Consider an under-determined system of nonlinear equations F(x)=0, F:R^m→R^n, where F is continuously differentiable and m > n. This system appears in a variety of applications, including parameter-dependent systems, dynamical systems with periodic solutions, and nonlinear eigenvalue problems. Robust, efficient numerical methods are often required for the solution of this system. Newton's method is an iterative scheme for solving the nonlinear system of equations F(x)=0, F:R^n→R^n. Simple to implement and theoretically sound, it is not, however, often practical in its pure form. Inexact Newton methods and globalized inexact Newton methods are computationally efficient variations of Newton's method commonly used on large-scale problems. Frequently, these variations are more robust than Newton's method. Trust region methods, thought of here as globalized exact Newton methods, are not as computationally efficient in the large-scale case, yet notably more robust than Newton's method in practice. The normal flow method is a generalization of Newton's method for solving the system F:R^m→R^n, m > n. Easy to implement, this method has a simple and useful local convergence theory; however, in its pure form, it is not well suited for solving large-scale problems. This dissertation presents new methods that improve the efficiency and robustness of the normal flow method in the large-scale case. These are developed in direct analogy with inexact-Newton, globalized inexact-Newton, and trust-region methods, with particular consideration of the associated convergence theory. Included are selected problems of interest simulated in MATLAB.

Cables are highly nonlinear structural members under transverse loading. This nonlinearity is mainly due to the close relationship between the final geometry under transverse loads and the resulting stresses in its equilibrium state rather than the material properties. In practice, the cables are usually used as isolated single-segment elements fixed at the ends. Various studies and solution procedures suggested by researchers are available in the literature for such isolated cables. However, not much work is available for continuous cables with multiple supports. In this study, a multi-segment continuous cable is defined as a cable fixed at the ends and supported by a number of stationary roller supports in between. Total cable length is assumed constant and the intermediate supports are assumed to be frictionless. Therefore, the critical issue is to find the distribution of the cable length among its segments in the final equilibrium state. Since the solution of single-segment cables is available the additional condition to be satisfied for multi-segment continuous cables with multiple supports is to have stress continuity at intermediate support locations where successive cable segments meet. A predictive/corrective iteration procedure is proposed for this purpose. The solution starts with an initially assumed distribution of total cable length among the segments and each segment is analyzed as an independent isolated single-segment cable. In general, the stress continuity between the cable segments will not be satisfied unless the assumed distribution of cable length is the correct distribution corresponding to final equilibrium state. In the subsequent iterations the segment lengths are readjusted to eliminate the unbalanced tensions at segment junctions. The iterations are continued until the stress continuity is satisfied at all junctions. Two alternative approaches are proposed for the segment length adjustments: Direct stiffness method and tension distribution method. Both techniques have been implemented in a software program for the analysis of multi-segment continuous cables and some sample problems are analyzed for verification. The results are satisfactory and compares well with those obtained by the commercial finite element program ANSYS.

In visually guided control of a robot, a large residual problem occurs when the robot configuration is not in the neighborhood of the target acquisition configuration. Most existing uncalibrated visual servoing algorithms use quasi-Gauss-Newton methods which are effective for small residual problems. The solution used in this study switches between a full quasi-Newton method for large residual case and the quasi-Gauss-Newton methods for the small case. Visual servoing to handle large residual problems for tracking a moving target has not previously appeared in the literature. For large residual problems various Hessian approximations are introduced including an approximation of the entire Hessian matrix, the dynamic BFGS (DBFGS) algorithm, and two distinct approximations of the residual term, the modified BFGS (MBFGS) algorithm and the dynamic full Newton method with BFGS (DFN-BFGS) algorithm. Due to the fact that the quasi-Gauss-Newton method has the advantage of fast convergence, the quasi-Gauss-Newton step is used as the iteration is sufficiently near the desired solution. A switching algorithm combines a full quasi-Newton method and a quasi-Gauss-Newton method. Switching occurs if the image error norm is less than the switching criterion, which is heuristically selected. An adaptive forgetting factor called the dynamic adaptive forgetting factor (DAFF) is presented. The DAFF method is a heuristic scheme to determine the forgetting factor value based on the image error norm. Compared to other existing adaptive forgetting factor schemes, the DAFF method yields the best performance for both convergence time and the RMS error. Simulation results verify validity of the proposed switching algorithms with the DAFF method for large residual problems. The switching MBFGS algorithm with the DAFF method significantly improves tracking performance in the presence of noise. This work is the first successfully developed model independent, vision-guided control for large residual with capability to stably track a moving target with a robot.

Mémoire (M.Sc. A.)-- Université du Québec à Chicoutimi, 1984. / "Mémoire présenté comme exigence partielle de la maîtrise en sciences appliquées en ressources et systèmes" CaQCU bibliographie: p. 56-58. Document électronique également accessible en format PDF. CaQCU

Thesis (Ph. D.)--Ohio State University, 2005. / Available online via OhioLINK's ETD Center; full text release delayed at author's request until 2006 Aug 15.

