Neutron Noise Source Research Articles

Classification and Location of Neutron Noise Perturbations Using Convolutional Neural Networks

With the aging of the nuclear reactor fleet in Europe, and especially in Spain, monitoring these reactors through complex models has become of great interest to maintain the safety and operational capability of these nuclear power plants. It is of particular interest to locate the place where a possible anomaly has occurred, as well as the type, to guarantee the safety of the reactor through the analysis of neutron flux fluctuations. Therefore, we propose a deep learning framework for the deconvolution of reactor transfer functions from perturbation-induced neutron noise sources. The main objective of this work is to develop tools based on deep learning techniques to classify the type and to locate the perturbation, working with simulated data with different noise levels, and to study the number of detectors that need to be active. In particular, the data used have been simulated for the BIBLIS 2D reactor using FEMFFUSION. This work has been carried out using the Keras library based on tensor flow, managing to develop two convolutional neural networks that adapt well to the data model. High-accuracy results are obtained both when predicting the type of the perturbation and when locating the place of the perturbation, with a low error rate even when only four to eight detectors are available.

Investigation of VVER-1000 fuel assembly bowing effect on power distribution during cycle using neutron noise adiabatic approximation

Thermomechanical and radiation loads in the reactor core cause lateral changes in the shape of Fuel Assemblies (FAs). This phenomenon, known as FA bowing, has significant implications for reactor safety and operation. Bowing results in alterations to the spacing between FAs, which in turn leads to neutron flux perturbations affecting power distribution. These perturbations are time-dependent due to variations in boric acid concentration during the cycle. Neutron noise theory is employed to analyze these time-dependent neutron perturbations. In this research, it is investigated the bowing effect during the cycle in a VVER-1000 reactor using the neutron noise adiabatic approximation. It was initially considered a VVER-1000 reactor core to verify the calculations algorithm without bowed FAs. Results had acceptable accuracy in power, initial boric acid, and cycle length. Subsequently, it was explored various modes of FA bowing as neutron noise sources the results revealed that the power noise caused by bowing varies throughout the cycle, as expected. The noise amplitude during the cycle depends on changes in boric acid concentration, burnup, size, and the direction of bowing.

Modelling and simulations of reactor neutron noise induced by mechanical vibrations

Mechanical vibrations of core internals are among the main perturbations that induce oscillations in the neutron flux field, also known as neutron noise. In this work, different simulation models for the study of the influence of the mechanical vibrations of fuel assemblies on the neutron flux in the reactor core have been discussed. These methodologies employ the diffusion approximation, with or without a previous homogenization model, to simulate the neutron noise in the time or the frequency domain. The diffusion-based approach is expected to be less accurate in the vicinity of the vibrating fuel assemblies, but correct when considering distances larger than a few diffusion lengths away from the perturbation. All methodologies provide consistent results and can reproduce typical features of the neutron noise induced by mechanical vibrations of core components. First, FEMFFUSION can perform simulations in both the time and frequency domains. Second, CORE SIM + can be used to study various neutron noise scenarios in realistic three-dimensional reactor configurations. The third methodology is centred on using commercial codes as CASMO-5, SIMULATE-3 and SIMULATE-3K. This methodology allows time domain simulations of the neutron noise induced by different neutron noise sources in a nuclear reactor. Finally, a model for time-dependent geometry is implemented for the code system ATHLET/QUABOX-CUBBOX employing a cross-section-based approach for encoding water gap width variations at the reflector.

