Monitoraggio di strutture Aeronautiche basato su misure di vibrazioni Luigi Balis Crema, Giuliano...
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Monitoraggio di strutture Aeronautiche basato su misure di vibrazioni Luigi Balis Crema, Giuliano Coppotelli, Franco Mastroddi Dipartimento di Ingegneria Aerospaziale ed Astronautica Via Eudossiana, 18 00184 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 Damage identification techniques based on the evaluation of the change of an Output the evaluation of the change of an Output signal wrt the reference: signal wrt the reference: Response Model Response Model Uncertainties minimized through Uncertainties minimized through reduction reduction of data handling and manipulation of data handling and manipulation Health of the structure monitored evaluating Health of the structure monitored evaluating changing in design parameter related to mass changing in design parameter related to mass and stiffness distribution and stiffness distribution ge identification techniques based on the evaluation of e 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, Ultrasound Modal Model, Response Model, Sound, Ultrasound Theoretical Background Theoretical Background 1/1 1/1 [Grafe, 1998] [Grafe, 1998] X X ,A = Experimental, Analytical = Experimental, Analytical Sensitivity of the system to changes in the design parameters: Correlation functions: ifferences between the reference and the actual strucure: Unknown changes of design parameters, , given for each i-th iteration step by: Introducing Introducing 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 Background Theoretical Background 2/3 2/3 Theoretical Background Theoretical Background 3/3 3/3 Localized and small entities of structural Localized and small entities of structural damage requires high number of damage requires high number of DOFs in FEM DOFs in FEM Design parameters Design parameters Damage identification process divided into Damage identification process divided into consecutive steps: consecutive steps: For each iteration step, only the most For each iteration step, only the most sensitive design parameters to actual sensitive design parameters to actual dynamic difference are retained dynamic difference are retained Those parameters could differ from one Those parameters could differ from one iteration to another iteration to another Small structural changes identified with Small structural changes identified with acceptable computational costs acceptable computational costs Experimental Analysis based on Output Only Dynamic Response model Added masses Undamaged Structure Damaged Structure Variation of global parameters Damage Identification Heath monitoring with OO approach Heath monitoring with OO approach Results: experimental investigation Results: experimental investigation 1/6 1/6 Initial Initial correlation correlation Experimental analysis: Experimental analysis: Modal impact Modal impact Free-Free B.C. Free-Free B.C. Freq. Band: 0-640 Hz Freq. Band: 0-640 Hz 4096 Spectral lines 4096 Spectral lines 81 DOFs (trasversal) 81 DOFs (trasversal) Reduction of Reduction of 20% of 20% of thickness thickness at the center at the center of the plate of the plate (corresponding to the (corresponding to the 28° element) 28° element) 0.6% 0.6% average change average change in in f n No effects on damping No effects on damping ratios ratios Results: experimental investigation Results: experimental investigation 2/6 2/6 Looking for damage in both mass and Looking for damage in both mass and stiffness stiffness 64 + 64 design parameters 64 + 64 design parameters 12 Experimental Dofs considered 12 Experimental Dofs considered The method do NOT identify the correct parameter (# 28) The method do NOT identify the correct parameter (# 28) Results: experimental investigation Results: experimental investigation 3/6 3/6 a) Stiffness related design parameters a) Stiffness related design parameters b) Mass related design parameters b) Mass related design parameters Convergence history Convergence history Wrong Wrong stiffness-related design parameters identified stiffness-related design parameters identified Immaterial Immaterial changes in the mass-related design parameters # 28,33,60 changes in the mass-related design parameters # 28,33,60 Results: experimental investigation Results: experimental investigation 4/6 4/6 OPEN QUESTION OPEN QUESTION Localization process Localization process identified correct damaged identified correct damaged region for mass region for mass distribution, not for distribution, not for stiffness stiffness Actual damage involves Actual damage involves mostly the stiffness mostly the stiffness characteristics, the mass characteristics, the mass changes are H.O.T. changes are H.O.T. Mass-related design Mass-related design parameters reduces the parameters reduces the stability of the numerical stability of the numerical algorithm algorithm (Least Square solution) (Least Square solution) Lack of damage Lack of damage identification due to NON identification due to NON optimal selection of optimal selection of design parameters? design parameters? (from numerical point of view) (from numerical point of view) Results: experimental investigation Results: experimental investigation 5/6 5/6 Looking for damage in stiffness Looking for damage in stiffness distribution only distribution only 64 design parameters 64 design parameters 12 Experimental Dofs considered 12 Experimental Dofs considered Procedure speed up using a sensitivity Procedure speed up using a sensitivity matrix built on a frequency band of [0,300] matrix built on a frequency band of [0,300] Hz (final dimensions: 2450 Hz (final dimensions: 2450 £ £ 64) 64) After 4 steps, the number of design After 4 steps, the number of design parameters useful to describe the damage parameters useful to describe the damage condition reduces to 2 condition reduces to 2 Results: experimental investigation Results: experimental investigation 6/6 6/6 Convergency history of Convergency history of stiffness related design stiffness related design