Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 181548, 16 pages
Research Article

Identification of Stochastic Loads Applied to a Nonlinear Dynamical System Using an Uncertain Computational Model

C. Soize1 and A. Batou1,2

1Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME FRE3160 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France
2R&D Department Analyse Mecanique et Acoustique, EDF, 1 avenue du Géneral de Gaulle, 92140 Clamart Cedex, France

Received 6 April 2008; Accepted 4 June 2008

Academic Editor: Jose Balthazar

Copyright © 2008 C. Soize and A. Batou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the identification of stochastic loads applied to a nonlinear dynamical system for which a few experimental responses are available using an uncertain computational model. Uncertainties are induced by the use of a simplified computational model to predict the responses of the real system. A nonparametric probabilistic approach of both parameter uncertainties and model uncertainties is implemented in the simplified computational model in order to take into account uncertainties. The level of uncertainties is identified using the maximum likelihood method. The identified stochastic simplified computational model which is obtained is then used to perform the identification of the stochastic loads applied to the real nonlinear dynamical system. A numerical validation of the complete methodology is presented.