Characterization of High Harmonic Frequencies in Reactor Noise Experiments Within the CORTEX Project

We present a novel technique of neutron noise detection and experimental data interpretation developed during the EU H2020 project CORTEX aiming to improve the capabilities for identification and localization of neutron noise sources. The experimental data analysis is performed in the frequency domain by extracting the spectral power density and the phase angle using a novel spectral variance reduction technique based on per cycle-based bootstrapping with replacement. This technique allows for variance reduction of measured spectral power and phase angle not only at base frequency, but at higher harmonic frequency contributions as well. This allows for a more representative treatment of experimental data and validation of codes for neutron noise propagation, some of which have been developed within the project. The detector response is not necessarily linearly dependent on the oscillator movement, and the study of nonlinear terms provides additional information which can improve the accuracy of neutron noise source identification and localization. Moreover, these terms can be used in a Taylor series to identify a more complex dependence. The process is simplified in the sense that these contributions are linearized in the frequency domain as higher harmonic frequency contributions and can be easily identified and extracted due to spectral peaks prominence provided by the bootstrapping with replacement method. Combined with the spectral power and phase, we present a preliminary investigation of usability of higher-order terms for noise source identification and localization. In this article, we outline the CORTEX project, the experiments, and the measurement analysis methodology based on the bootstrapping with replacement along with the initial developments on the study of nonlinear terms in CROCUS reactor, using several different noise source configurations at a set frequency.

Development of SD-HACNEM neutron noise simulator based on high order nodal expansion method for rectangular geometry

In this study, the SD-HACNEM (Sharif Dynamic - High order Average Current Nodal Expansion Method) neutron noise simulator in two energy groups using a second-order flux expansion method for two-dimensional rectangular X Y-geometry has been developed. In the first step, the calculations were performed for the steady state and results of ACNEM (Average Current Nodal Expansion Method) and HACNEM (High order Average Current Nodal Expansion Method) were examined and compared. To solve the problem, the power iteration algorithm has been used to calculate the distribution of neutron flux and neutron multiplication factor by considering the coarse-mesh (each fuel assembly one node). To validate the steady state calculations, the results were compared with the western nuclear reactor BIBLIS-2D (reference model). In the next step, dynamic calculations were performed in the frequency domain. For this purpose, after discretizing the neutron noise equations by the high-order average current nodal expansion method (NEM), a neutron noise source of absorber with variable strength was simulated. The results were verified by performing simulation at zero frequency and adjoint calculations. Then, the distribution of neutron noise for Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position (ILOFAIP) is obtained. The numerical results showed that the use of HACNEM compared with ACNEM, without reducing the size of the meshes in neutron noise simulation, presented more accurate.

Neutron noise simulator based on the boundary element method (BEM)

The purpose of the present study is to develop the neutron diffusion solver and neutron noise simulator based on the Boundary Element Method (BEM). The 2-D, 2-G neutron/adjoint diffusion equation and corresponding neutron/adjoint noise equation were solved using the mentioned method. The developed neutron static and noise simulator based on the finite element method gives accurate results when the more number of the elements is used. The motivation of the present research is to use the boundary element method to reduce the computational cost. The boundary element method attempts to use the givenboundary conditionsto fit boundary values into the integral equation, rather than values throughout the space defined by a partial differential equation.The results of static calculation were then benchmarked against the valid data for BIBLIS-2D and IAEA-2D benchmark problems. The neutron noise calculation due to the absorber of variable strength neutron noise source was performed using BEM and the Green's function technique. The adjoint of noise equation was also solved using the same method applied to the forward calculation. Comparison of the calculated neutron noise at zero frequency with the results of static calculation, utilizing the result of adjoint noise calculation and qualitative comparison with similar reported results are three different procedures to validate the neutron noise calculation.The analysis of the results obtained from the BEM shows that the boundary element method alone, or coupled with the finite element method, is ideally suited for the static and neutron noise calculation from both the accuracy and efficiency viewpoints.

