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.     

BNIF-1长中子计数器探测效率的刻度

长中子计数器是在一定的中子能量范围内,中子探测器效率恒定,不随中子能量变化的一种中子探测装置。本工作的长中子计数器为Hanson结构。采用含氢正比计数器与半导体望远镜法,用静电加速器中子源分别为220 keV、500 keV、1.000 MeV、1.403 MeV、3.270 MeV、4.000 MeV与5.000 MeV单能中子束,对本单位制作的BNIF-1长中子计数器进行了刻度。刻度结果表明,在220 keV～5.000 MeV区间,中子探测器效率为2.8810×10^-4（1±4.8%）。     

An Optimized Design of Anode Shape Based on Artificial Neural Network for Achieving Highest X-ray Yield in Plasma Focus Device

In this paper, an optimized design of anode shape in order to achieve highest X-ray yield in a plasma focus device filled with nitrogen gas based on artificial neural networks (ANNs) is presented. Multi-layer perceptron neural network structure with the back-propagation algorithm is used for the training of the proposed model. The model has achieved good agreement with the training data and has yielded satisfactory generalization. This shows that the ANN model is an accurate and reliable approach to predict the highest X-ray yield in plasma focus devices.     

秦山一期反应堆的中子计数率监测

应用高效涂硼计数管,结合改变次级中子源在堆芯的位置,解决了由于堆内中子源衰减过多而导致堆外源量程对中子计数率的监测出现盲区的问题,并以秦山核电厂第五循环装料的实际情况为实例作了阐述。     

Identification and localization of absorbers of variable strength in nuclear reactors

This paper investigates the possibility of localising a noise source of the type “absorber of variable strength” (or reactor oscillator) from as few as five neutron detectors evenly distributed throughout the core of a commercial nuclear reactor. The novelty of this investigation lies with the fact that the calculations are performed for a realistic 2-D heterogeneous reactor in the 2-group diffusion approximation, via the prior determination of the corresponding reactor transfer function. It is first demonstrated that the response of such a reactor to a localized perturbation deviates significantly from point-kinetics. The space-dependence of the induced neutron noise thus carries enough information about the location of the noise source, which makes it possible to determine its position from a few detector readings. The identification of the type of noise source is easily performed from the in-phase behaviour of the induced neutron noise. Different unfolding techniques are finally tested. All these techniques rely on the use of the reactor transfer function. One of these techniques is based on the comparison between the actual measured neutron noise and the neutron noise calculated for every possible location of the noise source. This technique is very reliable and almost insensitive to the contamination of the detector signals by background noise, but also extremely CPU consuming. Another technique, based on the piece-wise inversion of the reactor transfer function and requiring little CPU effort, was developed. Although this technique is much less reliable when background noise is present, this technique is useful to indicate a region of the reactor where a noise source is likely to be located.     

On the space dependence of neutron density noise and the problem of malfunction localization

The space dependence of neutron noise is investigated as a function of reactor size and frequency of excitation, with regard to malfunction localization. An analytical expression for the relative importance of the higher harmonics of the Greens function is given and evaluated for typical sizes of commercial power reactors. It is concluded that localization of thermal hydraulic excitations through neutron noise signals is practically impossible. The case of rod vibration excitations is examined in detail. A 3-dimensional analytical expression is derived for the neutron density response to rod vibrations; it is concluded that rod malfunction localization through neutron noise is not a practical proposition.     

Simulation of start-up measurements with the KIKO3D code and its application for determining the scram rod worth uncertainty in the VVER-440 reactor

The reasons for large discrepancies between the computed and measured values of the efficiency of control rods observed during start-up experiments on the Russian pressurized water type VVER reactors are discussed. The numerical simulation of the measurements including the prediction of the ex-core detector signals was used to resolve the discrepancies. The time and space dependent neutron flux in the core during these measurements have been calculated by the KIKO3D nodal kinetic code. For calculating the ionization chamber signals the Green function technique has been applied. The Green functions of ionization chambers have been evaluated via solving the neutron transport equation in the reflector regions with the MCNP Monte Carlo code. The detector signals have been calculated and compared with measured ones using the inverse point kinetics transformation. Large number of asymmetric rod drop measurements (with one rod stuck) and some differential rod worth measurements from the Zero Power Physics Tests were provided by the Paks NPP for validation. The experiments cover different fuels (without and with enrichment zoning) and loading patterns. The intermediate range ionization chambers have been used during the scram measurements. The newly developed method provides fairly sufficient match of measured and calculated results. The time behavior of the detector readings observed in the measurements are described by the code in a consistent manner.As a further application the uncertainty of scram rod worth of the KARATE-440 code system was determined by static calculations and subsequent simulation of rod drop with the KIKO3D code. The calculated results were compared to measurements carried out by the Paks NPP. The uncertainty of scram rod worth is established by statistical analysis.     

