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Page 1: Monitoraggio di strutture Aeronautiche basato su misure di vibrazioni Luigi Balis Crema, Giuliano Coppotelli, Franco Mastroddi Dipartimento di Ingegneria.

Monitoraggio di strutture Aeronautiche basato su misure di vibrazioniLuigi Balis Crema, Giuliano Coppotelli, Franco MastroddiDipartimento di Ingegneria Aerospaziale ed Astronautica

Via Eudossiana, 1800184 Roma

[email protected]

Sommario – L’aumento dell’affidabilità e la riduzione dei costi operativi associati alla gestione di elicotteri, aerei, strutture spaziali, ma anche di infrastrutture civili o di altro tipo, rappresentano delle richieste che stanno assumendo un peso sempre più importante nell’ambito della progettazione strutturale. L'aumento dell'affidabilità e la riduzione dei costi operativi associati alla gestione di elicotteri, aerei, strutture spaziali, ma anche di infrastrutture civili o di altro tipo, rappresentano delle richieste che stanno assumendo un peso sempre più importante nell'ambito della progettazione strutturale. Oltre alla presenza di danni localizzati, è anche possibile rilevare un danneggiamento di tipo diffuso e/o ampiamente distribuito il cui rilevamento è praticamente impossibile utilizzando le tradizionali tecniche non distruttive (Non Destructive Evaluation - NDE). In questa categoria di danneggiamento è possibile far rientrare, ad esempio, gli effetti della fatica in strutture composite ed il danneggiamento multiplo che si rileva in strutture aerospaziali in seguito all'invecchiamento delle leghe di alluminio. Attualmente, le tecniche non distruttive per l'identificazione del danneggiamento impiegate nella manutenzione di elicotteri ed aerei prevedono un intervento manuale nei vari sottosistemi. Pertanto, la qualità della verifica strutturale è fortemente influenzata dall'abilità dell'operatore ed inoltre queste tecniche richiedono un elevato periodo di in operatività dell'intero sistema. La possibilità di unire i recenti sviluppi compiuti sia in ambito di identificazione di danneggiamento strutturale tramite l'analisi delle vibrazioni del sistema (indicate in genere come tecniche "Structural Health Monitoring" - SHM), sia in ambito di identificazione dei parametri dinamici globali attraverso la valutazione delle sole risposte dinamiche del sistema (tecniche di stima a cui in genere va l'appellativo di "Output-Only" o "Natural Input Modal Analysis") potrebbe migliorare sensibilmente l'affidabilità di strutture aerospaziali. Sebbene sia già possibile stimare la firma dinamica di un sistema attraverso le diverse metodologie Output-Only (ed in questo ambito il gruppo di ricerca ha contribuito e continua a fornire il suo apporto per ulteriori sviluppo di tali metodologie) queste non sono ancora impiegate per la valutazione del danneggiamento strutturale. Tali tecniche Output-Only, permettendo la stima delle proprietà dinamiche del sistema direttamente nel corso delle diverse fasi di volo, ossia "in situ", potrebbero sensibilmente ridurre non solo i tempi, ma anche i costi associati a tali analisi dinamiche sperimentali. Inoltre, è possibile immaginare un uso congiunto delle metodologie appena descritte con l'uso di sensori distribuiti, del tipo "Active Fiber Composite - AFC attualmente disponibili in commercio, per aumentare sensibilmente il numero dei punti di misura e quindi lasciare intravedere la possibilità di sviluppare delle metodologie innovative di identificazione di danneggiamento distribuito. Come risulta dai riferimenti bibliografici, tale proposta di ricerca si inserisce nel quadro di attività sviluppate dal gruppo proponente negli ultimi anni nel settore dell'analisi dinamica di strutture aerospaziali.

Damage identification techniques based on the Damage identification techniques based on the evaluation of the change of an Output signal wrt the evaluation of the change of an Output signal wrt the reference:reference:

Response ModelResponse Model

Uncertainties minimized through reduction Uncertainties minimized through reduction

of data handling and manipulationof data handling and manipulation

Health of the structure monitored evaluating changing in Health of the structure monitored evaluating changing in design parameter related to mass and stiffness design parameter related to mass and stiffness distributiondistribution

Damage identification techniques based on the evaluation of Damage identification techniques based on the evaluation of

the change of an Output signal wrt the reference:the change of an Output signal wrt the reference:

Modal Model, Response Model, Sound, UltrasoundModal Model, Response Model, Sound, Ultrasound

Theoretical BackgroundTheoretical Background 1/11/1[Grafe, 1998][Grafe, 1998]

Theoretical BackgroundTheoretical Background 1/11/1[Grafe, 1998][Grafe, 1998]

X X ,,AA = Experimental, Analytical= Experimental, Analytical

Sensitivity of the system to changes in the design parameters:

Correlation functions:

Differences between the reference and the actual strucure:

Unknown changes of design parameters, , given for each i-th iteration step by:

