A comparative study of uncertainty propagation methods for black-box-type problems

Structural and Multidisciplinary Optimization

Volumn 37, Issue 3, 2009, Pages 239-253

  Lee, S H ^a   Chen, W ^a  

^a Northwestern University   (United States)

Author keywords

Comparative study; Design under uncertainty; Dimension reduction method; Full factorial numerical integration; Polynomial chaos expansion; Uncertainty propagation

Indexed keywords

CLUSTER ANALYSIS; DESIGN; INTEGRATION; INTERPOLATION; MACHINE DESIGN; METHOD OF MOMENTS; NUMERICAL ANALYSIS; OPTIMIZATION; POLYNOMIAL APPROXIMATION; PROBABILITY; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; RANDOM VARIABLES; SYSTEMS ANALYSIS;

COMPARATIVE STUDY; DESIGN UNDER UNCERTAINTY; DIMENSION REDUCTION METHOD; FULL FACTORIAL NUMERICAL INTEGRATION; POLYNOMIAL CHAOS EXPANSION; UNCERTAINTY PROPAGATION;

PROBABILITY DENSITY FUNCTION;

EID: 56449100211     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-008-0234-7     Document Type: Review

References (41)

1. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions (10th edn.). Dover, New York
2. CG Bucher 1988 Adaptive sampling-an iterative fast Monte Carlo procedure Struct Saf 5 119 126
3. SK Choi RV Grandhi RA Canfield 2004 Structural reliability under non-Gaussian stochastic behavior Comput Struct 82 1113 1121
4. Christensen P, Baker MJ (1982) Structural reliability theory and its applications. Springer, New York
5. Creveling CM (1997) Tolerance design: a handbook for developing optimal specifications. Addison-Wesley, Reading, MA
6. JR D'Errico NA Zaino 1988 Statistical tolerancing using a modification of Taguchi's method Technometrics 30 397 405
7. X Du W Chen 2000 Towards a better understanding of modeling feasibility robustness in engineering design J Mech Des 122 385 394
8. X Du A Sudjianto W Chen 2004 An integrated framework for optimization under uncertainty using inverse reliability strategy J Mech Des 126 562 570
9. S Engelund R Rackwitz 1993 A benchmark study on importance sampling techniques in structural reliability Struct Saf 12 255 276
10. DH Evans 1972 An application of numerical integration techniques to statistical tolerancing, III: general distributions Technometrics 14 23 35
11. B Fiessler R Rackwitz H Neumann 1979 Quadratic limit states in structural reliability J Eng Mech 105 661 676
12. Ghanem RG, Spanos PD (1991) Stochastic finite elements: a spectral approach. Springer, New York
13. AM Hasofer NC Lind 1974 Exact and invariant second order code format J Eng Mech 100 NEM1 111 121
14. Hahn GJ, Shapiro SS (1967) Statistical models in engineering. Wiley, New York
15. GA Hazelrigg 1998 A framework for decision-based engineering design J Mech Des 120 653 658
16. Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions (vol 1). Wiley, New York
17. AD Kiureghian 1996 Structural reliability methods for seismic safety assessment: a review Eng Struct 18 412 424
18. M Kokkolaras ZP Mourelatos PY Papalambros 2006 Design optimization of hierarchically decomposed multilevel system under uncertainty J Mech Des 128 503 508
19. Law AM, Kelton WD (1982) Simulation modeling ands analysis. McGraw-Hill, New York
20. TW Lee BM Kwak 1987-88 A reliability-based optimal design using advanced first order second moment method Mech Struct Mach 15 523 542
21. SH Lee BM Kwak 2006 Response surface augmented moment method for efficient reliability analysis Struct Saf 28 261 272
22. Lee I, Choi KK, Du L (2007) A new inverse reliability analysis method using MPP-based dimension reduction method (DRM). In: Proceedings of ASME 2007 international design engineering technical conference and computers and information in engineering conference (IDETC/CIE2007), Las Vegas, NV, USA
23. W Liu T Belytschko A Mani 1986 Random field finite elements Int J Numer Methods Eng 23 1831 1845
24. H Liu W Chen M Kokkolaras PY Papalambros HM Kim 2006 Probabilistic analytical target cascading: a moment matching formulation for multilevel optimization under uncertainty J Mech Des 128 991 1000
25. Madsen HO, Krenk S, Lind NC (2006) Methods of structural safety. Dover, Mineola, NY
26. CD McAllister TW Simpson 2003 Multidisciplinary robust design optimization of an internal combustion engine J Mech Des 125 124 130
27. RE Melchers 1989 Importance sampling in structural systems Struct Saf 6 3 10
28. R Rackwitz B Fiessler 1978 Structural reliability under combined random load sequences Comput Struct 9 489 494
29. S Rahman D Wei 2006 A univariate approximation at most probable point for higher-order reliability analysis Int J Solids Struct 43 2820 2839
30. S Rahman H Xu 2004 A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics Probab Eng Mech 19 393 408
31. HS Seo BM Kwak 2002 Efficient statistical tolerance analysis for general distributions using three-point information Int J Prod Res 40 931 944
32. Shoutens W (2000) Stochastic processes and orthogonal polynomials. Springer, New York
33. G Taguchi 1978 Performance analysis design Int J Prod Res 16 521 530
34. Tatang MA (1995) Direct incorporation of uncertainty in chemical and environmental engineering systems. Ph.D. thesis, MIT
35. X Wan GE Karniadakis 2006 Multi-element generalized polynomial chaos for arbitrary probability measure SIAM J Sci Comput 28 901 928
36. YT Wu 1994 Computational methods for efficient structural reliability and reliability sensitivity analysis AIAA J 32 1717 1723
37. D Xiu 2007 Efficient collocatioal approach for parametric uncertainty analysis Commun Comput Phys 2 293 309
38. D Xiu GE Karniadakis 2003 Modeling uncertainty in flow simulations via generalized polynomial chaos J Comput Phis 187 137 167
39. H Xu S Rahman 2004 A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics Int J Numer Methods Eng 61 1992 2019
40. BD Youn KK Choi YH Park 2003 Hybrid analysis method for reliability-based design optimization J Mech Des 125 221 232
41. Youn BD, Xi Z, Wells LJ, Wang P (2006) Enhanced dimension reduction (eDR) method for sensitivity-free uncertainty quantification. In: Proceedings of 11th AIAA/ISSMO multidisciplinary analysis and optimization conference, Portsmouth, VA, USA