CORE SIM+: A flexible diffusion-based solver for neutron noise simulations

The paper presents CORE SIM+, a tool developed for diffusion-based neutron noise simulations. The simulator is based on the 3-dimensional, two-energy group neutron diffusion equation in the frequency domain. The tool includes the necessary solvers to calculate the criticality problems associated with the system and then the response to a variety of perturbations such as absorbers of variable strength, perturbations travelling with the coolant flow and vibrations of core components. Numerical methods suitable for different types of problems have been implemented. A capability that allows to apply non-uniform computational meshes is available so that the discretization of the domain can be optimized with respect to the characteristics of the neutron noise sources. The simulator can generate neutron noise databases for nuclear power reactors via the Green’s function method in a fully automated manner. These databases can be useful when studying the neutron noise response in a reactor and when training machine learning algorithms for core monitoring and diagnostics. As part of the verification process, the CORE SIM+ response of a realistic reactor model to a given perturbation at various frequencies is used to estimate the corresponding point-kinetic component, compared to an exact analytical expression. In addition, the Green’s function generator is used to calculate the response of a system to a fuel cell vibration. The solution is then compared to the one of the direct solver of CORE SIM+. As part of the validation work, a neutron noise experiment with vibrations of fuel rods is simulated, showing a reasonable agreement with the measurements. A representative neutron noise database generated for a generic pressurized water reactor is described. From the database the simulations of fuel assembly and core barrel vibrations are chosen as illustrative examples for demonstrating the capabilities of the tool.

Precise localization of neutron noise sources based on transport theory and comparison with diffusion theory

In an attempt to explore the significance of transport theory in neutron noise, localization of a noise source by Green’s function based on transport theory is investigated. There are considerable differences between Green’s functions based on diffusion and transport, such as small dimensions, near edges, high heterogeneity medium and high-frequency source of perturbation. These differences are expected to significantly impact unfolding, reconstruction, and identification of the neutron noise source. Improvement in noise source unfolding methods is essential in terms of safety aspects and reactor performance enhancement. Since gaining the ability to monitor nuclear reactor based on noise diagnostics principle using few numbers of detectors is a challenging problem, more accurate methods of calculation of neutron noise can help reduce the detectors in number and sensitivity to location. This study revealed that inverse Green’s function based on diffusion and transport is fundamentally different in concept. The inverse Green’s function based on diffusion theory requires applying complicated reconstruction methods to gain more accurate results. This means that a large number of detectors must be used for noise source reconstruction. In contrast, in the case of inverse Green’s function based on transport theory, each mesh's shape function is strongly correlated with the adjacent mesh. As a result, simple methods can be used to reconstruct the noise source. Therefore, the noise source can be identified and reconstructed with a smaller number of detectors in practical terms.

Frequency domain Monte Carlo simulations of void velocity measurements in an actual experimental setup using a neutron noise technique

ABSTRACT Monte Carlo simulations of the void velocity measurement in a light-water moderated critical assembly CROCUS are performed using a continuous energy Monte Carlo code that has a special function to conduct frequency domain calculations using complex-valued weights of neutron noise. In the measurements that are simulated in this paper, two vertically aligned fission chambers detected the neutron noise caused by the upward moving void in a rectangular channel. The neutron noise transport calculations in the frequency domain are performed for the measurement simulations. Using the cross power spectral density between two chambers, the void velocities are calculated at frequencies from 0.1 to 12 Hz. The void velocity is overestimated at lower frequencies, and accurately predicted at higher frequencies. This frequency dependence is explained using a simple model that takes neutron noise spatial attenuation and source intensity distribution into consideration.

Time-frequency analysis of non-stationary neutron noise in a small modular nuclear reactor

