Digital Twin Workshop

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Digital Twin Workshop

• Harry Millwater
• University of Texas at San Antonio
• Sept. 10-11, 2012

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Topics

• FAA Probabilistic Damage Tolerance Analysis
• System Reliability Analysis
• Sensitivity Methods

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Damage Tolerance Methodology
Loading
EVD
RS
Insp 2
Insp 1
Time
Material Prop.
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POF Calculations
Survival t-1
POF Flight t
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EVD Results
Frechet Gumbel Weibull
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EVD Results
Usage Location Scale Shape Distribution
Single Engine Unpress. Basic Inst. 14.49 1.75 0.01 Frechet
Single Engine Unpress. Personal 12.03 1.15 0.00 Gumbel
Single Engine Unpress. Executive 11.68 0.90 -0.04 Weibull
Twin Engine Unpress. Basic Inst. 13.93 1.42 0.00 Gumbel
Twin Engine Unpress. General 12.05 1.16 0.02 Frechet
Pressurized 13.41 1.26 0.02 Frechet
Agric/Special 12.07 0.94 -0.12 Weibull
Special Usage Survey 14.56 1.32 -0.05 Weibull
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Probabilistic Modeling of Systems
POF contours
L. Domyancic, D. Sparkman, and H.R. Millwater, L.
Smith and D. Wieland, A Fast First-Order Method
for Filtering Limit States, 50th AIAA AIAA
Nondeterministic Approaches Conference, May 4-7,
2009, Palm Springs, CA, AIAA 2009-2260
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Pair-wise Filtering Criteria

• Pair-wise filtering neglect limit states that
  dont contribute significantly to the system POF
  relative to the dominant limit states

g1 dominant limit state, serves as a benchmark
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Filtering Procedure

• Pair-wise comparison of each limit state with
  dominant
• Each limit state is assigned a filtering error,
  i.e. the relative error incurred if the limit
  state were filtered

• is calculated using the bivariate normal

• User decides how much error to allow and set
  tolerance
• (typical values 1E-4 1E-6)

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Second Order Bounds

• Examine the cumulative effect of the filtered
  limit states using 2nd order bounds

• Compare bounds from a) all limit states vs. b)
  only unfiltered limit states

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Aircraft Model

• Lower wing skin analyzed, 900 limit states

LS Beta Corr. Filt. Error
292 0.297 1 0
277 0.65 0.99 2.50E-04
256 0.949 0.98 2.20E-09
g1

• Root radius Element 292 and 277 left unfiltered
  (?TOL 1E-6)
• Bounds on entire system vs. only critical
  locations widen by 1E-5

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Sensitivity Methods

• Numerical Differentiation ()
• Visual
• Linear Regression
• Score Function partial derivatives
• Local probabilistic partial derivatives ()
• Global Sensitivity Analysis

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Local Prob. Sensitivity
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ZFEM Complex Variable FE Method
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Abaqus 2D Verification
Analytical
Abaqus
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Strain Energy Release Rate
Double Cantilever Beam (DBC)
Exact 0.800
Exact 0.8
of Contours Perturbation Method Abaqus CTSE
20 Tip only 0.7914
8 Tip only 0.7918
4 Tip only 0.7914
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Higher Order Sensitivities
Thick walled cylinder