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Uncertainty Analysis in Aircraft Structures

Jason GruenwaldUniversity of Illinois-Urbana/Champaign

Dr. Mark BrandyberryMSSC, CSAR

Air Frame Finite Element Modeling for Uncertainty Analysis and Large-Scale Numerical Simulation Validation

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Goal

• Create a Methodology – Better Predicts Performance of aircraft structure– Using uncertain input variables– Minimizes computation expense (number of runs)

• Need to be able to answer probabilistic questions– 99% confident satisfies requirement rather than use

safety factor• Predictive Analysis:

– Reduce experiments needed– Reduce the number of Prototypes built– Increase Cost effectiveness

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Uncertainty Analysis

• Variation of the structure’s response due to collective variation of input parameters– i.e. Aircraft wing

• Better understand change in response

• Apply methodology used for Computational Fluid Dynamics in rockets

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Overview of Methodology

Determine Input Uncertainties and probability

distributions

Create Sample Sets using

sampling method

Create Surrogate Model

Predict output trends quickly

Create Clusters of Similar Predictions

Simulate a few specific sample sets

Interpolate results over entire range

Cumulative Probabilities of

Output Variables

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Wing Box Model

• Modeled in ABAQUS– Solid Mechanics Finite

Element Program

• Chosen for simplicity– Short Simulation time

• Material assumptions:– Entire model is 7075-

T6 Al– Behaves linearly

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Input Parameters & Sample Sets

• Young’s Modulus– 10400 ksi ± 5%– Normal Distribution

• Poisson’s Ratio– 0.33 ± 5%– Normal Distribution

• Load Reference Case– FALSTAFF Spectrum– Assumed loads change

in phase• Latin Hypercube

Sampling– Samples values from

extremes– 50 sample sets

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Set Prediction

1 1.327

2 0.779

3 0.746

48 1.223

49 0.921

50 1.06

Surrogate Model

434 3424

LxLxEI

qy o

I

clqo2

2

max

Cluster 1

Cluster 2

Cluster 9

Cluster 10

Wing Box

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Clusters and SimulationFront Spar Max Stress Prediction

0.00

0.50

1.00

0 60000 120000

Max Stress (psi)

Cu

mu

lati

ve

Pro

bab

ilit

yPrediction

Cluster 3Cluster 3Cluster 1Cluster 1

Cluster 10Cluster 10

Cluster 4Cluster 4

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Results

Front Spar Max Stress Distribution

0.00

0.25

0.50

0.75

1.00

0 50000 100000

Rear Spar Max Stress Distribution

0 50000 100000

Maximum Stress (psi)

Cum

ulat

ive

Pro

babi

lity

Te

nsi

le Y

ield

Te

nsi

le Y

ield

Ulti

ma

te Y

ield

Ulti

ma

te Y

ield

Interpolation ABAQUS Sims

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Conclusion

• Cluster Methodology accurately predicts performance

• Engineers ability to answer probabilistic questions

• Minimal computational expense• Predictive Analysis:

– Reduce the number of Prototypes built– Reduce experiments needed– Cost effective

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Future Work

• Investigate techniques to validate computational model – Compare uncertain simulation with uncertain

experiments– Multiple points of comparison– Weighted comparisons– Multi-Attribute Decision Tree Methods

• Incorporate other uncertainties– i.e. Geometric tolerances, Friction, Boundary

Conditions Uncertainties

• Apply to entire aircraft wing