Aquilino Senra Martinez

Basic investigations related to genetic algorithms in core designs

Abstract The use of genetic algorithms as a tool to improve nuclear reactor core design optimization is proposed. A method based on genetic algorithms are developed to solve optimization problems that involve cell parameters adjustment. In this paper we address a global optimization approach to nuclear reactor core design problems. In previous work, a great variety of local optimization method have been applied in such a kind of problems. In order to illustrate the performance, we apply the method based on genetic algorithms to two traditional test problems that have been considered in literature. These test problems describe the principal framework of the approach proposed, because they have known optimal solutions. Due to the global exploitation capacity and independence of prior knowledge of the search space characteristics proportioned by the genetic algorithms the application scope was extended. The method was applied to optimize a more complex problem, to which traditional methods do not apply. The goal of this third problem is to minimize the average peak factor in a three enrichment zone reactor by the adjust of the fuel radii, cladding thickness, equivalent radii, the three zone enrichments, fuel material and cladding material. In this case a qualitative analysis of the results is made.

Formulation for the Calculation of Reactivity Without Nuclear Power History

This paper presents a new method for the solution of the inverse point kinetics equation. This method is based on the integration by parts of the integral of the inverse point kinetics equation, which results in a power series in terms of the nuclear power in time dependence. With the imposition of conditions to the nuclear power, the reactivity is represented as first and second derivatives of this nuclear power. This new calculation method for reactivity has very special characteristics, amongst which the possibility of using longer sampling period, and the possibility of restarting the calculation, after its interruption, allowing the calculation of reactivity in a non-continuous way. Beside that, the reactivity can be obtained independent of the nuclear power memory.

Adaptive vector quantization optimized by genetic algorithm for real-time diagnosis through fuzzy sets

The accurate diagnosis of accidents in a nuclear power plant has fundamental importance for decision making necessary to mitigate their consequences for the power plant as well as for the general public, on the basis of emergency planning. Two main characteristics should be achieved in this kind of diagnostics, namely, real-time features and adaptive capacity. The first characteristic gives the operators the possibility of predicting degraded operations and monitoring critical safety functions related to that specific situation. The second one allows the system to be able to deal with accidents that were not incorporated in the training sample set, in which case the operators are unprepared because they were not trained to face an event that they did not observe even in simulator training. The Three Mile Island accident is a classic one to demonstrate that these kinds of events are possible. Several methodologies have been tried to match those characteristics. While the first one is achieved through the permanent evolution ofnew faster processors, the second one can only be achieved through the simulation of human cognitive processes, which show higher adaptive behavior. Our model utilizes a neural network, fuzzy sets, and a genetic algorithm to simulate that behavior. We have used a neural network activated by an additive model and trained with an unsupervised competitive training law. Once trained with three accidents (steam generator tube rupture, blackout, and loss-of-coolant accident), a synaptic matrix was obtained, in which the elements represent the interchanging weights between neurons in the concatenated input/output space and the competitive neurons that fight to encode the input-output vector. This kind of competition establishes a statistical classification of the state variables, changing with time, clustering them in centroids labeling the kind of accident for which variables are being sampled. Thus, the accident identification is done in real time with the synaptic matrix. However, the centroids are located in the same time value, in view of the fact that the neural network algorithm treats the variable time as an independent one. Therefore, a genetic algorithm is applied to a fuzzy system formed by the partition of the variables space with fuzzy sets determined by the neural network centroids, in order to estimate the optimal positions in the time variable where the fuzzy system centroids must be located. As a consequence, the diagnostic can be done in representative regions of each accident with maximum confidence.

The dependence of practical width on temperature

Abstract Practical width has frequently been used to establish the type of resonance in determining the cell neutron flux according to NR, IR or WR (narrow, intermediate and wide Resonance) approximations. The literature on the subject disregards the dependence on temperature for practical width calculation, mainly if it aims at determining the type of resonance. This paper presents a method for practical width calculation including temperature dependence. It also introduces a new procedure for Doppler broadening function calculation. The results provide evidence that practical width varies considerably with temperature.

