DIAGNOSTICS OF IN-CORE NEUTRON MONITORING SYSTEM BASED ON ARTIFICIAL NEURAL NETWORK

В.І. Борисенко, В.В. Горанчук, А.В. Носовський. Діагностика внутрішньозонного нейтронного контролю на основі застосування нейронних мереж. Однією з задач діагностики внутрішньозонного нейтронного контролю є задача діагностики детекторів прямого заряду, а саме визначення достовірності сигналів, тобто визначення детектора прямого заряду якій відмовив. Важливо мати змогу оцінити енерговиділення в тепловидільній збірці з цим детектором прямого заряду. В статті обговорюються особливості відновлення сигналу детекторів прямого заряду на основі застосування технології нейронних мереж. Під відновленням сигналу відмовившиго детектора прямого заряду мається на увазі модельне відтворення сигналу, відсутнього через фізичне пошкодження детектора. Навчена нейронна мережа, на основі моніторингу вхідної інформації, може з високим ступенем точності передбачити появу дефектів в обладнанні й оцінити ступінь його технічного стану. Розглянуто мережі трьох різних архітектур: без прихованих шарів, з одним прихованим шаром та з двома прихованими шарами. На вхід нейронної мережі подавалися сигнали детекторів прямого заряду від різної кількості каналів нейтронних вимірювань – від 3 до 63, у якості вихідного сигналу слугували детектори прямого заряду каналів нейтронних вимірювань, що перевірявся. Моделювання було проведено для різних детекторів прямого заряду як за роком використання, так і за місцем розташування в активній зоні, а також для різних енергоблоків та паливних кампаній (26 та 27 кампанії ЗАЕС-5, 27 та 28 кампанії ХАЕС-1, 11 та 12 кампанії ХАЕС-2). Був досліджений вплив кількості вхідних сигналів, а також вплив кількості прихованих шарів на похибку визначення вихідного сигналу. Проведено порівняння алгоритмів навчання нейронних мереж: Левенберга-Марквардта та L-BFGS. Показана важливість вибору для нейронної мережі таких вхідних сигналів, що найбільше визначають характер вихідного сигналу. Показано, що відновлення сигналів детекторів прямого заряду можливе з похибкою не більше 2 % за умови навчання на широкому діапазоні даних, що дозволяє забезпечити контроль енергорозподілу в тепловидільній збірці з даним детектором прямого заряду. Ключові слова: детектор прямого заряду, канал нейтронних вимірювань, система внутрішньореакторного контролю, нейронна мережа, діагностика систем, достовірність сигналів


Introduction
An in-core monitoring system is provided to control the distribution of energy in the VVER reactor core. This system provides the operator with operational information on energy release in the core based on the signals of self-powered neutron detectors (SPND) and coolant temperature sensors. The output signal of the SPND is proportional to the density of the neutron flux at its location, which in turn also determines the energy release in the nearest fuel elements. In order to control the linear energy release of fuel when operating at rated power, it is necessary to ensure compliance with the regulatory requirements for the number of operational SPND. Detectors that malfunction should be detected in in-core monitoring system (ICMS) and be able to evaluate energy generation in a fuel assembly (FA) in which energy control was lost due to damage to the SPND or for other reasons.

Analysis of recent publications
The reliability of the input information in the ICMS was investigated in [1,2]. In this article, the reliability of information that is defined in the ICMS is the property of information to be correctly perceived and uniquely interpreted for making management decisions. In [2], similar algorithms were used to analyze the reliability of the input information as in [1], but in real time. Estimates were performed on the basis of: analysis of statistical characteristics of channels, comparison with regime values and setpoints, comparison with information in parallel control channels [2]. At the same time, the technology of neural networks [3 -5] showed its perspective for the analysis of the reliability of the input information of NPP control systems, which is considered in this paper in the problem of ICMS diagnostics.
The purpose and objectives of the study The purpose of the study is to ensure the control of the reliability of the information of the measuring channels in the ICMS. The task of diagnosing SPND is to search for a failed SPND. This paper presents the results of a study on the possibility of model recovery of a failed SPND signal based on the use of neural network technology. When the signal of the failed SPND is restored, the model reproduces the signal missing due to physical damage to the detector.

