Quantificação de Incertezas
Professor:
Americo Barbosa da Cunha Junior
americo@ime.uerj.br
Tel.: (21) 2334-0323 ramal: 208
Sala 6032, Bloco B
Turma:
- 2ª feira de 16:10 às 19:30h -- Sala 6142, Bloco F
Ementa:
1 - Noções Básicas de Quantificação de Incertezas
2 - Noções de Probabilidade e Processos Estocásticos
3 - Noções de Inferência Estatística
4 - Métodos de Amostragem
5 - Modelagem Probabilística de Incertezas
6 - Rudimentos de Polinômio Caos
Avaliação:
A avaliação do curso será feita com base em:
- testes ao final das aulas
- um trabalho final
Sendo a nota final do curso calculada da seguinte forma:
NF = 0.3*Testes + 0.7*Trabalho
O aluno que obtiver nota final maior ou igual a sete,
i.e. NF >= 7,0 estará aprovado.
De acordo com a nota do curso, o aluno receberá um dos seguintes conceitos:
A - Excelente (nota de 9,0 a 10,0)
B - Bom (nota de 8,0 a 8,9)
C - Regular (nota 7,0 a 7,9)
D - Deficiente (nota inferior a 7,0)
GNU Octave:
Neste curso iremos desenvolver algumas atividades computacionais.
Para tal, os alunos poderão utilizar o ambiente de programação GNU Octave.
UQ Software:
Referências do curso:
|
R. Smith,
Uncertainty Quantification: Theory, Implementation, and Applications,
SIAM: Society for Industrial and Applied Mathematics, 2013
Disponível na SIAM
|
|
C. Soize,
Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering, Springer, 2017
Disponível na Amazon
|
Referências para estudos complementares:
|
R. Ghanem, D. Higdon, H. Owhadi (Editors),
Handbook of Uncertainty Quantification,
Springer, 2017
Disponível na Amazon
|
|
T. J. Sulivan,
Introduction to Uncertainty Quantification,
Springer, 2015
Disponível na Amazon
|
|
C. Soize,
Stochastic Models of Uncertainties in Computational Mechanics,
American Society of Civil Engineers, 2012.
Disponível na Amazon
|
|
J. E. S. de Cursi and R. Sampaio,
Modelagem Estocástica e Quantificação de Incertezas,
Sociedade Brasileira de Matemática Aplicada e Computacional, 2012
http://dx.doi.org/10.5540/001.2012.0066.01
|
|
D. A. Castello and T. G. Ritto,
Quantificação de Incertezas e Estimação de Parâmetros em Dinâmica Estrutural: uma introdução a partir de exemplos computacionais, Sociedade Brasileira de Matemática Aplicada e Computacional, 2015
http://www.sbmac.org.br/arquivos/notas/livro_81.pdf
|
|
G. Grimmett and D. Welsh,
Probability: An Introduction,
Oxford University Press, 2 edition, 2014
Disponível na Amazon
|
|
A. Papoulis and S. U. Pillai,
Probability, Random Variables and Stochastic Processes,
McGraw-Hill Europe; 4th edition, 2002
Disponível na Amazon
|
|
E. Cataldo,
Introdução aos Processos Estocásticos,
Sociedade Brasileira de Matemática Aplicada e Computacional, 2012
http://dx.doi.org/10.5540/001.2012.0068.01
|
|
L. Wasserman,,
All of Statistics: A Concise Course in Statistical Inference,
Springer, 2004
Disponível na Amazon
|
|
D. P. Kroese, T. Taimre, and Z. I. Botev,
Handbook of Monte Carlo Methods,
Wiley, 2011
Disponível na Amazon
|
|
S. Asmussen and P. W. Glynn,
Stochastic Simulation: Algorithms and Analysis,
Springer, 2007
Disponível na Amazon
|
|
F. B. Ribeiro, E. C. Molina,
Uma Introdução ao Método de Monte Carlo,
Sociedade Brasileira de Matemática Aplicada e Computacional, 2017
http://www.sbmac.org.br/arquivos/notas/livro_86.pdf
|
|
L. Biegler, G. Biros, O. Ghattas et al. (Editors),
Large-Scale Inverse Problems and Quantification of Uncertainty,
Wiley, 2010
Disponível na Amazon
|
|
J. Kaipio and E. Somersalo,
Statistical and Computational Inverse Problems,
Springer, 2005
Disponível na Amazon
|
|
Inverse Problem Theory and Methods for Model Parameter Estimation,
SIAM, 2004
http://www.ipgp.fr/~tarantola/Files/Professional/Books/InverseProblemTheory.pdf |
|
L. Tenorio,
An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems,
SIAM, 2017
Disponível na SIAM
|
|
J. M. Bardsley,
Computational Uncertainty Quantification for Inverse Problems,
SIAM, 2018
Disponível na SIAM
|
|
R. G. Ghanem and P. D. Spanos,
Stochastic Finite Elements: A Spectral Approach,
Dover Publications, Revised Edition, 2012