IntroducingIntroducing the the weighting matrices:weighting matrices:

minimizing the functional:minimizing the functional:

The solution is given by:The solution is given by:

and therefore:and therefore:

Theoretical BackgroundTheoretical Background 2/32/3Theoretical BackgroundTheoretical Background 2/32/3 Theoretical BackgroundTheoretical Background 3/33/3Theoretical BackgroundTheoretical Background 3/33/3

Localized and small entities of structural damage requires Localized and small entities of structural damage requires high number of high number of

DOFs in FEMDOFs in FEM

Design parametersDesign parameters

Damage identification process divided into consecutive Damage identification process divided into consecutive steps:steps:

For each iteration step, only the most sensitive design For each iteration step, only the most sensitive design parameters to actual dynamic difference are retainedparameters to actual dynamic difference are retained

Those parameters could differ from one iteration to Those parameters could differ from one iteration to anotheranother

Small structural changes identified with acceptable Small structural changes identified with acceptable computational costs computational costs

Experimental Analysis based on

Output Only

Dynamic Response model

Added masses

UndamagedStructure

Damaged StructureVariation of

globalparameters

DamageIdentification

Heath monitoring with OO approachHeath monitoring with OO approachHeath monitoring with OO approachHeath monitoring with OO approach Results: experimental investigation Results: experimental investigation 1/6 1/6 Results: experimental investigation Results: experimental investigation 1/6 1/6

Initial Initial correlationcorrelation Experimental analysis:Experimental analysis:

Modal impactModal impact

Free-Free B.C.Free-Free B.C.

Freq. Band: 0-640 HzFreq. Band: 0-640 Hz

4096 Spectral lines4096 Spectral lines

81 DOFs (trasversal)81 DOFs (trasversal)

Reduction of Reduction of 20% of 20% of thicknessthickness at the center of the at the center of the plate (corresponding to the plate (corresponding to the 28° element)28° element)

0.6%0.6% average change in average change in ffnn

No effects on damping No effects on damping ratiosratios

Results: experimental investigationResults: experimental investigation 2/62/6 Results: experimental investigationResults: experimental investigation 2/62/6

Looking for damage in both mass and stiffnessLooking for damage in both mass and stiffness

64 + 64 design parameters64 + 64 design parameters

12 Experimental Dofs considered12 Experimental Dofs considered

The method do NOT identify the correct parameter (# 28)The method do NOT identify the correct parameter (# 28)

Results: experimental investigationResults: experimental investigation 3/63/6 Results: experimental investigationResults: experimental investigation 3/63/6

a) Stiffness related design parametersa) Stiffness related design parameters b) Mass related design parametersb) Mass related design parameters

Convergence historyConvergence history

WrongWrong stiffness-related design parameters identified stiffness-related design parameters identified

ImmaterialImmaterial changes in the mass-related design parameters # 28,33,60 changes in the mass-related design parameters # 28,33,60

Results: experimental investigationResults: experimental investigation 4/64/6 Results: experimental investigationResults: experimental investigation 4/64/6

OPEN QUESTIONOPEN QUESTION

Localization process identified Localization process identified correct damaged region for mass correct damaged region for mass distribution, not for stiffnessdistribution, not for stiffness

Actual damage involves mostly Actual damage involves mostly the stiffness characteristics, the the stiffness characteristics, the mass changes are H.O.T.mass changes are H.O.T.

Mass-related design parameters Mass-related design parameters reduces the stability of the reduces the stability of the

numerical algorithmnumerical algorithm(Least Square solution)(Least Square solution) Lack of damage identification Lack of damage identification

due to NON optimal selection of due to NON optimal selection of design parameters? design parameters? (from numerical point of view)(from numerical point of view)

Results: experimental investigationResults: experimental investigation 5/65/6 Results: experimental investigationResults: experimental investigation 5/65/6

Looking for damage in stiffness distribution Looking for damage in stiffness distribution onlyonly

64 design parameters64 design parameters

12 Experimental Dofs considered12 Experimental Dofs considered

Procedure speed up using a sensitivity matrix built on Procedure speed up using a sensitivity matrix built on a frequency band of [0,300] Hz (final dimensions: 2450 a frequency band of [0,300] Hz (final dimensions: 2450 ££ 64)64)

After 4 steps, the number of design parameters useful After 4 steps, the number of design parameters useful to describe the damage condition reduces to 2to describe the damage condition reduces to 2

Results: experimental investigationResults: experimental investigation 6/66/6 Results: experimental investigationResults: experimental investigation 6/66/6

Convergency history of stiffness Convergency history of stiffness related design parameter- Step #4related design parameter- Step #4

Effects on global parametersEffects on global parameters

Two adjacent elements identified (# 28 and 36) Two adjacent elements identified (# 28 and 36) corresponding to the actual damage locationcorresponding to the actual damage location

reduction in the eigenfrequency shiftsreduction in the eigenfrequency shifts

increase in the correlation among the FRFsincrease in the correlation among the FRFs

Experimental investigation: OO test on the undamaged structureExperimental investigation: OO test on the undamaged structure Experimental investigation: OO test on the undamaged structureExperimental investigation: OO test on the undamaged structure

(LSCE-FDD)

GENERALIZED MASSES (DIAA, [2002])

Experimental investigation: mode correlationExperimental investigation: mode correlation Experimental investigation: mode correlationExperimental investigation: mode correlation

Variation of thickness: 5%

Experimental investigation: damaged structureExperimental investigation: damaged structure Experimental investigation: damaged structureExperimental investigation: damaged structure

FREQUENCY SHIFT DAMAGED V.S.

