Inversion of probabilistic structural models using measured transfer functions M. Arnst* a , D. Clouteau a , M. Bonnet b , a MSSMat, UMR8579, Ecole Centrale Paris, Grande Voie des Vignes, F-92295 Chˆ atenay-Malabry Cedex, France. Fax:+33 1 41 13 14 42. Tel:+33 1 41 13 13 59. b LMS, UMR7649, Ecole Polytechnique, F-91128 Palaiseau Cedex, France. Fax:+33 1 69 33 30 26. Abstract This paper addresses the inversion of probabilistic models for the dynamical be- haviour of structures using experimental data sets of measured frequency-domain transfer functions. The inversion is formulated as the minimization, with respect to the unknown parameters to be identified, of an objective function that measures a distance between the data and the model. Two such distances are proposed, based on either the loglikelihood function, or the relative entropy. As a comprehensive example, a probabilistic model for the dynamical behaviour of a slender beam is inverted using simulated data. The methodology is then applied to a civil and en- vironmental engineering case history involving the identification of a probabilistic model for ground-borne vibrations from real experimental data. Key words: probabilistic modelling, inverse problem, identification, relative entropy, likelihood, non-parametric probabilistic model 1 Introduction Predictive models for the dynamical behaviour of complex structures are inevitably confronted to data uncertainties and modelling errors. Uncertain data include mate- rial properties, geometric parameters and boundary conditions. Modelling errors are introduced by the assumptions and approximations made in the modelling process. The data uncertainties and modelling errors may sometimes result in significant un- certainties in the model predictions. Probabilistic models then are desirable, since Email address: maarten.arnst@ecp.fr (M. Arnst*). Preprint submitted to CMAME 18 September 2007