In vibration-based damage detection in structures, often changes in the dynamic properties such as natural frequencies, modeshapes, and derivatives of modeshapes are used to identify the damaged elements. If only a partial list of natural frequencies is known, optimization methods may need to be used to identify the damage. In this research, the algorithm proposed by Podlevskyi & Yaroshko (2013) is used to determine the stiffness distribution in shear building models. The lateral load resisting elements are presented as a single equivalent spring, and masses are lumped at floor levels. The proposed method calculates stiffness values directly, i.e., without optimization, from the known partial list of natural frequency data and mass distribution. It is shown that if the number of stories with reduced stiffness is smaller than the number of known natural frequencies, the stories with reduced stiffnesses can be identified. Numerical studies on building models with two stories and four stories are used to illustrate the solution method. Effect of error or noise in given natural frequencies on stiffness estimates and, conversely, sensitivity of natural frequencies to changes in stiffness are studied using 7-, 15-, 30-, and 50-story numerical models. From the studies, it is learnt that as the number of stories increases, the natural frequencies become less sensitive to stiffness changes. Additionally, eight laboratory experiments were conducted on a five-story aluminum structural model. Ten slender columns were used in each story of the specimen. Damage was simulated by removing columns in one, two, or three stories. The method can locate and quantify the damage in cases presented in the experimental studies. It is also applied to a 1/3 scaled 18-story steel moment frame building tested on an earthquake simulator (Suita et al., 2015) to identify the reduction in the stiffness due to fractures of beam flanges. Only the first two natural frequencies are used to determine the reductions in the stiffness since the third mode of the tower is torsional and no reasonable planar spring-mass model can be developed to present all of the translational modes. The method produced possible cases of the softening when the damage was assumed to occur at a single story.

The Faber-Krahn theorem states that among all bounded domains with the same volume in Rn (with the standard Euclidean metric), a ball that has lowest first Dirichlet eigenvalue. Recently it has been shown that a similar result holds for (semi-)regular trees. In this article we show that such a theorem also hold for other classes of (not necessarily non-regular) trees. However, for these new results no couterparts in the world of the Laplace-Beltrami-operator on manifolds are known. / Series: Preprint Series / Department of Applied Statistics and Data Processing

Many methods for computing eigenvalues of a large sparse matrix involve shift-invert transformations which require the solution of a shifted linear system at each step. This thesis deals with shift-invert iterative techniques for solving eigenvalue problems where the arising linear systems are solved inexactly using a second iterative technique. This approach leads to an inner-outer type algorithm. We provide convergence results for the outer iterative eigenvalue computation as well as techniques for efficient inner solves. In particular eigenvalue computations using inexact inverse iteration, the Jacobi-Davidson method without subspace expansion and the shift-invert Arnoldi method as a subspace method are investigated in detail. A general convergence result for inexact inverse iteration for the non-Hermitian generalised eigenvalue problem is given, using only minimal assumptions. This convergence result is obtained in two different ways; on the one hand, we use an equivalence result between inexact inverse iteration applied to the generalised eigenproblem and modified Newton's method; on the other hand, a splitting method is used which generalises the idea of orthogonal decomposition. Both approaches also include an analysis for the convergence theory of a version of inexact Jacobi-Davidson method, where equivalences between Newton's method, inverse iteration and the Jacobi-Davidson method are exploited. To improve the efficiency of the inner iterative solves we introduce a new tuning strategy which can be applied to any standard preconditioner. We give a detailed analysis on this new preconditioning idea and show how the number of iterations for the inner iterative method and hence the total number of iterations can be reduced significantly by the application of this tuning strategy. The analysis of the tuned preconditioner is carried out for both Hermitian and non-Hermitian eigenproblems. We show how the preconditioner can be implemented efficiently and illustrate its performance using various numerical examples. An equivalence result between the preconditioned simplified Jacobi-Davidson method and inexact inverse iteration with the tuned preconditioner is given. Finally, we discuss the shift-invert Arnoldi method both in the standard and restarted fashion. First, existing relaxation strategies for the outer iterative solves are extended to implicitly restarted Arnoldi's method. Second, we apply the idea of tuning the preconditioner to the inner iterative solve. As for inexact inverse iteration the tuned preconditioner for inexact Arnoldi's method is shown to provide significant savings in the number of inner solves. The theory in this thesis is supported by many numerical examples.

