Nonlinear Gaussian inversion applied to structural parameter identification

In this paper we apply, in the general context of structural parameter identification using vibrational data (measured values of eigenfrequencies and modal displacements), the nonlinear Gaussian inversion approach as proposed by Tarantola. The available prior information on vibrational measured data, unknown parameters and physical model is modelled using Gaussian multidimensional random variables. The distributed error in constitutive equation, which provides approximate prior information on the spatial localization of structural perturbations, is included in the prior information. The unknown parameters (here, non-dimensional multiplicative factors to element stiffness and mass matrices of a finite element model) are then searched for as a maximum likelihood point of a certain probability density. An adjoint problem is formulated for evaluating the cost function gradient. The a posteriori covariance matrix allows to some degree a quantitative evaluation of the uncertainty attached to the inversion result. Numerical results are presented using both simulated and experimental data, on a FE model with about 3800 degrees of freedom.