New Set-membership Techniques for Parameter Estimation in Presence of Model Uncertainty

This paper introduces new methods for estimating parameters and their uncertainty in the context of inverse problems. The new techniques are capable of dealing with both measurement and modelling errors but also with uncertainty in parameters of the model that are assumed known. All the uncertain quantities are taken as unknown but bounded. In such a bounded-error context, reliable set-membership techniques are used to characterize, in a guaranteed way, the set of the unknown physical parameters that are compatible with the collected experimental data, the model and the prior error bounds. This ensures that no solution is lost. The methodology described will be applied to the simultaneous identification of thermal conductivity and diffusivity of polymer materials by a periodic method from actual experimental data. The guaranteed approaches provide a natural description of the uncertainty associated with the identified parameters.