In this work, for the first time, the time-frequency analysis technique is proposed to analyze a non-stationary neutron noise. The work investigates on an appropriate way to solve the neutron noise equation in the time-frequency domain in an SMR reactor. To actualize this procedure, a computer program has been developed. This program is based on the use of three main modules. The first is a static calculation by a finite difference method and a power iteration algorithm for providing a database of the required neutronic parameters. The second is the neutron noise calculations in the time-frequency domain and the extraction of the noise characteristics by using the Wigner-Ville distribution. The third is the categorization of the neutron noise sources based on their extracted characteristics such as the source type, the source location, the number of sources, the time of the occurrence, the instance frequency and the noise amplitude.In the first module, the static calculations are benchmarked by the referenced values. Then, in order to validate the static noise calculation, the obtained result is compared to the result of the noise calculation in zero frequency. The results of adjoint and direct methods are compared with each other to confirm the validity of the dynamic noise calculation. The obtained results show a good agreement with each other. In addition, the obtained results of the proposed method and Fourier method are compared with each other at the initial time. Moreover, various noise sources, including mono and multi-frequency, are solved in the time-frequency domain to evaluate the proposed method’s capability.All results show that the proposed method has a good capability to solve neutron noise equation. The results obtained show that the time-frequency method gives comprehensive results in comparison with frequency methods.Finally, it is concluded that analyzing the noise sources in the time-frequency domain can be used as a remarkable approach to investigate the core behavior and to recognize the non-stationary processes in the core.

Decomposition of neutron noise in a reactor into higher-order mode components and investigation of the space and frequency dependence

It is a well-known fact that the frequency characteristics of neutron noise induced by the fluctuation of nuclear cross sections have space-dependence that departs from the point kinetics behavior. In this paper, the neutron noise distribution in a two-dimensional BWR core model, which is calculated by solving a two-energy group neutron noise diffusion equation, is decomposed into higher-order mode components using α-mode eigenfunctions. The amplitude and the phase shift of the higher-order mode components have a minor dependence on the frequency, compared to the fundamental mode. Near the neutron noise source, the higher-order mode components account for a major portion of the neutron noise, thereby causing a minor dependence of the neutron noise on the frequency. Near the nodes of the higher-order modes, the fundamental mode is dominant, and the neutron noise exhibits almost the point kinetics behavior. The space dependence and the frequency characteristics of the neutron noise are elucidated by examining the higher order components that are decomposed from the neutron noise distribution.

High accurate three-dimensional neutron noise simulator based on GFEM with unstructured hexahedral elements

Abstract The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

PARCS vs CORE SIM neutron noise simulations

In a nuclear reactor, even operating at full power and steady-state conditions, fluctuations are detected in the recording of any process parameter. These fluctuations (also called noise) could be of various origins, such as, turbulence, mechanical vibrations, coolant boiling, etc. The monitoring and complete comprehension of those parameters should thus allow detecting, using existing instrumentation and without introducing any external perturbation to the system, possible anomalies before they have any inadvertent effect on plant safety and availability.In order to reproduce and study the induced neutron noise in a nuclear reactor core, it is compulsory to develop suitable tools. Existing time-domain codes were originally not developed for this type of calculations. Modifications of those codes and the development of an associated intricate methodology are necessary for enabling noise calculations. This involves, in some cases, changes in the source code and the development of new auxiliary tools to ensure accurate reproductions of the core behavior under the existence of a neutron noise source.In the proposed work, the time-domain neutron diffusion code PARCS is used to model the effect of stationary perturbations representative of given neutron noise sources. In order to validate the feasibility of the time-dependent methodology thus developed, comparisons with the results of simulations performed in the frequency domain, using the CORE SIM tool, developed at Chalmers University of Technology, are performed.The development of a few test cases based on a real reactor model are undertaken as the basis for such comparisons and a methodology aimed at assessing the time-domain simulations versus the frequency-domain simulations is established. It is demonstrated that PARCS, although not primarily developed for neutron noise calculations, can reproduce neutron noise patterns for reasonable frequencies. However, it is also observed that unphysical results are occasionally obtained.

3D convolutional and recurrent neural networks for reactor perturbation unfolding and anomaly detection

With Europe's ageing fleet of nuclear reactors operating closer to their safety limits, the monitoring of such reactors through complex models has become of great interest to maintain a high level of availability and safety. Therefore, we propose an extended Deep Learning framework as part of the CORTEX Horizon 2020 EU project for the unfolding of reactor transfer functions from induced neutron noise sources. The unfolding allows for the identification and localisation of reactor core perturbation sources from neutron detector readings in Pressurised Water Reactors. A 3D Convolutional Neural Network (3D-CNN) and Long Short-Term Memory (LSTM) Recurrent Neural Network (RNN) have been presented, each to study the signals presented in frequency and time domain respectively. The proposed approach achieves state-of-the-art results with the classification of perturbation type in the frequency domain reaching 99.89% accuracy and localisation of the classified perturbation source being regressed to 0.2902 Mean Absolute Error (MAE).

