Two-time-scale inverse problems: formulation and solution

International audience; The aim here is to study two-time-scale models and their associated parameter identification. When it is possible to consider two well-separated time scales, and when the fast component of the applied loading is periodic, a periodic time homogenization scheme, similar to what exists in space homogenization, can be used to derive a homogenized model. A parameter identification process for this latter is then proposed, consisting in homogenizing with respect to time a classical identification strategy based on the use of adjoint state formulations; it is then applied to an academic example showing the benefits of such a strategy.