<p>As parallel and distributed systems scale to hundreds of thousands of cores and beyond, fault tolerance becomes increasingly important -- particularly on systems with limited I/O capacity and bandwidth. Error correcting codes (ECCs) are used in communication systems where errors arise when bits are corrupted silently in a message. Error correcting codes can detect and correct erroneous bits. Erasure codes, an instance of error correcting codes that deal with data erasures, are widely used in storage systems. An erasure code addsredundancy to the data to tolerate erasures. </p> <p><br> </p> <p>In this thesis, erasure coded computations are proposed as a novel approach to dealing with processor faults in parallel and distributed systems. We first give a brief review of traditional fault tolerance methods, error correcting codes, and erasure coded storage. The benefits and challenges of erasure coded computations with respect to coding scheme, fault models and system support are also presented.</p> <p><br> </p> <p>In the first part of my thesis, I demonstrate the novel concept of erasure coded computations for linear system solvers. Erasure coding augments a given problem instance with redundant data. This augmented problem is executed in a fault oblivious manner in a faulty parallel environment. In the event of faults, we show how we can compute the true solution from potentially fault-prone solutions using a computationally inexpensive procedure. The results on diverse linear systems show that our technique has several important advantages: (i) as the hardware platform scales in size and in number of faults, our scheme yields increasing improvement in resource utilization, compared to traditional schemes; (ii) the proposed scheme is easy to code as the core algorithm remains the same; (iii) the general scheme is flexible to accommodate a range of computation and communication trade-offs. </p> <p><br> </p> <p>We propose a new coding scheme for augmenting the input matrix that satisfies the recovery equations of erasure coding with high probability in the event of random failures. This coding scheme also minimizes fill (non-zero elements introduced by the coding block), while being amenable to efficient partitioning across processing nodes. Our experimental results show that the scheme adds minimal overhead for fault tolerance, yields excellent parallel efficiency and scalability, and is robust to different fault arrival models and fault rates.</p> <p><br> </p> <p>Building on these results, we show how we can minimize, to optimality, the overhead associated with our problem augmentation techniques for linear system solvers. Specifically, we present a technique that adaptively augments the problem only when faults are detected. At any point during execution, we only solve a system with the same size as the original input system. This has several advantages in terms of maintaining the size and conditioning of the system, as well as in only adding the minimal amount of computation needed to tolerate the observed faults. We present, in details, the augmentation process, the parallel formulation, and the performance of our method. Specifically, we show that the proposed adaptive fault tolerance mechanism has minimal overhead in terms of FLOP counts with respect to the original solver executing in a non-faulty environment, has good convergence properties, and yields excellent parallel performance.</p> <p><br> </p> <p>Based on the promising results for linear system solvers, we apply the concept of erasure coded computation to eigenvalue problems, which arise in many applications including machine learning and scientific simulations. Erasure coded computation is used to design a fault tolerant eigenvalue solver. The original eigenvalue problem is reformulated into a generalized eigenvalue problem defined on appropriate augmented matrices. We present the augmentation scheme, the necessary conditions for augmentation blocks, and the proofs of equivalence of the original eigenvalue problem and the reformulated generalized eigenvalue problem. Finally, we show how the eigenvalues can be derived from the augmented system in the event of faults. </p> <p><br> </p> <p>We present detailed experiments, which demonstrate the excellent convergence properties of our fault tolerant TraceMin eigensolver in the average case. In the worst case where the row-column pairs that have the most impact on eigenvalues are erased, we present a novel scheme that computes the augmentation blocks as the computation proceeds, using the estimates of leverage scores of row-column pairs as they are computed by the iterative process. We demonstrate low overhead, excellent scalability in terms of the number of faults, and the robustness to different fault arrival models and fault rates for our method.</p> <p><br> </p> <p>In summary, this thesis presents a novel approach to fault tolerance based on erasure coded computations, demonstrates it in the context of important linear algebra kernels, and validates its performance on a diverse set of problems on scalable parallel computing platforms. As parallel systems scale to hundreds of thousands of processing cores and beyond, these techniques present the most scalable fault tolerant mechanisms currently available.</p><br>