UNDAMAGED MODELS

FRF COMPARISON ON THE FIRST

MEASUREMENT POINTS

0.88%

Experimental investigation: comparisonExperimental investigation: comparison Experimental investigation: comparisonExperimental investigation: comparison

The procedure has been developed and successfully The procedure has been developed and successfully applied to an aluminum plateapplied to an aluminum plate

Sensitivity-based approach (from structural updating Sensitivity-based approach (from structural updating discipline) enhanced with a “by-step” algorithmdiscipline) enhanced with a “by-step” algorithm

Reduction of numerical instability, from “Reduction of numerical instability, from “noisy data”noisy data”, , computer memory, and computational time achievedcomputer memory, and computational time achieved

Blind search is dangerous:Blind search is dangerous:Design parameters MUST describe the topology of Design parameters MUST describe the topology of the actual damagethe actual damageAnalysis speed up with a suitable frequency bandAnalysis speed up with a suitable frequency band

The proposed methods allow the damage The proposed methods allow the damage identification by means of the estimate of modal identification by means of the estimate of modal parametersparameters Approximated solution procedure: least square Approximated solution procedure: least square technique with not-unique solutionstechnique with not-unique solutionsThe effectiveness of the approach is based on the The effectiveness of the approach is based on the employments of critical points and on small structural employments of critical points and on small structural variationsvariationsThe OO technique (The OO technique (e.g., e.g., based on the use of the based on the use of the strain-gage) allows to estimate the variation of the strain-gage) allows to estimate the variation of the modal parameteres also for small structure modal parameteres also for small structure perturbationsperturbationsThe OO approach can be used for the (SHM) The OO approach can be used for the (SHM) Structural Health Monitoring of Aerospace structuresStructural Health Monitoring of Aerospace structures

Concluding Remarks:Concluding Remarks: Concluding Remarks:Concluding Remarks:

Component disembark Component disembark requiredrequired

• Low sensitivity to damage levelLow sensitivity to damage level• Fine tuning of the F.E. modelFine tuning of the F.E. model• Low accuracy of experimental data from estimating Low accuracy of experimental data from estimating processprocess

Various type of damage Various type of damage identifiable from identifiable from • the natural frequency shiftthe natural frequency shift• pattern modification of mode shapespattern modification of mode shapes

Theoretical BackgroundTheoretical Background 1/31/3Theoretical BackgroundTheoretical Background 1/31/3 Theoretical BackgroundTheoretical Background 2/32/3Theoretical BackgroundTheoretical Background 2/32/3

Damage identification by iteratively solving a non-linear Damage identification by iteratively solving a non-linear optimization procedure via least square algorithm optimization procedure via least square algorithm

F.E. model represents the reference structureF.E. model represents the reference structureA sensitivity matrix, and error vector built from the A sensitivity matrix, and error vector built from the correlation of the FRF analytical and experimentalcorrelation of the FRF analytical and experimental

Localized and small damage entity requiredLocalized and small damage entity required

Refined numerical model and high number of design Refined numerical model and high number of design parameters are neededparameters are needed

““by-step”by-step” enhancement is proposed for reduction of both enhancement is proposed for reduction of both computational time and computer memory amount computational time and computer memory amount

Numerical and experimental validation reportedNumerical and experimental validation reported

Theoretical BackgroundTheoretical Background 1/31/3Theoretical BackgroundTheoretical Background 1/31/3

Advantage of Output-Only technique for the estimate of the modal Advantage of Output-Only technique for the estimate of the modal parameters parameters

Only the output time responses of the structure are employedOnly the output time responses of the structure are employedMeasurements of the input loads of the structure are not Measurements of the input loads of the structure are not necessary necessary The used output data are those of the structure in operative The used output data are those of the structure in operative conditions conditions save costs and timesave costs and time

The approach is particularly convenient whenever the input is The approach is particularly convenient whenever the input is unknownunknown

Aerospace field: aeroelastic phenomenaAerospace field: aeroelastic phenomenaCivil field: vibrations of builds and bridgesCivil field: vibrations of builds and bridges

Heath monitoring with OO approachHeath monitoring with OO approachHeath monitoring with OO approachHeath monitoring with OO approach