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SUMMARY:A Random Set Based Identification Strategy
DTSTART:20231205T130000Z
DTEND:20231205T140000Z
DTSTAMP:20260505T071900Z
UID:indico-event-10551@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pierre Feissel (UTC - Roberval)\n\nThe identificatio
 n of model parameters from experimental test is a keypoint for the predict
 ivity of computations. The broad development of full-field measurement suc
 h 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). Suc
 h an identification though requires the use of an inverse approach to be p
 erformed and can still be sensitive to the measurement and model errors. D
 edicated identification strategies have therefore to be developed\, keepin
 g in mind special attention should be paid to the taking into account of t
 he uncertainty and the description of the available information.Several wa
 ys of dealing with the uncertainties have been developed in the past. A us
 ual approach is to use probabilities to describe the uncertainty on the av
 ailable information. It is the approach used in the bayesian inference fra
 mework\, where it is possible to deal with both the experimental uncertain
 ty and any prior knowledge on the model. Yet\, it can be argued that proba
 bilities are not suited for the description of any uncertainties (e.g. som
 e authors claim it is not adapted to epistemic uncertainties or to describ
 e a complete lack of knowledge). We therefore have wished to incestigate a
 lternative frameworks for the description of uncertainties.The framework w
 e 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 rand
 om sets. The merging of information is performed thanks to the Dempster-Sc
 häfer rule allowing to define a posterior random set. From a numerical po
 int of view\, the latter is described through samples coming from the merg
 ing of samples from the prior random set and measurement one. Then this po
 sterior random set sample can be post-processed to extract some informatio
 n on the solution of the inverse problem. For example\, a set of minimal s
 ide with a guarantee of belief or plausibility level can be computed.One k
 eypoint of the approach\, that allows the numerical efficiency of the appr
 oach\, is to describe the sets of the samples on a unique grid of points t
 hrough their discrete characteristic functions. It is then straightforward
  to compute intersections\, for example.The approach has been applied to t
 he identification of elastic properties from fullfield displacement data (
 on numerical examples). Monoscale and multiscale applications\, with or wi
 thout the taking into account of model errors\, will be presented to illus
 trate the proposed methodology.\n\nhttps://indico.math.cnrs.fr/event/10551
 /
LOCATION:UTC - GI
URL:https://indico.math.cnrs.fr/event/10551/
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