Quality Assurance Methods for Uncertainty Analysis in Reactor Physics with Applications

Risto Vanhanen

Research output: ThesisDoctoral ThesisCollection of Articles


The purpose of uncertainty analysis is to quantify the level of confidence one can have in calculated quantities of interest. In this respect, uncertainty is lack of confidence in the calculated values. In this Thesis uncertainty analysis is applied to reactor physics, which predicts the behavior of nuclear reactors based on radiation transport theories and nuclear data. The motivation is mainly twofold. First, in order to assess reliability of the computed results all calculated quantities of interest should have representative uncertainty estimates. Second, in its recent Regulatory Guides on Nuclear Safety the Finnish Radiation and Nuclear Safety Authority allows, instead of conservative estimates, the usage of realistic, best-estimate values of safety parameters augmented by uncertainty estimates. There are different sources of uncertainty and it is not always a priori obvious which of the components dominate the uncertainties in the quantities of interest. Therefore, an estimate for each component should be provided. It is usually presumed that uncertainty in nuclear data is the largest source of uncertainty. In this Thesis, this is verified in a few simple cases. In the course of the work some of the present uncertainty estimates of nuclear data were found to be mathematically and physically improper. The noted improper qualities were non-positivity, that is, negative generalized variances, and inconsistency with respect to the sum rules of nuclear data. This is a problem in quality of the data and of prime importance since the results of calculations are at most as good as data used in them. The problem in quality of the data was solved by developing and proposing quality assurance methods to detect improper covariances, and by developing and proposing methods to find nearby more proper energy-dependent covariances and methods to find the nearest proper covariances in multigroup form. There are several nuclear data evaluation projects in the world. Their evaluated nuclear data have discrepancies. The best-estimate values might differ or the nuclear data community does not agree on how well a piece of nuclear data is known. This is another quality assurance issue, which is considered in this Thesis. The most important practical implications of the work presented in this Thesis are introduction of quality assurance methods that can be and were implemented as computer routines and used to detect certain improper properties of covariances of nuclear data as a part of quality assurance programs. The other methods can be used to remove these improper components with minimal changes to the covariances of nuclear data. The methods have also other potential applications such as verifying that covariances of fission yields retain proper normalization.
Translated title of the contributionLaadunvarmistusmenetelmiä epävarmuusanalyysille reaktorifysiikassa sovelluksineen
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Tuomisto, Filip, Supervising Professor
  • Ala-Heikkilä, Jarmo, Thesis Advisor
Print ISBNs978-952-60-6729-2
Electronic ISBNs978-952-60-6730-8
Publication statusPublished - 2016
MoE publication typeG5 Doctoral dissertation (article)


  • quality assurance
  • uncertainty analysis
  • sensitivity analysis
  • nuclear data
  • covariance
  • positivity
  • consistency


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