Development of a methodology for nuclear data uncertainty propagation on isotopic evolution calculations for advanced nuclear systems

Una apropiada evaluación de los márgenes de seguridad de una instalación nuclear, por ejemplo, una central nuclear, tiene en cuenta todas las incertidumbres que afectan a los cálculos de diseño, funcionanmiento y respuesta ante accidentes de dicha instalación. Una fuente de incertidumbre son los datos nucleares, que afectan a los cálculos neutrónicos, de quemado de combustible o activación de materiales. Estos cálculos permiten la evaluación de las funciones respuesta esenciales para el funcionamiento correcto durante operación, y también durante accidente. Ejemplos de esas respuestas son el factor de multiplicación neutrónica o el calor residual después del disparo del reactor. Por tanto, es necesario evaluar el impacto de dichas incertidumbres en estos cálculos. Para poder realizar los cálculos de propagación de incertidumbres, es necesario implementar metodologías que sean capaces de evaluar el impacto de las incertidumbres de estos datos nucleares. Pero también es necesario conocer los datos de incertidumbres disponibles para ser capaces de manejarlos. Actualmente, se están invirtiendo grandes esfuerzos en mejorar la capacidad de analizar, manejar y producir datos de incertidumbres, en especial para isótopos importantes en reactores avanzados. A su vez, nuevos programas/códigos están siendo desarrollados e implementados para poder usar dichos datos y analizar su impacto. Todos estos puntos son parte de los objetivos del proyecto europeo ANDES, el cual ha dado el marco de trabajo para el desarrollo de esta tesis doctoral. Por tanto, primero se ha llevado a cabo una revisión del estado del arte de los datos nucleares y sus incertidumbres, centrándose en los tres tipos de datos: de decaimiento, de rendimientos de fisión y de secciones eficaces. A su vez, se ha realizado una revisión del estado del arte de las metodologías para la propagación de incertidumbre de estos datos nucleares. Dentro del Departamento de Ingeniería Nuclear (DIN) se propuso una metodología para la propagación de incertidumbres en cálculos de evolución isotópica, el Método Híbrido. Esta metodología se ha tomado como punto de partida para esta tesis, implementando y desarrollando dicha metodología, así como extendiendo sus capacidades. Se han analizado sus ventajas, inconvenientes y limitaciones. El Método Híbrido se utiliza en conjunto con el código de evolución isotópica ACAB, y se basa en el muestreo por Monte Carlo de los datos nucleares con incertidumbre. En esta metodología, se presentan diferentes aproximaciones según la estructura de grupos de energía de las secciones eficaces: en un grupo, en un grupo con muestreo correlacionado y en multigrupos. Se han desarrollado diferentes secuencias para usar distintas librerías de datos nucleares almacenadas en diferentes formatos: ENDF-6 (para las librerías evaluadas), COVERX (para las librerías en multigrupos de SCALE) y EAF (para las librerías de activación). Gracias a la revisión del estado del arte de los datos nucleares de los rendimientos de fisión se ha identificado la falta de una información sobre sus incertidumbres, en concreto, de matrices de covarianza completas. Además, visto el renovado interés por parte de la comunidad internacional, a través del grupo de trabajo internacional de cooperación para evaluación de datos nucleares (WPEC) dedicado a la evaluación de las necesidades de mejora de datos nucleares mediante el subgrupo 37 (SG37), se ha llevado a cabo una revisión de las metodologías para generar datos de covarianza. Se ha seleccionando la actualización Bayesiana/GLS para su implementación, y de esta forma, dar una respuesta a dicha falta de matrices completas para rendimientos de fisión. Una vez que el Método Híbrido ha sido implementado, desarrollado y extendido, junto con la capacidad de generar matrices de covarianza completas para los rendimientos de fisión, se han estudiado diferentes aplicaciones nucleares. Primero, se estudia el calor residual tras un pulso de fisión, debido a su importancia para cualquier evento después de la parada/disparo del reactor. Además, se trata de un ejercicio claro para ver la importancia de las incertidumbres de datos de decaimiento y de rendimientos de fisión junto con las nuevas matrices completas de covarianza. Se han estudiado dos ciclos de combustible de reactores avanzados: el de la instalación europea para transmutación industrial (EFIT) y el del reactor rápido de sodio europeo (ESFR), en los cuales se han analizado el impacto de las incertidumbres de los datos nucleares en la composición isotópica, calor residual y radiotoxicidad. Se han utilizado diferentes librerías de datos nucleares en los estudios antreriores, comparando de esta forma el impacto de sus incertidumbres. A