Moving least squares based sensitivity analysis for models with dependent variables

Applied Mathematical Modelling

Volumn 37, Issue 8, 2013, Pages 6097-6109

  Tian, Longfei ^a   Lu, Zhenzhou ^a   Hao, Wenrui ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Dependent inputs; Marginal contribution; Moving least squares; Sensitivity analysis; Total contribution; Variance decomposition

Indexed keywords

DEPENDENT INPUTS; MARGINAL CONTRIBUTION; MOVING LEAST SQUARES; TOTAL CONTRIBUTION; VARIANCE DECOMPOSITION;

SENSITIVITY ANALYSIS;

LEAST SQUARES APPROXIMATIONS;

EID: 84874568272     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.12.010     Document Type: Article

References (39)

1. Apostolakis G.E. How useful is quantitative risk assessment. Risk Anal. 2005, 24(3):515-520. 10.1111/j.0272-4332.2004.00455.x.
2. Saltelli A. Sensitivity analysis for importance assessment. Risk Anal. 2002, 22(3):579-590. 10.1111/0272-4332.00040.
3. McRae G.J., Tilden J.W., Seinfeld J.H. Global sensitivity analysis: a computational implementation of the Fourier amplitude sensitivity test (FAST). Comput. Chem. Eng. 1982, 6(1):15-25. 10.1016/0098-1354(82)80003-3.
4. Li G., Rabitz H., Yelvington P.E., Oluwole O.O., Bacon F., Kolb C.E., Schoendorf J. Global sensitivity analysis for systems with independent and/or correlated inputs. J. Phys. Chem. A 2010, 114(19):6022-6032. 10.1021/jp9096919.
5. Iman R.L., Hora S.C. A robust measure of uncertainty importance for use in fault tree system analysis. Risk Anal. 1990, 10(3):401-406. 10.1111/j.1539-6924.1990.tb00523.x.
6. Saltelli A. The role of sensitivity analysis in the corroboration of models and its link to model structural and parametric uncertainty. Reliab. Eng. Syst. Saf. 1997, 57(1):1-4.
7. Pörn K. A decision-oriented measure of uncertainty importance for use in PSA. Reliab. Eng. Syst. Saf. 1997, 56(1):17-27. 10.1016/S0951-8320(96)00136-6.
8. Rabitz H., Alis O.F., Shorter J., Shim K. Efficient input output model representation. Comput. Phys. Commun. 1998, 117(1-2):11-20. 10.1016/S0010-4655(98)00152-0.
9. Rabitz H., Alis O.F. General foundations of high-dimensional model representations. J. Math. Chem. 1999, 25(2-3):197-233. 10.1023/A:1019188517934.
10. Chun M.H., Han S.J., Tak N.I. An uncertainty importance measure using a distance metric for the change in a cumulative distribution function. Reliab. Eng. Syst. Saf. 2000, 70(3):313-321. 10.1016/S0951-8320(00)00068-5.
11. Sobol' I.M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 2001, 55(1-3):271-280. 10.1016/S0378-4754(00)00270-6.
12. Sobol' I.M. Theorem and examples on high-dimensional model representation. Reliab. Eng. Syst. Saf. 2003, 79(2):187-193. 10.1016/S0951-8320(02)00229-6.
13. Helton J.C., Johnson J.D., Sallaberry C.J., Storlie C.B. Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab. Eng. Syst. Saf. 2006, 91(10-11):1175-1209. 10.1016/j.ress.2005.11.017.
14. Borgonovo E. A new uncertainty importance measure. Reliab. Eng. Syst. Saf. 2007, 92(6):771-784. 10.1016/j.ress.2006.04.015.
15. De Rocquigny E., Devitor N., Tarantola S. Uncertainty in Industrial Practice 2008, Wiley, Chichester, England, UK. 10.1002/9780470770733.fmatter.
16. A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola, Global Sensitivity Analysis: The Primer, John Wiley & Sons Ltd, West Sussex, 2008.
17. Ratto M., Pagano A., Young P. State dependent parameter metamodelling and sensitivity analysis. Comput. Phys. Commun. 2007, 177(11):863-876. 10.1016/j.cpc.2007.07.011.
18. Cukier R., Levine H., Shuler K. Nonlinear sensitivity analysis of multi-parameter model systems. J. Comput. Phys. 1978, 26(1):1-42. 10.1016/0021-9991(78)90097-9.
