Goal-oriented updating of mechanical models using the adjoint framework

Abstract

In this paper, we introduce a goal-oriented procedure for the updating of mechanical models. It is based as usual on information coming from measurement data, but these data are post-processed in a convenient way in order to firstly update model parameters which are the most influent for the prediction of a given quantity of interest. The objective is thus to perform a partial model calibration that enables to obtain an approximate value of the quantity of interest with sufficient accuracy and minimal model identification effort. The updating method uses the constitutive relation error framework as well as duality and adjoint techniques. It leads to a convenient strategy, mainly based on sensitivity analysis, that selects the relevant parameter set to be updated and also provides for useful quantitative tools in order to define optimal experiments. Performances of the approach are analyzed on examples involving linear elasticity and transient thermal models.

Synergies between the constitutive relation error concept and PGD model reduction for simplified V&V procedures

“…It consists in selecting the highest local contributions to F(p) and updating first the associated parameters. Moreover, a goaloriented version of the model updating with mCRE, in which only parameters which have influence for the prediction of an output of interest are updated, can be constructed [48].…”

Comparison of deterministic and probabilistic approaches to identify the dynamic moving load and damages of a reinforced concrete beam

“…in which the displacement field u satisfies the kinematic conditions defined in U 0 and the dynamic equilibrium in Eq. (1). Note that the Tikhonov regularization term ||q|| corresponds to…”

“…In the deterministic sense, the regularisation is very often achieved by Tikhonov regularization [26]. However, other possible techniques also exist such as for example Error in the Constitutive Relation (ECR) regularization [10,2,1] previously studied by author. On the other hand, the ill-posed problem can be regularised in a probabilistic manner via Bayes rule by adding the prior expert knowledge on the parameter (model) set next to the observation data.…”

Model updating techniques for damage detection in concrete beam using optical fiber strain measurement device

“…Combining model updating techniques and the local strain information, the aim of this paper is at detecting, localizing and quantifying early damages with the help of deterministic and probabilistic numerical procedures. For this purpose three model updating techniques are discussed and compared naming: classical Tikhonov regularization [19], Constitutive Relation Error (CRE) based updating method [20,21,22,23] and Bayesian framework [10,18]. They are analyzed with respect to the measure of the information gain obtained after the updating procedure.…”