Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

Reliability Engineering and System Safety

Volumn 95, Issue 11, 2010, Pages 1216-1229

  Blatman, Graud ^a,b   Sudret, Bruno ^a,c  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b EDF R AND D   (France)

^c now at Phimeca Engineering   (France)

Author keywords

ANOVA; Global sensitivity analysis; Sequential experimental design; Sobol' indices; Sparse polynomial chaos; Stepwise regression

Indexed keywords

ANOVA; GLOBAL SENSITIVITY ANALYSIS; SEQUENTIAL EXPERIMENTAL DESIGN; SOBOL' INDICES; SPARSE POLYNOMIALS; STEPWISE REGRESSION;

ADAPTIVE ALGORITHMS; ANALYSIS OF VARIANCE (ANOVA); CHAOS THEORY; COMPUTER SIMULATION; DESIGN; MATHEMATICAL MODELS; MONTE CARLO METHODS; POLYNOMIALS; REGRESSION ANALYSIS; STATISTICS;

SENSITIVITY ANALYSIS;

EID: 78049421958     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2010.06.015     Document Type: Article

References (75)

1. Saltelli A, Chan K, Scott EM. Sensitivity analysis. John Wiley & Sons; 2000.
2. J.C. Helton, and F.J. Davies Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems Reliab Eng Syst Safety 81 1 2003 23 69
3. A. Saltelli, and I.M. Sobol' About the use of rank transformation in sensitivity of model output Reliab Eng Syst Safety 50 1995 225 239
4. B. Efron, and C. Stein The Jacknife estimate of variance Ann Stat 9 3 1981 586 596
5. H. Cukier, R.I. Levine, and K. Shuler Nonlinear sensitivity analysis of multiparameter model systems J Comput Phys 26 1978 1 42
6. A. Saltelli, S. Tarantola, and K. Chan A quantitative, model independent method for global sensitivity analysis of model output Technometrics 41 1 1999 39 56
7. I.M. Sobol' Sensitivity estimates for nonlinear mathematical models Math Model Comput Exp 1 1993 407 414
8. G.E. Archer, A. Saltelli, and I.M. Sobol' Sensitivity measures, ANOVA-like techniques and the use of bootstrap J. Stat. Comput. Simul. 58 1997 99 120
9. A. Saltelli, S. Tarantola, and K.P.-S. Chan A quantitative model-independent method for global sensitivity analysis of model output Technometrics 41 1 1999 39 56
10. I.M. Sobol', and S.S. Kucherenko Global sensitivity indices for nonlinear mathematical models. Review Wilmott Mag 1 2005 56 61
11. M.D. Morris Factorial sampling plans for preliminary computational experiments Technometrics 33 2 1991 161 174
12. J.C. Helton, J.D. Johnson, C.J. Sallaberry, and C.B. Storlie Survey of sampling-based methods for uncertainty and sensitivity analysis Reliab Eng Syst Safety 91 1011 2006 1175 1209
13. A. Saltelli, T.H. Andres, and T. Homma Sensitivity analysis of model output: performance of the iterated fractional factorial design method Comput Stat Data Anal 20 4 1995 387 407
14. D.L. Beres, and D.M. Hawkins PlackettBurman techniques for sensitivity analysis of many-parametered models Ecol Model 141 13 2001 171 183
15. C.B. Storlie, and J.C. Helton Multiple predictor smoothing methods for sensitivity analysis: description of techniques Reliab Eng Syst Safety 93 1 2008 28 54
16. C.B. Storlie, and J.C. Helton Multiple predictor smoothing methods for sensitivity analysis: example results Reliab Eng Sys Safety 93 1 2008 55 77
17. C.B. Storlie, L.P. Swiler, J.C. Helton, and C.J. Sallaberry Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models Reliab Eng Syst Safety 94 2009 1735 1763
18. J. Oakley, and A. O'Hagan Probabilistic sensitivity analysis of complex models: a Bayesian approach J R Stat Soc Ser B 66 2004 751 769
19. A. Marrel, B. Iooss, B. Laurent, and O. Roustant Calculations of Sobol indices for the Gaussian process metamodel Reliab Eng Syst Safety 94 3 2009 742 751
20. H. Rabitz,.F. Ali, J. Shorter, and K. Shim Efficient inputoutput model representations Comput Phys Commun 117 12 1999 11 20
21. G. Li, P. Wang, and H. Rabitz Practical approaches to construct RSHDMR component functions J Phys Chem A 106 2002 8721 8733
22. G Li, J Hu, S-W Wang, G Georgopoulos, J Shoendorf, and H Rabitz Random samplinghigh dimensional model representation (RSHDMR) and orthogonality of its different order component functions J Phys Chem A 110 7 2006 2474 2485