In-core coolant flow monitoring of pressurized water reactors using temperature and neutron noise

Noise measurements were performed at the Loss-of-Fluid-Test (LOFT) and Sequoyah-1 pressurized water reactors (PWRs) in order to investigate the possibility of inferring in-core coolant velocities from cross-power spectral density (CPSD) phases of core-exit thermocouple and in-core neutron detector signals. These noise measurements were used to investigate the effects of inlet coolant temperature, core flow, reactor power, and random heat transfer fluctuations on the noise-inferred coolant velocities. The effect on the inferred velocities of varying in-core neutron detector and core-exit thermocouple locations was also investigated. Theoretical models of temperature noise were developed, and the results were used to interpret the experimental measurements.Results of these studies indicate that the neutron detector/thermocouple phase is useful for monitoring core flow in PWRs. Our results show that the interpretation of the phase between these signals depends on the source of temperature noise, the response times and locations of the sensors, and the neutron dynamics of the reactor. At Sequoyah-1 we found that the in-core neutron detector/core-exit thermocouple phase can be used to infer in-core coolant velocities, provided that the measurements are corrected for the thermocouple response time.     

Recovery of saturated signal waveform acquired from high-energy particles with artificial neural networks

Artificial neural networks(ANNs) are a core component of artificial intelligence and are frequently used in machine learning. In this report, we investigate the use of ANNs to recover the saturated signals acquired in highenergy particle and nuclear physics experiments. The inherent properties of the detector and hardware imply that particles with relatively high energies probably often generate saturated signals. Usually, these saturated signals are discarded during data processing, and therefore, some useful information is lost. Thus, it is worth restoring the saturated signals to their normal form. The mapping from a saturated signal waveform to a normal signal waveform constitutes a regression problem. Given that the scintillator and collection usually do not form a linear system, typical regression methods such as multi-parameter fitting are not immediately applicable. One important advantage of ANNs is their capability to process nonlinear regression problems.To recover the saturated signal, three typical ANNs were tested including backpropagation(BP), simple recurrent(Elman), and generalized radial basis function(GRBF)neural networks(NNs). They represent a basic network structure, a network structure with feedback, and a network structure with a kernel function, respectively. The saturated waveforms were produced mainly by the environmental gamma in a liquid scintillation detector for the China Dark Matter Detection Experiment(CDEX). The training and test data sets consisted of 6000 and 3000 recordings of background radiation, respectively, in which saturation was simulated by truncating each waveform at 40% of the maximum signal. The results show that the GBRF-NN performed best as measured using a Chi-squared test to compare the original and reconstructed signals in the region in which saturation was simulated. A comparison of the original and reconstructed signals in this region shows that the GBRF neural network produced the best performance. This ANN demonstrates a powerful efficacy in terms of solving the saturation recovery problem. The proposed method outlines new ideas and possibilities for the recovery of saturated signals in high-energy particle and nuclear physics experiments. This study also illustrates an innovative application of machine learning in the analysis of experimental data in particle physics.     

Diagnostics of core barrel vibrations by in-core and ex-core neutron noise

Diagnostics of core-barrel vibrations has traditionally been made by use of ex-vessel neutron detector signals. We suggest that in addition to the ex-core noise, also the in-core noise, induced by core barrel vibrations, be also used. This would enhance the possibilities of diagnostics where the number of the ex-core detectors is not sufficient or their positions are disadvantageous for effective diagnostics, especially for shell-mode vibrations.

To this order, the theory of in-core noise induced by a fluctuating core boundary has been elaborated and applied to the diagnostics of beam and shell mode vibrations. The formulas were tested on some measurements taken in the Ringhals PWRs. The results confirm the validity of the model itself, and the possibilities for enhanced diagnostics were demonstrated. A more effective use of these novel possibilities requires more in-core detectors and/or better detector positioning.     

