N.S. Garis

Determination of PWR control rod position by core physics and neural network methods

A method is described by which the axial position of a control rod can be determined. The method is based on the influence of a partially inserted control rod on the axial flux profile. By measuring this flux profile, the control rod position can be in principle unfolded. One problem is however that the relationship between rod position and flux profile is rather implicit and cannot be explicitly inverted. Thus, it is suggested here to use neural network techniques to unfold the rod position from the measured flux profile. For training of the network, a large number of flux profiles are needed, corresponding to various known rod positions. These data can be generated by advanced core calculational codes. In this study, the Studsvik core master system SIMULATE was used. The method was tested with good results on both fully simulated data as well as on a measurement taken at the Swedish pressurized water reactor Ringhals 4.

Feasibility study on transient identification in nuclear power plants using support vector machines

Support vector machines (SVMs), a relatively new paradigm in statistical learning theory, are studied for their potential to recognize transient behavior of detector signals corresponding to various accident events at nuclear power plants (NPPs). Transient classification is a major task for any computer-aided system for recognition of various malfunctions. The ability to identify the state of operation or events occurring at an NPP is crucial so that personnel can select adequate response actions. The Modular Accident Analysis Program, version 4 (MAAP4) is a program that can be used to model various normal and abnormal events in an NPP. This study uses MAAP signals describing various loss-of-coolant accidents in boiling water reactors. The simulated sensor readings corresponding to these events have been used to train and test SVM classifiers. SVM calculations have demonstrated that they can produce classifiers with good generalization ability for our data. This in turn indicates that SVMs show promise as classifiers for the learning problem of identifying transients.

Some developments in core-barrel vibration diagnostics

Abstract Diagnostics of core-barrel motion, and notably that of beam mode vibrations, has been usually performed by two distinct concepts. One strategy is to perform a qualitative analysis in the time domain, using descriptors such as vibration trajectory, probability distributions etc. This approach is rather realistic in the sense that it allows for general anisotropic pendular vibrations. The other strategy is to use frequency analysis with the goal of quantifying certain vibration properties. However, this second approach could so far handle only isotropic and unidirectional vibrations. In this paper we propose a unification of these two approaches by introducing a model by which general anisotropic vibrations can be quantified in the frequency domain. However, when separating the noise components prior to the frequency analysis, we suggest the use of symmetry properties of the noise in the time domain, based on reactor physics assumptions, as opposed to the earlier methods that use statistical independence of the components. Due to the unified approach, a combination of time and frequency domain analysis methods can be used for presentation and maximum information extraction.

Spectrum of one-speed Neutron transport operator with reflective boundary conditions in slab geometry

Abstract The time eigenvalue spectrum of the one-speed neutron transport equation has been investigated in the case of an infinite slab with reflective boundary conditions and isotropic scattering. The region Re ( ) v Σ t , too, is mainly contained in the resolvent set of the operator, the continuous spectrum consisting of only a set of discrete lines. Further it is shown that a finite number of real decay constants also exist in this region. We also give an upper limit for the magnitude of these eigenvalues. The analysis is supported by numerical calculations.

Development of an encapsulated scintillating fiber detector as a 14-MeV neutron sensor☆

Abstract A scintillating fiber detector has been developed and tested for use as a 14-MeV neutron sensor. The detector, designated an “Encapsulated Scintillating Fiber Detector (EFD)”, is composed of a parallel array of 0.5 × 0.5 × 15 mm BCF-12 plastic scintillating fibers encapsulated in clear BC-600 optical cement. The 85 fibers from a 12 × 12 mm square array, with a separation gap of 0.8–1 mm, in the center of the 40 mm diameter × 15 mm thick hardened optical cement. It can be directly coupled to an ordinary 2 in. diameter photomultiplier tube and its simple electronics. The response of the detector to gamma-rays from isotopic sources, as well as to 2.6- and 14-MeV monoenergetic neutrons from a neutron generator has been evaluated. The detector shows 3 distinct properties simultaneously, i.e. (1) good gamma-ray pulse height reduction, (2) discrimination against 14-MeV neutrons entering at angles non-parallel to the fiber axis, and (3) production of a full energy peak of 14-MeV recoil protons in the direction of the fiber axes. Investigations by Monte Carlo simulation are also included.

