1 Residual Vectors & Error Estimation in Substructure based Model Reduction - A PPLICATION TO WIND...
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Transcript of 1 Residual Vectors & Error Estimation in Substructure based Model Reduction - A PPLICATION TO WIND...
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Residual Vectors & Error Estimation in Substructure based Model Reduction
- APPLICATION TO WIND TURBINE ENGINEERING -
MSc. Presentation
Bas Nortier
2
80 m
IntroductionTrends in wind industry
• Increase in size of wind turbines• `Going offshore`• More wind offshore
• Decrease wind energy costs• Decrease wind turbine costs
25 m
3
IntroductionCost reduction through optimisation
• Costs reduction cycle
Turbine design
Dynamicbehaviour
Structural dynamic analysis
Design changes
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IntroductionCreate accurate reduced model
• Reduced model• `Simplify` the model• Increase computational efficiency• Approximation of dynamic behaviour
• Dynamic behaviour is influenced by excitation• Current reduction methods• Do not take excitation into account
“Investigate and implement the modal truncation augmentation (MTA) method into the
current structural dynamic tools"
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IntroductionCreate accurate reduced assembly
“Investigate error estimation techniques for accuracy determination and refinement strategies"
Unreducedassembly
Reducedassembly
Which component models?
Needs exact solution
AccuracyEfficiency
Refinement
Comparison
Level of reduction
blades
tower
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Content• Introduction• MTA method• Application to an offshore support structure• Error estimation• Application to an offshore wind turbine• Conclusions & Recommendations
MTA – Application – EE – Application – Conclusions
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MTA methodWhat is it?
• Extension of current reduction methods• Taking excitation into account• Create improved reduced model
• Model reduction
¼ ++ +
Standard
`Standard` modes
MTA – Application – EE – Application – Conclusions
++ +
Extended
Force dependent modes
`Standard` modes
¼
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Blades
Tower
Application to an offshore support structureModel description
• Model• 5-MW offshore turbine• Jacket support structure• Excited by waves
Jacket
MTA – Application – EE – Application – Conclusions
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Application to an offshore support structureExperiment description
• Goal • Create reduced jacket model• Use standard and extended
reduction methods• 4 wave loads;
low, medium, high, freak waves
• One model for each wave type • One combined model
MTA – Application – EE – Application – Conclusions
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Application to an offshore support structureResults
Low Medium High Freak
Improved
Similar
Extended
Stan
dard
Combined
MTA – Application – EE – Application – Conclusions
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Content• Introduction• MTA method• Application to an offshore support structure• Error estimation• Application to an offshore wind turbine• Conclusions & Recommendations
MTA – Application – EE – Application – Conclusions
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Error estimationWhy, and what
• Estimate error• Without knowing exact response• Conservative Upper bound
• Determine refinement of components
Blades
Jacket Tower
Hub
Exact error Estimated error
Unreducedassembly
Reducedassembly
Refinement
Comparison
Time
Dis
plac
emen
t
ExactApproximation
Exact errorEstimated error
Error
MTA – Application – EE – Application – Conclusions
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Error estimationHow does it work?
• Error results in global residual force• Split global residual• Conservative scaling per component
MTA – Application – EE – Application – Conclusions
Residual
M Ä~u + K ~u = f + rAccelerations
Displacements Force
M Äu + K u = f
Interface
…
Tower
r =
2
64
r (0)
...r (n)
3
75 Exact
error
Scaling
Component residual
jkekj2 ·nP
s=0
1¸ ( s )
°°r (s)
°°2·
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Error estimationType of errors
• Errors for various situations• Global eigenmode & eigenfrequency• Accurate range• Single eigensolution
MTA – Application – EE – Application – Conclusions
: : :)
Eigenmode + Eigenfrequency = Eigensolution
Reduced assembly
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Error estimationIteration loop
1. Reduce model
2. Approximate response Global residual
3. Domain contribution
Tolerance?
4. Refinement strategy
Optimal reduced model
NoYes
MTA – Application – EE – Application – Conclusions
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Application to an offshore wind turbineModel description• Same turbine model• Rotor nacelle assembly (RNA)• Tower• Jacket• Interface
MTA – Application – EE – Application – Conclusions
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Application to an offshore wind turbineExperiment description
MTA – Application – EE – Application – Conclusions
• Create a reduced assembly• Optimal component refinement• Upper bounds• Error on 10th eigenfrequency• Error on 10th eigenmode
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Application to an offshore wind turbineResults global eigensolution
Component error
MTA – Application – EE – Application – Conclusions
EigenfrequencyEigenmode
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Conclusions & RecommendationsConclusions
• MTA method• Able to produce more accurate reduced models• Implemented in dynamic analysis tools
• Error estimation• Can determine accuracy • Used for refinement strategy
“Investigate and implement the MTA method into the current structural dynamic tools"
“Investigate error estimation techniques for accuracy determination and refinement strategies"
MTA – Application – EE – Application – Conclusions
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Conclusions & RecommendationsRecommendations• MTA method• Generalise excitation
• Error estimation• Create a practical tool• Range of eigensolutions
• Combining the best of both worlds• Error estimation & MTA method
Component residuals force dependent modes
MTA – Application – EE – Application – Conclusions
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Thank you for your attention
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Backup slidesDynamic substructuring tools
• BHawC• Global turbine model used for multiple simulations• Simulation take half an hour• Hundreds of simulation have to be run
• Dynamic Substructuring tools• Counterpart of BHawC• Input large FE models• Use reduction methods to reduce large models• Create superelements for input in BHawC• 3 Tools
• Preparation Tool• Assembly Tool• Postprocessing Tool
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Backup slidesReduction method
• Craig-Bampton• Static constraint modes• Fixed interface modes
• Dual Craig-Bampton• Free vibration modes• Rigid body modes• Residual attachment modes
• …
• Both extended using MTA method
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Backup slidesMTA method
• Force dependent modes• Based on external loading• Based on interface loading
• Number equals interface DoF• Can become limiting Interface reduction
• Interface reduction• Interface displacements (substructure and assembly)• Interface forces• Rigid interface displacements• Effective modal mass• Post-selection
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Backup slidesMTA method 2
• Efficient computation• Using Lanczos algorithm• Postprocessing Lanczos iterations• Separate step using (Block) Lanczos
• Frequency shift• Create MTA vectors for specific frequency• Creates a dynamic stiffness matrix• Additional costs
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Backup slidesForce analysis using POD method
• Wave loads are time varying• Need to obtain time-invariant force vectors• Proper orthogonal decomposition (POD) method
• Used to obtain spatial force vector from time varying load data
• Proper orthogonal modes (POM); force shapes• Proper orthogonal values (POVs); energy captured by POMs
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Backup slidesExtended results dynamic response
High waves Freak waves
Medium wavesLow waves
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Backup slidesError estimation; which type
• Error estimation• A priori knowing error in advance• A posteriori computing error in hindsight (iteratively)
• Compatible with Craig-Bampton reduction• Assembly• Transformation• Reduction
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Backup slidesError estimation; different errors
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Backup slidesError estimation; refinement schemes
• 2 Refinement schemes• Selecting largest contributors (part of largest component
error)• Normal distribution• Divide number of available DoF accordingly
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Backup slidesUncoupling of component models
ui = ª C ;i ub + ui
• Compatible with Craig-Bampton reduction method• System description• Uncoupled component models• Component models Domains
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