23. Feil B, Kucherenko S, Shah N. Comparison of Monte Carlo and quasi Monte Carlo sampling methods in high dimensional model representation. In: Advances in system simulation, first international conference on advances in system simulation, Porto, Portugal, 2009.
24. R.G. Ghanem, and P.D. Spanos Stochastic finite elementsa spectral approach 1991 Springer Verlag [Reedited by Dover Publications, 2003]
25. D.M. Ghiocel, and R.G. Ghanem Stochastic finite element analysis of seismic soilstructure interaction J Eng Mech 128 2002 66 77
26. O.P. Le Matre, M. Reagan, H.N. Najm, R.G. Ghanem, and O.M. Knio A stochastic projection method for fluid flowII. Random process J Comput Phys 181 2002 9 44
27. Field RV. Numerical methods to estimate the coefficients of the polynomial chaos expansion. In: Proceeding of the 15th ASCE engineering mechanics division conference, Columbia University, New York, USA, 2002.
28. Keese A, Matthies H. Numerical methods and Smolyak quadrature for nonlinear stochastic partial differential equations. Technical Report, Technische Universitt Braunschweig; 2003.
29. S.K. Choi, R.V. Grandhi, R.A. Canfield, and C.L. Pettit Polynomial chaos expansion with Latin hypercube sampling for estimating response variability AIAA J 45 2004 1191 1198
30. H.G. Matthies, and A. Keese Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations Comput Methods Appl Mech Eng 194 2005 1295 1331
31. P.S. Beran, C.L. Pettit, and D.R. Millman Uncertainty quantification of limit-cycle oscillations J Comput Phys 217 2006 217 247
32. Berveiller M. Stochastic finite elements: intrusive and non-intrusive methods for reliability analysis. PhD thesis, Universit Blaise Pascal, Clermont-Ferrand; 2005.
33. M. Berveiller, B. Sudret, and M. Lemaire Stochastic finite elements: a non-intrusive approach by regression Eur J Comput Mech 15 13 2006 81 92
34. B. Sudret Global sensitivity analysis using polynomial chaos expansions Reliab Eng Syst Safety 93 2008 964 979
35. Berveiller M, Sudret B, Lemaire M. Nonlinear non-intrusive stochastic finite element methodapplication to a fracture mechanics problem. In: Augusti G, Schuller GI, Ciampoli M, editors. Proceedings of the 9th international conference on structural safety and reliability (ICOSSAR'2005), Roma, Italy, Millpress, Rotterdam, 2005.
36. G. Blatman, and B. Sudret Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach C R Mcanique 336 6 2008 518 523
37. G. Blatman, and B. Sudret An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis Probab Eng Mech 25 2010 183 197
38. Blatman G, Sudret B. Adaptive sparse polynomial chaos expansion based on least angle regression. J Comput Phys, 2010, under review.
39. W. Hoeffding A class of statistics with asymptotically normal distributions Ann Math Stat 19 1948 293 325
40. Griebel M. Sparse grids and related approximation schemes for higher dimensional problems. Technical Report, Technical University of Bonn, Germany; 2006.
41. T. Homma, and A. Saltelli Importance measures in global sensitivity analysis of nonlinear models Reliab Eng Syst Safety 52 1996 1 17
42. A. Saltelli Making best use of model evaluations to compute sensitivity indices Comput Phys Commun 145 2002 280 297
43. Sudret B. Global sensitivity analysis using polynomial chaos expansions. In: Spanos P, Deodatis G, editors. Proceedings of the 5th international conference on computation stochastic mechanics (CSM5), Rhodos, Greece, 2006.
44. W. Schoutens Stochastic processes and orthogonal polynomials 2000 Springer-Verlag New York
45. D. Xiu, and G.E. Karniadakis The WienerAskey polynomial chaos for stochastic differential equations SIAM J Sci Comput 24 2 2002 619 644
46. X. Wan, and G. Karniadakis Beyond WienerAskey expansions: handling arbitrary PDFs J Sci Comput 27 2006 455 464
47. J.A.S. Witteveen, S. Sarkar, and H. Bijl Modeling physical uncertainties in dynamic stall induced fluidstructure interaction of turbine blades using arbitrary polynomial chaos Comput Struct 85 2007 866 878
