The goal of this thesis is to develop a new, fast, adaptive load flow algorithm that "automatically alternates" numerical methods including Newton-Raphson method, Gauss-Seidel method and Gauss method for a load flow run to achieve less run time. Unlike the proposed method, the traditional load flow analysis uses only one numerical method at a time. This adaptive algorithm performs all the computation for finding the bus voltage angles and magnitudes, real and reactive powers for the given generation and load values, while keeping track of the proximity to convergence of a solution. This work focuses on finding the algorithm that uses multiple numerical techniques, rather than investigating programming techniques and programming languages. The convergence time is compared with those from using each of the numerical techniques. The proposed method is implemented on the IEEE 39-bus system with different contingencies and the solutions obtained are verified with PowerWorld Simulator, a commercial software for load flow analysis.

by Hau-Leung Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 41-42). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Paper I --- p.5 / Chapter 1.2 --- Paper II --- p.6 / Chapter 2 --- The Inexact Newton-Like Method for Inverse Eigen- value Problem --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- The Newton-Like Method --- p.9 / Chapter 2.3 --- The Inexact Newton-Like Method --- p.11 / Chapter 2.4 --- Convergence Analysis --- p.14 / Chapter 2.5 --- Numerical Experiments --- p.22 / Chapter 3 --- A DCT Based Watermarking Scheme for Copyright Protection of Images --- p.26 / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Preliminary --- p.28 / Chapter 3.2.1 --- Gray-level image --- p.28 / Chapter 3.2.2 --- Color image --- p.29 / Chapter 3.2.3 --- The Discrete Cosine transform --- p.30 / Chapter 3.3 --- Watermarking Approaches --- p.31 / Chapter 3.3.1 --- Insertion procedures --- p.31 / Chapter 3.3.2 --- Retrieval procedures --- p.33 / Chapter 3.4 --- Experimental results --- p.34 / Chapter 3.5 --- Other Applications --- p.38 / Chapter 3.5.1 --- Data Hiding --- p.38 / Chapter 3.5.2 --- Authentication --- p.39 / Chapter 3.5.3 --- Fingerprinting --- p.39 / Chapter 3.5.4 --- Copy Control --- p.39 / Chapter 3.6 --- Conclusion --- p.40 / Bibliography --- p.41

<p>The steadily increasing demand of wood forces sawmills to increase the efficiency and effectiveness of their equipments. The weak parts and the twist in wooden logs have been documented as the most common and crucial defect in sawn lumber.</p><p>In this thesis we are going to implement a program which is able to determine the weak parts in wooden logs. The implementation will be in two languages C++ and Matlab. Parts of the program are going to be implemented sometimes by C++ and sometimes by Matlab therefore different designs are going to be tested. The aim of this thesis is to check whether these designs will meet the real time bound of 10 m/s.</p><p>The result shows that there is a huge difference in time performance for the different designs. Therefore, different discretization levels were used in order to meet the deadline of 10m/s. We found that in order to get better speed one should calculate the matrix for the function <em>F </em>and the Jacobian function <em>J </em>by using C++ not by Matlab. Also we found that when we called functions from one language to another an extra time is added.</p>

Methods for estimating vehicle-terrain interaction parameters for small scale robotic vehicles have been formulated and evaluated using both simulation and experimental studies. A model basis was developed, guided by experimental studies with an iRobot PackBot. The intention was to demonstrate whether a nominally instrumented robotic vehicle could be used as a test platform for generating data for vehicle-terrain parameter estimation. A comprehensive skid-steered model was found to be sensitive enough to distinguish between various forms of unknown terrains. This simulation study also verified that the Bekker model for large scale vehicles adopted for this research was applicable to the small scale robotic vehicle used in this work. This fact was also confirmed by estimating coefficients of friction and establishing their dependence on forward velocity and turning radius as the vehicle traverses different terrains. On establishing that mobility measurements for this robotic were sufficiently sensitive, it was found that estimates could be made of key dynamic variables and vehicle-terrain interaction parameters. Four main contributions are described for reliably and robustly using PackBot data for vehicle-terrain property estimation. These estimation methods should contribute to efforts in improving mobility of small scale tracked vehicles on uncertain terrains. The approach is embodied in a multi-tiered algorithm based on the dynamic and kinematic models for skid-steering as well as tractive force models parameterized by key vehicle-terrain parameters. In order to estimate and characterize the key parameters, nonlinear estimation techniques such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and a General Newton Raphson (GNR) method are integrated into this multi-tiered algorithm. A unique idea in using an EKF with an added State Noise Compensation algorithm is presented which shows its robustness and consistency in estimating slip variables and other parameters for deformable terrains. In the multi-tiered algorithm, a kinematic model of the robotic vehicle is used to estimate slip variables and turning radius. These estimated variables are stored in a truth table and used in a skid-steered dynamic model to estimate the coefficients of friction. The total estimated slip on the left and right track, along with the total tractive force computed using a motor model, are then used in the GNR algorithm to estimate the key vehicle-terrain parameters. These estimated parameters are cross-checked and confirmed with EKF estimation results. Further, these simulation results verify that the tracked vehicle tractive force is not dependent on cohesion for frictional soils. This sequential algorithm is shown to be effective in estimating vehicle-terrain interaction properties with relatively good accuracy. The estimated results obtained from UKF and EKF are verified and compared with available experimental data, and tested on a PackBot traversing specified terrains at the Southwest Research Institute (SwRI), Small Robotics Testbed in San Antonio, Texas. In the end, based on the development and evaluation of small scale vehicle testing, the effectiveness of on-board sensing methods and estimation techniques are also discussed for potential use in real time estimation of vehicle-terrain parameters. / text

