References
- Alefeld, G. , & Mayer, G. (2000). Interval analysis: Theory and applications. Journal of Computational and Applied Mathematics, 121 (1–2), 421–464. Retrieved from http://dx.doi.org/10.1016/S0377-0427(00)00342-3
- Apostolakis, G. (1990). The concept of probability in safety assessments of technological systems. Science, 250 (4986), 1359–1364. doi:10.1126/science.2255906
- Baraldi, P. , Compare, M. , & Zio, E. (2013). Component ranking by Birnbaum importance in presence of epistemic uncertainty in failure event probabilities. Reliability, IEEE Transactions on, 62 (1), 37–48. doi:10.1109/TR.2013.2240885
- Baraldi, P. , Zio, E. , & Compare, M. (2009). A method for ranking components importance in presence of epistemic uncertainties. Journal of Loss Prevention in the Process Industries, 22 (5), 582–592. Retrieved from http://dx.doi.org/10.1016/j.jlp.2009.02.013
- Borgonovo, E. (2007). A new uncertainty importance measure. Reliability Engineering & System Safety, 92 (6), 771–784. Retrieved from http://dx.doi.org/10.1016/j.ress.2006.04.015
- Borgonovo, E. , Apostolakis, G.E. , Tarantola, S. , & Saltelli, A. (2003). Comparison of global sensitivity analysis techniques and importance measures in PSA. Reliability Engineering & System Safety, 79 (2), 175–185. Retrieved from http://dx.doi.org/10.1016/S0951-8320(02)00228-4
- Byrd, R.H. , Lu, P. , Nocedal, J. , & Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16 (5), 1190–1208. doi:10.1137/0916069
- Campolongo, F. , Cariboni, J. , & Saltelli, A. (2007). An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software, 22 (10), 1509–1518. Retrieved from http://dx.doi.org/10.1016/j.envsoft.2006.10.004
- Campolongo, F. , Saltelli, A. , & Cariboni, J. (2011). From screening to quantitative sensitivity analysis. A unified approach. Computer Physics Communications, 182 (4), 978–988. Retrieved from http://dx.doi.org/10.1016/j.cpc.2010.12.039
- Chun, M.-H. , Han, S.-J. , & Tak, N.-I.L. (2000). An uncertainty importance measure using a distance metric for the change in a cumulative distribution function. Reliability Engineering & System Safety, 70 (3), 313–321. Retrieved from http://dx.doi.org/10.1016/S0951-8320(00)00068-5
- Couckuyt, I. , Dhaene, T. , & Demeester, P. (2014). Oodace toolbox: A flexible object-oriented Kriging implementation. Journal of Machine Learning Research, 15 (1), 3183–3186.
- Dai, H. , & Wang, W. (2009). Application of low-discrepancy sampling method in structural reliability analysis. Structural Safety, 31 (1), 55–64. Retrieved from http://dx.doi.org/10.1016/j.strusafe.2008.03.001
- Der Kiureghian, A.D. , & Ditlevsen, O. (2009). Aleatory or epistemic? Does it matter? Structural Safety, 31 (2), 105–112. Retrieved from http://dx.doi.org/10.1016/j.strusafe.2008.06.020
- Dubois, D. (2006). Possibility theory and statistical reasoning. Computational Statistics & Data Analysis, 51 (1), 47–69. Retrieved from http://dx.doi.org/10.1016/j.csda.2006.04.015
- Dubois, D. , & Prade, H. (2001). Possibility theory, probability theory and multiple-valued logics: A clarification. Annals of Mathematics and Artificial Intelligence, 32 (1–4), 35–66. doi:10.1023/A:1016740830286
- Fine, T.L. (1973). Theories of probability: An examination of foundations . New York: Academic Press.
