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Volumn 197, Issue 43-44, 2008, Pages 3584-3592

Probabilistic equivalence and stochastic model reduction in multiscale analysis

Author keywords

Multiscale modeling; Stochastic homogenization; Stochastic inverse analysis; Stochastic model reduction; Uncertainty quantification; Upscaling

Indexed keywords

LAW ENFORCEMENT; MATHEMATICAL MODELS; MECHANICS; PROBABILITY; SEPARATION; SPEED; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC PROGRAMMING; STRUCTURAL DYNAMICS;

EID: 48849110024     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.03.016     Document Type: Article
Times cited : (56)

References (49)
  • 1
    • 48849100283 scopus 로고    scopus 로고
    • W. Gibbs, On the equilibrium of heterogeneous substances. Trans. Connecticut Academy III, 1875-1878.
    • W. Gibbs, On the equilibrium of heterogeneous substances. Trans. Connecticut Academy III, 1875-1878.
  • 3
    • 25444456701 scopus 로고    scopus 로고
    • A comprehensive overview of non-parametric probabilistic approach of random uncertainties for predictive models in structural dynamics
    • Soize C. A comprehensive overview of non-parametric probabilistic approach of random uncertainties for predictive models in structural dynamics. J. Sound Vib. 288 (2005) 623-652
    • (2005) J. Sound Vib. , vol.288 , pp. 623-652
    • Soize, C.1
  • 4
    • 33646514831 scopus 로고    scopus 로고
    • Maximum likelihood estimation of stochastic chaos representations from experimental data
    • Desceliers C., Ghanem R., and Soize C. Maximum likelihood estimation of stochastic chaos representations from experimental data. Int. J. Numer. Methods Engrg. 66 (2006) 978-1001
    • (2006) Int. J. Numer. Methods Engrg. , vol.66 , pp. 978-1001
    • Desceliers, C.1    Ghanem, R.2    Soize, C.3
  • 5
    • 33746495084 scopus 로고    scopus 로고
    • On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data
    • Ghanem R.G., and Doostan A. On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data. J. Comput. Phys. 217 (2006) 63-81
    • (2006) J. Comput. Phys. , vol.217 , pp. 63-81
    • Ghanem, R.G.1    Doostan, A.2
  • 6
    • 48849112479 scopus 로고    scopus 로고
    • S. Das, R. Ghanem, J. Spall, Asymptotic sampling distribution for polynomial chaos representation of data: a maximum entropy and Fisher information approach, SIAM J. Scient. Comput., in press.
    • S. Das, R. Ghanem, J. Spall, Asymptotic sampling distribution for polynomial chaos representation of data: a maximum entropy and Fisher information approach, SIAM J. Scient. Comput., in press.
  • 7
    • 16244409214 scopus 로고    scopus 로고
    • Physical systems with random uncertainties: chaos representations with arbitrary probability measure
    • Soize C., and Ghanem R. Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM J. Scient. Comput. 26 (2004) 395-410
    • (2004) SIAM J. Scient. Comput. , vol.26 , pp. 395-410
    • Soize, C.1    Ghanem, R.2
  • 8
    • 34548420549 scopus 로고    scopus 로고
    • Modeling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multiscale method
    • Ganapathysubramanian B., and Zabaras N. Modeling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multiscale method. J. Comput. Phys. 226 (2007) 326-353
    • (2007) J. Comput. Phys. , vol.226 , pp. 326-353
    • Ganapathysubramanian, B.1    Zabaras, N.2
  • 15
    • 33846262371 scopus 로고
    • Structural dynamics with parameter uncertainties
    • Ibrahim R.A. Structural dynamics with parameter uncertainties. ASME Appl. Mech. Rev. 40 (1987) 309-328
    • (1987) ASME Appl. Mech. Rev. , vol.40 , pp. 309-328
    • Ibrahim, R.A.1
  • 16
    • 0032640334 scopus 로고    scopus 로고
    • Progress in structural dynamics with stochastic parameter variations 1987-1998
    • Manohar C.S., and Ibrahim R.A. Progress in structural dynamics with stochastic parameter variations 1987-1998. ASME Appl. Mech. Rev. 52 (1999) 177-197
    • (1999) ASME Appl. Mech. Rev. , vol.52 , pp. 177-197
    • Manohar, C.S.1    Ibrahim, R.A.2
  • 18
    • 0035441628 scopus 로고    scopus 로고
    • Computational stochastic mechanics - recent advances
    • Schueller G.I. Computational stochastic mechanics - recent advances. Comput. Struct. 79 (2001) 2225-2234
    • (2001) Comput. Struct. , vol.79 , pp. 2225-2234
    • Schueller, G.I.1
  • 19
    • 0033737120 scopus 로고    scopus 로고
    • A non-parametric model of random uncertainties for reduced matrix models in structural dynamics
    • Soize C. A non-parametric model of random uncertainties for reduced matrix models in structural dynamics. Probab. Engrg. Mech. 15 (2000) 277-294
    • (2000) Probab. Engrg. Mech. , vol.15 , pp. 277-294
    • Soize, C.1
  • 20
    • 0035041285 scopus 로고    scopus 로고
    • Maximum entropy approach for modeling random uncertainties in transient elastodynamics