Eigenvalues for reflecting boundary conditions in one-speed neutron transport theory

Abstract The spectrum of criticality eigenvalues for the one-speed neutron transport equation has been studied for an infinite slab with reflexion coefficients R 1 and R 2 at the surfaces. For R 1 = R 2 = −1 or +1 the problem can be solved exactly. In another case, R 1 = −1 and R 2 = 0, the problem is simplified considerably. When both reflexion coefficients are close to unity the criticality eigenvalues follow a very accurate approximation formula. For the high-order eigenvalues a semi-empirical formula is given. Some results have also been obtained for the corresponding time-dependent problems.

The feasibility of using plastic scintillation fibers for fast neutron spectrometry

The response functions of a plastic scintillation fiber for a fast neutron beam have been studied in detail using Monte Carlo technique. The study shows that a bundle of plastic scintillation fibers can be used as a simple and high efficiency fast neutron spectrometer when high energy resolution is not required. The efficiency and resolution, for 14 MeV incident neutrons, of a bundle of 100 square fibers at thickness of 0.25 mm are estimated at (4.2±0.2)×10−5 cm2 and (8.7±0.1)%, respectively, for extra mural absorber (EMA) coated fiber (4.7% for a fiber without EMA).

Simulation of the neutron and proton transport in the 14 MeV neutron time-of-flight spectrometer, TANSY

A Monte Carlo code simulating the neutron and proton transport in the spectrometry TANSY has been written in order to obtain more accurate knowledge of the response functions. TANSY is a combined proton-recoil and neutron time-of-flight spectrometer for 14 MeV neutrons to be used for fusion plasma diagnostics at the Joint European Torus (JET). In the code developed, the simulation starts with a sampled neutron scattering point in a polyethylene foil followed by a uniformly sampled position of the surface of one of 16 neutron detectors. In the foil an (n,p) scattering occures and the transport of the recoil proton and the scattered neutron is simulated. For the recoil proton, passing through the foil, effects of stopping power and energy straggling are considered. The neutron transport in the scintillator detector is simulated until either a signal has occured or the remaining neutron energy is less than 100 keV. Multiply scattered neutrons in the neutron detector are allowed to “build up” a signal until a bias level is exceeded. The results from Monte Carlo calculations have been compared with measurements using 14 MeV neutrons from a neutron generator, and a good agreement was obtained. Comparing Monte Carlo calculations and measurements it has also been possible to estimate the energy spread of the neutron generator to 173 keV at a beam energy of 300 keV and a reaction angle of 90°. For a foil thickness of 0.95 mg/cm2 the Monte Carlo calculations gave as result the efficiency (1.38 ± 0.01) × 10−5cm2 and the resolution 155.1 ± 0.2 keV for the complete spectrometer.

On the Neutron Noise Diagnostics of Pressurized Water Reactor Control Rod Vibrations —IV: Application of Neural Networks

A neutron noise-based technique for the localization of excessively vibrating control rods is elaborated upon in the previous three papers of this series. The method is based on the inversion of a formula that expresses the auto- and cross spectra of three neutron detector signals through the parameters of the vibrating rod, i.e., equilibrium position and displacement components. Successful tests of the algorithm with both simulated and real data were reported in the previous papers. The algorithm had nevertheless certain drawbacks, namely, that its use requires expert knowledge, the redundancy of extra detectors cannot be utilized, and with realistic transfer functions the calculations are rather lengthy. The use of neural networks offers an alternative way of performing the inversion procedure. This possibility was investigated by constructing a network that was trained to determine the rod position from the detector spectra. It was found that all shortcomings of the traditional localization method can be eliminated. The neural network-based identification was also tested with success.

Modelling of a vibrating reactor boundary and calculation of the induced neutron noise

Abstract Three different models of a moving (vibrating) reactor boundary in time-dependent diffusion theory are investigated. The models are: (a) a localized absorber of variable strength at the boundary (equivalent to a perturbational treatment); (b) a time-varying extrapolation length; (c) explicit treatment of the moving boundary with a new transformation technique. The induced neutron noise was calculated in first order of the perturbation parameter both exactly and in the adiabatic approximation. All three models lead to equivalent results, confirming the applicability of perturbation techniques in treating moving perturbations (e.g. vibrating control rods). Application of the adiabatic approximation in model (c) required the extension of the Henry formalism, i.e. the use of orthogonality relations expressed as integrals over the system, to cases with non-constant system volume. The incentives for investigating a time-varying boundary arose from problems related to vibrating control rods; however, the results have some general relevance for systems with a varying volume such as gaseous core or liquid fuel reactors.