- Forrester, A.I.J. , & Keane, A.J. (2009). Recent advances in surrogate-based optimization. Progress in Aerospace Sciences, 45 (1–3), 50–79. Retrieved from http://dx.doi.org/10.1016/j.paerosci.2008.11.001
- Ge, Q. , Ciuffo, B. , & Menendez, M. (2015). Combining screening and metamodel-based methods: An efficient sequential approach for the sensitivity analysis of model outputs. Reliability Engineering & System Safety, 134 , 334–344. Retrieved from http://dx.doi.org/10.1016/j.ress.2014.08.009
- Haaker, M.P.R. , & Verheijen, P.J.T. (2004). Local and global sensitivity analysis for a reactor design with parameter uncertainty. Chemical Engineering Research and Design, 82 (5), 591–598. Retrieved from http://dx.doi.org/10.1205/026387604323142630
- Hofer, E. , Kloos, M. , Krzykacz-Hausmann, B. , Peschke, J. , & Woltereck, M. (2002). An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties. Reliability Engineering & System Safety, 77 (3), 229–238. Retrieved from http://dx.doi.org/10.1016/S0951-8320(02)00056-X
- Homma, T. , & Saltelli, A. (1996). Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering & System Safety, 52 (1), 1–17. Retrieved from http://dx.doi.org/10.1016/0951-8320(96)00002-6
- Iman, R.L. , & Hora, S.C. (1990). A robust measure of uncertainty importance for use in fault tree system analysis. Risk Analysis, 10 (3), 401–406. doi:10.1111/j.1539-6924.1990.tb00523.x
- Iman, R.L. , Johnson, M.E. , & Watson, C.C. (2005). Sensitivity analysis for computer model projections of hurricane losses. Risk Analysis, 25 (5), 1277–1297. doi:10.1111/j.1539-6924.2005.00673.x
- Ishigami, T. , & Homma, T. (1990, December 3–5). An importance quantification technique in uncertainty analysis for computer models. The Uncertainty Modeling and Analysis, 1990. Proceedings. First International Symposium on .
- Jansen, M.J.W. (1999). Analysis of variance designs for model output. Computer Physics Communications, 117 (1–2), 35–43. Retrieved from http://dx.doi.org/10.1016/S0010-4655(98)00154-4
- Jiang, C. , Han, X. , Li, W.X. , Liu, J. , & Zhang, Z. (2012). A hybrid reliability approach based on probability and interval for uncertain structures. Journal of Mechanical Design, 134 (3), 031001–031001. doi:10.1115/1.4005595
- Jiang, C. , Li, W.X. , Han, X. , Liu, L.X. , & Le, P.H. (2011). Structural reliability analysis based on random distributions with interval parameters. Computers & Structures, 89 (23–24), 2292–2302. doi:10.1016/j.compstruc.2011.08.006
- Krzykacz-Hausmann, B. (2006). An approximate sensitivity analysis of results from complex computer models in the presence of epistemic and aleatory uncertainties. Reliability Engineering & System Safety, 91 (10–11), 1210–1218. Retrieved from http://dx.doi.org/10.1016/j.ress.2005.11.019
- Li, L. , & Lu, Z. (2017). Importance analysis for model with mixed uncertainties. Fuzzy Sets and Systems . Retrieved from http://dx.doi.org/10.1016/j.fss.2015.12.020
- Li, G. , Lu, Z. , Li, L. , & Ren, B. (2016). Aleatory and epistemic uncertainties analysis based on non-probabilistic reliability and its kriging solution. Applied Mathematical Modelling, 40 (9–10), 5703–5716. Retrieved from http://dx.doi.org/10.1016/j.apm.2016.01.017
- Liu, Q. , & Homma, T. (2010). A new importance measure for sensitivity analysis. Journal of Nuclear Science and Technology, 47 (1), 53–61. doi:10.1080/18811248.2010.9711927
- McKay, M.D. , Beckman, R.J. , & Conover, W.J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21 (2), 239–245. doi:10.2307/1268522
- Morris, M.D. (1991). Factorial sampling plans for preliminary computational experiments. Technometrics, 33 (2), 161–174. doi:10.2307/1269043
- Myers, R.H. , Montgomery, D.C. , & Anderson-Cook, C.M. (2008). Response surface methodology: Process and product in optimization using designed experiments (3rd edition) . Hoboken, NJ: Wiley.
