Abstract
We introduce a goal-oriented procedure for the updating of mechanical models. It exploits as usual information coming from experimental data, but these are post-processed in a specific 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 updating 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, and defines dedicated cost functions. It leads to a convenient strategy that automatically selects the relevant parameter set to be updated. Performances of the approach are analyzed on examples involving linear elasticity and transient thermal models with possible noisy measurements.
Highlights
We introduce a goal-oriented procedure for the updating of mechanical models
A major concern with mathematical models is their capability to represent a faithful abstraction of the real world
To address this issue and control the error between physical and mathematical models, model validation methods have been used for a long time [13]
Summary
A major concern with mathematical models is their capability to represent a faithful abstraction of the real world. We define a goal-oriented version of updating methods performed using the CRE, focusing on the sensitivity of the considered quantity of interest with respect to parameters and measurements. The constitutive relation error (CRE) is a concept with strong mechanical content [11] It defines an energy measure, denoted E, of the distance between a given stress field and another stress field obtained from a given displacement field v using (3) : E2(p, v,. The inverse problem is defined as : psol = argmin F (p) ; p∈P It leads to an iterative method, each iteration consisting of two minimizations steps : – the first minimization step involved in (7), i.e. the computation of F(p) is called the localization step.
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