用于在线测量反应堆内热中子相对通量密度分布的闪烁体光纤探测器研究

闪烁体光纤探测器采用双探头甄别中子信号,利用252 Cf裂变源对探测器系统进行了测试,并与3 He计数管的计数进行了对比。在启明星1#上进行了热中子相对通量密度分布的测量,结合Geant4得到的不同能量段的中子转化率及MCNPX模拟得到的反应堆中子能谱,对探测器进行了相对效率刻度,测试结果与固体核径迹探测器测得的裂变率分布进行了对比。测量结果表明,闪烁体光纤探测器对于252 Cf中子源的响应基本符合点源的衰减趋势,与3 He计数管的测量结果符合较好。在启明星1#热区测得的热中子相对通量密度分布与固体核径迹探测器测量到的结果一致,快区测得的热中子相对通量密度分布与3 He计数管的测量结果及MCNPX的模拟结果符合较好。测量结果为闪烁体光纤探测器的研究提供了较好的实验依据。     

组合式核测量探测器研究

通过合理组合涂硼计数管和γ补偿电离室,在计算机辅助分析和改进涂硼技术的基础上,研制能够覆盖反应堆中子通量的全量程中子核测量探测器。该探测器保持了计数管和电离室的灵敏度,可减少堆外探测孔道和探测器数量,为源区中子测量的准确性和可靠性提供冗余通道,确保反应堆临界安全和核安全。     

Application of forward and adjoint Monte Carlo coupling technique to detector system designs

Forward and adjoint Monte Carlo coupling technique has been developed for analyzing neutron streaming in a system with large geometry. Particles (neutron and adjoint particle) are scored by surface type estimators such as the next event surface crossing estimators and the boundary crossing estimators. The detector response is calculated by folding the calculated neutron and adjoint angular fluxes. The reliability and efficiency for this method were studied by solving a sample problem of neutron streaming through narrow sodium pipe embedded in an iron shield. This method turned out to give a figure of merit several times better than the conventional method. The applicability of the method to detector system design has been demonstrated by calculating the signal to noise ratio for the fuel failure detector with delayed neutron detection method, which is located behind the reactor shield of concrete. This method gives an advantage in clarifying the spatial channels for neutron streaming.     

Borssele PWR noise: Measurements, analysis and interpretation

In the Borssele reactor — a 450 MWe PWR — reactor noise measurements have been performed during four fuel cycles. Measurements were made with a set of ex-core neutron detectors, on one occasion an in-core displacement transducer, and with primary coolant pressure sensors. Digital analysis was applied, where the most powerful tool was the computer programme FAST, which computes auto and cross power spectra for all combinations from a set of many simultaneously recorded signals.

Analyses of neutronic signals show a reactivity noise peak at 9.2 Hz, core barrel motion peaks at about 12 and 15 Hz, a damped oscillation at about 2 Hz. Results are given for begin and end of each fuel cycle. The r.m.s. value of the low frequency noise appears to depend linearly on the boron concentration over a wide range.

Also some results of primary coolant pressure noise are presented, with coherent peaks below 15 Hz and incoherent peaks above.

The second part of the paper describes an alternative way of analyzing and interpreting noise spectra, namely attempts to decompose the neutronic power spectra into physical components, using the information present in the CPSD's of all detector combinations. The components are characterized by their detector position dependency. Effects considered are: uncorrelated noise, global reactivity noise, core motion attenuation noise, and a possible coupling between reactivity and core motion. Results show excellent separation into reactivity and core motion components with possibilities to separate overlapping peaks. Weak peaks become more easily detectable. At low frequencies the decomposition of the spectra is not yet complete, however.     

球形^3He正比计数器物理性能研究

~3He正比计数器是理想的热中子探测器。本文给出了两种气压条件下球形~3He正比计数器的热中子探测效率、能最响应、几何响应等物理性能的计算和测量结果。为更好地设计和使用此类探测器提供了依据。     

Development of Prototype Neutron Flux Monitor for ITER

The prototype neutron flux monitor consists of a high purity 235U fission chamber detector and a “blank” detector, which is a fissile material free detector with the same dimension as the fission chamber detector to identify noise issues such as noise coming from gamma rays. The main parameters of the fission chamber assembly that have been measured in the laboratory are confirmed to approach the technological level of the International Thermonuclear Experimental Reactor (ITER) in the near future. This prototype neutron flux monitor will be further developed to become a neutron flux monitor suitable for the operation phase of D-D fusion on the ITER.     

Noise analysis performed at the sodium cooled power reactor KNK I for malfunction diagnosis and plant surveillance

In order to use neutron noise analysis as an effective tool for early malfunction detection it is necessary to identify the driving forces and to calculate their contributions to the power fluctuations. In this paper the influence of a considerable number of measured noise sources on neutron noise within a large frequency range (10⁻³ Hz to 10³ Hz) is investigated for the sodium cooled power reactor KNK I (thermal core, 58 MW_th).