su vez, mediante dichos estudios, se han comparando las distintas aproximaciones del Método Híbrido y otras metodologías para la porpagación de incertidumbres de datos nucleares: Total Monte Carlo (TMC), desarrollada en NRG por A.J. Koning y D. Rochman, y NUDUNA, desarrollada en AREVA GmbH por O. Buss y A. Hoefer. Estas comparaciones demostrarán las ventajas del Método Híbrido, además de revelar sus limitaciones y su rango de aplicación. ABSTRACT For an adequate assessment of safety margins of nuclear facilities, e.g. nuclear power plants, it is necessary to consider all possible uncertainties that affect their design, performance and possible accidents. Nuclear data are a source of uncertainty that are involved in neutronics, fuel depletion and activation calculations. These calculations can predict critical response functions during operation and in the event of accident, such as decay heat and neutron multiplication factor. Thus, the impact of nuclear data uncertainties on these response functions needs to be addressed for a proper evaluation of the safety margins. Methodologies for performing uncertainty propagation calculations need to be implemented in order to analyse the impact of nuclear data uncertainties. Nevertheless, it is necessary to understand the current status of nuclear data and their uncertainties, in order to be able to handle this type of data. Great eórts are underway to enhance the European capability to analyse/process/produce covariance data, especially for isotopes which are of importance for advanced reactors. At the same time, new methodologies/codes are being developed and implemented for using and evaluating the impact of uncertainty data. These were the objectives of the European ANDES (Accurate Nuclear Data for nuclear Energy Sustainability) project, which provided a framework for the development of this PhD Thesis. Accordingly, first a review of the state-of-the-art of nuclear data and their uncertainties is conducted, focusing on the three kinds of data: decay, fission yields and cross sections. A review of the current methodologies for propagating nuclear data uncertainties is also performed. The Nuclear Engineering Department of UPM has proposed a methodology for propagating uncertainties in depletion calculations, the Hybrid Method, which has been taken as the starting point of this thesis. This methodology has been implemented, developed and extended, and its advantages, drawbacks and limitations have been analysed. It is used in conjunction with the ACAB depletion code, and is based on Monte Carlo sampling of variables with uncertainties. Different approaches are presented depending on cross section energy-structure: one-group, one-group with correlated sampling and multi-group. Differences and applicability criteria are presented. Sequences have been developed for using different nuclear data libraries in different storing-formats: ENDF-6 (for evaluated libraries) and COVERX (for multi-group libraries of SCALE), as well as EAF format (for activation libraries). A revision of the state-of-the-art of fission yield data shows inconsistencies in uncertainty data, specifically with regard to complete covariance matrices. Furthermore, the international community has expressed a renewed interest in the issue through the Working Party on International Nuclear Data Evaluation Co-operation (WPEC) with the Subgroup (SG37), which is dedicated to assessing the need to have complete nuclear data. This gives rise to this review of the state-of-the-art of methodologies for generating covariance data for fission yields. Bayesian/generalised least square (GLS) updating sequence has been selected and implemented to answer to this need. Once the Hybrid Method has been implemented, developed and extended, along with fission yield covariance generation capability, different applications are studied. The Fission Pulse Decay Heat problem is tackled first because of its importance during events after shutdown and because it is a clean exercise for showing the impact and importance of decay and fission yield data uncertainties in conjunction with the new covariance data. Two fuel cycles of advanced reactors are studied: the European Facility for Industrial Transmutation (EFIT) and the European Sodium Fast Reactor (ESFR), and response function uncertainties such as isotopic composition, decay heat and radiotoxicity are addressed. Different nuclear data libraries are used and compared. These applications serve as frameworks for comparing the different approaches of the Hybrid Method, and also for comparing with other methodologies: Total Monte Carlo (TMC), developed at NRG by A.J. Koning and D. Rochman, and NUDUNA, developed at AREVA GmbH by O. Buss and A. Hoefer. These comparisons reveal the advantages, limitations and the range of application of the Hybrid Method.

