Comparison between the basic least squares and the bayesian approach for elastic constants identification

Christian Gogu; Raphael Haftka; Rodolphe Le Riche; Jérôme Molimard; Alain Vautrin; Bhavani V. Sankar

doi:10.1088/1742-6596/135/1/012045

Journal articles

Comparison between the basic least squares and the bayesian approach for elastic constants identification

Christian Gogu ^{1, 2} Raphael Haftka ³ Rodolphe Le Riche ^{4, 5, 6, 7, 8, 9} Jérôme Molimard ^{1, 6, 10, 11, 12, 13} Alain Vautrin ^{1, 10} Bhavani V. Sankar ³

1 MPE-ENSMSE - Département Mécanique et Procédés d'Elaboration

2 Département d'Ingénierie Mécanique et Aérospatiale

3 Department of Mechanical and Aerospace Engineering [Gainesville]

4 3MI-ENSMSE - Département Méthodes et Modèles Mathématiques pour l'Industrie

5 CROCUS-ENSMSE - Equipe : Calcul de Risque, Optimisation et Calage par Utilisation de Simulateurs

6 LCG-ENSMSE - UMR 5146 - Laboratoire Claude Goux

7 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne

8 SITE-ENSMSE - Centre Sciences, Information et Technologies pour l'Environnement

9 CNRS - Centre National de la Recherche Scientifique

10 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

11 DB2M-ENSMSE - Département Biomécanique et Biomatériaux

12 IFRESIS-ENSMSE - Institut Fédératif de Recherche en Sciences et Ingénierie de la Santé

13 CIS-ENSMSE - Centre Ingénierie et Santé

Abstract : The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.

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Journal articles

Domain :

Mathematics [math]

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https://hal.archives-ouvertes.fr/hal-00409731
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Submitted on : Wednesday, August 12, 2009 - 3:15:00 PM
Last modification on : Wednesday, March 10, 2021 - 5:48:03 PM

Comparison between the basic least squares and the bayesian approach for elastic constants identification

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Comparison between the basic least squares and the bayesian approach for elastic constants identification

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