Science and Technology of Nuclear Installations

Volume 2016, Article ID 4720685, 6 pages

http://dx.doi.org/10.1155/2016/4720685

## Prediction Study on PCI Failure of Reactor Fuel Based on a Radial Basis Function Neural Network

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Received 24 December 2015; Revised 11 February 2016; Accepted 10 April 2016

Academic Editor: Alejandro Clausse

Copyright © 2016 Xinyu Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Pellet-clad interaction (PCI) is one of the major issues in fuel rod design and reactor core operation in water cooled reactors. The prediction of fuel rod failure by PCI is studied in this paper by the method of radial basis function neural network (RBFNN). The neural network is built through the analysis of the existing experimental data. It is concluded that it is a suitable way to reduce the calculation complexity. A self-organized RBFNN is used in our study, which can vary its structure dynamically in order to maintain the prediction accuracy. For the purpose of the appropriate network complexity and overall computational efficiency, the hidden neurons in the RBFNN can be changed online based on the neuron activity and mutual information. The presented method is tested by the experimental data from the reference, and the results demonstrate its effectiveness.

#### 1. Introduction

The reactor core of Light Water Reactors (LWRs) holds fuel assemblies of fuel rods, which consist of zirconium alloy tubes containing uranium dioxide pellets. The Zr-alloy cladding is the first containment barrier for fission products. Due to water pressure, the cladding creeps down until contact with the pellet occurs after a few operating cycles. In the case of a power increase, this Pellet-Cladding Interaction (PCI) induces large stresses in the cladding that might lead to fuel rod failure [1]. PCI-induced clad tube failure is caused by a combination of stresses in the Zr-alloy clad due to the pellet-clad contact pressure and chemical reaction of corrosive fission products, such as iodine released during operation, with Zr-alloy under a power ramp. If the induced stresses in the clad are sufficiently large and the concentration of the fission product is high, clad failure may occur [2, 3]. PCI has been a topic of numerous experimental and computational studies with a great amount of accumulated field experience. This has led to PCI-resistant designs and operation guidelines, which have dramatically reduced the propensity for such failures in recent years. Overviews, from industrial perspective, on PCI testing and computations relating to reactor fuels can be found in the literatures [4, 5].

It is well known that the development of the crack before clad failure is difficult to detect. The usual methods for calculating PCI mainly are finite elements models [6–8]. Nevertheless, the probability of PCI failure is hard to assess. The present study aims at this purpose. In this paper, we present a neural network method to predict PCI failure. The reduction of the calculation complexity of the present method may contribute to the online calculation and prediction of the PCI failure in operating reactors. The transients will be calculated during the entire lifetime of the pins and for each of them the PCI failure probability will be predicted. Firstly, the radial basis function neural network (RBFNN) will be trained by sufficient experimental data. Before a transient, the PCI failure probability (failure or not) will be predicted by the trained network. After the transient, the actual result and its inputs will be used to replace one of the initial experimental data; then a new RBFNN will be trained by the new data. In this way, after every transient, the REFNN will be retrained. In this study, a self-organized one RBFNN is used, which can vary its structure dynamically in order to maintain its accuracy. The hidden neurons in the RBFNN can be added or removed online based on the neuron activity and mutual information, to achieve the appropriate network complexity and maintain overall computational efficiency. In this manner, the PCI failure probability can be predicted online by the simple and fast neural network method, which allow for straightforward implementation within a transient analysis methodology and core monitoring systems, and only the input parameters of the transient are considered in this method.

This paper is structured as follows. Section 2 illustrates the design of the self-organized RBFNN. Section 3 presents the calculation process of the PCI failure probability. The calculation results are discussed in Section 4. Finally, conclusion is given in Section 5.

#### 2. A Self-Organized RBFNN

Taking into account that the performance of an RBFNN is heavily dependent on its architecture, many researchers have focused on self-organizing methods that can be used to design the architecture of three-layered RBFNN. In order to design the structure of the RBFNN automatically, Han et al. [9] presented a flexible structure radial basis function neural network (FS-RBFNN) by using a dynamic tuning strategy. The strategy changes the topology of the RBFNN by measuring the average firing rate of the neurons and the mutual information (MI) in the training process. The firing rate is similar to the spiking frequency of the presynaptic neuron in the biological neural system [10]. When the rate value of the hidden neuron is bigger than a given threshold value, new neurons will be inserted into the hidden layer. MI is used to measure the connectivity of hidden neurons and to obtain the connectivity between hidden neurons [11].

##### 2.1. Radial Basis Function Neural Network

Figure 1 shows the structure of a basic RBFNN consisting of one input layer, one output layer, and one hidden layer [12]. In order to simplify the discussion, the RBF model used for analysis is multi input and single output (MISO). A single-output RBFNN with hidden layer neurons can be described bywhere denotes the input of the network, is the number of input variables, denotes the output of the network, is the connecting weights between the hidden neuron and the output layer, and is the output value of the th hidden neuron and can be calculated bywhere denotes the center vector of the th hidden neuron and is the Euclidean distance between and ; is the radius or width of the th hidden neuron.