Two novel procedures for aggregating randomized model ensemble outcomes for robust signal reconstruction in nuclear power plants monitoring systems

Detecting anomalies in sensors and reconstructing the correct values of the measured signals is of paramount importance for the safe and reliable operation of nuclear power plants. Auto-associative regression models can be used for the signal reconstruction task but in real applications the number of sensors signals may be too large to be handled effectively by one single model. In these cases, one may resort to an ensemble of reconstruction models, each one handling a small group of sensor signals; the outcomes of the individual models are then combined to produce the final reconstruction. In this work, three methods for aggregating the outcomes of a feature-randomized ensemble of Principal Components Analysis (PCA)-based regression models are analyzed and applied to two case studies concerning the reconstruction of 215 signals monitored at a Finnish nuclear Pressurized Water Reactor (PWR) and 920 simulated signals of the Swedish Forsmark-3 Boiling Water Reactor (BWR). Based on the insights gained, two novel aggregation procedures are developed for optimal signal reconstruction.     

Sensor monitoring using a fuzzy neural network with an automatic structure constructor

The performance of fuzzy neural networks applied to sensor monitoring strongly depends on the selection of input signals. A large number of input signals may be involved to estimate an output signal for failure detection. However, as the number of input signals increases, the required training time increases exponentially and the uncertainty of the model increases significantly due to the irrelevant and/or the redundant inputs. In this paper, a fuzzy neural network with an optimal structure constructor has been successfully developed to achieve a reliable and efficient sensor monitoring system. A fuzzy neural network is used to estimate an output signal from the selected input signals. Correlation analysis and genetic algorithm (GA) are combined for automatic input selection. In addition, the optimal number of fuzzy rules is accomplished automatically by the GA integrated along with the automatic input selection. The status of sensor health is determined by applying sequential probability ratio test to the residuals between the measured signals and the estimated signals. The proposed sensor monitoring system has been validated by using a variety of sensor signals acquired from Yonggwang units 3 and 4 pressurized water reactors.     

An ensemble approach to sensor fault detection and signal reconstruction for nuclear system control

To efficiently control a process, accurate sensor measurements must be provided of the signals used by the controller to decide which actions to actuate in order to maintain the system in the desired conditions. Noisy or faulty sensors must, then, be promptly detected and their signals corrected in order to avoid wrong control decisions. In this work, sensor diagnostics is tackled within an ensemble of Principal Component Analysis (PCA) models whose outcomes are aggregated by means of a local fusion (LF) strategy. The aggregated model thereby obtained is used for both the early detection and identification of faulty sensors, and for correcting their measured values. The fault detection decision logic is based on the Sequential Probability Ratio Test (SPRT). The proposed approach is demonstrated on a simulated case study concerning the pressure and level control in the pressurizer of a Pressurized Water Reactor (PWR). The obtained results show the possibility to achieve an adequate control of the process even when a sensor failure occurs.     

Determination of the minimal number and optimal sensor location in a nuclear system with fixed incore detectors

The determination of the minimal number of sensors and the optimal sensor location in a nuclear system with fixed incore detectors, which is represented by a linear stochastic distributed parameter system, was studied in this work. The partial differential equation representing nuclear reactor dynamics was approximated to the finite dimensional ordinary differential equation by the modal expansion. A scalar measure of the covariance matrix error in the optimal filter was minimized with respect to the sensor locations. The necessary conditions for optimal sensor location were derived using the matrix minimum principle, thus making the calculations computationally more attractive. The locations of sensors were guessed initially through sensitivity analysis to reach solutions of the optimal location quickly. A method to determine the minimum number of sensors is suggested based on the observability and admissible error bound. Several numerical simulations are performed to determine the minimal number and optimal sensor location for a one-dimensional slab reactor and a two-dimensional ABB Combustion Engineering type reactor with fixed incore detectors. Through the simulations the possibility of practical implementation and the rapid convergence of the algorithm are verified.     