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-01-26T09:20:52Z No. of bitstreams: 2 Dissertação - Jânio Alves dos Santos Júnior - 2016.pdf: 3798217 bytes, checksum: c2acd93260ead52c126f4b37d994825f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-30T10:25:56Z (GMT) No. of bitstreams: 2 Dissertação - Jânio Alves dos Santos Júnior - 2016.pdf: 3798217 bytes, checksum: c2acd93260ead52c126f4b37d994825f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-01-30T10:25:56Z (GMT). No. of bitstreams: 2 Dissertação - Jânio Alves dos Santos Júnior - 2016.pdf: 3798217 bytes, checksum: c2acd93260ead52c126f4b37d994825f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-12-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work aims to study some topics of graph theory in order to solve some problems. In order to complement, we approached a light study of matrices, eigenvalues and eigenvectors. The first problem is known as Königsberg Bridge Problem, where this was considered the problem that gave rise to the study on graphs. The House Problem is a joke, which shows us several propositions about planar and bipartite graphs. Some models we can relate graphs, such as we can observe in the problem of cannibals and in the game of chess. Finally, we will work with applications in the adjacency matrix as in the Problem of the Condominium of Farms and in the Number of Possible Paths in a graph, where we will work with geometric figures, apparently resolving a counting problem using eigenvalues and graph. As a methodological support will be approached Linear Algebra. / O objetivo deste trabalho é estudar alguns tópicos da teoria de grafos com o intuito de resolver alguns problemas. Para complementar, abordamos um leve estudo de matrizes, autovalores e autovetores. O primeiro problema é conhecido como o Problema da Ponte de Königsberg, onde tal, foi considerado o problema que deu origem ao estudo sobre grafos. O Problema das Casas que é uma brincadeira, que nos mostra várias proposições sobre grafos planares e bipartidos. Alguns modelos que podemos relacionar grafos, tais como veremos no problema dos canibais e no jogo de xadrez. Por fim, trabalharemos com aplicações na matriz de adjacência como no problema do Condomínio de Chácaras e no Número de Caminhos Possíveis em um Grafo, onde trabalharemos com figuras geométricas, resolvendo aparentemente um problema de contagem, utilizando autovalores e grafos. Como suporte metodológico será abordado Álgebra Linear.

<p>This study investigates the most important reasons behind the rst-year students' decision to select University of the Western Cape (UWC) as higher education institution.<br /> These reasons were organized into a few factors for easy interpretation. The data to be analyzed for this project is a subsection of the data collected during the orientation period of 2008. During the orientation week of 2008, the questionnaires were completed on a voluntary basis by new rst-year students. All questionnaires were anonymously completed and therefore the data does not contain any information that could be linked to any individual. For the purpose of this study, only the black African and coloured students were considered. The other racial groups were not analyzed due to too small sample sizes. Questionnaires with missing information on the reasons for selecting UWC were not&nbsp / nalyzed. We ended up with a sample of size 600. The data were statistically analyzed, using descriptive statistics, bivariate analyses, factor analysis, coefficient of congruence and bootstrap factor analysis. The results indicated that the most important reasons aecting students to choose UWC were identied as good academic reputation, family member's advice, UWC graduates are successful and UWC graduates get good jobs. The least important reasons were found to be not accepted anywhere, parents / family members graduated from UWC, recruited by UWC and wanted to study near to home. The results also indicated that there were significant differences among students according to population groups, parent's monthly income and grade 12 average. Factor analysis of 12 variables yielded three extracted factors upon which student decisions were based. Similarities of these three factors were tested, and a high similarity among demographic characteristics and grade 12 average were found. Additional analyses were conducted to measure the accuracy of factor analyses models constructed using Spearman and Polychoric correlation matrices. The results indicated that both correlation matrices were&nbsp / nbiased, with higher variance and higher loadings when the Polychoric correlation matrix was used to construct a factor analysis model for categorical data.</p>

