuousbeamtest.
Table5:Parametersforupdating. 0.2
Num. Parameter Originalvalues Updatingvalues
1 (𝐸)Mpa 3.2𝑒4 2.67𝑒4
2 (𝐷)kg/m3 2.5𝑒3 2.53𝑒3 0.15
3 (𝐾1)N⋅m/rad 1000 48320.33 on
4 (𝐾2)N⋅m/rad 1000 2448.81 ncti
5 (𝐾3)N⋅m/rad 1000 87109.14 e fu 0.1
6 (𝐾4)N⋅m/rad 1000 233.8 ctiv
e
bj
O
0.05
theappropriateoperatingparameters,the𝑚scriptautomati-
callyperformedthetasksuccessfully.Theobjectivefunction
approximately reached convergence and the convergence
process is shown in Figure5. The parameters searched are
0 250 500 750 1000 1250 1500 1750 2000
shown in Table5. A comparison of the model parameters
Iterations
beforeandafterupdatingisshowninTable6.
Table6showsthattheupdatedfrequencywasveryclose Figure5:Convergencecurveoftheobjectivefunction.
to the measured frequency and the testing frequency error
wasbelow1%,withtheexceptionofthethirddegree.Allfour accelerationrecordsautomaticallyusingacompiled𝑚script,
MAC values were above 0.9, which shows that the updated
identifiedthecablevibrationfrequencyautomatically,called
model correlated well with the measured model, and this
the ANSYS program automatically for model analyses by
also demonstrated the effectiveness of the updating results.
building a finite element model, inputted the measured
The updating process was simple to write in the MATLAB
frequency and the calculated frequency into the objective
script where the main contents of the script were model
function automatically, selected the PSO algorithm from
selection,theobjectivefunctionandoptimizationalgorithm,
the intelligent optimizationalgorithm library, automatically
configuring the input parameters of the calling functions,
updatedthecablemodelonline,selectedthecableforceand
callingANSYS,monitoringANSYSperformance,andfinally
bending stiffness as the updating parameters, and finally
outputting the calculated results file. After launching, the
providedtheupdatedresults.
wholeprocessranautomaticallyandtherewerenorequire-
Based on the parameters of the cable obtained from
ments for manual intervention. This example demonstrates
thedesigndata,theseparametersweregivencorresponding
the feasibility of our proposed automatic model updating
inputvariableswhencallingtheparameterizedfiniteelement
softwareframework.
model.ThePSOalgorithmwasselectedforupdatingandthe
objectivefunctionapproximatelyconvergedafter20iteration
5.2. Online Verification of the Prototype Software Intelligent steps. The results for the cable force and bending stiffness
UpdatingPlatform:CableForceMonitoring. Intheprevious areshowninTable7,wherethereferencevalueofthecable
example, the feasibility of automated model updating was force was obtained using the frequency formula and the
verified offline with measured data. However, it is more error between the identified cable force and the calculated
challenging and useful to update the structure online using cable force was 3.3%. EI0 represents the identified bending
ongoing experimental data. Therefore, we considered the stiffness, while EI1 and EI2 represent the bending stiffness
selection of real-time cable monitoring devices on a cable- when the steel cable was treated as a fully bonding model
stayed bridge, which was equipped with structure mon- andasanobindingmodel,respectively.Acomparisonofthe
itoring system. We connected the prototype software to frequenciesderivedfrommodelupdatingandtheidentified
the monitoring system using a MATLAB program that we frequencies is shown in Table8. The curve of the updating
developed,whichreadthedatafromtheremoteweb-based processobjectivefunctionisshowninFigure6.
bridgemonitoringsystem[27],establishedawebconnection AsshowninTable8,thefrequencysequencescalculated
to a specific cable acceleration channel, captured the cable by the automatic model updating prototype software and
10 MathematicalProblemsinEngineering
Table6:Frequenciesandmodalshapeparametersafterupdating.
Testfrequency Original Updating Errorbefore Errorafter MACbefore MACafter
Degree
(Hz) frequency(Hz) frequency(Hz) updating(%) updating(%) updating updating
1 26.38 25.02 26.26 4.76 0.5 0.995 0.98
2 57.68 54.75 58.37 5.06 1.2 0.937 0.989
3 65.22 64.54 65.15 1.05 0.1 0.955 0.979
4 88.49 93.11 87.89 5.22 0.7 0.817 0.901
Table7:Identifiedcableforcesandflexiblestiffness. ×10−3
1.1
/ Cableforces(kN) / Flexiblestiffness(kN⋅m2)
Updatedvalue 2900 EI 486 1.08
0
Referencevalue 3000 EI 511
1
1.06
Error(%) 3.3 EI 3.4
2 n
o
cti 1.04
Table8:Frequenciesafterupdating. un
e f 1.02
v
Order Measuredfrequencies Updatedfrequency Error ecti
(Hz) (Hz) (%) bj 1
O
1 1.27 1.304 2.61
0.98
2 2.637 2.609 1.07
3 3.906 3.915 0.23 0.96
4 5.273 5.223 0.96 0 20 40 60 80 100
5 6.543 6.533 0.15 Iterations
6 7.91 7.848 0.79
Figure6:Convergencecurveforthetargetfunction.
7 9.18 9.166 0.15
the measured frequency sequences were approximately the monitoring system. The results demonstrated the feasibility
same; that is, maximum error was 2.61% and the bending ofourmethodformonitoring-basedonlineintelligentmodel
stiffnessestimatewasalsoreasonable.Theseresultsindicate updating.
that the proposed model updating prototype software also
performswellandreliablyinanonlineenvironment,which ConflictofInterests
isimportantforitsfurtherdevelopment.
The authors declare that there is no conflict of interests
6.ConclusionsandProspects regardingthepublicationofthispaper.
In this study, we developed an intelligent model updating Acknowledgment
prototype software framework platform, which is based
on the commercial finite element software, ANSYS, and This project was supported by The Project of National Key
the scientific computing software, MATLAB. The proposed TechnologyR&DPrograminthe12thFiveYearPlanofChina
parameterized ANSYS finite element modeling scheme is (Grantno.2012BAJ11B01).
suitable for updating different bridge structure models. We
builtastandardobjectivefunctionlibraryfordifferentupdat-
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