Deterministic sampling method using simplex ensemble and scaling method for efficient and robust uncertainty quantification

ABSTRACT

Uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. Although the random sampling method is a practical and useful UQ method, a large computational cost is required to reduce the statistical error of the estimated uncertainty. Furthermore, if an input variable follows a normal distribution with a large standard deviation, the perturbed input variable by the random sampling method may become a physically inappropriate or negative value. To address these issues for the efficient and robust UQ, a modified deterministic sampling method using the simplex ensemble and the scaling method is proposed. The features of the proposed method are summarized as follows: The sample size is $\left(\mathit{r}+2\right)$, where $\mathit{r}$ corresponds to the effective rank of the covariance matrix between the input variables; depending on a situation of target UQ, the amounts of perturbations for the input parameters can be arbitrarily given by the scaling factor method; the scaling factor can be updated to avoid physically inappropriate in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ of the neutron multiplication factor due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation.

GRAPHICAL ABSTRACT

KEYWORDS:

• Uncertainty
• uncertainty quantification
• deterministic sampling method
• simplex ensemble
• scaling method
• criticality
• burnup calculation

Acknowledgments

The authors would like to sincerely appreciate Dr. Tatsuya Fujita of the Nuclear Regulation Authority for his valuable advice and comments on the uncertainty quantification in this study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Scientific Research (C) (Grant Number 21K04940).