A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models

Reliability Engineering and System Safety

Volumn 111, Issue , 2013, Pages 232-240

  Echard, B ^a   Gayton, N ^a   Lemaire, M ^a   Relun, N ^b  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b Grande Voie des Vignes   (France)

Author keywords

Importance sampling; Kriging metamodel; Reliability; Small failure probability; Surrogate model

Indexed keywords

INTERPOLATION; MECHANICAL ENGINEERING; MONTE CARLO METHODS; NUMERICAL MODELS; PROBABILITY; RELIABILITY;

ACTIVE LEARNING; COMPLEX STRUCTURE; FAILURE PROBABILITY; IMPORTANCE SAMPLING METHOD; KRIGING; MECHANICAL BEHAVIOUR; MECHANICAL MODEL; META MODEL; MODEL COMPUTATION; MONTE CARLO SIMULATION; PROBABILITY LEVELS; RELIABILITY METHODS; SAFETY MARGIN; SMALL PROBABILITY EVENTS; STOCHASTIC PROPERTIES; STRUCTURAL SAFETY; SURROGATE MODEL;

IMPORTANCE SAMPLING;

EID: 84871135242     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2012.10.008     Document Type: Article

References (42)

1. O. Ditlevsen, and H.O. Madsen Structural reliability methods 1996 John Wiley & Sons
2. M. Lemaire Structural reliability 2009 ISTE
3. R. Melchers Radial importance sampling for structural reliability Journal of Engineering Mechanics 116 1 1990 189 203
4. G. Matheron The intrinsic random functions and their applications Advances in Applied Probability 5 3 1973 439 468
5. B.J. Bichon, M.S. Eldred, L.P. Swiler, S. Mahadevan, and J.M. McFarland Efficient global reliability analysis for nonlinear implicit performance functions AIAA Journal 46 2008 2459 2468
6. B. Echard, N. Gayton, and M. Lemaire AK-MCS an active learning reliability method combining Kriging and Monte Carlo simulation Structural Safety 33 2 2011 145 154
7. P.A. Boucard, and L. Champaney A suitable computational strategy for the parametric analysis of problems with multiple contact International Journal for Numerical Methods in Engineering 57 9 2003 1259 1281
8. Ladevèze P. Nonlinear Computational structural methods: new approaches and non-incremental methods of calculation. Mechanical engineering series. Springer-Verlag, 1999.
9. S.K. Au, and J.L. Beck Estimation of small failure probabilities in high dimensions by subset simulation Probabilistic Engineering Mechanics 16 4 2001 263 277
10. N. Gayton, J.M. Bourinet, and M. Lemaire CQ2RS a new statistical approach to the response surface method for reliability analysis Structural Safety 25 1 2003 99 121
11. R.G. Ghanem, and P.D. Spanos Stochastic finite elements a spectral approach 1991 Springer Berlin
12. B. Sudret, and A. Der Kiureghian Comparison of finite element reliability methods Probabilistic Engineering Mechanics 17 4 2002 337 348
13. G. Blatman, and B. Sudret An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis Probabilistic Engineering Mechanics 25 2 2009 183 197
14. J.E. Hurtado An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory Structural Safety 26 3 2004 271 293
15. J.M. Bourinet, F. Deheeger, and M. Lemaire Assessing small failure probabilities by combined subset simulation and support vector machines Structural Safety 33 6 2011 343 353
16. A. O'Hagan Bayesian analysis of computer code outputs a tutorial Reliability Engineering & System Safety 91 10-11 2006 1290 1300 (The fourth international conference on Sensitivity Analysis of Model Output (SAMO 2004)
17. M.C. Kennedy, C.W. Anderson, S. Conti, and A. O'Hagan Case studies in Gaussian process modelling of computer codes Reliability Engineering & System Safety 91 10-11 2006 1301 1309 (The fourth international conference on sensitivity analysis of model output (SAMO 2004) - SAMO 2004)
18. A. Marrel, B. Iooss, B. Laurent, and O. Roustant Calculations of Sobol' indices for the Gaussian process metamodel Reliability Engineering & System Safety 94 3 2009 742 751
19. D.R. Jones, M. Schonlau, and W.J. Welch Efficient global optimization of expensive black-box functions Journal of Global Optimization 13 4 1998 455 492
