Uncertainty estimation and hierarchical Bayesian analysis of mechanical dynamic tests
Résumé
A methodology is presented to quantify uncertainties resulting from the analysis of dynamic tests performed on classic split Hopkinson pressure bar system in order to improve material parameter estimation within the framework of Bayesian inference. Since the experimental setup is imperfectly known, the proposed methodology consists in modeling experimental parameters as random variables. Then, cumulative effects of all experimental uncertainties are estimated by a statistical analysis based on one-dimensional wave interpretation. For each test, results consist in stress and strain-rate given as normal random variables. In addition, an experimental campaign is performed on the aluminum alloy AA7075-O, in order to identify material variability and repeatability of tests. Then, material parameters of a simple Steinberg-Cochran-Guinan model are estimated by standard Bayesian estimation techniques. In addition, a hierarchical Bayesian model is also developed in order to exploit the available information in more details. The fitted model agrees well with the measurements and model uncertainties are easily quantified. Results are presented in the form of posterior probability density functions and suggest that the standard inference tends to underestimate uncertainties compared to the hierarchical model. The systematic quantification of uncertainties in dynamic tests opens interesting perspectives to analyze the response of structures and materials to impact.
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