This thesis presents a novel approach for a power system to find a practical power flow solution when all the generators in the system have hit their real power output limits, such as some generator units shutting down or load outages. The approach assumes the frequency of the system is unable to be kept at the rated value (usually 60 or 50 Hz) and accordingly, the generator real power outputs are affected by the system frequency deviation. The modification aims to include the system frequency deviation as a new state variable in the power flow so that the power system can be described in a more precise way when the generation limits are hit and the whole system is not operated under the normal condition. A new mathematical formulation for power flow is given by modified the conventional power flow mismatch equation and Jacobian matrix. The Newton – Raphson method is particularly chose to be modified because Newton – Raphson method is most widely used and it is a fast convergent and accurate method. The Jacobian matrix will be augmented by adding a column and a row. Matlab is used as a programming tool to implement the Power Flow for Long Term Frequency Stability (PFLTFS) method for a simple 4-bus system and the IEEE 118-bus system. And PSS/E Dynamic simulation is used to verify the steady state solution from PFLTFS is reasonable. The PSS/E Dynamic Simulation plots are used to analyze the long term frequency response. The PFLTFS method provides a technique for solving an abnormal state system power flow. From the results we can conclude that the PFLTFS method is reasonable for solving power flow of a real power unbalanced system.

Thesis (M.S. )--Duquesne University, 2007. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 59-61) and index.

Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2018-07-25T14:02:43Z No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2018.pdf: 2985862 bytes, checksum: 893b26d388119df4da6d373c1ce19d3b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-07-26T10:43:33Z (GMT) No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2018.pdf: 2985862 bytes, checksum: 893b26d388119df4da6d373c1ce19d3b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-07-26T10:43:33Z (GMT). No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2018.pdf: 2985862 bytes, checksum: 893b26d388119df4da6d373c1ce19d3b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-07-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Determining roots of polynomial functions is a quite frequent content in the subject of Mathematics in Primary and Higher Education. But Galois has shown that it is not possible to develop algebraic formulas to find such roots in polynomials with a degree greater than 4. The present work aims to use Newton-Raphson’s Numerical and Iterative method to find roots of polynomial function. For this, the GeoGebra software is used as a computational and pedagogical tool to illustrate the procedure adopted by the mentioned method through spreadsheets, Geometry and algebraic calculations. Thus, the proposed methodology can help in the understanding of the Newton-Raphson Method and contribute to the process of teaching and learning the content of polynomials for teachers and students of Basic Education. / Determinar raízes de funções polinomiais é um conteúdo bastante frequente na disciplina de Matemática do Ensino Básico e Superior. Mas, Galois demonstrou que não é possível desenvolver fórmulas algébricas para encontrar tais raízes em polinômios com grau maior que 4. Então o presente trabalho tem o objetivo de utilizar o Método Numérico e Iterativo de Newton-Raphson para encontrar raízes de função polinomial. Para isto, utiliza-se o software GeoGebra como ferramenta computacional e pedagógica para ilustrar o procedimento adotado pelo método citado por meio de planilhas eletrônicas, da Geometria e de cálculos algébricos. Assim, a metodologia proposta pode auxiliar na compreensão do Método de Newton-Raphson e colaborar para o processo de ensino e aprendizagem do conteúdo de polinômios para professores e alunos do Ensino Básico.

The steadily increasing demand of wood forces sawmills to increase the efficiency and effectiveness of their equipments. The weak parts and the twist in wooden logs have been documented as the most common and crucial defect in sawn lumber. In this thesis we are going to implement a program which is able to determine the weak parts in wooden logs. The implementation will be in two languages C++ and Matlab. Parts of the program are going to be implemented sometimes by C++ and sometimes by Matlab therefore different designs are going to be tested. The aim of this thesis is to check whether these designs will meet the real time bound of 10 m/s. The result shows that there is a huge difference in time performance for the different designs. Therefore, different discretization levels were used in order to meet the deadline of 10m/s. We found that in order to get better speed one should calculate the matrix for the function F and the Jacobian function J by using C++ not by Matlab. Also we found that when we called functions from one language to another an extra time is added.

