Estimation of the Power Peaking Factor in a Nuclear Reactor Using Support Vector Machines and Uncertainty Analysis

The monitoring of detailed 3-Dimensional (3D) core power distribution is a prerequisite for the operation of nuclear power reactors to ensure that various safety limits imposed on the fuel pellets and fuel clad barriers, such as the Local Power Density (LPD) and the Departure from the Nucleate Boiling Ratio (DNBR), are not violated during the reactor’s operation. The LPD and DNBR need to be calculated in order to perform the two major functions of the Core Protection Calculator System (CPCS) and the Core Operation Limit Supervisory System (COLSS) [1], each of which plays a role in the protection and monitoring systems of the Optimized Power Reactor 1000 (OPR1000) and the Advanced Power Reactor 1400 (APR1400). After the CPCS calculates safety-critical parameters, such as the LPD and the DNBR, it protects a nuclear reactor by tripping the reactor when its operating limits are exceeded. On the other hand, after the COLSS calculates the parameters of interest, such as the LPD and the DNBR, by using algorithms that are different from those of the CPCS, it helps plant operators to monitor the Limiting Conditions for Operation (LCOs) specified in the technical specifications. The LPD needs to be estimated accurately to prevent nuclear fuel rods from melting. The LPD at the hottest part of a hot fuel rod, which is related to the Power Peaking Factor (PPF, Fq), is more important than the LPD located at any other position in the reactor core. On-line monitoring techniques that use artificial intelligence and its applications to the nuclear engineering field have been explained and reviewed by Garvey et al. [2] and Heo [3]. A lot of research [4-12] has been performed to calculate safety-critical parameters, such as the DNBR and the LPD, by using artificial intelligence methods that have been extensively used in a variety of engineering problems. Support Vector Machines (SVMs) have been applied to classification problems. However, along with the introduction of Vapnik’s ε-insensitive loss function [13], SVMs have also been extended and been widely used to solve nonlinear regression estimation problems. In SVM regression, the input data is mapped onto a high dimensional feature space, and subsequently, the linear regression is carried out in the feature space. Knowing more about the Local Power Density (LPD) at the hottest part of a nuclear reactor core can provide more important information than knowledge of the LPD at any other position. The LPD at the hottest part needs to be estimated accurately in order to prevent the fuel rod from melting in a nuclear reactor. Support Vector Machines (SVMs) have successfully been applied in classification and regression problems. Therefore, in this paper, the power peaking factor, which is defined as the highest LPD to the average power density in a reactor core, was estimated by SVMs which use numerous measured signals of the reactor coolant system. The SVM models were developed by using a training data set and validated by an independent test data set. The SVM models’ uncertainty was analyzed by using 100 sampled training data sets and verification data sets. The prediction intervals were very small, which means that the predicted values were very accurate. The predicted values were then applied to the first fuel cycle of the Yonggwang Nuclear Power Plant Unit 3. The root mean squared error was approximately 0.15%, which is accurate enough for use in LPD monitoring and for core protection that uses LPD estimation.