The derivation of the doppler broadening function using frobenius method

An analytical approximation of the Doppler broadening function ψ(ξ,x) is proposed. This approximation is based on the solution of the differential equation for ψ(ξ,x) using the methods of Frobenius and parameters variation. The analytical form derived for ψ(ξ,x) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances, mainly for calculations of multigroup parameters and resonances self-protection factors, the latter being used to correct microscopic cross section measurements by the activation technique.

Intelligent soft computing in nuclear engineering in Brazil

Abstract Nuclear reactor design and operation often involve important human cognition and decisions. Design optimization, transient diagnosis and core reload optimization, are examples of complex tasks faced during a nuclear reactor design or operation. In order to handle such kind of tasks expert knowledge is required. Due to the complexity involved in the cognition and decisions to be taken, computerized systems have been intensely explored in order to aid design and operation. Following hardware advances, soft computing has been improved and, nowadays, intelligent technologies, such as evolutionary programming, neural networks, expert systems and fuzzy systems are being used to support design and operation. This work presents applications of intelligent Soft Computing (ISC) to three important cognition problems which are: the nuclear reactor design, the core reload optimization and transient diagnosis.

On Approximations to the Neutron Escape Probability from an Absorbing Body

AbstractThe mathematical problem of approximating the neutron escape probability junction is studied through an analysis of the moment expansion of the junction. The problem with possible divergence of the expansion is identified and avoided by devising an alternative based on physical arguments. An approximation of general validity for any convex geometry is thus deduced that is simple, accurate, and convenient for use. As examples, numerical results are presented for three geometries: a sphere, a cylinder, and a slab.

Depletion Calculation for a Nodal Reactor Physics Code

This paper deals with an alternative numerical method for calculating depletion and production chains of the main isotopes found in a pressurized water reactor. It is based on the use of the exponentiation procedure coupled to orthogonal polynomial expansion to compute the transition matrix associated with the solution of the differential equations describing isotope concentrations in the nuclear reactor. Actually, the method was implemented in an automated nuclear reactor core design system that uses a quick and accurate 3D nodal method, the Nodal Expansion Method (NEM), aiming at solving the diffusion equation describing the spatial neutron distribution in the reactor. This computational system, besides solving the diffusion equation, also solves the depletion equations governing the gradual changes in material compositions of the core due to fuel depletion. The depletion calculation is the most time-consuming aspect of the nuclear reactor design code, and has to be done in a very precise way in order to obtain a correct evaluation of the economic performance of the nuclear reactor. In this sense, the proposed method was applied to estimate the critical boron concentration at the end of the cycle. Results were compared to measured values and confirm the effectiveness of the method for practical purposes.Copyright

A New Approach for Transient Identification with “Don’t Know” Response Using Neural Networks

In the last years, many different approaches based on neural network (NN) have been proposed for transient identification in nuclear power plants (NPPS). Some of them focus the dynamic identification using recurrent neural networks, however, they are not able to deal with unrecognized transients. Other kind of solution uses competitive learning in order to allow the “don’t know” response. In this case, dynamic features are not well represented.

Correcting the Cusping Problem in Three-Dimensional Transients through NEM Modification

Abstract Cross sections are homogenized over an entire node in nodal model implementation. The presence of a control rod (CR) partially inserted in the node has occasioned axial heterogeneity and generates a homogenization problem. If the homogenization process is only the volume-weighted average for nuclear parameters, the calculation of the multiplication factor and power in steady-state problems may mean relevant errors and for time-dependent problems may have caused the well-known cusping problem, which arises in three-dimensional transient simulations with CR motions. The major purpose of this technical note is to introduce an alternative method, based on the nodal expansion method, to deal with partially inserted CRs in nodes. One-dimensional equations, acquired through transverse integration of the neutron diffusion equation, have been modified to formulate the alternative method, which was evaluated in a transient problem. Furthermore, the alternative method gives satisfactory results and corrects the cusping effect in the case analyzed in this technical note.