Disponível na Amazon
|
|
D. Xiu,
Numerical Methods for Stochastic Computations: A Spectral Method Approach,
Princeton University Press, 2010
Disponível na Amazon
|
|
O. Le Maitre and O. Knio,
Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics,
Springer, 2010
Disponível na Amazon
|
|
M. P. Pettersson, G. Iaccarino and J. Nordström,
Polynomial Chaos Methods for Hyperbolic Partial Differential Equations: Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties, Springer, 2015
Disponível na Amazon
|
|
W. L. Oberkampf and C. J. Roy,
Verification and Validation in Scientific Computing,
Cambridge University Press, 2010
Disponível na Amazon
|
Periódicos com publicações sobre quantificação de incertezas:
Artigos interessantes:
- T. Oden, R. Moser and O. Ghattas,
Computer Predictions with Quantified Uncertainty, Part I,
SIAM News vol. 43, 2010
- T. Oden, R. Moser and O. Ghattas,
Computer Predictions with Quantified Uncertainty, Part II,
SIAM News vol. 43, 2010
- G. I. Schueller,
A state-of-the-art report on computational stochastic mechanics,
Probabilistic Engineering Mechanics, vol. 12, pp. 197-321, 1997.
https://doi.org/10.1016/S0266-8920(97)00003-9
- C. J.Roy and W. L. Oberkampf,
A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing,
Computer Methods in Applied Mechanics and Engineering vol 200 pp. 2131-2144, 2011.
https://doi.org/10.1016/j.cma.2011.03.016
- W. L. Oberkampf, T. G. Trucano and C. Hirsch,
Verification, validation, and predictive capability in computational engineering and physics,
Applied Mechanics Review, vol. 57, pp. 345-384, 2004
https://doi.org/10.1115/1.1767847
- C. Soize,
A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics,
Journal of Sound and Vibration, vol. 288, pp.623-65, 2005.
https://dx.doi.org/10.1016/j.jsv.2005.07.009
- C. Soize,
Stochastic modeling of uncertainties in computational structural dynamics - Recent theoretical advances,
Journal of Sound and Vibration, vol. 332, pp. 2379-2395, 2013.
https://dx.doi.org/10.1016/j.jsv.2011.10.010
- C. Soize and C. Farhat,
A nonparametric probabilistic approach for quantifying uncertainties in low-dimensional and high-dimensional nonlinear models,
International Journal for Numerical Methods in Engineering, vol. 109, pp. 837-888, 2017.
https://dx.doi.org/10.1002/nme.5312
- C. Soize and R. Ghanem,
Data-driven probability concentration and sampling on manifold,
Journal of Computational Physics, vol. 321, pp. 242-258, 2016.
https://doi.org/10.1016/j.jcp.2016.05.044
- C. Soize and R. Ghanem,
Polynomial chaos representation of databases on manifolds,
Journal of Computational Physics, vol. 335, pp. 201-221, 2017.
https://doi.org/10.1016/j.jcp.2017.01.031
- R. Ghanem,
Ingredients for a general purpose stochastic finite elements implementation,
Computer Methods in Applied Mechanics and Engineering, vol. 168, pp. 19-34, 1999.
https://doi.org/10.1016/S0045-7825(98)00106-6
- R. Ghanem and J. Red-Horse,
Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach,
Physica D: Nonlinear Phenomena, vol. 133, pp. 137-144, 1999.
https://doi.org/10.1016/S0167-2789(99)00102-5
- A. Doostan, R. Ghanem and J. Red-Horse,
Stochastic model reduction for chaos representations,
Computer Methods in Applied Mechanics and Engineering, vol. 196, pp. 3951-3966, 2007.
https://doi.org/10.1016/j.cma.2006.10.047
- R. Ghanem and A Doostan,
On the construction and analysis of stochastic models: characterization and propagation of the errors associated with limited data,
Journal of Computational Physics, vol 217, pp. 63-81, 2008.
https://doi.org/10.1016/j.jcp.2006.01.037
- R. Ghanem, A. Doostan and J. Red-Horse,
A probabilistic construction of model validation,
Computer Methods in Applied Mechanics and Engineering, vol. 197, pp. 2585-2595, 2008.
https://doi.org/10.1016/j.cma.2007.08.029
- K. Sargsyan, H. N. Najm and R. Ghanem,
On the statistical calibration of physical models,
International Journal of Chemical Kinetics, vol. 47, pp. 246-276, 2015.
https://doi.org/10.1002/kin.20906
|
|
