Application of transport techniques to the analysis of NERVA shadow shields

A radiation shield internal to the NERVA nuclear rocket reactor required to limit the neutron and photon radiation levels at critical components located external to the reactor was evaluated. Two significantly different shield mockups were analyzed: BATH, a composite mixture of boron carbide, aluminum and titanium hydride, and a borated steel-liquid hydrogen system. Based on the comparisons between experimental and calculated neutron and photon radiation levels, the following conclusions were noted: (1) The ability of two-dimensional discrete ordinates code to predict the radiation levels internal to and at the surface of the shield mockups was clearly demonstrated. (2) Internal to the BATH shield mockups, the one-dimensional technique predicted the axial variation of neutron fluxes and photon dose rates; however, the magnitude of the neutron fluxes was about a factor of 1.8 lower than the two-dimensional analysis and the photon dose rate was a factor of 1.3 lower

Implementation of radiation shielding calculation methods. Volume 1: Synopsis of methods and summary of results

The work performed in the following areas is summarized: (1) Analysis of Realistic nuclear-propelled vehicle was analyzed using the Marshall Space Flight Center computer code package. This code package includes one and two dimensional discrete ordinate transport, point kernel, and single scatter techniques, as well as cross section preparation and data processing codes, (2) Techniques were developed to improve the automated data transfer in the coupled computation method of the computer code package and improve the utilization of this code package on the Univac-1108 computer system. (3) The MSFC master data libraries were updated

K-means for massive data

The $K$-means algorithm is undoubtedly one of the most popular clustering analysis techniques, due to its easiness in the implementation, straightforward parallelizability and competitive computational complexity, when compared to more sophisticated clustering alternatives. However, the progressive growth of the amount of data that needs to be analyzed, in a wide variety of scientific fields, represents a significant challenge for the $K$-means algorithm, since its time complexity is dominated by the number of distance computations, which is linear with respect to both the number of instances, $n$, and dimensionality of the problem, $d$. This fact hinders its scalability on such massive data sets. Another major drawback of the $K$-means algorithm corresponds to its high dependence on the initial conditions, which not only may affect the quality of the obtained solution, but may also have a major impact on its computational load, as for instance, a poor initialization could lead to an exponential running time in the worst case scenario. In this dissertation, we tackle all these difficulties. Initially, we propose an approximation to the $K$-means problem, the Recursive Partition-based $K$-means algorithm (RP$K$M). This approach consists of recursively applying a weighted version of $K$-means algorithm over a sequence of spatial-based partitions of the data set, for which each cell of the partition is represented by the center of mass of the points that lie on it. From one iteration to the next, a more refined partition is constructed and the process is repeated using the optimal set of centroids, obtained at the previous iteration, as initialization. From a practical standpoint, such a process reduces the computational load of $K$-means algorithm as the number of representatives, at each iteration, is commonly much smaller than the number of instances of the data set. On the other hand, both phases of the algorithm are embarrasingly parallel. From a theoretical standpoint, and in spite of the selected partition strategy, one can guarantee the non-repetition of the clusterings generated at each RP$K$M iteration, which ultimately implies the reduction of the total amount of $K$-means algorithm iterations, as well as leading, in most of the cases, to a monotone decrease of the overall error function. Afterwards, we present a RP$K$M-type approach, the Boundary Weighted $K$-means algorithm (BW$K$M). For this technique, the data set partition is based on an adaptative mesh, that adjusts the size of each grid cell to maximize the chances of each cell having only instances of the same cluster. The goal is to focus most of the computational resources on those regions where it is harder to determine the correct cluster assignment of the original instances (which is the main source of error for our approximation). For such a construction, it can be proved that if all the cells of a spatial partition are well assigned (have instances of the same cluster) at the end of a BW$K$M step, then the obtained clustering is actually a fixed point of the $K$-means algorithm over the entire data set. Furthermore, if, for a certain step of BW$K$M, this property can be verified at consecutive weighted Lloyd’s iterations, then the error of our approximation also decreases monotonically. From a practical stand point, BW$K$M was compared to the state-of-the-art: $K$-means++, Forgy $K$-means, Markov Chain Monte Carlo $K$-means and Minibatch $K$-means. The obtained results show that BW$K$M commonly converged to solutions, with a relative error of under $1\%$ with respect to the considered methods, while using a much smaller amount of distance computations (up to 7 orders of magnitude lower). Even when the computational cost of BW$K$M is linear with respect to the dimensionality, its error quality guarantees are mainly related to the diagonal length of the grid cells, meaning that, as we increase the dimensionality of the problem, it will be harder for BW$K$M to have such a competitive performance. Taking this into consideration, we developed a fully-parellelizable feature selection technique intended for the $K$-means algorithm, the Univariate $K$-means relevance for feature selection algorithm ($K$MR). This approach consists of applying any heuristic for the $K$-means problem over multiple subsets of dimensions (each of which is bounded by a predefined constant, $m\ll d$) and using the obtained clusterings to upper-bound the increase in the $K$-means error when deleting a given feature. We then select the features with the $m$ largest error increases. Not only can each step of $K$MR be simply parallelized, but its computational cost is dominated by that of the selected heuristic (on $m$ dimensions), which makes it a suitable dimensionality reduction alternative for BW$K$M on large data sets. Besides providing a theoretical bound for the obtained solution, via $K$MR, with respect the optimal $K$-means clustering, we analyze its performance in comparison to well-known feature selection and feature extraction techniques. Such an analysis shows $K$MR to consistently obtain results with lower $K$-means error than all the considered feature selection techniques: Laplacian scores, maximum variance and random selection, while also requiring similar or lower computational times than these approaches. On the other hand, $K$MR, when compared to feature extraction techniques, such as Random Projections, also shows a noticeable improvement in both error and computational time. As a response to the high dependency of $K$-means algorithm to its initialization, we finally introduce a cheap and yet effective Split-Merge step that can be used to re-start the $K$-means algorithm after reaching a fixed point, Split-Merge $K$-means (SM$K$M). Under some settings, one can show that this approach reduces the error of the given fixed point without requiring any further iteration of the $K$-means algorithm. Moreover, experimental results show that this strategy is able to generate approximations with an associated error that is hard to reach for different multi-start methods, such as multi-start Forgy $K$-means, $K$-means++ and Hartigan $K$-means. In particular, SM$K$M consistently generated the local minima with the lowest $K$-means error, reducing, on average, over 1 and 2 orders of magnitude of relative error with respect to $K$-means++ and Hartigan $K$-means and Forgy $K$-means, respectively. We have observed that SM$K$M improves the previously commented methods in terms of the number of distances computed and the error of the obtained solutions

