Events Calendar

Inversion of probabilistic models of structures using measured transfer functions

Speaker:
Maarten Arnst
Department of Civil and Environmental Engineering,
University of Southern California,
3620SVermontAvenue, KAP130,
phone: (213) 740-9165,
mail: arnst@usc.eduAbstract:
Predictive models for the dynamical behavior of complex structures are inevitably confronted to data uncertainties and modeling errors. Uncertain data include material properties, geometric parameters and boundary conditions. Modeling errors are introduced by the assumptions and approximations made in the modeling process. The data uncertainties and modeling errors may sometimes result in significant uncertainties in the model predictions. Probabilistic models then are desirable, since theyprovide a way to quantify the impact of the data uncertainties and modeling errors on the predictions.
Probabilistic mechanics is nowadays a rich and well-developed domain of research, in which a wide variety of methods for constructing probabilistic structural models has been proposed, see e.g. [1, 2, 3, 4]. Compared to deterministic structural models, an important difficulty is that probabilistic models introduce supplementary parameters, e.g. dispersion levels, spatial correlations lengths, or coefficients of chaos decompositions.An active areaof researchis thereforethedevelopmentof methodologies guidingthe choice of these parameters.
This presentation concerns the experimental identification of probabilistic structural models from measured transfer functions. The classical methods of estimation from the theory of mathematical statistics, such as the method of maximum likelihood, see e.g. [5], are not well-adapted to formulate and solve this inverse problem. In particular,numerical difficulties and conceptual problems due to model misspecification prohibit the application of the classical methods. In this talk, we propose to formulate the inversion alternatively as the minimization, with respect to the parameters to be identified, of an objective function measuring a distance between the experimental data and the probabilistic model. Two principles of construction for the definition of this distance are proposed, based on either the loglikelihood function, or the relative entropy, see e.g. [6]. The limitation of the distance to low-order marginal laws is shown to allow circumventing the aforementioned difficulties. The methodology is applied to simple illustrative examples featuring simulated data and to a civil and environmental engineering case history featuring real experimental data.
This work has been performed in the frame of a PhD thesis at Ecole Centrale Paris in France, under the supervision of Dr. Didier Clouteau and Dr. Marc Bonnet. The manuscript can be downloaded from www.mssmat.ecp.fr/rubrique.php3?id rubrique=354.

Audiences: Everyone Is Invited

Contact: Evangeline Reyes