A probabilistic construction of model validation
Tóm tắt
Từ khóa
Tài liệu tham khảo
1970
Babuška, 2003, Solving stochastic partial differential equations based on the experimental data, Math. Models Methods Appl. Sci., 13, 10.1142/S021820250300257X
Babuška, 2004, Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM J. Numer. Anal., 42, 800, 10.1137/S0036142902418680
Černy, 1985, A thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm, J. Optimiz. Theory Appl., 45, 41, 10.1007/BF00940812
Debusschere, 2004, Numerical challenges in the use of polynomial chaos representations for stochastic processes, SIAM J. Sci. Comput., 26, 698, 10.1137/S1064827503427741
Descelliers, 2006, Maximum likelihood estimation of stochastic chaos representation from experimental data, Int. J. Numer. Methods Engrg., 66, 978, 10.1002/nme.1576
DoD. Verification, Validation, and Accreditation (VV&A) recommended practices guide. Technical report, Defense Modeling and Simulation Office, Office of the Director of Defense Research and Engineering, 1996. www.dmso.mil/docslib.
Fang, 1997, Some methods for generating both an NT-net and the uniform distribution on a Stiefel manifold and their applications, Comput. Stat. Data Anal., 24, 29, 10.1016/S0167-9473(96)00057-6
Gelman, 2003
Ghanem, 1998, Probabilistic characterization of transport in heterogeneous porous media, Comput. Methods Appl. Mech. Engrg., 158
Ghanem, 1998, Scales of fluctuation and the propagation of uncertainty in random porous media, Water Resour. Res., 34, 2123, 10.1029/98WR01573
Ghanem, 1999, Ingredients for a general purpose stochastic finite elements formulation, Comput. Methods Appl. Mech. Engrg., 168, 19, 10.1016/S0045-7825(98)00106-6
Ghanem, 1999, The nonlinear gaussian spectrum of lognormal stochastic processes and variables, ASME J. Appl. Mech., 66, 964, 10.1115/1.2791806
Ghanem, 1998, Stochastic finite element analysis for multiphase flow in heterogeneous porous media, Transport Porous Med., 32, 239, 10.1023/A:1006514109327
Ghanem, 2006, On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data, J. Comp. Phys., 217, 63, 10.1016/j.jcp.2006.01.037
Ghanem, 2002, Mid-frequency structural dynamics with parameter uncertainty, Comput. Methods Appl. Mech. Engrg., 191, 5499, 10.1016/S0045-7825(02)00465-6
Ghanem, 2003, Reduced models for the medium-frequency dynamics of stochastic systems, JASA, 113, 834, 10.1121/1.1538246
Ghanem, 2002
Guadagnini, 2004, Probabilistic reconstruction of geologic facies, J. Hydrol., 294, 57, 10.1016/j.jhydrol.2004.02.007
Hall, 1992
Hatcher, 2002
R.G. Hills, T.G. Trucano, Statistical validation of engineering and scientific models: Background. Technical report, Sandia National Laboratories, SAND99-1256, Albuquerque, NM, 1999.
Kirkpatrick, 1983, Optimization by simulated annealing, Science, 220, 671, 10.1126/science.220.4598.671
Kolmogorov, 1957
Le Maitre, 2004, Multi-resolution analysis of Wiener-type uncertainty propagation schemes, J. Comp. Phys., 197, 502, 10.1016/j.jcp.2003.12.020
Le Maitre, 2004, Uncertainty propagation using Wiener-Haar expansions, J. Comp. Phys., 197, 28, 10.1016/j.jcp.2003.11.033
Loeve, 1977
Mahadevan, 2005, Validation of reliability computational models using Bayes networks, Reliab. Engrg. Syst. Safety, 87, 223, 10.1016/j.ress.2004.05.001
Le Maitre, 2001, A stochastic projection method for fluid flow. I: basic formulation, J. Comp. Phys., 173, 481, 10.1006/jcph.2001.6889
McLachlan, 1997
Meilijson, 1989, A fast improvement to the EM algorithm on its own terms, J.R. Statist. Soc., Ser. B, 51, 127
Oberkampf, 2006, Measures of agreement between computation and experiment: validation metrics, J. Comp. Phys., 217, 5, 10.1016/j.jcp.2006.03.037
Oberkampf, 2002, Verification and validation in computational fluid mechanics, Progress Aaerospace Sci., 38, 209, 10.1016/S0376-0421(02)00005-2
Papoulis, 1991
Poor, 1994
Puig, 2002, Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms, Probabilist. Engrg. Mech., 17, 253, 10.1016/S0266-8920(02)00010-3
Red-Horse, 2004, A probabilistic approach to uncertainty quantification with limited information, Reliab. Engrg. Syst. Safety, 85, 183, 10.1016/j.ress.2004.03.011
J.R. Red-Horse, T.L. Paez, Sandia National Laboratories validation workshop: structural dynamics application, May 2006. Personal communication and http://www.esc.sandia.gov/VCWwebsite/vcwhome.html.
Roache, 1998
Sakamoto, 2002, Polynomial chaos decomposition for the simulation of non-Gaussian non-stationary stochastic processes, ASCE J. Engrg. Mech., 128, 190, 10.1061/(ASCE)0733-9399(2002)128:2(190)
Scott, 2002, Maximum likelihood estimation using the empirical Fisher information matrix, J. Statist. Comput. Simulat., 72, 599, 10.1080/00949650213744
Spall, 2003
Efronand, 1993
Xiu, 2003, Modeling uncertainty in flow simulations via generalized polynomial chaos, J. Comp. Phys., 187, 137, 10.1016/S0021-9991(03)00092-5
Xiu, 2004, A two-scale nonperturbative approach to uncertainty analysis of diffusion in random composites, J. Multiscale Model. Simulat., 2, 662, 10.1137/03060268X
Young, 1997