parameter- Step #4 parameter- Step #4 Effects on global Effects on global parameters parameters Two adjacent elements identified (# 28 Two adjacent elements identified (# 28 and 36) corresponding to the actual and 36) corresponding to the actual damage location damage location reduction in the eigenfrequency reduction in the eigenfrequency shifts shifts increase in the correlation among increase in the correlation among the FRFs the FRFs Experimental investigation: OO test on the undamaged Experimental investigation: OO test on the undamaged structure structure (LSCE-FDD) GENERALIZED MASSES (DIAA, [2002]) Experimental investigation: mode correlation Experimental investigation: mode correlation Variation of thickness: 5% Experimental investigation: damaged structure Experimental investigation: damaged structure FREQUENCY SHIFT DAMAGED V.S. UNDAMAGED MODELS FRF COMPARISON ON THE FIRST MEASUREMENT POINTS 0.88% Experimental investigation: comparison Experimental investigation: comparison The procedure has been developed and The procedure has been developed and successfully applied to an aluminum plate successfully applied to an aluminum plate Sensitivity-based approach (from Sensitivity-based approach (from structural updating discipline) structural updating discipline) enhanced with a “by-step” algorithm enhanced with a “by-step” algorithm Reduction of numerical instability, from Reduction of numerical instability, from “ “ noisy data” noisy data” , computer memory, and , computer memory, and computational time achieved computational time achieved Blind search is dangerous: Blind search is dangerous: Design parameters MUST describe the Design parameters MUST describe the topology of the actual damage topology of the actual damage Analysis speed up with a suitable Analysis speed up with a suitable frequency band frequency band The proposed methods allow the damage The proposed methods allow the damage identification by means of the estimate identification by means of the estimate of modal parameters of modal parameters Approximated solution procedure: least Approximated solution procedure: least square technique with not-unique square technique with not-unique solutions solutions The effectiveness of the approach is The effectiveness of the approach is based on the employments of critical based on the employments of critical points and on small structural points and on small structural variations variations The OO technique ( The OO technique ( e.g., e.g., based on the use based on the use of the strain-gage) allows to estimate of the strain-gage) allows to estimate the variation of the modal parameteres the variation of the modal parameteres also for small structure perturbations also for small structure perturbations The OO approach can be used for the The OO approach can be used for the (SHM) Structural Health Monitoring of (SHM) Structural Health Monitoring of Aerospace structures Aerospace structures Concluding Remarks: Concluding Remarks: Component disembark Component disembark required required • Low sensitivity to damage level Low sensitivity to damage level • Fine tuning of the F.E. model Fine tuning of the F.E. model • Low accuracy of experimental data from Low accuracy of experimental data from estimating process estimating process Various type of damage Various type of damage identifiable from identifiable from • the natural frequency shift the natural frequency shift • pattern modification of mode pattern modification of mode shapes shapes Theoretical Background Theoretical Background 1/3 1/3 Theoretical Background Theoretical Background 2/3 2/3 Damage identification by iteratively solving Damage identification by iteratively solving a non-linear optimization procedure via least a non-linear optimization procedure via least square algorithm square algorithm F.E. model represents the reference F.E. model represents the reference structure structure A sensitivity matrix, and error vector A sensitivity matrix, and error vector built from the correlation of the FRF built from the correlation of the FRF analytical and experimental analytical and experimental Localized and small damage entity required Localized and small damage entity required Refined numerical model and high number of Refined numerical model and high number of design parameters are needed design parameters are needed “ “ by-step” by-step” enhancement is proposed for reduction enhancement is proposed for reduction of both computational time and computer of both computational time and computer memory amount memory amount Numerical and experimental validation Numerical and experimental validation reported reported Theoretical Background Theoretical Background 1/3 1/3 Advantage of Output-Only technique for the estimate of Advantage of Output-Only technique for the estimate of the modal parameters the modal parameters Only the output time responses of the structure are Only the output time responses of the structure are employed employed Measurements of the input loads of the structure are Measurements of the input loads of the structure are not necessary not necessary The used output data are those of the structure in The used output data are those of the structure in operative conditions operative conditions save costs and time save costs and time The approach is particularly convenient whenever the The approach is particularly convenient whenever the input is unknown input is unknown Aerospace field: aeroelastic phenomena Aerospace field: aeroelastic phenomena Civil field: vibrations of builds and bridges Civil field: vibrations of builds and bridges Heath monitoring with OO approach Heath monitoring with OO approach
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Transcript of Monitoraggio di strutture Aeronautiche basato su misure di vibrazioni Luigi Balis Crema, Giuliano...
Monitoraggio di strutture Aeronautiche basato su misure di vibrazioniLuigi Balis Crema, Giuliano Coppotelli, Franco MastroddiDipartimento di Ingegneria Aerospaziale ed Astronautica
Via Eudossiana, 1800184 Roma
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
