Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

Reliability Engineering and System Safety

Volumn 138, Issue , 2015, Pages 59-72

  Shah, Harsheel ^a   Hosder, Serhat ^a   Winter, Tyler ^b  

^a Architectural and Environmental Engineering   (United States)

^b M4 Engineering Inc   (United States)

Author keywords

Evidence theory; Margins and uncertainty quantification; Point collocation; Polynomial chaos; Reliability; Representation of uncertainty; System safety

Indexed keywords

CHAOS THEORY; COMPUTATION THEORY; FORMAL LOGIC; RELIABILITY; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; UNCERTAINTY ANALYSIS;

EVIDENCE THEORIES; POINT COLLOCATION; POLYNOMIAL CHAOS; REPRESENTATION OF UNCERTAINTY; SYSTEM SAFETY; UNCERTAINTY QUANTIFICATIONS;

RELIABILITY THEORY;

EID: 84922698811     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2015.01.012     Document Type: Article

References (65)

1. D.H. Sharp, and M.M. Wood-Schultz QMU and nuclear weapons certification. Whats's under the hood Los Alamos Sci. 28 2003 47 53
2. Goodwin BT, Juzaitis RJ. National certification methodology for the nuclear weapon stockpile. Draft Working Paper; 2003.
3. Eardley D. Quantification of margins and uncertainties (QMU). Technical Report, JSR-04-330 (JASON); March 2005.
4. U.S. GAO (U.S. Government Accountability Office). Nuclear weapons: NNSA needs to refine and more effectively manage its new approach for assessing and certifying nuclear weapons. GAO-06-261. Washington, DC: U.S. Government Accountability Office; 2006.
5. NAS/NRC (National Academy of Science/National Research Council). Evaluation of quantification of margins and uncertainties for assessing and certifying the reliability of the nuclear stockpile. Washington, DC: National Academy Press; 2008.
6. M. Pilch, T.G. Trucano, and J.C. Helton Ideas underlying the quantification of margins and uncertainties Reliab Eng Syst Saf 96 2011 965 975
7. Pepin JE, Rytherford AC, Hemez FM. Defining a practical QMU metric. In: 49th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, AIAA Paper 2008-1717, Schaumburg, IL; April 2008.
8. L.J. Lucas, H. Owhadi, and M. Ortiz Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities Comput Methods Appl Mech Eng 197 October (51-52) 2008 4591 4609
9. Iaccariono G, Pecnik R, Glimm J, Sharp D. A QMU approach for characterizing operability limits of air-breathing hypersonic vehicles. LANL Report, LA-UR 09-01863; 2009.
10. National Research Council evaluation of quantification of margins and uncertainties methodology for assessing and certifying the reliability of the nuclear stockpile. Washington, DC: The National Academies Press; 2009.
11. J.C. Helton Quantification of margins and uncertainties conceptual and computational basis Reliab Eng Syst Saf 96 9 2011 976 1013
12. W.L. Oberkampf, S.M. DeLand, B.M. Rutherford, K.V. Diegert, and K.F. Alvin Error and uncertainty in modeling and simulation Reliab Eng Syst Saf 75 2002 333 357
13. A. Urbina, S. Mahadevan, and T.L. Paez Quantification of margins and uncertainties of complex systems in the presence of aleatory and epistemic uncertainty Reliab Eng Syst Saf 96 2011 1114 1125
14. T.C. Wallstrom Quantification of margins and uncertainties: a probabilistic framework Reliab Eng Syst Saf 96 2011 1053 1062
15. J.C. Helton, J.D. Johnson, W.L. Oberkampf, and C.B. Storlie A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory Comput Methods Appl Mech Eng 196 37-40 2007 3980 3998
16. H. Owhadi, C. Scovel, T.J. Sullivan, M. McKerns, and M. Ortiz Optimal uncertainty quantification SIAM Rev 55 2 2013 271 345
17. G. Shafer A mathematical theory of evidence 1976 Princeton University Press Princeton, NJ
