Two multifidelity kriging-based strategies to control discretization error in reliability analysis exploiting a priori and a posteriori error estimators
Tài liệu tham khảo
Ainsworth, 1998, A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains, Numerische Mathematik, 80, 325, 10.1007/s002110050370
Ainsworth, 1997, A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics Engineering, 142, 1, 10.1016/S0045-7825(96)01107-3
Alvin, 2000, Method for treating discretization error in nondeterministic analysis, AIAA Journal, 38, 910, 10.2514/2.1047
Au, 2001, Estimation of small failure probabilities in high dimensions by subset simulation, Probabilistic Engineering Mechanics, 16, 263, 10.1016/S0266-8920(01)00019-4
Babuska, 1982, On the rates of convergence of the finite element method, International Journal of Numerical Methods in Engineering, 18, 323, 10.1002/nme.1620180302
Babuška, 1978, Error estimates for adaptative finite element computation, SIAM Journal on Numerical Analysis, 15, 736, 10.1137/0715049
Becker, 1996, A feed-back approach to error control in finite element methods: Basic analysis and examples, Journal of Numerical Mathematics, 237
Bect, 2012, Sequential design of computer experiments for the estimation of a probability of failure, Statistics and Computing, 22, 773, 10.1007/s11222-011-9241-4
Bichon, 2008, Efficient global reliability analysis for nonlinear implicit performance functions, AIAA Journal, 46, 2459, 10.2514/1.34321
Bjerager, 1988, Probability integration by directional simulation, Journal of Engineering Mechanics, 114, 1285, 10.1061/(ASCE)0733-9399(1988)114:8(1285)
Breitung, 1984, Asymptotic approximations for multinormal integrals, Journal of Engineering Mechanics, 110, 357, 10.1061/(ASCE)0733-9399(1984)110:3(357)
C.G. Bucher, Y.M. Chen, and G.I. Schuëller. Time variant reliability analysis utilizing response surface approach. In Reliability and Optimization of Structural Systems’ 88, pages 1–14. Springer, 1989.
Clerc, 2019, Scap-1d: A spatial correlation assessment procedure from unidimensional discrete data, Reliability Engineering & System Safety, 191, 106498, 10.1016/j.ress.2019.106498
Couckuyt, 2014, ooDACE toolbox: a flexible object-oriented kriging implementation, Journal of Machine Learning Research, 15, 3183
De Rocquigny, 2009, Structural reliability under monotony: Properties of form, simulation or response surface methods and a new class of monotonous reliability methods (mrm), Structural Safety, 31, 363, 10.1016/j.strusafe.2009.02.002
Echard, 2011, AK-MCS: an active learning reliability method combining kriging and Monte Carlo simulation, Structural Safety, 33, 145, 10.1016/j.strusafe.2011.01.002
Forrester, 2008
Gallimard, 2011, Error bounds for the reliability index in finite element reliability analysis, Int ernational Journal of Numerical Methods in Engineering, 87, 781, 10.1002/nme.3136
Gallimard, 2017, Towards error bounds of the failure probability of elastic structures using reduced basis models, International Journal of Numerical Methods in Engineering, 112, 1216, 10.1002/nme.5554
Gallimard, 2006, Error estimation of stress intensity factors for mixed-mode cracks, International Journal of Numerical Methods in Engineering, 68, 299, 10.1002/nme.1705
Gaspar, 2015, A study on a stopping criterion for active refinement algorithms in kriging surrogate models, 1219
Ghavidel, 2018, The effect of fem mesh density on the failure probability analysis of structures, KSCE Journal of Civil Engineering, 22, 2370, 10.1007/s12205-017-1437-5
Ghavidel, 2020, Reliability mesh convergence analysis by introducing expanded control variates, Frontiers of Structural and Civil Engineering, 14, 1012, 10.1007/s11709-020-0631-6
Giles, 2008, Multilevel monte carlo path simulation, Operational Research, 56, 607, 10.1287/opre.1070.0496
Griffith, 1921, The phenomena of rupture and flow in solids, Philosiphical Transactions Royal Society London, 221, 163
Hasofer, 1974, Exact and invariant second-moment code format, Journal of the Engineering Mechanics Division, 100, 111, 10.1061/JMCEA3.0001848
Krige, 1951, A statistical approach to some basic mine valuation problems on the witwatersrand, Journal of the Southern African Institute of Mining and Metallurgy, 52, 119
Ladevèze, 2006, Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems, Comptes Rendus Académie des Sciences - Mécanique, Paris, 334, 399, 10.1016/j.crme.2006.04.004
Ladevèze, 2008, Strict upper error bounds on computed outputs of interest in computational structural mechanics, Computational Mechanics, 42, 271, 10.1007/s00466-007-0201-y
Ladeveze, 1983, Error estimate procedure in the finite element method and applications, SIAM Journal on Numerical Analysis, 20, 485, 10.1137/0720033
Ladevèze, 2005, volume 171
Ladevèze, 2005, volume 171
Lefebvre, 2015, Failure probability assessment using co-kriging surrogate models, Procedia Engineering, 133, 622, 10.1016/j.proeng.2015.12.640
L. Li, J. Bect, and E. Vazquez. A numerical comparison of kriging-based sequential strategies. Applications of Statistics and Probability in Civil Engineering, page 187, 2011.
