1. Problem

We want to estimate numerically the behavior at any point of a structure based on measurements made at a few points in the structure. Given the costs and accessibility constraints, the experimental measures are generally limited in number and located in places that are not necessarily the most requested. Thus, in dynamics, knowledge of stress concentration areas and local stress values is crucial to verify the mechanical strength of the equipment. It is then necessary to extrapolate the results of localized measurements over the entire digital mesh of the structure.

The proposed extrapolation approach is based on a representation of the structure on a carefully chosen projection basis (natural modes, static response,…). It consists in determining the generalized coordinates relating to this projection base. The proposed resolution uses a minimization, in the sense of least squares, by decomposition into LUs or into singular values (SVD), of a functional that may be regularized via the addition of a criterion of proximity to a solution known a priory. In the case of temporal identification, an explicit formulation of the a priory information is proposed.