18. L.C. Pereira, L.J.N. Guimaraes, B. Horowitz, and M. Sanchez Coupled hydro-mechanical fault reactivation analysis incorporating evidence theory for uncertainty quantification Comput Geotech 56 2014 202 215
19. J.C. Helton, J.D. Johnson, W.L. Oberkampf, and C.J. Sallaberry Representation of analysis results involving aleatory and epistemic uncertainty Int J Gen Syst 39 6 2010 605 646
20. J.C. Helton, W.L. Oberkampf, and J.D. Johnson Competing failure risk analysis using evidence theory Risk Anal 25 4 2005 973 995
21. J.C. Helton, and J.D. Johnson Quantification of margins and uncertainties alternative representations of epistemic uncertainty Reliab Eng Syst Saf 96 9 2011 1034 1052
22. Swiler LP, Paez TL, Mayes RL, Eldred MS. Epistemic uncertainty in the calculation of margins. In: 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, AIAA Paper 2009-2249, Palm Springs, CA; May 2009.
23. H. Bae, R.V. Grandhi, and R.A. Canfield An approximation approach for uncertainty quantification using evidence theory Reliab Eng Syst Saf 86 2004 215 225
24. H. Bae, R.V. Grandhi, and R.A. Canfield Epistemic uncertainty quantification techniques including evidence theory for large-scale structures Reliab Eng Syst Saf 82 2004 1101 1112
25. H. Agarwal, J.E. Renaud, and D. Padmanabhan Uncertainty quantification using evidence theory in multidisciplinary design optimization Reliab Eng Syst Saf 85 2004 281 294
26. Hosder S, Walters RW, Balch M. Efficient sampling for non-intrusive polynomial chaos applications with multiple input uncertain variables. In: 9th AIAA non-deterministic approaches conference, AIAA Paper 2007-1939, Honolulu, HI; April 2007.
27. S. Hosder, R.W. Walters, and M. Balch Point-collocation non-intrusive polynomial chaos method for stochastic computational fluid dynamics AIAA J 48 December (12) 2010 2721 2730
28. Bettis BR, Hosder S, Winter T. Efficient uncertainty quantification in multidisciplinary analysis of a reusable launch vehicle. In: 17th AIAA international space planes and hypersonic systems and technologies conference, AIAA Paper 2011-2393, San Francisco, CA; April 2011.
29. S. Hosder Stochastic response surfaces based on non-intrusive polynomial chaos for uncertainty quantification Int J Math Model Numer Optim 3 January (1-2) 2012 117 139
30. S. Hosder, and B.R. Bettis Uncertainty and sensitivity analysis for reentry flows with inherent and model-form uncertainties J Spacecr Rocket. 49 March-April (2) 2012 193 206
31. M.S. Eldred, L.P. Swiler, and G. Tang Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation Reliab Eng Syst Saf 96 2011 1092 1113
32. J.C. Helton, J.D. Johnson, and C.J. Sallaberry Quantification of margins and uncertainties example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty Reliab Eng Syst Saf 96 9 2011 1014 1033
33. K. Sentz, and S. Ferson Probabilistic bounding analysis in the quantification of margins and uncertainties Reliab Eng Syst Saf 96 2011 1126 1136
34. Ferson S, Kreinovich V, Ginzburg L, Meyers DS, Sentz K. Constructing probability boxes and Dempster-Shafer structures. Sandia National Laboratories SAND2002-4015, Albuquerque, NM; 2002.
35. Shah HR, Hosder S, Winter T. A mixed uncertainty quantification approach with evidence theory and stochastic expansions. In: AIAA SciTech 2014, AIAA Paper 2014-0298, National Harbor, MD; January 2014.
36. G.W. Parry, and P.W. Winter Characterization and evaluation of uncertainty in probabilistic risk analysis Nucl Saf 22 1 1981 28 42
37. G.W. Parry The characterization of uncertainty in probabilistic risk assessments of complex systems Reliab Eng Syst Saf 54 2-3 1996 119 126
38. M.E. Pate-Cornell Uncertainties in risk analysis six levels of treatment Reliab Eng Syst Saf 54 2-3 1996 95 111
39. F.O. Hoffman, and J.S. Hammonds Propagation of uncertainty in risk assessments the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability Risk Anal. 14 5 1994 707 712