The Monte Carlo method is, practically, the only approach capable of giving detail insight into complex neutron transport problems. In reactor physics, the method has been used mainly for determining the keff in criticality calculations. In the last decade, the continuously growing computer performance has allowed to apply the Monte Carlo method also on simple burnup simulations of nuclear systems. Nevertheless, due to its extensive computational demands the Monte Carlo method is still not used as commonly as deterministic methods. One of the reasons for the large computational demands of Monte Carlo criticality calculations is the necessity to carry out a number of inactive cycles to converge the fission source. This thesis presents a new concept of fission matrix based Monte Carlo criticality calculations where inactive cycles are not required. It is shown that the fission matrix is not sensitive to the errors in the fission source, and can be thus calculated by a Monte Carlo calculation without inactive cycles. All required results, including keff, are then derived via the final fission matrix. The confidence interval for the estimated keff can be conservatively derived from the variance in the fission matrix. This was confirmed by numerical test calculations of Whitesides's ``keff of the world problem'' model where other Monte Carlo methods fail to estimate the confidence interval correctly unless a large number of inactive cycles is simulated.   Another problem is that the existing Monte Carlo criticality codes are not well shaped for parallel computations; they cannot fully utilise the processing power of modern multi-processor computers and computer clusters. This thesis presents a new parallel computing scheme for Monte Carlo criticality calculations based on the fission matrix. The fission matrix is combined over a number of independent parallel simulations, and the final results are derived by means of the fission matrix. This scheme allows for a practically ideal parallel scaling since no communication among the parallel simulations is required, and no inactive cycles need to be simulated.   When the Monte Carlo criticality calculations are sufficiently fast, they will be more commonly applied on complex reactor physics problems, like non-linear steady-state calculations and fuel cycle calculations. This thesis develops an efficient method that introduces thermal-hydraulic and other feedbacks into the numerical model of a power reactor, allowing to carry out a non-linear Monte Carlo analysis of the reactor with steady-state core conditions. The thesis also shows that the major existing Monte Carlo burnup codes use unstable algorithms for coupling the neutronic and burnup calculations; therefore, they cannot be used for fuel cycle calculations. Nevertheless, stable coupling algorithms are known and can be implemented into the future Monte Carlo burnup codes. / QC 20100709

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

Today the multisensor array signal processing of noisy measurements has received much attention. The classical problem in array signal processing is determining the location of an energy-radiating source relative to the location of the array, in other words, direction-of-arrival (DOA) estimation. One is considering the signal estimation problem when together with the signal(s) of interest some noise and interfering signals are present. In this report a direction-of-arrival estimation system is described based on an antenna array for detecting arrival angles in azimuth plane of signals pitched by the antenna array. For this, the Multiple Signal Classication (MUSIC) algorithmis first of all considered. Studies show that in spite of its good reputation and popularity among researches, it has a certain limit of its performance. In this subspace-based method for DOA estimation of signal wavefronts, the term corresponding to additive noise is initially assumed spatially white. In our paper, we address the problem of DOA estimation of multiple target signals in a particular noise situation - in correlated spherically isotropic noise, which, in many practical cases, models a more real context than under the white noise assumption. The purpose of this work is to analyze the behaviour of the MUSIC algorithm and compare its performance with some other algorithms (such as the Capon and the Classical algorithms) and, uppermost, to explore the quality of the detected angles in terms of precision depending on different parameters, e.g. number of samples, noise variance, number of incoming signals. Some modifications of the algorithms are also done is order to increase their performance. Program MATLAB is used to conduct the studies. The simulation results on the considered antenna array system indicate that in complex conditions the algorithms in question (and first of all, the MUSIC algorithm) are unable to automatically detect and localize the DOA signals with high accuracy. Other algorithms andways for simplification the problem (for example, procedure of denoising) exist and may provide more precision but require more computation time.

Aeroelastic behavior prediction is often confined to analytical or highly computational methods, so I developed a low degree of freedom computational method using structural finite elements and unsteady loading to cover a gap in the literature. Finite elements are readily suitable for determination of the free vibration characteristics of eccentric, elastic structures, and the free vibration characteristics fundamentally determine the aeroelastic behavior. I used Theodorsen’s unsteady strip loading formulation to model the aerodynamic loading on linear elastic structures assuming harmonic motion. I applied Hassig’s ‘p-k’ method to predict the flutter boundary of nonsymmetric, aeroelastic systems. I investigated the application of a quintic interpolation assumed displacement shape to accurately predict higher order characteristic effects compared to linear analytical results. I show that quintic interpolation is especially accurate over cubic interpolation when multi-modal interactions are considered in low degree of freedom flutter behavior for high aspect ratio HALE aircraft wings.