The identification of model parameters from experimental test is a keypoint for the predictivity of computations. The broad development of full-field measurement such as fullfield measurements enable to tackle the identification from more complex tests, in particular tests with heterogeneous strain fields (due to either the loading, the material or the geometry of the specimen). Such an identification though requires the use of an inverse approach to be performed and can still be sensitive to the measurement and model errors. Dedicated identification strategies have therefore to be developed, keeping in mind special attention should be paid to the taking into account of the uncertainty and the description of the available information.
Several ways of dealing with the uncertainties have been developed in the past. A usual approach is to use probabilities to describe the uncertainty on the available information. It is the approach used in the bayesian inference framework, where it is possible to deal with both the experimental uncertainty and any prior knowledge on the model. Yet, it can be argued that probabilities are not suited for the description of any uncertainties (e.g. some authors claim it is not adapted to epistemic uncertainties or to describe a complete lack of knowledge). We therefore have wished to incestigate alternative frameworks for the description of uncertainties.
The framework we have chosen is the one of the theory of random set and belief functions, that is general enough to include the particular cases of probabilities or possibilities. We therefore tried to transcript the methodology of the bayesian inference to the framework of random set. The prior knowledge and the knowledge coming from the experiment are described thanks to two random sets. The merging of information is performed thanks to the Dempster-Schäfer rule allowing to define a posterior random set. From a numerical point of view, the latter is described through samples coming from the merging of samples from the prior random set and measurement one. Then this posterior random set sample can be post-processed to extract some information on the solution of the inverse problem. For example, a set of minimal side with a guarantee of belief or plausibility level can be computed.
One keypoint of the approach, that allows the numerical efficiency of the approach, is to describe the sets of the samples on a unique grid of points through their discrete characteristic functions. It is then straightforward to compute intersections, for example.
The approach has been applied to the identification of elastic properties from fullfield displacement data (on numerical examples). Monoscale and multiscale applications, with or without the taking into account of model errors, will be presented to illustrate the proposed methodology.
