Uncertainty Analysis in Aircraft Structures

1
Uncertainty Analysis in Aircraft Structures
Air Frame Finite Element Modeling for Uncertainty
Analysis and Large-Scale Numerical Simulation
Validation

• Jason Gruenwald
• University of Illinois-Urbana/Champaign
• Dr. Mark Brandyberry
• MSSC, CSAR

2
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

3
Uncertainty Analysis

• Variation of the structures 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

4
Overview of Methodology
Determine Input Uncertainties and probability
distributions
Create Sample Sets using sampling method
Create Surrogate Model
Simulate a few specific sample sets
Create Clusters of Similar Predictions
Predict output trends quickly
Cumulative Probabilities of Output Variables
Interpolate results over entire range
5
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

6
Input Parameters Sample Sets

• Youngs Modulus
• 10400 ksi 5
• Normal Distribution
• Poissons 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

7
Surrogate Model
Wing Box
Cluster 1
Cluster 2
Cluster 9
Cluster 10
8
Clusters and Simulation
Front Spar Max Stress Prediction
1.00
Prediction
Cluster 10
Cluster 4
Cumulative
Probability
0.50
Cluster 3
Cluster 1
0.00
0
60000
120000
Max Stress (psi)
9
Results
Tensile Yield
Tensile Yield
Ultimate Yield
Ultimate Yield
10
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

11
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