Efficient reliability analysis based on Bayesian framework under input variable and metamodel uncertainties

Structural and Multidisciplinary Optimization

Volumn 46, Issue 4, 2012, Pages 533-547

  An, Dawn ^a   Choi, Joo Ho ^a  

^a Hankuk Aviation University   (South Korea)

Author keywords

Bayesian approach; Gaussian process model; Markov Chain Monte Carlo; Metamodel uncertainty; Reliability analysis; Statistical uncertainty

Indexed keywords

BAYESIAN APPROACHES; GAUSSIAN PROCESS MODELS; MARKOV CHAIN MONTE CARLO; META MODEL; STATISTICAL UNCERTAINTY;

BAYESIAN NETWORKS; PROBABILITY DENSITY FUNCTION;

RELIABILITY ANALYSIS;

EID: 84870379838     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-012-0776-6     Document Type: Article

References (30)

1. Andrieu C, de Freitas N, Doucet A, Jordan MI (2003) An introduction to MCMC for machine learning. Mach Learn 50:5-43
2. Bae HR, Grandhi RV, Canfield RA (2006) Sensitivity analysis of structural response uncertainty propagation using evidence theory. Struct Multidisc Optim 31(4):270-279
3. Choi JH, An D, Won JH (2010) Bayesian approach for structural reliability analysis and optimization using the Kriging Dimension Reduction Method. ASME J Mech Des 132(5):051003
4. Cruse TA, Brown JM (2007) Confidence interval simulation for systems of random variables. ASME J Eng Gas Turbine Power 129(3):836-842
5. Der Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Struct Saf 31(2):105-112
6. Du L, Choi KK, Youn BD (2006) Inverse possibility analysis method for possibility based design optimization. AIAA J 44(11):2682-2690
7. Etman LFP (1994) Design and analysis of computer experiments: The method of Sacks et al. Engineering Mechanics report WFW 94.098, Eindhoven University of Technology
8. Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. Chapman & Hall/CRC, New York
9. Gunawan S, Papalambros PY (2006) A Bayesian approach to reliability-based optimization with incomplete information. ASME J Mech Des 128(4):909-918
10. Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design. Wiley, New York
11. Iman RL (1999) Latin hypercube sampling. In: Encyclopedia of statistical sciences, vol 3, pp 408-411
12. Kennedy MC, O'Hagan A (2001) Bayesian calibration of computer models (with discussion). J R Stat Soc Ser B 63(3):425-464
13. Lee I, Choi KK, Du L, Gorsich D (2008) Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems. Comput Methods Appl Mech Eng 198(1):14-27
14. Lee I, Choi KK, Gorsich D (2010) System reliability-based design optimization using MPP-based dimension reduction method. Struct Multidisc Optim 41(6):823-839
15. Martz HF,Waller RA (1982) Bayesian reliability analysis.Wiley, New York
16. Mourelatos ZP, Zhou J (2006) A design optimization method using evidence theory. ASME J Mech Des 128(4):901-908
17. Noh Y, Choi KK, Lee I, Gorsich D, Lamb D (2011) Reliabilitybased design optimization with confidence level under input model uncertainty due to limited test data. Struct Multidisc Optim 43:443-458
18. O'Hagan A (2006) Bayesian analysis of computer code outputs: A tutorial. Reliab Eng Syst Saf 91(10-11):1290-1300
19. Qiu Z, Ma Y, Wang X (2004) Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters. Commun Numer Methods Eng 20(4):279-290
20. Rahman S (2008) A polynomial dimensional decomposition for stochastic computing. Int J Numer Methods Eng 76:2091-2116
21. Rahman S (2009) Extended polynomial dimensional decomposition for arbitrary probability distributions. J Eng Mech 135(12):1439-1451
22. Rahman S,Wei D (2008) Design sensitivity and reliability-based structural optimization by univariate decomposition. Struct Multidisc Optim 35:245-261
23. Rahman S, Xu H (2004) A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics. Probab Eng Mech 19(4):393-408
24. Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. The MIT Press
25. Sacks J,Welch WJ, Mitchell TJ,Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409-435
26. Sasena MJ, Papalambros P, Goovaerts P (2002) Exploration of metamodeling sampling criteria for constrained global optimization. Eng Optim 34(3):263-278
27. Youn BD, Wang PF (2008) Bayesian reliability-based design optimization using Eigenvector Dimension Reduction (EDR) method. Struct Multidisc Optim 36(2):107-123
28. Xu H, Rahman S (2004) A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics. Int J Numer Methods Eng 61:1992-2019
29. Xu H, Rahman S (2005) Decomposition methods for structural reliability analysis. Probab Eng Mech 20:239-250
30. Zhou J, Mourelatos ZP (2008) A sequential algorithm for possibilitybased design optimization. ASME J Mech Des 130(1): 011001