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Illustrating the advantages of a Bayesian over a least squares approach to material properties identification

Abstract : Identifying parameters of a model using experimental data has been extensively studied in various areas, including for determining mechanical material properties from strain measurements or modal vibration data. In order to find the parameters that make the model agree best with the experiments, the most widely used method is based on minimizing the least-squares error between the experimental data and the model predictions. An alternative way to identify the material properties is through statistical frameworks, based on maximum likelihood or on Bayes' rule. The Bayesian framework is more general since it can include prior knowledge. Isenberg proposed the application of the Bayesian framework for parameter estimation in 1979 and several articles have been published since on the application of this approach to frequency or modal identification in particular, i.e. identifying material properties from vibration test data. Here we compare the least-squares and the Bayesian approach to material properties identification, seeking situations where the properties identified by the two approaches are significantly different. We chose a simple, didactic example of a three bar truss so that the results of the comparison are not clouded by unnecessary complexity or computational issues. For the three bar truss example we seek to identify the Young modulus of the bars from strain measurements on these bars. Due to uncertainty in the loads applied on the truss, which propagate to variability in the strains, the different strain measurements provide conflicting information. The least-squares approach and the Bayesian approach combine this conflicting information differently to come up with the identified Young modulus. We found that the least-squares method can be negatively affected by differences in magnitudes of the experimental data, by differences in uncertainty and by correlation among the experimental data. The least-squares method does indeed implicitly weight strains depending on their sensitivity to Young's modulus. This negatively impacts the results found by the least-squares approach. Different uncertainty in the strains in each bar also negatively affects the least-squares approach, which does not differentiate between a strain with low uncertainty and one with high. Last, the least-squares approach does not handle correlation between the strain measurements. On the other hand the Bayesian correctly handles these three situations, namely different strain magnitude, uncertainty and correlation. We found that in each situation the Bayesian approach systematically outperforms the least-squares approach. In the case when all three effects act combined, we found that the Young modulus identified by the Bayesian approach is on average almost 10 times closer than least-squares to the true value of the Young modulus.
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Contributor : Florent Breuil <>
Submitted on : Friday, April 13, 2012 - 4:54:00 PM
Last modification on : Friday, May 21, 2021 - 7:46:01 PM


  • HAL Id : emse-00687650, version 1


Christian Gogu, Raphael T. Hafkta, Rodolphe Le Riche, Jérôme Molimard, Alain Vautrin. Illustrating the advantages of a Bayesian over a least squares approach to material properties identification. ESM Centennial Mechanics Conference: Liviu Librescu Session, May 2008, Blacksburg, United States. ⟨emse-00687650⟩



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