How Neural Networks Work
Neural networks are a simplified model of the biological nervous system. They are used in solving classification and forecasting problems and can be applied to almost any task when there is a relationship between input variables and output (predicted), even when the relationship has a complex structure. A neural network is a collection of neural elements that are somehow connected to each other by relationships determined by weighting factors. The peculiarity of neural networks is that they are capable of learning. The learning process involves adjusting the weights.
The block diagram of the neuron model is presented in Fig. 1 Each synapse (ligament) is characterized by its weight. The signal x j at the input of a synapse J that is associated with a neuron k is multiplied by weight ω kj . The synaptic weight of the neuron can be both positive and negative.
The adder u k sums the input signals weighted relative to the corresponding neuron synapses. An externally added offset may be included in the model of the neuron, denoted as b k . The offset value b k determines the decrease or increase of the input signal supplied to the activation function.
The activation function ϕ limits the amplitude of the output signal of the neuron. For example, the normalized range of neuron output amplitudes may lie in the range [0, 1] or [-1, 1]. Therefore, the model of the neuron is described by the following equations: The neural network can be described using architecture and synaptic scales. There are three fundamental classes of architecture: single-layer direct distribution networks, multi-layer direct distribution networks, recurrent networks [6].

Modeling based on the use of neural network technology
The simulation was performed using the alglib cross-platform numerical analysis library [7]. The alglib library supports C ++, C #, Pascal, VBA, and Windows, Linux, Solaris. It used the C # programming language and the Windows operating system.
Neural networks were built with no hidden layers, with one hidden layer and two hidden layers. Network connections go from the input layer to the first hidden (if any), then to the second (if any), then to the original layer. Research on different neural network models was conducted to select the optimal neural network model.
Neural network training was conducted on the first five datasets and testing on the next fifteen. The time interval between the datasets was one week.
The simulation was performed for different SPND both by year of use and by location in the core area, as well as for different power units and fuel campaigns (26 and 27 ZNPP campaigns-5, 27 and 28 KhNPP campaigns-1, 11 and 12 KhNPP campaigns-2).
The influence of the number of input signals and the influence of the number of hidden layers on the error of determining the output signal was investigated. Comparison of learning algorithms of neural networks: Levenberg-Marquardt and L-BFGS.
Choosing the optimal neural network scheme for the recovery of SPND signals The choice of the neural network scheme was performed according to the criterion of minimum deviation of the recovered SPND signal from the real SPND signal by 10 -20 steps after simulating the fact of physical damage of the SPND.
The influence of the number of input signals.
On example 11 of the KhNPP-2 fuel campaign (see Fig. 2) three cases were considered (see Table 1): in the first calculation, the SPND signals from 63 NFMC were given, in the second calculation -from In all the considered cases, the current of the SPND NFMC-57, FA-114 served as the output signals (see Fig. 3). It is worth noting that the nearest neighboring NFMC to NFMC-57 is located through one fuel assembly, and FA-114 is located in the penultimate row -on the periphery of the core.   Tables 2 -4 present an error in the recovery of currents of the SPND NFMC-57 using neuralnetworks. The neural network architecture with no hidden layers was selected. The Levenberg-Marquardt algorithm was used to train neural networks. Training was conducted on the first five datasets and testing on the subsequent fifteen. Table 2 The deviation of the calculated value of the current of the SPND from the actual according to item No. 1 of Table 1 № set Datas type Deviation, % SPND-1 SPND-2 SPND-3 SPND-4 SPND-5 SPND-6 SPND-7 1  Table 3 Deviation of the calculated value of the current of the SPND from the actual according to item No. 2 Table 1 № set Datas tape Deviation, % SPND-1 SPND-2 SPND-3 SPND-4 SPND-5 SPND-6 SPND-7 1  Table 4 The deviation of the calculated value of the current SPND from the actual according to item No. 3 Table 1 № set Datas tape Deviation. % SPND-1 SPND-2 SPND-3 SPND-4 SPND-5 SPND-6 SPND-7 1 From the given data (Table 1) it is clear that the higher number of input signals of the neural network does not lead to better evaluation of the output signals. Therefore, we recommend that you limit yourself to only those inputs that most determine the output ones. A decrease in the number of NFMC inputs from 63 to 7 adjacent to the NFMC output resulted in a decrease of the maximum deviation of 1.53 %, and the use of NFMC inputs symmetrically located with the NFMC output in the 30° symmetry sectors resulted in a decrease in the maximum deviation by 3.17 %.

