Probabilistic nonparametric model of impedance matrices
Application to the seismic design of a structure
Keywords:
nonparametric model, impedance, probabilistic mechanics, uncertaintiesAbstract
Economic and legal pressures on the structural engineers force them to consider uncertainty in the domains interacting, through boundary impedances, with their design structure. A probabilistic model of this impedance is constructed around a mean hidden state variables model using a nonparametric method. This mean model is constructed using only deterministic tools. The methodology is applied to the design of a gas tank on a layered soil.
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References
Allemang R. J., Brown D. L., « A unied matrix polynomial approach to modal identication »,
Journal of Sound and Vibration, vol. 211, p. 301-322, 1998.
Arnst M., Clouteau D., Bonnet M., « Identication of probabilistic structural dynamics model:
application to Soize's nonparametric model », in C. Soize, G. I. Schuëller (eds), Eurodyn
: Proceedings of the 6th International Conference on Structural Dynamics, vol. 2,
Millpress, Paris, France, p. 823-828, September, 2005.
Bultheel A., van Barel M., « Vector orthogonal polynomials and least squares approximation »,
SIAM Journal of Matrix Analysis and its Applications, vol. 16, p. 863-885, 1995.
Chabas F., Soize C., « Modeling mechanical subsystems by boundary impedance in the nite
element method », La Recherche Aérospatiale (english edition), vol. 5, p. 59-75, 1987.
Chebli H., Soize C., « Experimental validation of a nonparametric probabilistic model of non
homogeneous uncertainties for dynamical systems », Journal of the Acoustical Society of
America, vol. 115, p. 697-705, 2004.
Clouteau D., Miss 6.3 : Manuel Utilisateur : version 2.2, École Centrale Paris, Châtenay-
Malabry, France. 2003, in french.
Cornell A. C., « First order uncertainty analysis of soils deformation and stability », Proceedings
of the rst International Conference on Applications of Statistics and Probability to Soil and
Structural Engineering, Hong-Kong, p. 129-144, 1971.
Desceliers C., Soize C., Cambier S., « Nonparametric-parametric model for random uncertainties
in nonlinear structural dynamics: Application to earthquake engineering », Earthquake
Engineering and Structural Dynamics, vol. 33, p. 315-327, 2003.
Favre J.-L., « Errors in Geotechnics and their impact on safety », Computers & Structures, vol.
, p. 37-45, 1998.
Ghanem R. G., Spanos P. D., Stochastic Finite Elements: A Spectral Approach, Springer-Verlag,
Guillaume P., Pintelon R., Schoukens J., « Parametric identication of multivariable systems
in the frequency domain - a survey », Proceedings of the 21st International Conference on
Noise and Vibration Engineering (ISMA), Leuven (Belgium), p. 1069-1082, 1996.
Jaynes E. T., « Information theory and statistical mechanics », Physical Review, vol. 106, p. 620-
, 1957.
Kramers H. A., « La diffusion de la lumière par les atomes », Resoconto del Congresso Internazionale
dei Fisíci, vol. 2, Como, Italy, p. 545-557, 1927. in french.
Kronig R. d., « On the theory of dispersion of X-rays », Journal of the Optical Society of
America, vol. 12, p. 547-557, June, 1926.
Pierce L. B., Hardy Functions, Junior paper, Princeton University, 2001.
http://www.princeton.edu/~lbpierce/.
Pintelon R., Rolain Y., Bultheel A., van Barel M., « Frequency domain identication of multivariable
systems using vector orthogonal polynomials », Proceedings of the 16th International
Symposium on Mathematical Theory of Networks and Systems, Leuven (Belgium),
July, 2004.
Pintelon R., Schoukens J., System identication: a frequency domain approach, IEEE Press,
Piscataway, 2001.
Ratier L., Cambier S., Berthe L., « Analyse probabiliste du désaccordement de roue de turbine »,
in , R. Ohayon, J.-P. Grellier, A. Rassineux (eds), Comptes-Rendus du 7ème Colloque National
en Calcul des Structures, vol. 1, Hermès-Lavoisier, Giens, France, May, 2005. in
french.
Savin E., Clouteau D., « Coupling a bounded domain and an unbounded heterogeneous domain
for elastic wave propagation in three-dimensional random media », International Journal
for Numerical Methods in Engineering, vol. 24, p. 607-630, 2002.
Schuëller G. I., « A state-of-the-art report on computational stochastic mechanics », Probabilistic
Engineering Mechanics, vol. 12, p. 197-321, 1997.
Soize C., « A nonparametric model of random uncertainties in linear structural dynamics », Publications
du LMA-CNRS, vol. 152, p. 109-138, Juin 1999. Journée Nationale Dynamique
Stochastique des Structures, Châtillon, France.
Soize C., « A nonparametric model of random uncertainties for reduced matrix models in structural
dynamics », Probabilistic Engineering Mechanics, vol. 15, p. 277-294, 2000.
Soize C., « Maximum entropy approach for modeling random uncertainties in transient elastodynamics
», Journal of the Acoustical Society of America, vol. 109, p. 1979-1996, May,
a.
Soize C., « Nonlinear dynamical systems with nonparametric model of random uncertainties »,
Uncertainties in Engineering Mechanics, vol. 1, p. 1-38, 2001b. http://www.resonancepub.
com.
Soize C., « Uncertain dynamical systems in the medium-frequency range », Journal of Engineering
Mechanics, vol. 129, p. 1017-1027, 2003.
Soize C., « Random matrix theory for modeling uncertainties in computational mechanics »,
Computer Methods in Applied Mechanics and Engineering, vol. 194, p. 1333-1366, 2005.
Soize C., Chebli H., « Random uncertainties model in dynamics substructuring using a nonparametric
probabilistic model », Journal of Engineering Mechanics, vol. 128, p. 449-457,
April, 2003.
Wolf J. P., Dynamic soil-structure interaction, Prentice-Hall, Inc., Englewood Cliffs, N. J.,