In the non-probabilistic uncertainty structural analysis, the input uncertain variables of it, such as loads and material properties, will be propagated to the output responses, which include the displacement, stress and compliance, etc. To measure the effect of these non-probabilistic input variables on the output response, two new uncertainty importance measures on the non-probabilistic reliability index are discussed. For the linear limit state function, the analytical solutions of the importance measures are derived. To reduce computational effort, the discretization method and the surrogate model method are presented to calculate the two importance measures in case of the non-linear limit state. Finally, four examples demonstrate that the proposed importance measures can effectively describe the effect of the input variables on the reliability of the structure system, and the established methods can effectively obtain the two importance measures.
YuWHarrisTJ. Parameter uncertainty effects on variance-based sensitivity analysis. Reliab Eng Syst Saf2009; 94(6): 596–603.
2.
HeltonJCJohnsonJDSallaberryCJ. Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf2006; 91(10–11): 1175–1209.
3.
BjeragerPKrenkS. Parametric sensitivity in first order reliability analysis. ASCE J Eng Mech1989; 115(7): 1577–1582.
4.
SatlelliA. Sensitivity analysis for importance assessment. Risk Anal2002; 22(3): 579–590.
5.
ImanRLHoraSC. A robust measure of uncertainty importance for use in fault tree system analysis. Risk Anal1990; 10(3): 401–406.
6.
ImanRL. A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal1987; 7(1): 21–33.
7.
ImanRLConoverWJ. A measure of top-down correlation. Technometrics1987; 29(3): 351–357.
8.
HeltonJC. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliab Eng Syst Saf1993; 42(2–3): 327–367.
9.
SaltelliA. The role of sensitivity analysis in the corroboration of models and its link to model structural and parametric uncertainty. Reliab Eng Syst Saf1997; 57(1): 1–4.
10.
HeltonJCDavisFJ. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf2003; 81(1): 23–69.
11.
SaltelliATarantolaSCampolongoF. Sensitivity analysis as an ingredient of modeling. Stat Sci2000; 15(4): 377–395.
12.
LiuQHommaT. A new computational method of a moment-independent uncertainty importance measure. Reliab Eng Syst Saf2009; 94(6): 1205–1211.
13.
BorgonovoE. Measuring uncertainty importance: investigation and comparison of alternative approaches. Risk Anal2006; 26(5): 1349–1461.
14.
ChunMHHanSJTakNIL. An uncertainty importance measure using a distance metric for the change in a cumulative distribution function. Reliab Eng Syst Saf2000; 70(3): 313–321.
15.
BorgonovoE. A new uncertainty importance measure. Reliab Eng Syst Saf2007; 92(6): 771–784.
16.
SongSFLuZZZhangWW. Uncertainty importance measure by fast Fourier transform for wing transonic flutter. J Aircraft2011; 48(2): 449–455.
17.
LiLYLuZZFengJ. Moment-independent importance measure of basic variable and its state dependent parameter solution. Struct Saf2012; 38: 40–47.
18.
Ben-HaimY. Convex models of uncertainty in radial pulse bucking of shells. J Appl Mech1993; 60: 683–688.
19.
Ben-HaimY. A non-probabilistic concept of reliability. Struct Saf1994; 14(4): 227–245.
20.
Ben-HaimY. A non-probabilistic measure of reliability of linear systems based on expansion of convex models. Struct Saf1995; 17(2): 91–109.
21.
ElishakoffI. Essay on uncertainties in elastic and viscoelastic structures: from A. M. Freudenthal’s criticisms to modern convex modeling. Comput Struct1995; 56(6): 871–895.
22.
ElishakoffI. Discussion on: A non-probabilistic concept of reliability. Struct Saf1995; 17(2): 195–199.
23.
CremonaCGaoY. The possibilistic reliability theory: theoretical aspects and applications. Struct Saf1997; 19(2): 173–201.
24.
GuoSXLuZZFengYS. A non-probabilistic model of structural reliability based on interval analysis. Chin J Comput Mech2001; 18(1): 56–60.
25.
GuoSXZhangLLiY. Procedures for computing the non-probabilistic reliability index of uncertain in structures. Chin J Comput Mech2005; 22(2): 227–231.
26.
JonesDRSchonlauMandWelchWJ. Efficient global optimization of expensive black-box functions. J Global Optim1998; 13(4): 455–492.
27.
MartinJDSimpsonTW. Use of kriging models to approximate deterministic computer models. AIAA J2005; 43(4): 853–863.
28.
JanssonNWakemanWDMansonJAE. Optimization of hybrid thermoplastic composite structures using surrogate models and genetic algorithms. Compos Struct2007; 80(1): 21–31.
29.
BangIKHanDSHanGJ. Structural optimization for a jaw using iterative kriging metamodels. J Mech Sci Technol2008; 22(9): 1651–1659.
30.
DavisEIerapetritouM. A kriging based method for the solution of mixed-integer nonlinear programs containing black-box functions. J Global Optim2009; 43(2–3): 191–205.
31.
LophavenSNNielsenHBSondergaardJ. DACE: a Matlab kriging toolbox, 2003.
32.
ObadageASHarnpornchaiN. Determination of point of maximum likelihood in failure domain using genetic algorithms. Int J Press Pip2006; 83(4): 276–282.