Lophaven, 2002, Aspects of the matlab toolbox DACE, Citeseer
Mahadevan, 2006, Inclusion of Model Errors in Reliability-Based Optimization, Journal of Mechanical Design, 128(4), 936–944, 01
Mallik, 2020, Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers, Journal of Computational and Applied Mathematics, 366, 112367, 10.1016/j.cam.2019.112367
Mell, 2020, Multifidelity adaptive kriging metamodel based on discretization error bounds, International Journal of Numerical Methods in Engineering, 121, 4566, 10.1002/nme.6451
Metropolis, 1949, The Monte Carlo method, Journal of the American Statistical Association, 44, 335, 10.1080/01621459.1949.10483310
Morse, 2019, A multi-fidelity boundary element method for structural reliability analysis with higher-order sensitivities, Engineering Analysis with Boundary Elements, 104, 183, 10.1016/j.enganabound.2019.03.036
Pan, 2017, An efficient reliability method combining adaptive support vector machine and monte carlo simulation, Structural Safety, 67, 85, 10.1016/j.strusafe.2017.04.006
Parés, 2006, Subdomain-based flux-free a posteriori error estimators, Computer Methods in Applied Mechanics and Engineering, 195, 297, 10.1016/j.cma.2004.06.047
Picheny, 2010, Adaptive designs of experiments for accurate approximation of a target region, Journal of Mechanical Design, 132, 071008, 10.1115/1.4001873
Pled, 2011, On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples, International Journal for Numerical Methods in Engineering, 88, 409, 10.1002/nme.3180
Ranjan, 2008, Sequential experiment design for contour estimation from complex computer codes, Technometrics, 50, 527, 10.1198/004017008000000541
Rey, 2014, Study of the strong prolongation equation for the construction of statically admissible stress fields: implementation and optimization, Computer Methods in Applied Mechanics and Engineering, 268, 82, 10.1016/j.cma.2013.08.021
Rüter, 2006, Goal-oriented a posteriori error estimates in linear elastic fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 195, 251, 10.1016/j.cma.2004.05.032
Schoefs, 2008, Sensitivity approach for modelling the environmental loading of marine structures through a matrix response surface, Reliability Engineering and System Safety, 93, 1004, 10.1016/j.ress.2007.05.006
Schueremans, 2005, Benefit of splines and neural networks in simulation based structural reliability analysis, Structural Safety, 27, 246, 10.1016/j.strusafe.2004.11.001
Stern, 1976, A contour integral computation of mixed-mode stress intensity factors, International Journal of Fracture, 12, 359, 10.1007/BF00032831
Strouboulis, 2000, A posteriori estimation and adaptive control of the error in the quantity of interest. part i: A posteriori estimation of the error in the von mises stress and the stress intensity factor, Computer Methods in Applied Mechanics and Engineering, 181, 261, 10.1016/S0045-7825(99)00077-8
Sudret, 2004, Eléments finis stochastiques en élasticité linéaire, C.R. Mec., 332, 531, 10.1016/j.crme.2004.02.024
Thomas, 2020, Reliability of inflatable structures: challenge and first results, European Journal of Environmental and Civil Engineering, 24, 1533, 10.1080/19648189.2018.1474807
Tong, 2015, A hybrid algorithm for reliability analysis combining kriging and subset simulation importance sampling, Journal of Mechanical Science and Technology, 29, 3183, 10.1007/s12206-015-0717-6
Vapnik, 2013
Wang, 2019, ESC: an efficient error-based stopping criterion for kriging-based reliability analysis methods, Structural Multidisciplinary Optimization, 59, 1621, 10.1007/s00158-018-2150-9
Wang, 2020, On confidence intervals for failure probability estimates in kriging-based reliability analysis, Reliability Engineering and System Safety, 196, 106758, 10.1016/j.ress.2019.106758
Wasserman, 2013
Yi, 2020, An active-learning method based on multi-fidelity kriging model for structural reliability analysis, Structural Multidisciplinary Optimization, 1
Zhu, 2016, Reliability analysis with monte carlo simulation and dependent kriging predictions, Journal of Mechanical Design, 138, 10.1115/1.4034219
Zienkiewicz, 1987, A simple error estimator and adaptive procedure for practical engineering analysis, International Journal for Numerical Methods in Engineering, 24, 337, 10.1002/nme.1620240206