40. J.C. Helton, and D.E. Burmaster Guest editorial treatment of aleatory and epistemic uncertainty in performance assessments for complex systems Reliab Eng Syst Saf 54 2-3 1996 91 94
41. J.C. Helton Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty J Stat Comput Simul 57 1-4 1997 3 76
42. J.C. Helton Treatment of uncertainty in performance assessments for complex systems Risk Anal 14 4 1994 483 511
43. Oberkampf WL, Helton JC, Sentz K. Mathematical representation of uncertainty. In: 3rd AIAA non-deterministic approaches forum, AIAA Paper 2001-1645, Seattle, WA; April 2001.
44. D. Xiu, and G.E. Karniadakis The Wiener-Askey polynomial chaos for stochastic differential equations SIAM J Sci Comput 24 2 2003 619 644
45. D. Xiu, and G.E. Karniadakis Modeling uncertainty in flow simulations via generalized polynomial chaos J Comput Phys 187 1 2003 137 167
46. H.N. Najm Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics Ann Rev Fluid Mech 41 2009 35 52
47. R.G. Ghanem, and P. Spanos Stochastic finite elements: a spectral approach 1991 Springer Berlin
48. Eldred MS, Webster CG, Constantine PG. Evaluation of non-intrusive approaches for Wiener-Askey generalized polynomial chaos. In: 10th AIAA non-deterministic approaches forum, AIAA-Paper 2008-1892, Schaumburg, IL; April 2008.
49. R. Yager Arithmetic and other operations on Dempster Shafer structures Int J Man-Mach Stud 25 1986 357 366
50. L.A. Zadeh Review of books a mathematical theory of evidence AI Mag 5 3 1984 81 83
51. Sentz K, Ferson S. Combination of evidence in Dempster-Shafer theory. Sandia National Laboratories SAND2002-0835, Albuquerque, NM; April 2002.
52. L.A. Zadeh A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination AI Mag 7 1986 85 90
53. J.C. Helton, J.D. Johnson, and W.L. Oberkampf An exploration of alternative approaches to the representation of uncertainty in model predictions Reliab Eng Syst Saf 85 2004 39 71
54. E. Nikolaidis, D.M. Ghiocel, and S. Singhal Engineering design reliability handbook 1st ed 2004 CRC Press Boca Raton, FL [July, Chapter 10]
55. Adams BM, Ebeida MS, Eldred MS, Jakeman JD, Swiler LP, Bohnnhoff WJ, et al. Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Sandia National Laboratories SAND2010-2183, Albuquerque, NM, Updated March 6, 2014.
56. Doyle S, PMP KA, Winter T. Developing the aerodynamics module for the integrated multidisciplinary optimization object system. In: 49th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition. AIAA Paper 2011-8, Orlando, FL; January 2011.
57. Raymondson C, Baker M, Doyle S, Young S, Tejtel D. Geometry manipulation by automatic parameterization (GMAP). AIAA MDAO conference; September 2008.
58. Andrew Dahlin, and Myles L. Baker GMAP mesh user's manual s.1 2010 M4 Engineering Long Beach, CA
59. Daniel Stuewe, and Myles L. Baker Rapid FEM user's manual 2010 M4 Engineering Long Beach, CA
60. High Speed Research Program HSR II Airframe Task 20, Task 2.1 Technology Integration, Sub-task 2.1.1.2 Refine Technology Concept Airplane: Configuration Description Document; April 1996.
61. Saaris GR, Tinoco EN, Lee JL, Rubbert PE. User's guide PAN AIR technology program for solving potential flow about arbitrary configurations; 1992.
62. Johnson FT, Rubbert PE. Advanced panel-type influence coefficient methods applied to subsonic flows. s.l. AIAA 75-50; January 1975.
63. Ehlers FE, Johnson FT, Rubbert PE. A higher order panel method for linearized supersonic flow. s.l. AIAA 76-381; July 1976.
64. Ehlers FE, et al. A higher order panel method for linearized supersonic flow. NASA Contractor Report 3062; 1979.
65. R.W. Claus, A.L. Evans, J.K. Lylte, and L.D. Nichols Numerical propulsion system simulation. 4 Comput Syst Eng 2 1991 357 364