Sensitivity study of dynamic systems using polynomial chaos

Reliability Engineering and System Safety

Volumn 104, Issue , 2012, Pages 15-26

  Haro Sandoval, Eduardo ^a   Anstett Collin, Floriane ^b   Basset, Michel ^c  

^a UNIVERSIDAD PANAMERICANA   (Mexico)

^b UNIVERSITÉ DE LORRAINE   (France)

^c UNIVERSITÉ DE HAUTE ALSACE   (France)

Author keywords

Dynamic system; Global sensitivity analysis; Polynomial chaos expansion; Sensitivity functions

Indexed keywords

DIRECT SIMULATION; GLOBAL ANALYSIS; GLOBAL SENSITIVITY; GLOBAL SENSITIVITY ANALYSIS; NON-INTRUSIVE METHOD; PARAMETER SENSITIVITIES; PC DECOMPOSITION; PHYSICAL SYSTEMS; POLYNOMIAL CHAOS; POLYNOMIAL CHAOS EXPANSION; SENSITIVITY FUNCTIONS; SENSITIVITY INDICES; SENSITIVITY STUDIES; STATIC MODEL;

DIFFERENTIAL EQUATIONS; DYNAMIC MODELS; MODELS; POLYNOMIALS; SENSITIVITY ANALYSIS;

DYNAMICAL SYSTEMS;

EID: 84860663770     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2012.04.001     Document Type: Article

References (35)

1. G. Blatman, and B. Sudret Sparse polynomial chaos expansion and adaptive stochastic finite element using a regression approach Comptes Rendus de Mécanique 336 6 2008 518 523
2. E. Borgonovo A new uncertainty importance measure Reliability Engineering & System Safety 92 2007 771 784 (Pubitemid 46135960)
3. R.I. Cukier, R.I. Levine, and K.E. Shuler Nonlinear sensitivity analysis of multiparameter model systems Journal of Computational Physics 26 1978 1 42
4. H. Frey, and S.R. Patil Identification and review of sensitivity analysis methods Risk Analysis 22 3 2002 553 578 (Pubitemid 34655123)
5. A. Saltelli Sensitivity analysis for importance assessment Risk Analysis 22 3 2002 579 590 (Pubitemid 34655124)
6. A. Saltelli, S. Tarantola, F. Campolongo, and N. Ratto Sensitivity analysis in practice. A guide to assessing scientific models 2004 Wiley
7. I.M. Sobol Sensitivity estimates for nonlinear mathematical models Mathematical Modelling and Computing Experiments 1 1993 407 414
8. Turyani T, Rabitz H. In: Saltelli A, Chan K, Scott EM, editors. Local methods in sensitivity analysis. Chichester: John Wiley and Sons; 2000.
9. T. Homma, and A. Saltelli Importance measures in global sensitivity analysis of model output Reliability Engineering & System Safety 52 1 1996 1 17 (Pubitemid 126374988)
10. A. Saltelli, S. Tarantola, and K. Chan A quantitative model independent method for global sensitivity analysis of model output Technometrics 41 1999 39 56
11. Borgonovo E, Castaings W, Tarantola S. Model emulation and moment-independent sensitivity analysis: an application to environmental modelling. Environmental Modelling & Software 2011, http://dx.doi.org/10. 1016/j.envsoft.2011.06.006.
12. M. Ratto, and A. Pagano Using recursive algorithms for the efficient identification of smoothing spline anova models Advances in Statistical Analysis 94 4 2010 367 388
13. J. Jacques, C. Lavergne, and N. Devictor Sensitivity analysis in presence of model uncertainty and correlated inputs Reliability Engineering & System Safety 91 2006 1126 1134 (Pubitemid 44055917)
14. T.A. Mara, and S. Tarantola Application of global sensitivity analysis of model output to building thermal simulations Journal of Building Simulation 1 2008 290 302
15. M.D. McKay, J.D. Morrison, and S.C. Upton Evaluating prediction uncertainty in simulation models Computer Physics Communications 117 1-2 1999 44 51
16. N. Wiener The homogeneous chaos American Journal of Mathematics 60 4 1938 897 936
17. R. Ghanem, and J. Red-Horse Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach Physica D 133 1999 137 144 (Pubitemid 30505386)
18. R. Ghanem, and P. Spanos Stochastic finite elements - a spectral approach 1991 Springer Verlag
19. T. Crestaux, O.L. Maitre, and J. Martinez Polynomial chaos expansion for sensitivity analysis Reliability Engineering & System Safety 94 2009 1161 1172
20. B. Sudret Global sensitivity analysis using polynomial chaos expansion Reliability Engineering & System Safety 93 2008 964 979 (Pubitemid 351313888)
21. G. Blatman, and B. Sudret Efficient computation of global sensitivity indices using sparse polynomial chaos expansions Reliability Engineering & System Safety 95 11 2010 1216 1229
22. Buzzard GT. Global sensitivity analysis using sparse grid interpolation and polynomial chaos. Reliability Engineering & System Safety 2011, http://dx.doi.org/10.1016/j.ress.2011.07.011.
23. S. Rahman Global sensitivity analysis by polynomial dimensional decomposition Reliability Engineering & System Safety 96 7 2011 825 837
24. D.J.W.D. Pauw, and P.A. Vanrolleghem Practical aspects of sensitivity function approximation for dynamic models Mathematical and Computer Modelling of Dynamical Systems 12 2006 395 414 (Pubitemid 44181270)
25. M. Perry, H.P. Wynn, and R.A. Bates Principal components analysis in sensitivity studies of dynamic systems Probabilistic Engineering Mechanics 21 4 2006 454 460 (Pubitemid 44332623)
26. Witteveen J, Bijl H. Modeling arbitrary uncertainties using Gram-Schmidt polynomial chaos. In: 44th AIAA aerospace sciences meeting and exhibit; 2006.
27. D. Xiu, and G. Karniadakis The Wiener-Askey polynomials chaos for stochastic differential equations Journal of Scientific Computing 24 2002 2 9
28. D. Xiu, and G. Karniadakis Modeling uncertainty in flow simulations via generalized polynomial chaos Journal of Computational Physics 187 1 2002 137 167
29. Field R. Numerical methods to estimate the coefficients of the polynomial chaos expansion. In: 15th ASCE engineering mechanics conference; 2002.
30. M. Berveiller, B. Sudret, and M. Lemaire Stochastic finite element: a non intrusive approach by regression European Journal of Computational Mechanics 15 2006 81 92
31. B. Sudret, M. Berveiller, and M. Lemaire Application of a stochastic finite element procedure to reliability analysis European Journal of Computational Mechanics 15 7-8 2006 825 866
32. Eldred M. Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design. Technical report, 50th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference; 2009.
33. Agusti G, Schueller GI, Ciampoli M, editors. Nonlinear nonintrusive stochastic finite element method - application to a fracture mechanics problem. In: 9th international conference on structure, safety and reliability. Roma, Italy: Mill Press; 2005.
34. Sudret B. Uncertainty propagation and sensitivity analysis in mechanical models - contributions to structural reliability and stochastic spectral methods, habilitation à diriger des recherches. Clermont-Ferrand, France: Université Blaise Pascal; 2007.
35. Baudin M, Martinez J. Polynômes de chaos sous Scilab via librarie NISP. In: 42èmes journées de statistique; 2010.