19. Saltelli, Tarantola S., Chan K.P.S. A quantitative model-independent method for global sensitivity analysis of model output. Technometrics 1999, 41(1):39-56. 10.2307/1270993.
20. Oakley J., O'Hagan A. Probabilistic sensitivity analysis of complex models: a Bayesian approach. J. Roy. Stat. Soc. B 2004, 66(3):751-769. 10.1111/j.1467-9868.2004.05304.x.
21. Sobol' I.M. Sensitivity analysis for non-linear mathematical models. Math. Model. Comput. Exp. 1993, 1(4):407-414.
22. Saltelli A., Tarantola S., Campolongo F., Ratto M. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models 2004, Wiley, West-Sussex, England, UK.
23. McKay M.D. Nonparametric variance-based methods of assessing uncertainty importance. Reliab. Eng. Syst. Saf. 1997, 57(3):267-279. 10.1016/S0951-8320(97)00039-2.
24. Fang S., Gertner G.Z., Anderson A. Estimation of sensitivity coefficients of nonlinear model input parameters which have a multinomial distribution. Comput. Phys. Commun. 2004, 157(1):9-16. 10.1016/S0010-4655(03)00488-0.
25. Xu C., Gertner G.Z. Uncertainty and sensitivity analysis for models with correlated parameters. Reliab. Eng. Syst. Saf. 2008, 93(6):1563-1573. 10.1016/j.ress.2007.06.003.
26. T.A. Mara, S. Tarantola, Variance-based sensitivity indices for models with dependent inputs, Reliab. Eng. Syst. Saf., in press. doi:10.1016/j.ress.2011.08.008.
27. Lancaster P., Salkauskas K. Surfaces generated by moving least squares methods. Math. Comput. 1981, 37(155):141-158. 10.1090/S0025-5718-1981-0616367-1.
28. Breitkpf P., Naceur H., Rassineux A., Villon P. Moving least squares response surface approximation: formulation and metal forming applications. Comput. Struct. 2005, 83(17-18):1411-1428. 10.1016/j.compstruc.2004.07.011.
29. Kim C., Wang S., Choi K.K. Efficient response surface modeling by using moving least-squares method and sensitivity. AIAA J. 2005, 43(11):2404-2411. 10.2514/1.12366.
30. Iman R.I., Conover W.J. A distribution-free approach to inducing rank correlation among input variables. Commun. Stat. Simul. Comput. 1982, 11(3):311-334. 10.1080/03610918208812265.
31. Lebrun R., Dutfoy A. A generalization of the Nataf transformation to distributions with elliptical copula. Probab. Eng. Mech. 2009, 24(2):172-178. 10.1016/j.probengmech.2008.05.001.
32. Rosenblatt M. Remarks on a multivariate transformation. Ann. Math. Stat. 1952, 23(3):470-472.
33. Der Kiureghian A., Liu P.L. Structural reliability under incomplete probability information. J. Eng. Mech. 1986, 112(1):85-104. 10.1061/(ASCE)0733-9399(1986)112:1(85).
34. Liu P.L., Der Kiureghian A. Multivariate distribution models with prescribed marginals and covariances. Probab. Eng. Mech. 1986, 1(2):105-112. 10.1016/0266-8920(86)90033-0.
35. Li H.S., Lu Z.Z., Yuan X.K. Nataf transformation based point estimate method. Chin. Sci. Bull. 2008, 53(17):2586-2592. 10.1007/s11434-008-0351-0.
36. Stein M. Large sample properties of simulations using Latin hypercube sampling. Technometrics 1987, 29(2):143-151. 10.2307/1269769.
37. Seung-Kyum C., Robert C., Ramana G., Chris P. Polynomial chaos expansion with Latin hypercube sampling for estimating response variability. AIAA J. 2004, 42(6):1191-1198. 10.2514/1.2220.
38. Lian Y., Kim N.H. Reliability-based design optimization of a transonic compressor. AIAA J. 2006, 44(2):368-375. 10.2514/1.16262.
39. Cheraghi S.H. Effect of variations in the riveting process on the quality of riveted joints. Int. J. Adv. Manuf. Technol. 2008, 39(11-12):1144-1155. 10.1007/s00170-007-1291-6.