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DINAME2019
DINAME2019
Analytical approximation of the uncertainty of an identification problem with chaos polynomials
Submission Author:
Roberta Lima , RJ , Brazil
Co-Authors:
Emmanuel Pagnacco, Rubens Sampaio, Eduardo Souza de Cursi, Roberta Lima
Presenter: Roberta Lima
doi://10.26678/ABCM.DINAME2019.DIN2019-0026
Abstract
We aim at taking into account measurement uncertainties in an identification process with errors in the measurements. We understand that uncertainty is the cumulative distribution function (CDF). In the case of a continuous distribution the probability distribution function (PDF) characterizes the CDF and we want to find an analytical approximation of the PDF. Uncertainties are taken into account by modeling them as random variables and the distribution of the identified parameter is an unknown of an inverse problem, which is a result of an optimization process. More precisely, to focus on this branch of optimization, we are concerned by a four point bending static test applied to a beam, and we model the identified elastic modulus with polynomial chaos expansions, using Hermite, and Chebyshev of 2nd kind, polynomials to see the influence of the polynomial used in the identification. Two different hypotheses are made about the uncertainties in the loading, leading to the investigation of two applications. This spectral theory for the quantification of uncertainties of this kind of identification problems is verified practically on both of these applications with successful results for an adequate order of truncation of the expansion basis.
Keywords
identification, Inverse problem, quantification of uncertainty, polynomial chaos expansion
