Excitation considerations for attractor property analysis in vibration-based damage detection

ExcitationConsiderationsforAttractorProp ertyAnalysisinVibrationBasedDamageDetectionStephenTrickey,Michael Todd,MarkSeaver,andJon NicholsCo de5673, Fib er Optic SmartStructuresSection,U.S.Naval ResearchLab oratory,Washington, DC20375ABSTRACTInpast work, wehave presented a metho dology for vibration based damage detection derived from the char-acterization of changes in the geometric prop erties of the time domain resp onse of a structure.In brief, inputforcingsignalsandoutputresp onsecanbetransformedintostatespacegeometricalrepresentations.When allowed to evolve to a steady state, the geometric ob ject is called an attractor.Certain prop erties of theattractor,such as the lo cal variance ofneighb orho o ds of p ointsorprediction errors b etweenattractors, havebeen shown to correlate directly with damage.Whilemostinputswillgeneratesometyp eofattractinggeometricob ject,prescribingalowdimensionalinput forcing signal helps to maintain a low dimensional output signal which in turn simpli es the calculationofattractor prop erties.Work todate has incorp oratedtheuse ofachaotic inputforcing signal based onitslowdimensionalityetusefulfrequencycontent.Inthisorkeevaluatevariousformsofshap ednoiseasalternative e ectively low dimensional inputs.We assess whether the intrinsic prop erties of the chaotic inputleadstob etterdamagedetectioncapabilitiesthanvariousshap ednoiseinputs.Theexp erimentalstructureconsidered is a thin plate with weld line damage.Keywords:Attractor Prop erty Analysis, Chaotic Input, Band Limited Noise Input1. INTRODUCTIONFor the problem of damage detection or more generally structural health monitoring, a standard approachistopro ceedwithsomeformofsystemidenti cationtifyinitiallyhealthysystems andlaterp otentiallydamagedsystems.Bycomparingafeatureofinterestfromtheidenti edtestsystemwiththehealthy baselinesystem,anassessmentofsystem's healthcan b emade.Attractor prop erty analysismetho ds for damage detection pro ceed with a di erent fo cus than other metho ds particularly with regard to theactual system identi cation.Currenttechniques underconsideration for health monitoring problems pro ceedwith their resp ective system identi cations with well established metho ds such as ARMA, neural networks,1, 2and subspace metho ds3, 4as well as metho dsthatreturnvarious mo dalprop erties such as frequencies,mo deshap es, damping and strain energy.5, 6Attractor prop erty analysis metho ds tend to distinguish themselves from other metho ds due to the fact thatthe attractor is essentially the mo del.The attractor, comp osed directly from the dynamic output resp onse ofa system, is the source of the features intended for the assessing of damage.Alternatively, the attractor can b ethought of a as a geometric realization of the steady state dynamics of the system.The system identi cationthus reduces to recording the resp onse of a system to an input.The goal of the metho d then is to determine afeature of the attractor and thus a feature of the steady state dynamics that characterizes damage.Two e ective damage detection features that can b e generated from attractors are lo cal variance ratio7andprediction error.8The variance ratio feature indicates how the disp ersion of the input forcing signal relates tothe disp ersion of the output resp onse signal.Given a xed input signal, anychanges in the ratio are due to achange inthesystem.Thisfeature e ectivelymonitors changesinasystem'senergy dissipationmechanism.Theprediction error feature,the featureusedinthispap er,is ameasure of howell thedynamics ofatestattractor can b e predicted based on the dynamics of a baseline attractor.Much simpler than an ARMA mo del,