Tomographic Algorithms for General Line Integrals

This paper extends the constrained optimization image reconstruction techniques to curved-ray projections for a number of scanning systems and for 2-D and 3-D reconstructions. Teh treatment presented is general in that it includes the previous results on parallel-ray and divergent-ray geometries as special casss. Employing the projection data as constraints, the reconstruction problem is expressed as a generalized constrained optimization problem whose solution leads to a relationship (model) between the reconstruction and the associate Lagrange multiplier functions, thus introducting the models for a number of prescribed cost criteria and scanning systems involing curved-ray projections. Using these new models a category of subspaces of a Hirbert space, the elements of which are the functions (objects) for reconstruction, is presented. The projections and the minimum energy reconstruction are shown to be projections of the object into these new subspaces. The projection slice theorem is extended by introducing a new transform, a slice of which is equal to the Fourier series of the corresponding projection, irrespective of the projection geometry. The ART methods are extended to curved-ray scanning systems. Also a convergent iterative algorithms which evaluates the Lagrange multipliers from general line integrals and then calculates the reconstruction, is introduced. The iterations of this algorithm are identical to those of the additive ART, thus resulting in the same solution.     

Calculation of the power peaking factor in a nuclear reactor using support vector regression models

Local power density (LPD) at the hottest part of a hot nuclear fuel rod should be estimated accurately to confirm that the rod does not melt. The power peaking factor (PPF) is defined as the highest LPD divided by the average power density in the reactor core. In this paper, the PPF is calculated by support vector regression (SVR) models using numerous measured signals from the reactor cooling system. SVR models are regression analysis models using a kernel function for artificial neural networks. Their neural network weights are found by solving a quadratic programming problem under linear constraints. SVR models are trained using a training data set and then verified against another test data set. The proposed SVR models were applied to the first fuel cycle of the Yonggwang nuclear power plant unit 3. The root mean square errors of the SVR model, with and without in-core neutron flux sensor signal inputs, were 0.1113% and 0.0968%, respectively. This level of errors is sufficiently low for use in LPD monitoring.     

The autoassociative neural network in signal analysis: I. The data dimensionality reduction and its geometric interpretation

In complex and risky plants, such as the nuclear reactors, the analysis of the signals released by the many sensors which monitor the plant represents a difficult task due to the high-dimensionality of the data. This paper is the first of two in which we tackle the problem of the dimensionality reduction by the nonlinear principal components analysis as performed by an autoassociative neural network (AANN). This network filters the many input data and releases at the bottleneck output a relatively small number of signals which capture the significant properties of the original data, thus realizing the data reduction.In the present paper, we show that the network ability in correctly reproducing as output the given input after a passage through the bottleneck layer (which by definition should have fewer nodes than either input or output layers) could be conceived as a topological mapping between abstract spaces. Apart from the less critical choice of the number of nodes in the mapping and demapping layers, the topological mapping will be successful – and the AANN will be able to perform the required data reconstruction – provided that the number of nodes of the bottleneck layer is related to the dimensionality d of the abstract projection space. We show how to obtain a numerical estimate d* for the real dimension d. This numerical estimate will firmly base the choice of the number of nodes f of the bottleneck layer, thus avoiding the usual troubling trial-and-error procedure. The power of the proposed approach is demonstrated firstly on a few geometrical cases and then on the analysis of nuclear transients simulated by the classic Chernick’s model.     

Assessment of linear and non-linear autoregressive methods for BWR stability monitoring

A benchmark has been performed to compare the performances of exponential autoregressive (ExpAR) models against linear autoregressive (AR) models with respect to boiling water reactor stability monitoring. The well-known March-Leuba reduced-order model is used to generate the time-series to be analysed, since this model is able to reproduce the most significant non-linear behaviour of boiling water reactors (i.e. converging, diverging and limit-cycle oscillations). In this way the stability characteristics of the signals to be analysed are known a priori. An application to experimental time-traces measured on a thermalhydraulic natural circulation loop is reported as well. All methods perform equally well in determining the stability characteristics of the analysed signals.     