48. C. Soize, and R. Ghanem Physical systems with random uncertainties: chaos representations with arbitrary probability measure SIAM J Sci Comput 26 2 2004 395 410
49. J. An, and A. Owen Quasi-regression J Complexity 17 4 2001 588 607
50. M.D. McKay, R.J. Beckman, and W.J. Conover A comparison of three methods for selecting values of input variables in the analysis of output from a computer code Technometrics 2 1979 239 245
51. H. Niederreiter Random number generation and quasi-Monte Carlo methods 1992 SIAM Philadelphia, PA, USA
52. G. Blatman, B. Sudret, and M. Berveiller Quasi-random numbers in stochastic finite element analysis Mcanique Industries 8 2007 289 297
53. S.A. Smolyak Quadrature and interpolation formulas for tensor products of certain classes of functions Soviet Math Dokl 4 1963 240 243
54. T. Gerstner, and M. Griebel Dimension-adaptive tensor-product quadrature Computing 71 2003 65 87
55. Nobile F, Tempone R, Webster C. A sparse grid stochastic collocation method for elliptic partial differential equations with random input data. Technical Report MOX Report 85, Politecnico di Milano; 2006.
56. Klimke WA. Uncertainty modeling using fuzzy arithmetic and sparse grids. PhD thesis, University of Stuttgart; 2006.
57. B. Ganapathysubramanian, and N. Zabaras Sparse grid collocation schemes for stochastic natural convection problems J Comput Phys 225 2007 652 685
58. Isukapalli SS. Uncertainty analysis of transport-transformation models. PhD thesis, The State University of New Jersey; 1999.
59. . Bjorck Numerical methods for least squares problems 1996 SIAM Press Philadelphia, PA
60. Blatman G. Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis. PhD thesis, Universit Blaise Pascal, Clermont-Ferrand; 2009.
61. V.N. Vapnik The nature of statistical learning theory 1995 Springer-Verlag New York
62. Allen D. The prediction sum of squares as a criterion for selecting prediction variables. Technical Report 23, Department of Statistics, University of Kentucky; 1971.
63. Saporta G. Probabilits, analyse des donnes et statistique. Editions Technip, 2nd ed., 2006.
64. G.G. Wang Adaptive response surface method using inherited Latin hypercube design points J Mech Design 125 2003 210 220
65. C. Tong Refinement strategies for stratified sampling methods Reliab Eng Syst Safety 91 1011 2006 1257 1265
66. C.J. Sallaberry, J.C. Helton, and S.C. Hora Extension of Latin hypercube samples with correlated variables Reliab Eng Syst Safety 93 2008 1047 1059
67. Ishigami T, Homma T. An importance quantification technique in uncertainty analysis for computer models. In: Proceedings of the ISUMA'90, first International symposium on uncertainty modeling and analysis, University of Maryland, 1990. p. 398403.
68. I.M. Sobol' Theorems and examples on high dimensional model representation Reliab Eng Syst Safety 79 2003 187 193
69. R.L. Iman Statistical methods for including uncertainties associated with the geologic isolation of radioactive waste which allow for a comparison with licensing criteria Proceedings of the symposium on uncertainties associated with the regulation of the geologic disposal of high-level radioactive waste 1981
70. J.C. Helton, and C.J. Sallaberry Computational implementation of sampling-based approaches to the calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada Reliab Eng Syst Safety 94 2009 699 721
71. P.-L. Liu, and A. Der Kiureghian Optimization algorithms for structural reliability Struct Safety 9 1991 161 177
72. D. Wei, and S. Rahman Structural reliability analysis by univariate decomposition and numerical integration Probab Eng Mech 22 2007 27 38
73. A. Nataf Dtermination des distributions dont les marges sont donnes C R Acad Sci Paris 225 1962 42 43
74. C. Xu, and G.Z. Gertner Uncertainty and sensitivity analysis for models with correlated parameters Reliab Eng Syst Safety 93 2008 1563 1573
75. B. Efron, and R.J. Tibshirani An introduction to the bootstrap 1993 Chapman & Hall New York