Fully adaptive gaussian mixture metropolis-hastings algorithm

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples from generic multimodal and multidimensional target distributions. The proposal density is a mixture of Gaussian densities with all parameters (weights, mean vectors and covariance matrices) updated using all the previously generated samples applying simple recursive rules. Numerical results for the one and two-dimensional cases are provided.

Mode matches and their locations in the hydrophobic free energy sequences of peptide ligands and their receptor eigenfunctions

Patterns in sequences of amino acid hydrophobic free energies predict secondary structures in proteins. In protein folding, matches in hydrophobic free energy statistical wavelengths appear to contribute to selective aggregation of secondary structures in “hydrophobic zippers.” In a similar setting, the use of Fourier analysis to characterize the dominant statistical wavelengths of peptide ligands’ and receptor proteins’ hydrophobic modes to predict such matches has been limited by the aliasing and end effects of short peptide lengths, as well as the broad-band, mode multiplicity of many of their frequency (power) spectra. In addition, the sequence locations of the matching modes are lost in this transformation. We make new use of three techniques to address these difficulties: (i) eigenfunction construction from the linear decomposition of the lagged covariance matrices of the ligands and receptors as hydrophobic free energy sequences; (ii) maximum entropy, complex poles power spectra, which select the dominant modes of the hydrophobic free energy sequences or their eigenfunctions; and (iii) discrete, best bases, trigonometric wavelet transformations, which confirm the dominant spectral frequencies of the eigenfunctions and locate them as (absolute valued) moduli in the peptide or receptor sequence. The leading eigenfunction of the covariance matrix of a transmembrane receptor sequence locates the same transmembrane segments seen in n-block-averaged hydropathy plots while leaving the remaining hydrophobic modes unsmoothed and available for further analyses as secondary eigenfunctions. In these receptor eigenfunctions, we find a set of statistical wavelength matches between peptide ligands and their G-protein and tyrosine kinase coupled receptors, ranging across examples from 13.10 amino acids in acid fibroblast growth factor to 2.18 residues in corticotropin releasing factor. We find that the wavelet-located receptor modes in the extracellular loops are compatible with studies of receptor chimeric exchanges and point mutations. A nonbinding corticotropin-releasing factor receptor mutant is shown to have lost the signatory mode common to the normal receptor and its ligand. Hydrophobic free energy eigenfunctions and their transformations offer new quantitative physical homologies in database searches for peptide-receptor matches.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.

Sintonia automática do filtro de kalman unscented.

O filtro de Kalman estendido tem sido a mais popular ferramenta de filtragem não linear das últimas quatro décadas. É de fácil implementação e apresenta baixo custo computacional. Nos casos nos quais as não linearidades do sistema dinâmico são significativas, porém, o filtro de Kalman estendido pode apresentar resultados insatisfatórios. Nessas situações, o filtro de Kalman unscented substitui com vantagens o filtro de Kalman estendido, pois pode apresentar melhores estimativas de estado, embora ambos os filtros exibam complexidade computacional de mesma ordem. A qualidade das estimativas de estado do filtro unscented está intimamente ligada à sintonia dos parâmetros que controlam a transformada unscented. A versão escalada dessa transformada exibe três parâmetros escalares que determinam o posicionamento dos pontos sigma e, consequentemente, afetam diretamente a qualidade das estimativas produzidas pelo filtro. Apesar da importância do filtro de Kalman unscented, a sintonia ótima desses parâmetros é um problema para o qual ainda não há solução definitiva. Não há nem mesmo recomendações heurísticas que garantam o bom funcionamento do filtro unscented na maior parte dos problemas tratáveis por meio de filtros Gaussianos. Essa carência e a importância desse filtro para a área de filtragem não linear fazem da busca por mecanismos de sintonia automática do filtro unscented área de pesquisa ativa. Assim, este trabalho propõe técnicas para sintonia automática dos parâmetros da transformada unscented escalada. Além da sintonia desses parâmetros, também é abordado o problema de sintonizar as matrizes de covariância dos ruídos de processo e de medida demandadas pelo modelo do sistema dinâmico usado pelo filtro unscented. As técnicas propostas cobrem então a sintonia automática de todos os parâmetros do filtro.

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (g(max)), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with g(max). In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution.

Cluster analysis of high-dimensional data: A case study

Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.

The cost of uniqueness in groundwater model calibration

Calibration of a groundwater model requires that hydraulic properties be estimated throughout a model domain. This generally constitutes an underdetermined inverse problem, for which a Solution can only be found when some kind of regularization device is included in the inversion process. Inclusion of regularization in the calibration process can be implicit, for example through the use of zones of constant parameter value, or explicit, for example through solution of a constrained minimization problem in which parameters are made to respect preferred values, or preferred relationships, to the degree necessary for a unique solution to be obtained. The cost of uniqueness is this: no matter which regularization methodology is employed, the inevitable consequence of its use is a loss of detail in the calibrated field. This, ill turn, can lead to erroneous predictions made by a model that is ostensibly well calibrated. Information made available as a by-product of the regularized inversion process allows the reasons for this loss of detail to be better understood. In particular, it is easily demonstrated that the estimated value for an hydraulic property at any point within a model domain is, in fact, a weighted average of the true hydraulic property over a much larger area. This averaging process causes loss of resolution in the estimated field. Where hydraulic conductivity is the hydraulic property being estimated, high averaging weights exist in areas that are strategically disposed with respect to measurement wells, while other areas may contribute very little to the estimated hydraulic conductivity at any point within the model domain, this possibly making the detection of hydraulic conductivity anomalies in these latter areas almost impossible. A study of the post-calibration parameter field covariance matrix allows further insights into the loss of system detail incurred through the calibration process to be gained. A comparison of pre- and post-calibration parameter covariance matrices shows that the latter often possess a much smaller spectral bandwidth than the former. It is also demonstrated that, as all inevitable consequence of the fact that a calibrated model cannot replicate every detail of the true system, model-to-measurement residuals can show a high degree of spatial correlation, a fact which must be taken into account when assessing these residuals either qualitatively, or quantitatively in the exploration of model predictive uncertainty. These principles are demonstrated using a synthetic case in which spatial parameter definition is based oil pilot points, and calibration is Implemented using both zones of piecewise constancy and constrained minimization regularization. (C) 2005 Elsevier Ltd. All rights reserved.