Investigation of the influence of the number of hidden layers
On the example of the KHPP-1 27th fuel campaign (see Fig. 4). three different neural network architectures (see Table 5) are considered: where no hidden layers, one hidden layer, and two hidden layers. The hidden layers included 20 neurons each.  Higher number of hidden layers does not necessarily result in better evaluation of the output signals. It may be advisable to use neural networks without hidden layers to solve this problem. Thus, in this case, the neural network without hidden layers showed the maximum deviation of the calculated current of the SPND NFMC-2 from the actual level of 1.45 %, the neural network with one hidden layer -3.22 %, and the neural network with two hidden layers -5.7 %.

Comparison of neural network training algorithms
On the example of the 26th and 27th fuel campaigns of ZAES-5 (see Figs. 6, 7) there two algorithms for training neural networks (Levenberg-Marquardt and L-BFGS (see Table 6)) are considered. To the input of the neural network were signaled SPND from NFMC, which were in sectors of symmetry 30 ° similar to the original NFMC.
For the 26th fuel campaign. the signals of the SPND NFMC in FA-76, FA-150, FA-156, FA-88, FA-14 were fed to the input, and the SPND NFMC in FA-8 served as the output signal (see Fig. 8).
For the 27th fuel campaign, the signals of the SPND NFMC in FA 141, FA-146, FA-87, FA-23, FA-18 were fed to the input, and the SPND NFMC in FA-8 served as the output signal (see Fig. 9).   The neural network architecture with no hidden layers was selected. Training was conducted on the first five datasets. and testing on subsequent ones. Fig. 7 presents the error of current recovery SPND NFMC-12 (FA-8) by the algorithm L-BFGS, and in Table, 8 according to the Levenberg-Marquardt algorithm for the ZAES-5 26th fuel campaign. As can be seen from the Table, 7, 8 Levenberg-Marquardt's training algorithm showed better recovery of DPF currents. This trend is observed for most calculations. although there are opposite cases.
It is worth noting that the current values of the SPND in the eighth data set are very different from those used in the training of the neural network.
As can be seen from the Table 9, 10, the L-BFGS training algorithm showed a much better recovery of SPND currents for the eighth data set. for other datasets with little advantage, the Levenberg-Marquardt algorithm turned out to be the best.
In the Table 9 presents the error of current recovery SPND NFMC-8 (FA-77) by the algorithm L-BFGS, and in Table 10 according to Levenberg-Marquardt algorithm for the ZAES-5 27th fuel campaign. Table 7 The deviation of the calculated value of the current of the SPND from the actual according to item No. 1 of  Table 9 The deviation of the calculated value of the current of the SPND from the actual according to item No. 3 of  Therefore. a neural network using the L-BFGS algorithm showed a better ability to generalize, that is, to return the correct result based on data that did not participate in the training sample.
For a good recovery of SPND currents it is necessary to train a neural network on a wide range of data. Also, do not seek to minimize the error in training the network. as the network can be converted and lose its ability to generalize.

Conclusions
The results of the calculations showed the suitability of the use of neural networks for the diagnosis of in-core neutron control. Recovery of SPND signals has been shown to be possible with a deviation of no more than 2 % provided that the neural network is trained over a wide range of data. This makes it possible to determine the current of the SPND that has failed, and also allows the control of the energy distribution in the fuel assembly even with the failed SPND.
The best results from the SPND signal recovery were obtained using the Levenberg-Marquardt training algorithm. The L-BFGS algorithm showed better speed than the Levenberg-Marquardt algorithm.
A neural network with no hidden layers has been identified as having the best architect. The importance of choosing for the neural network such input signals that most determine the nature of the output signal is shown.
Thus, when fed to the input of the neural network of SPND signals in the sectors of symmetry 30° to the output signal error was 3…4 times smaller than the case when the input signals were given to all SPND core. For a more accurate restoration of the currents of the SPND, it is necessary to train the neural network over a wide range of data.