A cheap feature selection approach for the K -means algorithm

The increase in the number of features that need to be analyzed in a wide variety of areas, such as genome sequencing, computer vision or sensor networks, represents a challenge for the K-means algorithm. In this regard, different dimensionality reduction approaches for the K-means algorithm have been designed recently, leading to algorithms that have proved to generate competitive clusterings. Unfortunately, most of these techniques tend to have fairly high computational costs and/or might not be easy to parallelize. In this work, we propose a fully-parellelizable feature selection technique intended for the K-means algorithm. The proposal is based on a novel feature relevance measure that is closely related to the K-means error of a given clustering. Given a disjoint partition of the features, the technique consists of obtaining a clustering for each subset of features and selecting the m features with the highest relevance measure. The computational cost of this approach is just O(m · max{n · K, log m}) per subset of features. We additionally provide a theoretical analysis on the quality of the obtained solution via our proposal, and empirically analyze its performance with respect to well-known feature selection and feature extraction techniques. Such an analysis shows that our proposal consistently obtains results with lower K-means error than all the considered feature selection techniques: Laplacian scores, maximum variance, multi-cluster feature selection and random selection, while also requiring similar or lower computational times than these approaches. Moreover, when compared to feature extraction techniques, such as Random Projections, the proposed approach also shows a noticeable improvement in both error and computational time.BERC 2014-201

Synthesis of calculational methods for design and analysis of radiation shields for nuclear rocket systems

Eight computer programs make up a nine volume synthesis containing two design methods for nuclear rocket radiation shields. The first design method is appropriate for parametric and preliminary studies, while the second accomplishes the verification of a final nuclear rocket reactor design

An efficient K-means clustering algorithm for tall data

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. Therefore, the development of efficient and parallel algorithms to perform such an analysis is a a crucial topic in unsupervised learning. Cluster analysis algorithms are a key element of exploratory data analysis and, among them, the K-means algorithm stands out as the most popular approach due to its easiness in the implementation, straightforward parallelizability and relatively low computational cost. Unfortunately, the K-means algorithm also has some drawbacks that have been extensively studied, such as its high dependency on the initial conditions, as well as to the fact that it might not scale well on massive datasets. In this article, we propose a recursive and parallel approximation to the K-means algorithm that scales well on the number of instances of the problem, without affecting the quality of the approximation. In order to achieve this, instead of analyzing the entire dataset, we work on small weighted sets of representative points that are distributed in such a way that more importance is given to those regions where it is harder to determine the correct cluster assignment of the original instances. In addition to different theoretical properties, which explain the reasoning behind the algorithm, experimental results indicate that our method outperforms the state-of-the-art in terms of the trade-off between number of distance computations and the quality of the solution obtained

An efficient approximation to the K-means clustering for Massive Data

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to manipulate and analyze such information. In spite of its dependency on the initial settings and the large number of distance computations that it can require to converge, the K-means algorithm remains as one of the most popular clustering methods for massive datasets. In this work, we propose an efficient approximation to the K-means problem intended for massive data. Our approach recursively partitions the entire dataset into a small number of subsets, each of which is characterized by its representative (center of mass) and weight (cardinality), afterwards a weighted version of the K-means algorithm is applied over such local representation, which can drastically reduce the number of distances computed. In addition to some theoretical properties, experimental results indicate that our method outperforms well-known approaches, such as the K-means++ and the minibatch K-means, in terms of the relation between number of distance computations and the quality of the approximation.MINECO (TIN2013-41272P), Spanish Ministry of Economy and Competitivenes

Formation Flying Control Implementation in Highly Elliptical Orbits

The Tschauner-Hempel equations are widely used to correct the separation distance drifts between a pair of satellites within a constellation in highly elliptical orbits [1]. This set of equations was discretized in the true anomaly angle [1] to be used in a digital steady-state hierarchical controller [2]. This controller [2] performed the drift correction between a pair of satellites within the constellation. The objective of a discretized system is to develop a simple algorithm to be implemented in the computer onboard the satellite. The main advantage of the discrete systems is that the computational time can be reduced by selecting a suitable sampling interval. For this digital system, the amount of data will depend on the sampling interval in the true anomaly angle [3]. The purpose of this paper is to implement the discrete Tschauner-Hempel equations and the steady-state hierarchical controller in the computer onboard the satellite. This set of equations is expressed in the true anomaly angle in which a relation will be formulated between the time and the true anomaly angle domains

Implementation of radiation shielding calculation methods. Volume 2: Seminar/Workshop notes

Detailed descriptions are presented of the input data for each of the MSFC computer codes applied to the analysis of a realistic nuclear propelled vehicle. The analytical techniques employed include cross section data, preparation, one and two dimensional discrete ordinates transport, point kernel, and single scatter methods