The stability of P in coral reef fishes

The constancy of phenotypic variation and covariation is an assumption that underlies most recent investigations of past selective regimes and attempts to predict future responses to selection. Few studies have tested this assumption of constancy despite good reasons to expect that the pattern of phenotypic variation and covariation may vary in space and time. We compared phenotypic variance-covariance matrices (P) estimated for Populations of six species of distantly related coral reef fishes sampled at two locations on Australia's Great Barrier Reef separated by more than 1000 km. The intraspecific similarity between these matrices was estimated using two methods: matrix correlation and common principal component analysis. Although there was no evidence of equality between pairs of P, both statistical approaches indicated a high degree of similarity in morphology between the two populations for each species. In general, the hierarchical decomposition of the variance-covariance structure of these populations indicated that all principal components of phenotypic variance-covariance were shared but that they differed in the degree of variation associated with each of these components. The consistency of this pattern is remarkable given the diversity of morphologies and life histories encompassed by these species. Although some phenotypic instability was indicated, these results were consistent with a generally conserved pattern of multivariate selection between populations.

Investigations into an optimal transmission scheme for a MIMO system operating in a ricain fading environment

This paper describes investigations into an optimal transmission scheme for a multiple input multiple output (MIMO) system operating in a Rician fading environment. The considerations are reduced to determining a covariance matrix of transmitted signals which maximizes the MIMO capacity under the condition that the receiver has perfect knowledge of the channel while the transmitter has the information about selected statistical quantities which are measured at the receiver. An optimal covariance matrix, which requires information of the Rice factor and the signal to noise ratio, is determined. The transmission scheme relying on the choice of the proposed covariance matrix outperforms the other transmission schemes which were reported earlier in the literature. The proposed scheme realizes an upper bound limit for the MIMO capacity under arbitrary Rician fading conditions. ©2005 IEEE

Pragmatic algorithms for implementing geostatistics with large datasets

With the ability to collect and store increasingly large datasets on modern computers comes the need to be able to process the data in a way that can be useful to a Geostatistician or application scientist. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively for likelihood-based Geostatistics. Various methods have been proposed and are extensively used in an attempt to overcome these complexity issues. This thesis introduces a number of principled techniques for treating large datasets with an emphasis on three main areas: reduced complexity covariance matrices, sparsity in the covariance matrix and parallel algorithms for distributed computation. These techniques are presented individually, but it is also shown how they can be combined to produce techniques for further improving computational efficiency.

A comprehensive portfolio construction under stochastic environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. ^ A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: (a) increase the efficiency of the portfolio optimization process, (b) implement large-scale optimizations, and (c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. ^ The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. ^ The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH). ^

A Comprehensive Portfolio Construction Under Stochastic Environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

Robust Stereo Visual Odometry through a Probabilistic Combination of Points and Line Segments

Most approaches to stereo visual odometry reconstruct the motion based on the tracking of point features along a sequence of images. However, in low-textured scenes it is often difficult to encounter a large set of point features, or it may happen that they are not well distributed over the image, so that the behavior of these algorithms deteriorates. This paper proposes a probabilistic approach to stereo visual odometry based on the combination of both point and line segment that works robustly in a wide variety of scenarios. The camera motion is recovered through non-linear minimization of the projection errors of both point and line segment features. In order to effectively combine both types of features, their associated errors are weighted according to their covariance matrices, computed from the propagation of Gaussian distribution errors in the sensor measurements. The method, of course, is computationally more expensive that using only one type of feature, but still can run in real-time on a standard computer and provides interesting advantages, including a straightforward integration into any probabilistic framework commonly employed in mobile robotics.