Point-kinetics neutron noise modeling and analysis via probabilistic finite state automata

Abstract

This paper addresses two issues for safety & performance analysis of nuclear reactors; these issues are: (i) Modeling of the neutron noise process, which is constructed as stochastic differential equations by augmenting deterministic dynamic models of point kinetics, thermal hydraulics, and mechanical vibrations in the reactor core, and (ii) Time-series analysis of nuclear reactor internals for early-stage anomaly detection by making use of the neutron noise model. The model is used to generate an ensemble of time series of neutron noise under both normal and anomalous operating conditions, where an anomaly in the postulated probability distribution of neutron noise is caused by abnormal vibration of the fuel assembly. A symbolic time series analysis (STSA) tool, called probabilisitc finite state automata (PFSA), has been selected to detect the anomalies, if any. The PFSA method symbolizes a time-series and then encodes the resulting symbol string into a state transition probability matrix, which is both stochastic and ergodic by construction. The discrimination function for anomaly detection is built upon the residual error of the principal (left) eigenvector of the state transition probability matrix, which is also the state probability vector of the PFSA. The accuracy of the proposed analysis and its capability for online anomaly detection is demonstrated by simulation on a low-order dynamic model of a 2,500 MWt PWR of the Three-Mile-Island type.