Two new methods for the simulation of gas turbine fuel systems, one based on an inter-component volume (ICV) method, and the other based on the iterative Newton Raphson (NR) method, have been developed in this study. They are able to simulate the performance behaviour of each of the hydraulic components such as pumps, valves, metering unit of a fuel system, using physics-based models, which potentially offer more accurate results compared with those using transfer functions. A transient performance simulation system has been set up for gas turbine engines based on an inter-component volume (ICV). A proportional- integral (PI) control strategy is used for the simulation of engine control systems. An integrated engine and its control and hydraulic fuel systems has been set up to investigate their coupling effect during engine transient processes. The developed simulation methods and the systems have been applied to a model turbojet and a model turboshaft gas turbine engine to demonstrate the effectiveness of both two methods. The comparison between the results of engines with and without the ICV method simulated fuel system models shows that the delay of the engine transient response due to the inclusion of the fuel system components and introduced inter-component volumes is noticeable, although relatively small. The comparison of two developed methods applied to engine fuel system simulation demonstrate that both methods introduce delay effect to the engine transient response but the NR method is ahead than the ICV method due to the omission of inter-component volumes on engine fuel system simulation. The developed simulation methods are generic and can be applied to the performance simulation of any other gas turbines and their control and fuel systems. A sensitivity analysis of fuel system key parameters that may affect the engine transient behaviours has also been achieved and represented in this thesis. Three sets of fuel system key parameters have been introduced to investigate their sensitivities, which are, the volumes introduced for ICV method applied to fuel system simulation; the time constants introduced into those first order lags tosimulate the valve movements delay and fuel spray delay effect; and the fuel system key performance and structural parameters.

Machine learning is a major source of interesting optimization problems of current interest. These problems tend to be challenging because of their enormous scale, which makes it difficult to apply traditional optimization algorithms. We explore three avenues to designing algorithms suited to handling these challenges, with a view toward large-scale ML tasks. The first is to develop better general methods for unconstrained minimization. The second is to tailor methods to the features of modern systems, namely the availability of distributed computing. The third is to use specialized algorithms to exploit specific problem structure. Chapters 2 and 3 focus on improving quasi-Newton methods, a mainstay of unconstrained optimization. In Chapter 2, we analyze an extension of quasi-Newton methods wherein we use block updates, which add curvature information to the Hessian approximation on a higher-dimensional subspace. This defines a family of methods, Block BFGS, that form a spectrum between the classical BFGS method and Newton's method, in terms of the amount of curvature information used. We show that by adding a correction step, the Block BFGS method inherits the convergence guarantees of BFGS for deterministic problems, most notably a Q-superlinear convergence rate for strongly convex problems. To explore the tradeoff between reduced iterations and greater work per iteration of block methods, we present a set of numerical experiments. In Chapter 3, we focus on the problem of step size determination. To obviate the need for line searches, and for pre-computing fixed step sizes, we derive an analytic step size, which we call curvature-adaptive, for self-concordant functions. This adaptive step size allows us to generalize the damped Newton method of Nesterov to other iterative methods, including gradient descent and quasi-Newton methods. We provide simple proofs of convergence, including superlinear convergence for adaptive BFGS, allowing us to obtain superlinear convergence without line searches. In Chapter 4, we move from general algorithms to hardware-influenced algorithms. We consider a form of distributed stochastic gradient descent that we call Leader SGD, which is inspired by the Elastic Averaging SGD method. These methods are intended for distributed settings where communication between machines may be expensive, making it important to set their consensus mechanism. We show that LSGD avoids an issue with spurious stationary points that affects EASGD, and provide a convergence analysis of LSGD. In the stochastic strongly convex setting, LSGD converges at the rate O(1/k) with diminishing step sizes, matching other distributed methods. We also analyze the impact of varying communication delays, stochasticity in the selection of the leader points, and under what conditions LSGD may produce better search directions than the gradient alone. In Chapter 5, we switch again to focus on algorithms to exploit problem structure. Specifically, we consider problems where variables satisfy multiaffine constraints, which motivates us to apply the Alternating Direction Method of Multipliers (ADMM). Problems that can be formulated with such a structure include representation learning (e.g with dictionaries) and deep learning. We show that ADMM can be applied directly to multiaffine problems. By extending the theory of nonconvex ADMM, we prove that ADMM is convergent on multiaffine problems satisfying certain assumptions, and more broadly, analyze the theoretical properties of ADMM for general problems, investigating the effect of different types of structure.