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Article | REF: BE8267 V2

Inverse problems in heat diffusion . Specific tools of inverse conduction and regularization

Authors: Denis MAILLET, Yvon JARNY, Daniel PETIT

Publication date: July 10, 2018

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ABSTRACT

The different components of the estimation error met when seeking to solve a problem of inversion of measurements are presented. A few approaches that allow their assessment and control are reviewed. The specific case of estimation of a function that has been given a parameterized form is studied through the introduction and detailed description of several regularization techniques that provide a necessary compromise between dispersion and bias of the estimation. The study of the errors caused by the parameters that are ‘assumed to be known’, and the guiding principles and utility of Bayesian techniques, are presented at the end of the article.

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AUTHORS

  • Denis MAILLET: Professor Emeritus. University of Lorraine (UL) - Laboratoire d'Énergétique et de Mécanique Théorique et Appliquée (LEMTA) – CNRS and UL

  • Yvon JARNY: Professor Emeritus. University of Nantes - Laboratoire de Thermique et énergie de Nantes (LTeN) – UMR CNRS 6607 Nantes

  • Daniel PETIT: Professor Emeritus. École Nationale Supérieure de Mécanique et d'Aérotechnique (ISAE-ENSMA) - Institut P' UPR CNRS 3346 Département Fluides, Thermique, Combustion – Poitiers

 INTRODUCTION

This dossier is the last in a series of three entitled "Inverse problems in thermal diffusion". We saw in [BE 8 265] "Diffusive models, measurements, sensitivities" and [BE 8 266] "Formulation and resolution of the least-squares problem", that simply applying numerical and analytical inversion methods is no guarantee of obtaining good results. In order to improve results, it is necessary to refine these methods for analyzing and solving this type of problem. This is what will be undertaken here, focusing first on the six components of the estimation error, then reviewing the "Specific tools for inverse conduction and regularization", before detailing the latter and highlighting some important questions that the thermal measurement inverter must ask itself, right from the start of its approach.

The symbols and notations used in this article are taken from Table 1 of [BE 8 265] . It should be noted that only the pdf version of this article provides fully relevant notation, as the electronic version does not make it possible to distinguish clearly between the different weights of the symbols.

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KEYWORDS

estimation errors   |   regularization   |   singular value décomposition   |   bayesian estimation

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Inverse problems in thermal diffusion
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