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Residual Vectors & Error Estimation in Substructure based Model Reduction

- APPLICATION TO WIND TURBINE ENGINEERING -

MSc. Presentation

Bas Nortier

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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

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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

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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

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Scaling

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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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