- Nocedal, J. (1980). Updating quasi-Newton matrices with limited storage. Mathematics of Computation, 35 (151), 773–773. doi:10.2307/2006193
- Queipo, N.V. , Haftka, R.T. , Shyy, W. , Goel, T. , Vaidyanathan, R. , & Kevin Tucker, P. (2005). Surrogate-based analysis and optimization. Progress in Aerospace Sciences, 41 (1), 1–28. Retrieved from http://dx.doi.org/10.1016/j.paerosci.2005.02.001
- Ryberg, A.-B. , Domeij Bäckryd, R. , & Nilsson, L. (2012). Metamodel-based multidisciplinary design optimization for automotive applications . Linköping: Linköping University Electronic Press.
- Sacks, J. , Welch, W.J. , Mitchell, T.J. , & Wynn, H.P. (1989). Design and analysis of computer experiments : Rejoinder, 4(4). doi:10.1214/ss/1177012413
- Sakata, S. , Ashida, F. , & Zako, M. (2003). Structural optimization using Kriging approximation. Computer Methods in Applied Mechanics and Engineering, 192 (7–8), 923–939. Retrieved from http://dx.doi.org/10.1016/S0045-7825(02)00617-5
- Saltelli, A. , Ratto, M. , Andres, T. , Campolongo, F. , Cariboni, J. , Gatelli, D. , & Tarantola, S. (2008). Global sensitivity analysis. The primer . New York, NY: John Wiley & Sons.
- Saltelli, A. , & Sobol', I.M. (1995). Sensitivity analysis for nonlinear mathematical models: Numerical experience. Mathematical Modelling, 7 (11), 16–28.
- Sobol', I.M. (1993). Sensitivity analysis for non-linear mathematical models. Mathematical Modeling & Computational Experiment, 1 , 407–414.
- Sobol', I.M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55 (1–3), 271–280. Retrieved from http://dx.doi.org/10.1016/S0378- 4754(00)00270-6
- Sundararajan, S. , & Keerthi, S.S. (2001). Predictive approaches for choosing hyperparameters in Gaussian processes. Neural Computation, 13 (5), 1103–1118.
- Tang, B. (1993). Orthogonal array-based Latin hypercubes. Journal of the American Statistical Association, 88 (424), 1392–1397. doi:10.1080/01621459.1993.10476423
- Wang, P. , Lu, Z. , & Tang, Z. (2013). An application of the kriging method in global sensitivity analysis with parameter uncertainty. Applied Mathematical Modelling, 37 (9), 6543–6555. Retrieved from http://dx.doi.org/10.1016/j.apm.2013.01.019
- Welch, W.J. , Robert, J.B. , Sacks, J. , Wynn, H.P. , Mitchell, T.J. , & Morris, M.D. (1992). Screening, predicting, and computer experiments. Technometrics, 34 (1), 15–25. doi:10.2307/1269548
- Xia, B. , Yin, S. , & Yu, D. (2015). A new random interval method for response analysis of structural–acoustic system with interval random variables. Applied Acoustics, 99 , 31–42. Retrieved from http://dx.doi.org/10.1016/j.apacoust.2015.05.002
- Zhang, Z. , Jiang, C. , Wang, G.G. , & Han, X. (2015). First and second order approximate reliability analysis methods using evidence theory. Reliability Engineering & System Safety, 137 , 40–49. Retrieved from http://dx.doi.org/10.1016/j.ress.2014.12.011
- Zhu, C. , Byrd, R.H. , Lu, P. , & Nocedal, J. (1997). Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Transactions on Mathematical Software, 23 (4), 550–560. doi:10.1145/279232.279236