LocFaults, a bounded constraint-based approach to aid for error localization
Correlation and Error Localization
description
Transcript of Correlation and Error Localization
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Correlation and Error LocalizationAnalytical versus Experimental Dynamicsof a Large Structural AssemblyThesis presentation, Herman Marquart, 2013
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Content
• Introduction• Theory• Methodology• Results• Discussion• Conclusion• Recommendations
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Department at ASML
• Structural Dynamics• Component
• Well defined modeling process
• Largely automated in software
• Assembly• Less defined modeling process
• Requires more subjective interferences
Mechanical Analysis
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Assignment from ASML
“Improve the correlation (process) of analytical and experimental structural assembly models”
•Procedure• First understand the current process
• Determine typical properties of a structural assembly
• Determine applicability of correlation tools
• Determine typical errors made during modeling
• Define specific research problem• Propose methodology
Formulated as…
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General development processSystem, subsystem, …, component level
Functional requirements Realized functions
System
design
Subsystem
design
Component
designRea
lizat
ion,
inte
grat
ion
and
Specification, decomposition and
definitionTimeline
System
assembly
Subsystem
assembly
Component
production
Feedback loops
valid
atio
n
Experimental
modelsAnalytical models
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Typical high tech case
• Assembly: set of many integrated components
ASML lithography machine
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Typical high tech case
• Typical properties of such an assembly• Complex base structure (master structure)
• Thin walled box structure
• Many thin ribs and spacers
• Many holes
• Many components attached (slave structures)• Several large components
• Many small components
• Cables, wires, pipes, channels, …
Positioning module
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General modeling processSystem, subsystem, …, component level
Analytical approach
Eigensolution computation
Spatial
M C K
Modal
Φ Λ
Response
H
Modal parameter identification
Experimental approach
1
1
T
T
- -
- -
=
=
M Φ Φ
K Φ ΛΦ
( )1 TH Φ Λ Ω Φ
-= -
102
103
10-2
100
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FREQUENCY [Hz]
MA
GN
ITU
DE
[kg
]
TP.V09 FRFS
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FREQUENCY [Hz]
MA
GN
ITU
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FREQUENCY [Hz]
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FREQUENCY [Hz]
MA
GN
ITU
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Analytical approach
• Substructure assembly into components• Natural approach• Enables parallel engineering• Possibly more attention to details• More flexible to local modifications
• Reduce each substructure• Approximation• Speeds up computation of eigensolutions• Easy reuse and exchange of components
• Assemble reduced substructures
Assembly
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• Setup• Structure• Suspension• Hammer• Accelerometer• Amplifiers• Data acquisition module• Computer
• Procedure• Roving hammer method
Experimental approach
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Theory discussion
• Practical issues• Many small components• Lots of effort required to perform such detailed analysis• Simpler models could be sufficient• Limited amount of time available
• Practical solutions• Omission of slave structures• Omission of structural dynamics of slave structures• Simplification of connections
• However, assumptions are not always valid…
Theory versus application
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Research problemFormulated as…
“What is the influence of a relatively lightweight resonating slave structure on the global structural dynamic behaviour of the master structure? How
could you find the location of an unmeasured resonating slave structure with existing correlation
tools and validation procedures, when multiple components are suspicious?”
“What is the influence of a relatively lightweight resonating slave structure on the global structural
dynamic behaviour of the master structure? How could you find the location of an unmeasured resonating slave structure with existing correlation tools and validation
procedures, when multiple components are suspicious?”