Neutron noise simulation using ACNEM in the hexagonal geometry

In the present study, the development of a neutron noise simulator, DYN-ACNEM, using the Average Current Nodal Expansion Method (ACNEM) in 2-G, 2-D hexagonal geometries is reported. In first stage, the static neutron calculation is performed. The neutron/adjoint flux distribution and corresponding eigen-values are calculated using the algorithm developed based on power iteration method by considering the coarse meshes. The results of the static calculation are validated against the well-known IAEA-2D benchmark problem. In the second stage, the dynamic calculation is performed in the frequency domain in which the dimension of the variable space of the noise equations is lower than the time dependent equations. Induced neutron/adjoint noise distribution due to the neutron noise source of type absorber of variable strength is calculated as well. Two different methods are used to validate the neutron noise calculation. The Inadvertent Loading and Operation of a Fuel Assembly in an Improper Position (ILOFAIP) as an important neutron noise source is investigated using ACNEM in this study.

On a various soft computing algorithms for reconstruction of the neutron noise source in the nuclear reactor cores

This paper presents a comparative study of various soft computing algorithms for reconstruction of neutron noise sources in the nuclear reactor cores. To this end, the computational code for reconstruction of neutron noise source is developed based on the Adaptive Neuro-Fuzzy Inference System (ANFIS), Decision Tree (DT), Radial Basis Function (RBF) and Support Vector Machine (SVM) algorithms. Neutron noise source reconstruction process using the developed computational code consists of three stages of training, testing and validation. The information of neutron noise sources and induced neutron noise distributions are used as output and input data of training stage, respectively. As input data, both the real and imaginary parts of numerical value of the neutron noise in the detector are used. In the present study, the neutron noise source of absorber of variable strength type is only considered. The neutron noise distributions in the detectors due to 2000 randomly generated neutron noise sources are calculated using the developed computational code based on Galerkin Finite Element Method (GFEM). As output data, the strength, frequency of occurrence and location (X and Y coordinates) of the considered neutron noise sources are used. The VVER-1000 reactor core is considered as the benchmarking problem for validation of performed simulation using developed computational code. All specifications of neutron noise source including strength, frequency and location of the neutron noise source are reconstructed with high accuracy. Finally, a sensitivity analysis of results to the number of active detectors in the reactor core is performed. A comparative study of the performance of different developed algorithms represents Decision Tree as the most appropriate one for reconstruction of the neutron noise source in the nuclear reactor cores.

Adaptive group of ink drop spread: a computer code to unfold neutron noise sources in reactor cores

Abstract The present paper reports the development of a computational code based on the Adaptive Group of Ink Drop Spread (AGIDS) for reconstruction of the neutron noise sources in reactor cores. AGIDS algorithm was developed as a fuzzy inference system based on the active learning method. The main idea of the active learning method is to break a multiple input–single output system into a single input–single output system. This leads to the ability to simulate a large system with high accuracy. In the present study, vibrating absorber-type neutron noise source in an International Atomic Energy Agency-two dimensional reactor core is considered in neutron noise calculation. The neutron noise distribution in the detectors was calculated using the Galerkin finite element method. Linear approximation of the shape function in each triangle element was used in the Galerkin finite element method. Both the real and imaginary parts of the calculated neutron distribution of the detectors were considered input data in the developed computational code based on AGIDS. The output of the computational code is the strength, frequency, and position ( X and Y coordinates) of the neutron noise sources. The calculated fraction of variance unexplained error for output parameters including strength, frequency, and X and Y coordinates of the considered neutron noise sources were 0.002682 #/cm 3 s, 0.002682 Hz, and 0.004254 cm and 0.006140 cm, respectively.

