Exploring Variability in Reflood Simulation Results: an Application of Functional Data Analysis

In this paper we followed the functional data analysis (FDA) paradigm to summarize the output of computer code simulating a reflood transient. The paradigm stands on the assumption that the data (code output) is generated by a smooth, albeit complex, process. As such, discrete points as output by the code can be represented as a function or a set of functions. We applied the approach to the analysis of cladding temperature evolution of reflood transient simulations using the thermal-hydraulics code TRACE. The dataset was generated from a computer experiment by random and independent sampling of the input model parameters. The steps taken for the subsequent analyses are the following: First, the dataset was represented as a set of functions using basis function expansion. Second, the functional dataset was aligned to a reference using landmark registration procedure to separate the amplitude and the phase variations. And third, the variations in the dataset were exposed using functional Principal Component Analysis (fPCA). The analysis resulted in a set of functions and scores that could explain the most variability or mode of variation exhibited by the functional dataset. The methodology was able to reveal five different modes of variations containing 90% of the sample variability both in amplitude and phase. A principal component score can attribute a certain mode of variation to a given run. As such, this set of scores and their statistics can be used as quantities of interest in sensitivity analysis of a code when the output is a function.