Improved Sampling Algorithms in the Risk-Informed Safety Margin Characterization Toolkit

Abstract

The RISMC approach is developing an advanced set of methodologies and algorithms in order to perform Probabilistic Risk Analyses (PRAs). In contract to classical PRA methods, which are based on Event-Tree and Fault-Tree methods, the RISMC approach largely employs system simulator codes applied to stochastic analysis tools. The fundamental approach via simulation is to randomly perturb (by employing sampling algorithms) timing and sequencing of events and uncertain parameters of the physics-based models (e.g., system codes such as RELAP-7) in order to estimate stochastic outcomes such as off-normal and damage states of the facility. Further, these outcomes can be used to estimate other useful metrics such as the plant core damage probability. This modeling approach applied to complex systems such as nuclear power plants requires the analyst to perform a series of computationally-expensive simulation runs given a large set of uncertain parameters. Consequently, these types of analysis are potentially affected by two issues. Firstly, the space of the possible solutions (the issue space or the response surface) can be sampled only sparsely and this precludes the ability to fully analyze the impact of uncertainties on the system dynamics. Secondly, large amounts of data are generated and tools to generate knowledge from such data sets have not typically been used for safety analysis approaches. This report focuses on the first issue and, in particular, describes how we can use novel methods that optimize the information generated by the sampling process by sampling unexplored or risksignificant regions of the issue space; we call this approach adaptive (smart) sampling algorithms. These methods infer the system response using surrogate models constructed from existing samples and predict the best location of the next sample. By using enhanced methods, it is possible to understand features of the issue space with a smaller number of carefully selected samples. In this report, we will present how it is possible to perform adaptive sampling using the RISMC toolkit and highlight the advantages compared to more classical sampling approaches such as Monte-Carlo. We will employ RAVEN to perform such statistical analyses applied to both analytical cases and more complex cases using RELAP-7.iii CONTENTS EXECUTIVE SUMMARY .

Data Analysis Approaches for the Risk-Informed Safety Margins Characterization Toolkit

“…Modeling of the thermal-hydraulic behavior of the plant [6] Modeling of external events such as flooding [7] Modeling of the operators responses to the accident scenario [8] Note that deterministic modeling of the plant or external events can be performed by employing specific simulator codes but also surrogate models [5], known as reduced order models (ROM). ROMs would be employed in order to decrease the high computational costs of employed codes.…”

“…In [5] we focused the development directly on the first two categories using RAVEN and we showed several applications that are of interest in the RISMC project. This report focuses on the third step of the RISMC method (see Figure 6): data clustering post-processing (in particular time-dependent data mining) and data visualization.…”

“…This implies that the covariance matrix needs to be computed prior determining . This can causes problems, from a computational efficiency point of view, if the data set changes (i.e., data points are added or removed) (5) o Z-Normalization: this normalization (also known as standard score normalization) transforms the data to have zero mean and unit variance:…”

“…In the past years, the development of the RISMC approach has covered the following topics Application of RISMC simulation based PRA methods on a BWR SBO test case [3] Comparisons of RISMC simulation based PRA against state of practice methods [4] Employment of reduced order model techniques [5]…”

“…http://scikit-learn.org/stable/5 This matching can be analytically performed using distance metrics that are described in Section 6.3…”