The experimental basis for the analysis is numerous records of the following signals at various power levels: neutron noise which has been measured with an in-core fission chamber and 3 ex-core ionisation chambers; the sodium inlet temperature and the coolant flow in both primary coolant loops and the movement of the control rods. In addition signals from acoustic-, seismic- and pressure transducers and the coolant outlet temperature were collected.

The influence of the thermohydraulic- and of the control system on neutron noise has also been calculated by means of the relations for linear and multiple-input systems. Important for this analysis is the reactivity-power transfer function. Calculations of this function could be confirmed by measurements using a pseudo-random binary signal as reactivity input.

The following results were obtained from the analysis of the auto-power spectral densities of the neutron flux: Fluctuations of the coolant inlet temperature and the coolant flow are relatively small sources for neutron noise. However, reactivity adjustments resulting from the automatic control system because of the inherent instability of the reactor turned out to be an important driving force.

The influence of still unknown driving forces increased considerably with the reactor power. Since the coolant flow was proportional to the reactor power in order to keep the coolant temperature constant, this result indicates that turbulent flow must have induced stochastical movements of core components. These movements are considered to have mainly caused the unknown reactivity driving forces. Their magnitude could be determined reliably only in the frequency range, in which external feedback mechanisms through the primary coolant system were negligible. For 30 to 50 % reactor power the contribution was about 30 % (for f > 5·10⁻³ Hz) and for full power it increased to about 80 % (for f > 5·10⁻² Hz) of the measured neutron noise. For frequencies > 5 Hz the white detection noise prevails. Single peaks in this frequency region could be explained by coherence function investigations between in-core and ex-core neutron detector signals and by correlation of these signals with displacement- and pressure fluctuations.

Though the measured neutron noise could not be unambiguously related to driving forces, the combination of analytical and empirical methods makes the results also applicable for the design of surveillance techniques for other sodium cooled reactors (e.g. LMFBRs). Examples for possible applications are given.     

Analysis of an MTC noise measurement performed in ringhals-2 using gamma-thermometers and in-core neutron detectors

A noise measurement in the Swedish Ringhals-2 PWR was performed in January 2002 by using twelve gamma-thermometers and two in-core neutron detectors, all located on the same axial level in the reactor. The gamma-thermometers are very versatile tools since they allow estimating the core-averaged moderator temperature noise throughout the core. This core-averaged temperature noise was then used to estimate the MTC by noise analysis, via a new MTC noise estimator. It was shown that whatever the location of the neutron detector might be, the MTC is always correctly estimated by this new MTC noise estimator, without any calibration to a known value of the MTC prior to the noise measurement. For the purpose of comparisons, the MTC was also estimated by using a single gamma-thermomemeter and a single core-exit thermocouple, together with an in-core neutron detector. In such cases, the MTC was systematically underestimated, with a stronger bias for the core-exit thermocouple than for the gamma-thermometer. This shows that the main reason of the MTC underestimation by noise analysis in all the experimental work until now was due to the radially non-homogeneous temperature noise throughout the core. The resulting deviation from point-kinetics of the reactor response has a negligible effect.     

Calculation of the ex-core neutron noise induced by individual fuel assembly vibrations in two PWR cores

Calculation of the neutron noise induced by fuel assembly vibrations in two pressurized water reactor(PWR) cores has been conducted to investigate the effect of cycle burnup on the properties of the ex-core detector noise. An extension of the method and the computational models of a previous work have been applied to two different PWR cores to examine a hypothesis that fuel assembly vibrations cause the corresponding peak in the auto power spectral density(APSD) increase during the cycle. Stochastic vibrations along a random two-dimensional trajectory of individual fuel assemblies were assumed to occur at different locations in the cores. Two models regarding the displacement amplitude of the vibrating assembly have been considered to determine the noise source. Then, the APSD of the ex-core detector noise was evaluated at three burnup steps. The results show that there is no monotonic tendency of the change in the APSD of ex-core detector; however, the increase in APSD occurs predominantly for peripheral assemblies. When assuming simultaneous vibrations of a number of fuel assemblies uniformly distributed over the core, the effect of the peripheral assemblies dominates the ex-core neutron noise.This behaviour was found similar in both cores.     

可控中子源中子-伽马测井仪中屏蔽结构的优化

本文设计了一种使用遗传算法调用蒙特卡罗计算软件MCNP的方案,用以优化设计中子-伽马测井仪中的屏蔽结构。以D-D聚变中子源和BGO探测器为研究对象,以最小化探测器内的辐照本底为优化目标,设计出了3种不同厚度的屏蔽结构。模拟结果表明,这些屏蔽结构具有优异的屏蔽性能,可有效地降低探测器中的辐射本底。