20. V.J. Romero, L.P. Swiler, and A.A. Giunta Construction of response surfaces based on progressive-lattice-sampling experimental designs with application to uncertainty propagation Structural Safety 26 2 2004 201 219
21. I. Kaymaz Application of Kriging method to structural reliability problems Structural Safety 27 2 2005 133 151
22. D. Busby Hierarchical adaptive experimental design for Gaussian process emulators Reliability Engineering & System Safety 94 7 2009 1183 1193 [Special Issue on Sensitivity Analysis]
23. A.H. Land, and A.G. Doig An automatic method of solving discrete programming problems Econometrica 28 3 1960 497 520
24. D.R. Jones, C.D. Perttunen, and B.E. Stuckman Lipschitzian optimization without the Lipschitz constant Journal of Optimization Theory and Applications 79 1 1993 157 181
25. P. Ranjan, D. Bingham, and G. Michailidis Sequential experiment design for contour estimation from complex computer codes Technometrics 50 4 2008 527 541
26. A. Dey, and S. Mahadevan Ductile structural system reliability analysis using adaptive importance sampling Structural Safety 20 2 1998 137 154
27. B.J. Bichon, J.M. McFarland, and S. Mahadevan Efficient surrogate models for reliability analysis of systems with multiple failure modes Reliability Engineering & System Safety 96 10 2011 1386 1395
28. Echard B, Gayton N, Lemaire M. A Kriging improvement of the Monte Carlo simulation: AK-MCS method. In: The eleventh International Conference on applications of statistics and probability in civil engineering. ETH Zurich; 2011.
29. B. Echard, N. Gayton, and M. Lemaire Structural reliability assessment using Kriging metamodel and Monte Carlo simulation D. Straub, Reliability and optimization of structural systems 2010 CRC Press 61 68
30. Lophaven SN, Nielsen HB, Sondergaard J. DACE, a matlab Kriging toolbox, version 2.0.Technical Report IMM-TR-2002-12. Technical University of Denmark; 2002. URL 〈 http://www2.imm.dtu.dk/∼hbn/dace/ 〉.
31. R. Rackwitz, and B. Fiessler Structural reliability under combined random load sequences Computers & Structures 9 5 1978 489 494
32. A. Marrel, B. Iooss, F. Van Dorpe, and E. Volkova An efficient methodology for modeling complex computer codes with Gaussian processes Computational Statistics & Data Analysis 52 10 2008 4731 4744
33. J.P.C. Kleijnen Kriging metamodeling in simulation: a review European Journal of Operational Research 192 3 2009 707 716
34. D.D. Cox, and S. John SDO A statistical method for global optimization M.N. Alexandrov, M.Y. Hussaini, Multidisciplinary design optimization: state-of-the-art 1997 SIAM Philadelphia 315 329
35. M.R. Rajashekhar, and B.R. Ellingwood A new look at the response surface approach for reliability analysis Structural Safety 12 3 1993 205 220
36. L. Schueremans, and D. Van Gemert Benefit of splines and neural networks in simulation based structural reliability analysis Structural Safety 27 3 2005 246 261
37. S. Thomas, G. Perroud, A. Bignonnet, and D. Monnet Fatigue design and reliability in the automotive industry G. Marquis, J. Solin, European Structural Integrity Society 1999 Elsevier 1 11
38. Echard B. Kriging-based reliability assessment of structures submitted to fatigue. PhD thesis. Blaise Pascal University-Clermont II; 2012 [written in English].
39. J.L. Chaboche Constitutive equations for cyclic plasticity and cyclic viscoplasticity International Journal of Plasticity 5 3 1989 247 302
40. AFNOR. A03-405, metal products - fatigue testing - data statistical processing; 1991.
41. Z. Guédé, B. Sudret, and M. Lemaire Life-time reliability based assessment of structures submitted to thermal fatigue International Journal of Fatigue 29 7 2007 1359 1373
42. K. Smith, P. Watson, and T. Topper A stress-strain function for the fatigue of metals Journal of Materials 5 4 1970 767 778