# Development and Application of Uncertainty Analysis Approaches for MELCOR Simulations of Severe Accidents

**Time: **
Wed 2024-04-24 09.30

**Location: **
FA32, Roslagstullsbacken 21, Stockholm

**Language: **
English

**Doctoral student: **
Wanhong Wang
, Kärnkraftssäkerhet

**Opponent: **
Florian Fichot,

**Supervisor: **
Weimin Ma, Kärnkraftssäkerhet

QC 2024-03-25

## Abstract

The contemporary needs in advancing safety analysis methods and the increasing stringency in light water reactor (LWR) safety in the post-Fukushima era require more advanced and systematical approaches for severe accident analyses. The best estimate plus uncertainty (BEPU) methods are among such approaches and have been widely used for deterministic safety analysis (DSA) of design basis accidents (DBAs). However, the BEPU analyses of severe accidents (SAs) are not straightforward due to the complexity of SA phenomena and the specialties of SA simulation tools. It is therefore necessary to develop BEPU approaches for severe accidents.

This thesis work starts from an application of the conventional BEPU approach using various uncertainty quantification (UQ) methods of 95/95 tolerance limits to MELCOR simulations of severe accidents, with the aim to identify their capabilities in MELCOR simulations of severe accidents. Both parametric and nonparametric UQ methods, including goodness-of-fit test, Wilks’ methods, Baren and Hall’s linear interpolation and Hutson fractional statistics, are applied to postulated severe accident scenarios in a Nordic boiling water reactor (BWR). It is found that (i) a small sample size or a low order in these UQ methods tends to cause conservative estimates, and (ii) a large sample size has many unsuccessful MELCOR calculation cases and fixing of the cases incurs an explosive computational cost. To solve this problem, two alternative approaches are supposed to be developed in the next step.

The first alternative approach is to develop a bootstrapped artificial neural network (ANN) model to be employed in UQ; and the second alternative approach is to couple deterministic sampling (DS) methods with a fixed/dynamic coverage factor. The first alternative approach overcomes the problem in the conventional BEPU approach, i.e. the explosive computation cost due to fixing many crashed MELCOR cases otherwise it ruins randomness of samples. The idea behind this approach is to use surrogate models (SMs) developed from successful MELCOR calculations to predict the relation between major uncertain inputs and outputs. As a result, an UQ with numerically equivalent estimate of 95/95 tolerance limits can be done. The approach is applied to a severe accident scenario due to station blackout (SBO) in a Nordic BWR and results are compared with those of the conventional approach. The second approach is proposed for realistic estimates with reduced computational costs. Its theoretical basis is that DS methods can use far fewer samples to produce approximately convergent estimates of the statistical moments of outputs (figures of merits). By introducing a fixed or dynamic coverage factor, the information on the first two statistical moments can be extended to 95th percentiles or so-called numerically equivalent estimates of 95/95 tolerance limits. The second approach is applied to a severe accident scenario of SBO in a Swedish PWR and compared with the conventional approach.

The comparative results show that the two alternative approaches work well in uncertainty quantification of MELCOR simulations of the postulated severe accident scenarios chosen. For instance, given the mass of H2 production and the timing of vessel failure as the figures of merit (FOMs), the first alternative approach predicts the 95/95 estimates similar to those of the conventional approach. Besides, a high order nonparametric method can be used in the bootstrapped ANN model for stable and realistic estimates, which is almost impossible for the conventional approach due to the requirement of numerous MELCOR calculations. For the second approach, a fixed coverage factor 1.65 should be used when the outputs (figures of merits) are symmetrically distributed like normal distribution. Otherwise, a dynamic coverage factor from a fitted beta distribution should be used to avoid unrealistic estimates when the outputs are strongly skewed. It is thus concluded that the two proposed alternative approaches have potentials to replace the conventional approach of uncertainty quantification for MELCOR simulations of severe accidents, in case of too high computational cost due to a large sample size or many unsuccessful MELCOR calculations incurred in the conventional approach.