Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties

A dynamic probabilistic safety margin characterization approach in support of Integrated Deterministic and Probabilistic Safety Analysis

“…The former type of uncertainty is often referred to as objective, aleatory, stochastic, whereas the latter is often referred to as subjective, epistemic, state of knowledge [Apostolakis 1990;Helton, 2011]. To deal with these uncertainties, traditional safety margins quantification in DSA analysis has implied conservatism in both the analysis of the TH code outputs and the evaluation criteria [Nutt et al, 2004]. Best Estimate (BE) methodologies have reduced the amount of conservatism for the evaluation of safety margins, but do not take into account all aleatory and epistemic uncertainties in the physical models stochastic behavior and model parameter values [US D.O.E., 2009].…”

“…For this, we introduce a novel definition of a DSM by the combined quantification of a percentile (e.g., 95 th ) of the safety parameter distribution (e.g., oil temperature, peak cladding temperature) and a percentile (e.g., 5 th ) of the distribution of the earliest time required to the safety parameter to reach the given percentile value. The uncertainties affecting the DSM are treated using Order Statistics (OS) (i.e., Bracketing and Coverage approach) [Nutt et al, 2004]. By doing so, we are able to compute the confidence that, for a selected accidental scenario of a Dynamic Event Tree (DET) obtained by a IDPSA analysis, the estimated 95 th percentile of the safety parameter cannot be reached before the 5 th percentile of the estimated time: if these estimated percentiles meet the safety criteria with the required confidence, the NPP can be licensed as "safe" to withstand the selected accidental scenario.…”

“…Traditionally, for an accidental scenario ' ', the safety margin ( , ) is defined as the difference between the conservatively computed values reached by a selected safety parameter ( ), j=1,2,…J, and a predefined upper (lower) threshold ( ) during an accidental scenario [Nutt et al, 2004;Secchi et al, 2008;Martorell et al, 2009].…”

“…By regulation, 1 is usually set equal to the 95 th percentile. Despite that, the estimation of the probability density function of y, ( ), and of its -th percentile 1 , ( 1 ), is a non-trivial task that requires guaranteeing a confidence 1 (e.g., 95% confidence), viz [Nutt et al, 2004;Zio et al, 2010]: The definition of probabilistic safety margin of equation (5) can be enriched by taking into account the resilience information related to the time required for reaching 1 .…”

“…The invaluable advantage of OS is that an unlimited number of model uncertainties can be explicitly considered simultaneously, especially when the Nutt-Wallis method [Nutt et al, 2004] is enforced (as done in this work) for capturing the uncertainties in multivariate cases: this is, indeed, the only approach for multivariate cases that can determine their individual coverage with a specified confidence level and an expression of the probability distribution is not required [Martin et al, 2011].…”