Calibration of fuel performance models – A hierarchical Bayesian approach to account for model inadequacy

Gustav Robertson1

Henrik Sjöstrand1, Peter Andersson1, Paul Blair2.

1Uppsala University – Department of Physics and Astronomy – Applied Nuclear Physics; 2Westinghouse Electric Sweden AB.


Fuel performance models [1] are approximations of their underlying physics. Hence they are not a perfect representation of the actual physical processes, and consequently, these models are said to be inadequate to some extent. This model inadequacy has an unfavorable impact on model calibration, with the most crucial result being that the uncertainties are underestimated and do not sufficiently represent the underlying error. One way to solve this is to adapt the covariance matrix of the model parameters so that the propagated uncertainty conforms with the spread of the residuals [2].

This work presents a method incorporating model inadequacy into the Bayesian framework by assuming a multivariate Gaussian irreducible variability among the calibration parameters. Calibration is then performed on the distribution parameters rather than on the model parameters directly. The result is an inflated uncertainty of the model parameters that account for the discrepancies of the model. Finally, the method is applied to various fuel performance synthetic test-beds (e.g., cladding oxidation, fission gas release, etc.) to demonstrate its applicability and compare with standard Bayesian calibration.


[1] P. Van Uffelen, J. Hales, W. Li, G. Rossiter, and R. Williamson, “A review of fuel performance modelling,” J. Nucl. Mater., vol. 516, pp. 373–412, 2019.
[2] P. Pernot and F. Cailliez, “A critical review of statistical calibration/prediction models handling data inconsistency and model inadequacy,” AIChE J., 2016.

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Wednesday – 15th September 2021
Gustav Robertson