Neutron noise source reconstruction using the Adaptive Neuro-Fuzzy Inference System (ANFIS) in the VVER-1000 reactor core

The neutron noise is defined as the stationary fluctuation of the neutron flux around its mean value due to the induced perturbation in the reactor core. The neutron noise analysis may be useful in many applications like noise source reconstruction. To identify the noise source, calculated neutron noise distribution of the detectors is used as input data by the considered unfolding algorithm. The neutron noise distribution of the VVER-1000 reactor core is calculated using the developed computational code based on Galerkin Finite Element Method (GFEM). The noise source of type absorber of variable strength is considered in the calculation. The computational code developed based on An Adaptive Neuro-Fuzzy Inference System (ANFIS) is used to unfold the neutron noise source. Complex neutron noise distribution (real and imaginary parts) in the detectors is considered as input data onto the developed computational code based on the ANFIS algorithm. All the characteristics of the neutron noise source, including strength, frequency and position (X and Y coordinates) are unfolded with excellent accuracy using the developed computational code.

Point flux nodal expansion scheme applied to the neutron noise analysis of the nuclear reactor core

In this paper, a neutron noise simulator based on the point flux nodal expansion method (PFNEM) for nuclear reactor cores with rectangular geometry is developed. The point flux scheme is a kind of nodal expansion method (NEM) which is based on keeping balance of neutrons in every node and has been proved very efficient for LWR analysis. The method can be applied to mesh volumes as coarse as the reactor subassemblies to speed up calculations. In this work, the PFNEM is implemented for spatial discretization of neutron diffusion equation in the frequency domain in order to obtain the neutron noise, fluctuation of neutron flux around its mean value. The fluctuations of the absorption macroscopic cross sections in both fast and thermal energy groups are assumed as the neutron noise source. The adjoint noise analysis is also carried out to validate forward noise calculation results. Three test problems including 2-region slab reactor, 2D TWIGL seed-blanket reactor and 2D LRA BWR are assessed for evaluating the noise results. In addition, an adopted iterative scheme is also presented for the solution of neutron noise equations. Altogether, static and dynamic calculations results demonstrate the good accuracy of proposed approach.

Noise source reconstruction using ANN and hybrid methods in VVER-1000 reactor core

The present paper consists of two separate sections. In the first section, the neutron noise source is reconstructed using Artificial Neural Network (ANN) in a typical VVER-1000 reactor core. In the first stage of this section, the neutron noise calculations are performed based on Galerkin Finite Element Method (GFEM). To this end, two types of noise sources including absorber of variable strength and vibrating absorber are considered. As the results of noise calculations, the neutron noise is obtained in the location of detectors. In the second stage, the multilayer perception neural network is developed for reconstruction of the noise source. Complex neutron noises (real and imaginary parts) in the location of detectors are considered as the inputs of ANN. The developed artificial neural network consists of two hidden layers of type hyperbolic tangent sigmoid transfer function and a linear transfer function in the output layer. Noise source characteristics including strength, frequency and the location (X and Y coordinates) are identified with high accuracy. The developed hybrid method which comprises scanning method and multilayer perception neural network is employed for reconstruction of two coincidence noise sources. The number, type and location of noise source are exactly reconstructed using the hybrid method. The strength and frequency of noise source(s) are also identified with high accuracy using the developed method. A sensitivity analysis of the reconstructed noise source to some ANN parameters like the number of hidden layers, neurons in each hidden layer and the applied transfer functions is performed. Variation of accuracy of reconstructed noise source versus number of detectors and their arrangement in the reactor core are investigated as well.In the second section of present work, neutron flux variations (neutron noise) due to absorber of variable strength and vibrating absorber noise sources are studied in both frequency and time domains. Time dependency of neutron noise was obtained using inverse Fourier transform.