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All issues Volume 24 (2023) Mechanics & Industry, 24 (2023) 42 References
Issue
Mechanics & Industry
Volume 24, 2023
History of matter: from its raw state to its end of life
Article Number 42
Number of page(s) 13
DOI https://doi.org/10.1051/meca/2023037
Published online 06 December 2023
  1. A. Asadpoure, M. Tootkaboni, J.K. Guest, Robust topology optimization of structures with uncertainties in stiffness – application to truss structures, Comput. Struct. 89, 1131–1141 (2011) [CrossRef] [Google Scholar]
  2. M. Tootkaboni, A. Asadpoure, J.K. Guest, Topology optimization of continuum structures under uncertainty – a polynomial chaos approach,. Comput. Methods Appl. Mech. Eng. 201–204, 263–275 (2012) [CrossRef] [Google Scholar]
  3. G. Stefanou, The stochastic finite element method: Past, present and future, Comput. Methods Appl. Mech. Eng. 198, 1031–1051 (2009) [CrossRef] [Google Scholar]
  4. D. Xiu, Fast numerical methods for stochastic computations: a review, Commun. Comput. Phys. 5, 242–272 (2009) [Google Scholar]
  5. G. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, Springer Science & Business Media (2013) [Google Scholar]
  6. R.E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica 7, 1–49 (1998) [CrossRef] [Google Scholar]
  7. R.G. Regis, C.A. Shoemaker, A stochastic radial basis function method for the global optimization of expensive functions, INFORMS J. Comput. 19, 497–509 (2007) [CrossRef] [MathSciNet] [Google Scholar]
  8. S. Volpi, M. Diez, N.J. Gaul, H. Song, U. Iemma, K.K. Choi, E.F. Campana, F. Stern, Development and validation of a dynamic metamodel based on stochastic radial basis functions and uncertainty quantification, Struct. Multidiscip. Optim. 51, 347–368 (2015) [CrossRef] [Google Scholar]
  9. J.P.C. Kleijnen, Regression and Kriging metamodels with their experimental designs in simulation: a review, Eur. J. Oper. Res. 256, 1–16 (2017) [CrossRef] [Google Scholar]
  10. H. Rostami, J.Y. Dantan, L. Homri, Review of data mining applications for quality assessment in manufacturing industry: Support vector machines, Int. J. Metrol. Qual. Eng. 6 (2015) [Google Scholar]
  11. E. Denimal, J.-J. Sinou, Advanced computational technique based on kriging and polynomial chaos expansion for structural stability of mechanical systems with uncertainties, J. Eng. Math. 130, 1–19 (2021) [CrossRef] [Google Scholar]
  12. M.A. El-Beltagy, A. Al-Juhani, A mixed spectral treatment for the stochastic models with random Parameters, J. Eng. Math. 132, 1–20 (2022) [CrossRef] [Google Scholar]
  13. N. Wiener, The homogeneous chaos, Am. J. Math. 60, 897–936 (1938) [CrossRef] [Google Scholar]
  14. R. Askey, J.A. Wilson, Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials, Vol. 319. American Mathematical Soc., 1985 [Google Scholar]
  15. D. Xiu, George Em Karniadakis, Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, Comput. Methods Appl. Mech. Eng. 191, 4927–4948 (2002) [CrossRef] [Google Scholar]
  16. E. Jacquelin, S. Adhikari, J.J. Sinou, M.I. Friswell, Polynomial chaos expansion in structural dynamics: accelerating the convergence of the first two statistical moment sequences, J. Sound Vib. 356, 144–154 (2015) [CrossRef] [Google Scholar]
  17. E. Jacquelin, O. Dessombz, J.-J. Sinou, S. Adhikari, M.I. Friswell, Steady-state response of a random dynamical system described with padé approximants and random eigenmodes. Procedia Eng. 199, 1104–1109 (2017) [CrossRef] [Google Scholar]
