Digital Twin Workshop Harry Millwater University of Texas

Digital Twin Workshop Harry Millwater University of Texas at San Antonio Sept. 10 -11, 2012 1

Topics FAA Probabilistic Damage Tolerance Analysis n System Reliability Analysis n Sensitivity Methods n 2

Damage Tolerance Methodology Loading 1 4 POD EVD 2 3 5 …n Crack Size RS Insp 1 Insp 2 EIFS Geometry Time Material Prop. SFPOF & CTPOF Sensitivities

POF Calculations Survival t-1 POF Flight t 4

EVD Results Flight 1 Flight 2 . . . Flight n Frechet Gumbel Weibull 5

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 6

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, ” 50 th AIAA Nondeterministic Approaches Conference, May 4 -7, 2009, Palm Springs, CA, AIAA 2009 -2260 7

Pair-wise Filtering Criteria n Pair-wise filtering – neglect limit states that don’t contribute significantly to the system POF relative to the dominant limit states i = 2, n g 1 – dominant limit state, serves as a benchmark 8

Filtering Procedure Pair-wise comparison of each limit state with dominant n 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 n n User decides how much error to allow and set tolerance (typical values: 1 E-4 – 1 E-6) 9

Second Order Bounds Examine the cumulative effect of the filtered limit states using 2 nd order bounds Compare bounds from a) all limit states vs. b) only unfiltered limit states 10

Aircraft Model n Lower wing skin analyzed, ~900 limit states LS # 292 277 256 n n Beta 0. 297 0. 65 0. 949 Corr. 1 0. 99 0. 98 Filt. Error 0 2. 50 E-04 2. 20 E-09 g 1 Root radius Element 292 and 277 left unfiltered ( TOL =1 E-6) Bounds on entire system vs. only critical locations widen by 1 E-5 11

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

Local Prob. Sensitivity Original CDF Modified CDF

ZFEM Complex Variable FE Method

Abaqus 2 D Verification Analytical Abaqus

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

Higher Order Sensitivities Thick walled cylinder