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Methodology… influence …
• Simulation• Create simplified structural assembly
• Master structure
• Slave structures
• Multiple non-resonating
• One resonating
• Compare and correlate models; observe typical effects• Intended design versus realized design
• Multiple positions of the resonating slave structure• Validation
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MethodologyDesign structural assembly
• Master structure• Plate
• Linear elastic material
• Out of plane dynamics
• Asymmetric
• Mounting positions
• Simple to manufacture• f1 ≈ 200 Hz
• Slave structures• 1 Sprung mass• 9 Unsprung masses
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MethodologyDesign slave structure
• Sprung mass• Linear elastic material• Out of plane vibration• Single mount• Simple to manufacture• f1 ≈ 500 Hz
• Unsprung mass• f1 > 2000 Hz
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… influence …
Intended design10 unsprung masses
• Compare and Correlate• Frequencies [Hz]
Mode Realized
design
Intended
design ∆ [%]
1 184 185 0.5 2 222 220 -0.8 3 425 433 0.3 4 432 454 8.3 5 549 607 0.4 6 605 624 -8.0 7 679 827 -5.0 8 870 971 -1.1 9 982 1203 0.7
10 1194 1242 0.7 11 1233 1350 -0.9 12 1362 1488 1.7 13 1463 1522 1.0 14 1507 1766
Results
Realized design1 sprung mass + 9 unsprung
masses
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• Compare and Correlate• Frequencies [Hz]• Mode shapes
Results… influence …
Realizeddesign
Intendeddesign
Realized design1 sprung mass + 9 unsprung
masses
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• Compare and Correlate• Frequencies [Hz]• Mode shapes
• MAC
Results… influence …
Inte
nded d
esi
gn
2Tr s
rs T Tr r s s
MAC φ φ
φ φ φ φ
%%
% %% %
Intended designRealized design
Realized design1 sprung mass + 9 unsprung
masses
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• Compare and Correlate• Frequencies [Hz]• Mode shapes
• MAC
• FRFs
Results… influence …
Intended design
Realized design
Magnit
ude [
kg-1]
Magnit
ude [
kg-1]
Frequency [Hz]
Frequency [Hz]
Realized design1 sprung mass + 9 unsprung
masses
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“What is the influence of a relatively lightweight resonating slave structure on the global structural dynamic behaviour of the master structure? How
could you find the location of an unmeasured resonating slave structure with existing correlation
tools and validation procedures, when multiple components are suspicious?”
Research problemFormulated as…
“What is the influence of a relatively lightweight resonating slave structure on the global structural
dynamic behaviour of the master structure? How could you find the location of an unmeasured resonating slave structure with existing correlation tools and validation
procedures, when multiple components are suspicious?”
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Methodology… localization…
• Systematically correct intended design• Known (approximately)
• Additional resonance frequency
• Slave structure mass
• Connection stiffness
• Unknown• Location
• Define objective functions to quantify model correlation• Localize the resonating slave structure with objective
function
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MethodologyProposed approach
• Isolate the master structure• Add the small slave structures as mass-spring-systems• Vary the connection stiffness of each slave structure
one by one• Recalculate the eigensolutions• Compute objective values
• Eigenfrequencies
• Mode shapes
• Weighted summation
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ResultsOne slave structure
owJωo Jφ●J‒R
Obje
ctiv
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valu
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Model
variant
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MODEL VARIANT
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LUE
Stiffness value
Obje
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ResultsAll slave structures
Obje
ctiv
e v
alu
e
Stiffness value
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ResultsAll slave structures
Obje
ctiv
e v
alu
e
Stiffness value
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ResultsAll slave structures
Obje
ctiv
e v
alu
e
Stiffness value
1 2 3 4 5 6 7 8 9 10
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ResultsAll slave structures
Obje
ctiv
e v
alu
e
Stiffness value
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Discussion
• Requirements• Validated master structure• Accurate measurements and mode shape identification
• Fortunate properties• No additional measurements required• Entire process performed with ANSYS and MATLAB• Clear systematic approach
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Conclusion
• The proposed procedure may help localizing the resonating component, when typical structural dynamic correlations as presented, are encountered during the monitoring of the assembly process
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Recommendations
• Research extension to more complex slave structures• Application to a case with multiple resonating slave
structures
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Questions?
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