  18. M.T. Reagan, H.N. Najm, R.G. Ghanem, O.M. Knio, Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection, Combust. Flame 132, 545–555 (2003) [CrossRef] [Google Scholar]
  19. R.A. Todor, C. Schwab, Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients, IMA J. Numer. Anal. 27, 232–261 (2007) [CrossRef] [MathSciNet] [Google Scholar]
  20. X. Wan, G.E. Karniadakis, Long-term behavior of polynomial chaos in stochastic flow simulations, Comput. Methods Appl. Mech. Eng. 195, 5582–5596 (2006) [CrossRef] [Google Scholar]
  21. X. Wan, G.E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, J. Comput. Phys. 209, 617–642 (2005) [Google Scholar]
  22. B. Chouvion, E. Sarrouy, Development of error criteria for adaptive multi-element polynomial chaos approaches, Mech. Syst. Signal Process. 66, 201–222 (2016) [CrossRef] [Google Scholar]
  23. D.H. Mac, Z. Tang, S. Chénet, E. Creusé, Residual-based a posteriori error estimation for stochastic magnetostatic problems, J. Comput. Appl. Math. 289, 51–67 (2015) [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Blatman, B. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Prob. Eng. Mech. 25, 183–197 (2010) [CrossRef] [Google Scholar]
  25. G. Blatman, B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle Regression, J. Comput. Phys. 230, 2345–2367 (2011) [CrossRef] [MathSciNet] [Google Scholar]
  26. C.V. Mai, B. Sudret, Hierarchical adaptive polynomial chaos expansions, in: UNCECOMP 2015 – 1st Int. Conf. Uncertain. Quantif. Comput. Sci. Eng., Vol. 229, May 2015, pp. 65–78, Crete, Greece, 2015 [Google Scholar]
  27. T. Duc Dao, Q. Serra, S. Berger, E. Florentin, Error estimation of polynomial chaos approximations in transient structural dynamics, Int. J. Comput. Methods 17, 2050003 (2020) [CrossRef] [MathSciNet] [Google Scholar]
  28. T. Butler, P. Constantine, T. Wildey, A posteriori error analysis of parameterized linear systems using spectral methods, SIAM J. Matrix Anal. Appl. 33, 195–209 (2012). [CrossRef] [MathSciNet] [Google Scholar]
  29. L. Mathelin, O. Le Maitre, Dual-based a posteriori error estimate for stochastic finite element Methods, Commun. Appl. Math. Comput. Sci. 2, 83–115 (2007) [CrossRef] [MathSciNet] [Google Scholar]
  30. K. Dammak, S. Koubaa, A. El Hami, L. Walha, M. Haddar, Numerical modelling of vibro-acoustic problem in presence of uncertainty: application to a vehicle cabin, Appl. Acoust. 144, 113–123 (2019) [CrossRef] [Google Scholar]
  31. M. Ghienne, C. Blanzé, L. Laurent, Stochastic model reduction for robust dynamical characterization of structures with random parameters, Comptes Rendus Méc. 345, 844–867 (2017) [Google Scholar]
  32. M. Berveiller, B. Sudret, M. Lemaire, Stochastic finite element: a non intrusive approach by regression, Eur. J. Comput. Mech. 15. 81–92 (2006) [CrossRef] [Google Scholar]
  33. G. Blatman, B. Sudret, Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach, Comptes Rendus Mec. 336, 518–523 (2008) [CrossRef] [Google Scholar]
  34. D.M. Allen, Mean square error of prediction as a criterion for selecting variables, Technometrics 13, 469–475 (1971) [CrossRef] [Google Scholar]
  35. A.M. Molinaro, R. Simon, R.M. Pfeiffer, Prediction error estimation: a comparison of resampling methods, Bioinformatics 21, 3301–3307 (2005) [CrossRef] [PubMed] [Google Scholar]
  36. M. Stone, Cross-validatory choice and assessment of statistical predictions, J. R. Stat. Soc. Ser. B 36, 111–147 (1974) [Google Scholar]
  37. B. Efron, R. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993 [Google Scholar]

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