Slice-wise reconstruction for low-dose cone-beam CT using a deep residual convolutional neural network

Because of the growing concern over the radiation dose delivered to patients, X-ray cone-beam CT(CBCT) imaging of low dose is of great interest. It is difficult for traditional reconstruction methods such as Feldkamp to reduce noise and keep resolution at low doses. A typical method to solve this problem is using optimizationbased methods with careful modeling of physics and additional constraints. However, it is computationally expensive and very time-consuming to reach an optimal solution. Recently, some pioneering work applying deep neural networks had some success in characterizing and removing artifacts from a low-dose data set. In this study,we incorporate imaging physics for a cone-beam CT into a residual convolutional neural network and propose a new end-to-end deep learning-based method for slice-wise reconstruction. By transferring 3D projection to a 2D problem with a noise reduction property, we can not only obtain reconstructions of high image quality, but also lower the computational complexity. The proposed network is composed of three serially connected sub-networks: a cone-to-fan transformation sub-network, a 2D analytical inversion sub-network, and an image refinement sub-network. This provides a comprehensive solution for end-to-end reconstruction for CBCT. The advantages of our method are that the network can simplify a 3D reconstruction problem to a 2D slice-wise reconstruction problem and can complete reconstruction in an end-to-end manner with the system matrix integrated into the network design. Furthermore, reconstruction can be less computationally expensive and easily parallelizable compared with iterative reconstruction methods.     

Constrained Optimization Algorithms for Divergent Ray Tomography

Using the projections as constraints, the reconstruction of an object from its fan beam projections is formulated and solved as a problem in constrained optimization. First a general cost criterion is optimized and the result is applied to several specific criteria. This produces a number of relationships (models) between the image and the Lagrange multipliers introduced by the Euler-Lagrange method. Utilizing these models, the ART methods are extended to fan beam projections. A non-recursive algorithm which exploits the speed of the block fast Fourier transform is given and compared with an existing convolution algorithm. The projection slice theorem for divergent ray geometry is given by introducing a new transform, the Angular Projection Transform.     

基于异构多GPU的锥束CT图像重建研究

针对锥束CT图像重建系统中GPU型号不一致问题,提出了基于异构多GPU的重建模型。该模型基于FDK算法进行重建,采用了按计算能力进行任务分配的方法,确保各GPU计算平衡。采用数据流分解的方法,实现了海量数据的图像重建。给出了该重建模型基于CUDA的实现方法,包括采用流管理和异步函数来实现多GPU并行计算以及滤波和反投影核函数的流程设计。利用高精度工业CT系统进行模型的实验验证。结果表明：所建立的重建模型正确有效,能充分发挥系统中异构多GPU的计算能力,执行效率高。     

Instability localization with artificial neural networks (ANNs)

The aim of this piece of research is to investigate the potential of artificial neural networks (ANNs) for tackling the problem of instability localization. The instability is modeled by a variable strength absorber (point-source) in a two-dimensional bare reactor model with a one neutron-energy group. The proposed approach constitutes an exercise in simplicity in that: (1) an arbitrarily simplified model is employed for ANN training and validation; (2) few training and validation patterns of low complexity are utilized; (3) the ANN inputs are derived directly from the neutron noise signals, the proposed location of instability is given on-line via an uncomplicated combination of ANN outputs; (4) the ANN architecture is independent of the number of possible locations of instability. In fact, unlike previous approaches which employ hundreds of outputs (one for each fuel assembly), only two ANN outputs are employed representing the X- and Y-coordinates (location) of instability; (5) the responses of only a few detectors are employed; (6) a measure of confidence in the prediction is assigned. The results of ANN testing, which is performed on patterns from both actual and simplified models, are reported and analyzed.     

Structural reliability in the continuous feedback process for model validation and regulations improvement

The connections between structural reliability and system reliability are reviewed, emphasizing their intimate dependence. The problem of model validation is then outlined; the importance of data in this respect is analyzed.The role of structural reliability in the set-up of regulations and standards is shown to be the statistical analysis of the ‘safety margin’ provided by component design.Furthermore the importance is stressed of implementing a continuous feedback between analysis and operational data on individual structures in order to improve and update prior estimates and models.     

Development of localization system using ultrasonic sensor for an underwater robot to survey narrow environment

This paper describes a localization system for a swimming robot to survey underwater narrow environments. In that environment, external sensors cannot be set up to localize the robot position, as there are many structures and the robot moves three-dimensionally. Therefore, the position needs to be calculated only by internal sensors. In this work, a new localization method based on map-matching is proposed, referring to cross-sectional shape data cut from a three-dimensional computer-aided design (CAD) data as an environmental map and structural shapes measured by a range sensor. As a range sensor, an ultrasonic sensor which is two-dimensional scanning-type was developed. The reflected signals of the ultrasonic sensor have some noise. Only structural shape data are extracted from the reflected signals. The image correlation is used as the matching method. Experiments to evaluate the performance of the proposed system were implemented at a mock-up environment. As a result, it was confirmed that the position was detected with an accuracy of 100 mm. The error is mainly caused by measurement error of the ultrasonic sensor that is used to calculate structural shapes. We concluded to improve the measurement accuracy of the ultrasonic sensor to reduce localization error.     

