An approach based on Support Vector Machines and a K-D Tree search algorithm for identification of the failure domain and safest operating conditions in nuclear systems

The safety of a Nuclear Power Plant (NPP) is verified by analyzing the system responses under normal and accidental conditions. This is done by resorting to a Best-Estimate (BE) Thermal-Hydraulic (TH) code, whose outcomes are compared to given safety thresholds enforced by regulation. This allows identifying the limit-state function that separates the failure domain from the safe domain. In practice, the TH model response is affected by uncertainties (both epistemic and aleatory), which make the limit-state function and the failure domain probabilistic. The present paper sets forth an innovative approach to identify the failure domain together with the safest plant operating conditions. The approach relies on the use of Reduced Order Models (ROMs) and K-D Tree. The model failure boundary is approximated by Support Vector Machines (SVMs) and, then, projected onto the space of the controllable variables (i.e., the model inputs that can be manipulated by the plant operator, such as reactor control-rods position, feed-water flow-rate through the plant primary loops, accumulator water temperature and pressure, repair times, etc.). The farthest point from the failure boundary is, then, computed by means of a K-D Tree-based nearest neighbor algorithm; this point represents the combination of input values corresponding to the safest operating conditions. The approach is shown to give satisfactory results with reference to one analytical example and one real case study regarding the Peak Cladding Temperature (PCT) reached in a Boiling Water Reactor (BWR) during a Station-Black-Out (SBO), simulated using RELAP5-3D

Aspects of Metric Spaces in Computation

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate