Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T19:41:48.949Z Has data issue: false hasContentIssue false
  • English
  • Français

MODELING EXPERIMENTAL DATA WITH POLYNOMIALS CHAOS

Published online by Cambridge University Press:  14 August 2018

Emeline Gayrard ,
Cédric Chauvière ,
Hacène Djellout  and
Pierre Bonnet
Emeline Gayrard
Affiliation:
Laboratoire de Mathématiques Blaise Pascal (LMBP), CNRS UMR 6620 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 3 place Vasarely, TSA 60026/CS 60026, 63 178 Aubière Cedex, France E-mail: [email protected]
Cédric Chauvière
Affiliation:
Laboratoire de Mathématiques Blaise Pascal (LMBP), CNRS UMR 6620 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 3 place Vasarely, TSA 60026/CS 60026, 63 178 Aubière Cedex, France E-mail: [email protected]
Hacène Djellout
Affiliation:
Laboratoire de Mathématiques Blaise Pascal (LMBP), CNRS UMR 6620 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 3 place Vasarely, TSA 60026/CS 60026, 63 178 Aubière Cedex, France E-mail: [email protected]
Pierre Bonnet
Affiliation:
Institut Pascal, CNRS UMR 6602 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 4 Avenue Blaise Pascal, TSA 60026/CS 60026, 63178 Aubière Cedex, France E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Given a raw data sample, the purpose of this paper is to design a numerical procedure to model this sample under the form of polynomial chaos expansion. The coefficients of the polynomial are computed as the solution to a constrained optimization problem. The procedure is first validated on samples coming from a known distribution and it is then applied to raw experimental data of unknown distribution. Numerical experiments show that only five coefficients of the Chaos expansions are required to get an accurate representation of a sample.

Keywords

Chaos expansionsexperimental data modelingnumerical methods
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020 , pp. 14 - 26
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Ahlfeld, R., Belkouchi, B., & Montomoli, F. (2016). SAMBA: sparse approximation of moment-based arbitrary polynomial chaos. Journal of Computational Physics 320: 1–16.Google Scholar
2.Arnst, M., Ghanem, R., & Soize, C. (2010). Identification of Bayesian posteriors for coefficients for chaos expansions. Journal of Computational Physics 229(9): 3134–3154.Google Scholar
3.Bonnini, S., Corain, L., Marozzi, M., & Salmaso, L (2014). Nonparametric hypothesis testing. Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons Ltd., Rank and permutation methods with applications in R, Presentation of the book by Fortunato Pesarin.Google Scholar
4.Chauvière, C., Hesthaven, J.S., & Lurati, L. (2006). Computational modeling of uncertainty in time-domain electromagnetics. SIAM Journal on Scientific Computing 28(2): 751–775.Google Scholar
5.Ghanem, R.G. & Spanos, P.D. (1991). Stochastic finite elements: a spectral approach. New York: Springer-Verlag.Google Scholar
6.Grady, D. (2006). Fragmentation of rings and shells. Shock wave and high pressure phenomena. New York, Berlin: Springer, The Legacy of N.F. Mott.Google Scholar
7.Lagarias, J.C., Reeds, J.A., Wright, M.H., & Wright, P.E. (1999). Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM Journal on Optimization 9(1): 112–147.Google Scholar
8.Le Maître, O.P., Reagan, M.T., Najm, H.N., Ghanem, R.G., & Knio, O.M. (2002). A stochastic projection method for fluid flow. II. Random process. Journal of Computational Physics 181(1): 9–44.Google Scholar
9.Levy, S., Molinari, J.F., Vicari, I., & Davison, A. (2010). Dynamic fragmentation of a ring: Predictable fragment mass distributions. Physics Review 82(6): 066105-1–066105-6.Google Scholar
10.Oladyshkin, S. & Nowak, W. (2012). Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion. Reliability Engineering & System Safety 106: 179–190.Google Scholar
11.Sudret, M. (2008). Global sensitivity analysis using polynomial Chaos expansion. Reliability Engineering & System Safety 93(7): 964–979.Google Scholar
12.Wasserman, L. (2004). All of statistics. Springer texts in statistics. New York: Springer-Verlag, A concise course in statistical inference.Google Scholar
13.Wiener, N. (1938). The homogeneous chaos. American Journal of Mathematics 60(4): 897–936.Google Scholar
14.Xiu, D. & Karniadakis, G.E. (2002). The Wiener–Askey polynomial chaos for stochastic differential equations. Journal on Scientific Computing 24(2): 619–644.Google Scholar