Pilot Study for Uncertainty Analysis in Probabilistic Fitness-for-Service Evaluations of Zr-2.5Nb Pressure Tubes: Identification of Influential Variables

Canadian Nuclear Standard CSA N285.8, “Technical requirements for in-service evaluation of zirconium alloy pressure tubes in CANDU® reactors”(1), permits the use of probabilistic methods when performing assessments of the reactor core. A non-mandatory annex has been proposed for inclusion in the CSA Standard N285.8, to provide guidelines for performing uncertainty analysis in probabilistic fitness-for-service evaluations within the scope of this Standard, such as the probabilistic evaluation of leak-before-break. The proposed annex outlines the general approach to uncertainty analysis as being comprised of the following major activities: identification of influential variables, characterization of uncertainties in influential variables, and subsequent propagation of these uncertainties through the evaluation framework or code. The application of the proposed guidelines for uncertainty analysis was exercised by performing a pilot study for one of the evaluations within the scope of the CSA Standard N285.8, the probabilistic evaluation of leak-before-break based on a postulated through-wall crack. The pilot study was performed for a representative CANDU reactor unit using the recently developed computer code P-LBB that complies with requirements of Canadian Nuclear Standard N286.7 for quality assurance of analytical, scientific, and design computer programs for nuclear power plants. This paper discusses the approach used and the results obtained in the first stage of this pilot study, the identification of influential variables. The proposed annex considers three approaches for identifying influential variables, which may be used separately or in combination: analysis of probabilistic evaluation outputs, sensitivity analysis and expert judgment. In this pilot study, local sensitivity analysis was used to identify and rank the influential variables. For each input variable in the probabilistic evaluation of leak-before-break, the local sensitivity coefficient was determined as the relative change in the output variable associated with a relative change of a small magnitude in the input variable. Each input variable was also varied across a large range to assess the linearity of the relationship between the input variable and the output variable. All relevant input variables were ranked according to the absolute value of their sensitivity coefficients to identify the influential variables. On the basis of the results obtained, the pressure tube wall thickness was found to be the most influential variable in the probabilistic evaluation of leak-before-break based on a postulated through-wall crack, followed by the fracture toughness of Zr-2.5Nb pressure tube material and the pressure tube inner diameter. The results obtained at this stage were then used at the second stage of this pilot study, the uncertainty characterization of influential variables, as discussed in the companion paper PVP2018-85011.