Direct Three-Dimensional Image Reconstruction from Divergent Rays

The solutions to the image reconstruction problem, in two and three dimensions, for both parallel and divergent ray geometries, are presented within a general linear reconstruction framework. It is shown that, with suitable parameterizations, each of these solutions reduces to a "convolve-and-backproject" algorithm. The exact solution to the three-dimensional divergent ray geometry problem is a new result and is treated in detail. This problem arises when the sensors are located around the object region in three-dimensional space, and the measurement rays diverge (i.e., fan out) from the individual sources. An approximation to the exact solution has been made in order to derive convenient and practical convolving functions for this geometry.     

基于遗传算法的钠冷快堆堆芯流量分区优化设计方法

钠冷快堆采用封闭组件,流量分区是实现堆芯出口温度展平的重要途径。传统的流量分区优化设计方法的计算量随组件数的增加呈指数增长,不适用于解决大型问题。本文建立了流量分区设计的最优化模型,并设计了基于最优个体保存策略的遗传算法,以燃料最高温度限值和包壳温度限值为边界条件,搜索出使活性区平均出口温度最高以及活性区总流量最小的最优流量分区方案,为解决大型钠冷快堆堆芯流量分区优化设计问题提供了新的途径。     

Optimized Design Method for Core Flow Zoning of Sodium-cooled Fast Reactor Based on Genetic Algorithm

Sodium-cooled fast reactors use closed assemblies, and flow zoning is an important means to achieve core outlet temperature flattening. The calculation amount of the traditional flow zoning optimization design method increases exponentially with the number of fuel assemblies, which is not suitable for solving large-scale problems. In this paper, an optimization model for flow zoning design was established, and a genetic algorithm based on the optimal individual preservation strategy was designed. The maximum fuel temperature limit and cladding temperature limit were used as the boundary conditions to search for the optimal flow zoning solution. The average outlet temperature of the active zone is the highest, and the total flow of the active zone reaches the minimum. It provides a new approach to solve the core flow zoning optimization design problem of large-scale sodium-cooled fast reactor.     

Practical use of the modified Bronnikov algorithm in micro-CT

Through the years, the resolution of X-ray Computed Tomography (CT) systems has increased rapidly, in particular for the newer micro- and nano-CT systems. With this increasing resolution, the limits of absorption contrast CT are being reached. At the same time, a new type of contrast becomes visible: phase contrast. Mainly for low-absorbing objects such as insects and wood, phase contrast can lead to a new type of CT reconstruction using the modified Bronnikov algorithm (MBA) [A. Groso, R. Abela, M. Stampanoni, Implementation of a fast method for high 297 resolution phase contrast tomography, Opt. Express 14 (18) (2006) 8103.] Despite it’s theoretical limitation to pure phase objects, the algorithm has some clear advantages with respect to filtered back-projection (FBP). The MBA is therefore commonly used at the Centre for X-ray Tomography of the Ghent University (UGCT) to obtain additional information for optimal scanning results.     

Determination of Optimal Process Variables for Two-Cycle Purex Process

The large and complicated system that is the Purex process is decomposed into units possessing common functions. Then, using the concentration plofile determined by linear search, the inputs, the outputs and the concentration profiles of all the individual units can be determined systematically. Using this approach, Powell's method and multilevel control theory is applied to the Purex process design problem, which is thereby reduced to a problem of optimization. Numerical calculations are carried out, resulting in optimal process variables well within the range of practicability. These process variables are calculated without taking into consideration such relevant but difficult factors as criticality and the instability of Pu solutions. These factors could, however be accounted for by adding appropriate penalty terms to the performance index. The computer program devised for the present calculations is given the code name POSER (Program for Optimization of Solvent Extraction Process).