    • Soize C. Maximum entropy approach for modeling random uncertainties in transient elastodynamics. J. Acoust. Soc. Am. 109 (2001) 1979-1996
    • (2001) J. Acoust. Soc. Am. , vol.109 , pp. 1979-1996
    • Soize, C.1
  • 21
    • 27244456853 scopus 로고    scopus 로고
    • Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators
    • Soize C. Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators. Comput. Methods Appl. Mech. Engrg. 195 (2006) 26-64
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 26-64
    • Soize, C.1
  • 22
    • 8744246329 scopus 로고    scopus 로고
    • Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations
    • Narayanan V.A.B., and Zabaras N. Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations. J. Comput. Phys. 202 (2005) 94-133
    • (2005) J. Comput. Phys. , vol.202 , pp. 94-133
    • Narayanan, V.A.B.1    Zabaras, N.2
  • 23
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R.H., and Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 48 (1947) 385-392
    • (1947) Ann. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 24
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Scient. Comput. 24 (2002) 619-644
    • (2002) SIAM J. Scient. Comput. , vol.24 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 25
    • 0001500115 scopus 로고
    • Functions of positive and negative type and their connection with the theory of integral equations
    • Mercer J. Functions of positive and negative type and their connection with the theory of integral equations. Philos. Trans. Roy. Soc. A 209 (1909) 415-446
    • (1909) Philos. Trans. Roy. Soc. A , vol.209 , pp. 415-446
    • Mercer, J.1
  • 26
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener N. The homogeneous chaos. Am. J. Math. 60 (1938) 897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 27
  • 35
    • 0000414660 scopus 로고
    • Large sample properties of generalized method of moments estimators
    • Hansen L.P. Large sample properties of generalized method of moments estimators. Econometrica 50 (1982) 1029-1054
    • (1982) Econometrica , vol.50 , pp. 1029-1054
    • Hansen, L.P.1
  • 36
    • 70350096085 scopus 로고
    • Large sample estimation and hypothesis testing
    • Engle R., and McFadden D. (Eds), Elsevier
    • Newey W., and McFadden D. Large sample estimation and hypothesis testing. In: Engle R., and McFadden D. (Eds). Handbook of Econometrics IV (1994), Elsevier 2113-2247
    • (1994) Handbook of Econometrics IV , pp. 2113-2247
    • Newey, W.1    McFadden, D.2
  • 37
    • 0000221293 scopus 로고
    • Minimum disparity estimation for continuous models: efficiency, distributions and robustness
    • Basu A., and Lindsay B.G. Minimum disparity estimation for continuous models: efficiency, distributions and robustness. Annals of the Institute of Statistical Mathematics 46 (1994) 683-705
    • (1994) Annals of the Institute of Statistical Mathematics , vol.46 , pp. 683-705
    • Basu, A.1    Lindsay, B.G.2
  • 38
    • 0000204608 scopus 로고
    • Minimum Hellinger distance estimates for parametric models
    • Beran R. Minimum Hellinger distance estimates for parametric models. Ann. Statist. 5 (1977) 445-463
    • (1977) Ann. Statist. , vol.5 , pp. 445-463
    • Beran, R.1
  • 39
    • 48849110126 scopus 로고    scopus 로고
    • A. Keziou, Utilisation des divergences entre mesures en statistique inférentielle, PhD thesis, Université Paris 6, France, 2003.
    • A. Keziou, Utilisation des divergences entre mesures en statistique inférentielle, PhD thesis, Université Paris 6, France, 2003.
  • 40
    • 0000489740 scopus 로고
    • Information type measures of difference of probability distributions and indirect observations
    • Csiszár I. Information type measures of difference of probability distributions and indirect observations. Stud. Scient. Math. Hungarica 2 (1967) 299-318
    • (1967) Stud. Scient. Math. Hungarica , vol.2 , pp. 299-318
    • Csiszár, I.1
  • 42
    • 0001473437 scopus 로고
    • On estimation of probability density function and mode
    • Parzen E. On estimation of probability density function and mode. Ann. Math. Stat. 33 (1962) 1065-1076
    • (1962) Ann. Math. Stat. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 43
    • 0001529784 scopus 로고
    • Remarks on some nonparametric estimates of a density function
    • Rosenblatt M. Remarks on some nonparametric estimates of a density function. Ann. Math. Stat. 27 (1956) 832-837
    • (1956) Ann. Math. Stat. , vol.27 , pp. 832-837
    • Rosenblatt, M.1
  • 45
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • Kirkpatrick S., Gelatt C.D., and Vecchi M.P. Optimization by simulated annealing. Science 220 (1983) 671-680
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.D.2    Vecchi, M.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.