Global sensitivity analysis by polynomial dimensional decomposition

Reliability Engineering and System Safety

Volumn 96, Issue 7, 2011, Pages 825-837

  Rahman, Sharif ^a  

^a University of Iowa   (United States)

Author keywords

ANOVA; Curse of dimensionality; Dimension reduction; Orthogonal polynomials; Sensitivity index

Indexed keywords

ANOVA; CURSE OF DIMENSIONALITY; DIMENSION REDUCTION; ORTHOGONAL POLYNOMIALS; SENSITIVITY INDEX;

ANALYSIS OF VARIANCE (ANOVA); COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; ORTHOGONAL FUNCTIONS; POLYNOMIAL APPROXIMATION; PROBABILITY DISTRIBUTIONS; STOCHASTIC SYSTEMS;

SENSITIVITY ANALYSIS;

EID: 79955522844     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2011.03.002     Document Type: Article

References (35)

1. A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, and D. Gatelli Global sensitivity analysis: the primer 2008 Wiley West Sussex
2. S. Tarantola, D. Gatelli, and T.A. Mara Random balance designs for the estimation of first-order global sensitivity indices Reliability Engineering and System Safety 91 l 2006 717 727
3. F.E. Satterthwaite Random balance experimentation Technometrics 1 2 1959
4. R.I. Cukier, H.B. Levine, and K.E. Shuler Nonlinear sensitivity analysis of multi-parameter model systems Journal of Computational Physics 26 1978 1 42
5. M. Ratto, A. Pagano, and P. Young State dependent parameter metamodelling and sensitivity analysis Computer Physics Communications 177 2007 863 876 (Pubitemid 47614975)
6. I.M. Sobol Sensitivity analysis for nonlinear mathematical models Mathematical Modelling & Computational Experiment 1 1993 407 414
7. A. Saltelli Making best use of model evaluations to compute sensitivity indices Computer Physics Communications 145 2002 280 297 (Pubitemid 34524628)
8. A. Saltelli, P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and S. Tarantola Variance based sensitivity analysis of model output: design and estimator for the total sensitivity index Computer Physics Communications 181 2010 259 270
9. B. Sudret Global sensitivity analysis using polynomial chaos expansions Reliability Engineering and System Safety 93 7 2008 964 979 (Pubitemid 351313888)
10. R.G. Ghanem, and P.D. Spanos Stochastic finite elements: a spectral approach 1991 Springer-Verlag New York
11. T. Crestaux, O. Le Maitre, and J.M. Martinez Polynomial chaos expansion for sensitivity analysis Reliability Engineering and System Safety 94 7 2008 1161 1172
12. J.C. Helton, and F.J. Davis Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems Reliability Engineering and System Safety 81 1 2003 23 69
13. I.M. Sobol On the distribution of points in a cube and the approximate evaluation of integrals USSR Computational Mathematics and Mathematical Physics 7 4 1967 86 112
14. W. Hoeffding A class of statistics with asymptotically normal distributions Annals of Mathematical Statistics 19 1948 293 325
15. B. Efron, and C. Stein The jackknife estimate of variance Annals of Statistics 9 1981 586 596
16. H. Rabitz, and O. Alis General foundations of high dimensional model representations Journal of Mathematical Chemistry 25 1999 197 233
17. G. Li, S.W. Wang, and H. Rabitz Practical approaches to construct RS-HDMR component functions Journal of Physical Chemistry A 106 2002 8721 8733 (Pubitemid 35382435)
18. S. Rahman, and H. Xu A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics Probabilistic Engineering Mechanics 19 2004 393 408
19. H. Xu, and S. Rahman A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics International Journal for Numerical Methods in Engineering 61 2004 1992 2019 (Pubitemid 39622519)
20. H. Xu, and S. Rahman Decomposition methods for structural reliability analysis Probabilistic Engineering Mechanics 20 2005 239 250 (Pubitemid 41145456)
21. Rahman S. Decomposition methods for structural reliability analysis revisited. Probabilistic Engineering Mechanic 2011;26:35763.
22. I.M. Sobol Theorems and examples on high dimensional model representations Reliability Engineering and System Safety 79 2003 187 193
23. S. Rahman A polynomial dimensional decomposition for stochastic computing International Journal for Numerical Methods in Engineering 76 2008 2091 2116
24. S. Rahman Extended polynomial dimensional decomposition for arbitrary probability distributions Journal of Engineering Mechanics 135 12 2009 1439 1451
25. A. Saltelli, S. Tarantola, F. Campolongo, and M. Ratto Sensitivity analysis in practice: a guide to assessing scientific models 2004 John Wiley & Sons
26. R.E. Caflisch, W. Morokoff, and A. Owen Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension Journal of Computational Finance 1 1997 27 46
27. S. Rahman Statistical moments of polynomial dimensional decomposition Journal of Engineering Mechanics 136 7 2010 923 927
28. M. Abramowitz, and I.A. Stegun Handbook of mathematical functions 9th ed 1972 Dover Publications Inc. New York
29. Rahman S, Yadav V. Orthogonal polynomial expansions for solving random eigenvalue problems. International Journal for Uncertainty Quantification 2011;1(2):16387.
30. E. Castillo, N. Sánchez-Maroo, A. Alonso, and C. Castillo Functional network topology learning and sensitivity analysis based on ANOVA decomposition Neural Computation 19 1 2007 231 257
31. T. Ishigami, and T. Homma An importance quantification technique in uncertainty analysis for computer models Proceedings of the ISUMA '90, first international symposium on uncertainty modeling and analysis, University of Maryland, 35 December 1990 398 403
32. A. Saltelli, and I.M. Sobol About the use of rank transformation in sensitivity analysis of model output Reliability Engineering and System Safety 50 3 1995 225 239
33. D. Gatelli, S. Kucherenko, M. Ratto, and S. Tarantola Calculating first-order sensitivity measures: a benchmark of some recent methodologies Reliability Engineering and System Safety 94 2009 1212 1219
34. J. Oakley, and A. O'Hagan Probabilistic sensitivity analysis of complex models: a Bayesian approach Journal of Royal Statistical Society: series B 66 2004 751 769 (Pubitemid 39015911)
35. ABAQUS Standard, Version 6.9. Dassualt Systems Simulia Corp., Providence, RI, 2010.