Hydrauliska högtryckskopplingar av typen FEM ½” studeras med avsikten att fastställa en effektiv beräkningsmetodik som kan användas till att prediktera kopplingarnas hållfasthet. Metodiken utgörs av finita element analyser (FEA), och valideras av experimentella trycktester utförda på kopplingstypen FEM ½”. Genom FEA kan kopplingarnas hållfasthetsbeteende och maximala belastningskapacitet studeras virtuellt, vilket minskar behovet av experimentella tester och medför potential för optimering av produkterna. Arbetet utförs på Parker Hannifin AB i Skövde. Experimentella tester utförs på 20 stycken kopplingspar av typen FEM ½” för att utöka förståelsen av kopplingarnas beteende under brottsförloppet och för att prediktera trycket som medför haveri. Testernas genomförande och struktur baseras på metodiken Design of Experiments (DOE). Kritiska komponenter identifieras utifrån experimentets resultat, vilka sedan studeras närmare via FEA. Analyserna valideras utifrån standarder som kopplingarna ska efterfölja, och mätdata insamlad under de experimentella testerna. Från de experimentella testerna är det komponenterna: kulhållaren, styrningen och nippelhuset som upptar belastning i störst utsträckning. Vid haveri framgår två brottmoder som vanliga, att kulhållaren slits isär samt att styrningen brister, båda fallen uppkommer vid approximativt samma tryck. FE-analyserna för styrningen och kulhållaren visar god överensstämmelse med experimentella resultat. Deformationerna skiljer sig dock mellan analyserna och de experimentella testerna, var nippelhusets analyser uppvisar störst avvikelser. FE-modellerna uppvisar god potential för att prediktera samt utvärdera kopplingarnas mekaniska beteende under tryckbelastning. Analyserna är dock helt beroende av ingående data, var saknaden av en verklig materialmodell medför avvikelser från experimentella resultat. Förhållandet framgår tydligt av nippelhuset, vars relaterade härdningsegenskaper saknas. / Hydraulic FEM ½" high pressure couplings are studied with the purpose of establishing an effective methodology that can be used to predict the strength of the couplings. The methodology consists of finite element analyzes (FEA) and is validated by experimental pressure tests, performed on the FEM ½” couplings pairs.  Using FEA, the couplings solid mechanical behavior and maximum load ability can be viewed virtual, reducing the need for experimental tests and gives the potential for optimized products. The work is performed at Parker Hannifin AB in Skovde. Experimental tests are performed on 20 FEM ½” couplings pairs, to understand the solid mechanical behavior of the couplings until failure occurs, and to predict the maximum pressure that can be applied. The experimental structure and performance is based on the method Design of Experiments (DOE). Critical components are identified based on the results from the experimental tests, which are then studied more closely through FEA. The analysis are validated based on the applied material model, and data collected during the experimental tests. From the experimental tests it is shown that the components: ball cage, guide and plug housing are the components in which failure occur. In case of failure, two failure modes appear as common, that the ball cage is worn apart and that the guide burst, both types of failure modes occur at a similar pressure. The analysis for the guide and ball cage corresponds with the experimental outcomes. Differences occurs however when looked at the deformations, in which the plug housing shows the largest deviation when compared to the experimental results. The usage of FE-models appears to be appropriate for predicting and evaluating the mechanical strengths of the couplings during pressure loads. The analysis are however entirely dependent on the input data, where an incorrect material model generates incorrect results. The relationship is shown for the plug housing, which lack the mechanical properties related to curing processes.

Orientadores: Márcia Aparecida Gomes Ruggiero, Sandra Augusta Santos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-21T10:21:10Z (GMT). No. of bitstreams: 1 Begiato_RodolfoGotardi_D.pdf: 3815627 bytes, checksum: 59584610cfd737a94e68dc5bf3735e25 (MD5) Previous issue date: 2012 / Resumo: O objetivo desta tese é tratar da resolução de sistemas não lineares de grande porte, em que as funções são continuamente diferenciáveis, por meio de uma abordagem híbrida que utiliza um método iterativo com duas fases. A primeira fase consiste de versões sem derivadas do método do ponto fixo empregando parâmetros espectrais para determinar o tamanho do passo da direção residual. A segunda fase é constituída pelo método de Newton inexato em uma abordagem matrix-free, em que é acoplado o método GMRES para resolver o sistema linear que determina a nova direção de busca. O método híbrido combina ordenadamente as duas fases de forma que a segunda é acionada somente em caso de falha na primeira e, em ambas, uma condição de decréscimo não-monótono deve ser verificada para aceitação de novos pontos. Desenvolvemos ainda um segundo método, em que uma terceira fase de busca direta é acionada em situações em que o excesso de buscas lineares faz com que o tamanho de passo na direção do método de Newton inexato torne-se demasiadamente pequeno. São estabelecidos os resultados de convergência dos métodos propostos. O desempenho computacional é avaliado em uma série de testes numéricos com problemas tradicionalmente encontrados na literatura. Tanto a análise teórica quanto a numérica evidenciam a viabilidade das abordagens apresentadas neste trabalho / Abstract: This thesis handles large-scale nonlinear systems for which all the involved functions are continuously differentiable. They are solved by means of a hybrid approach based on an iterative method with two phases. The first phase is defined by derivative-free versions of a fixed-point method that employs spectral parameters to define the steplength along the residual direction. The second phase consists of a matrix-free inexact Newton method that employs the GMRES to solve the linear system that computes the search direction. The proposed hybrid method neatly combines the two phases in such a way that the second is called only in case the first one fails. To accept new points in both phases, a nonmonotone decrease condition upon a merit function has to be verified. A second method is developed as well, with a third phase based on direct search, that should act whenever too many line searches have excessively decreased the steplenght along the inexact- Newton direction. Convergence results for the proposed methods are established. The computational performance is assessed in a set of numerical experiments with problems from the literature. Both the theoretical and the experimental analysis corroborate the feasibility of the proposed strategies / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Orientadores: Sandra Augusta Santos, Roberto Andreani / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T11:40:11Z (GMT). No. of bitstreams: 1 Shirabayashi_WesleyVagnerInes_D.pdf: 877226 bytes, checksum: a814cd9947431a0aee17517c4cc953f4 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho reformulamos o problema de complementaridade não linear generalizado (GNCP) em cones poliedrais como um sistema não linear com restrição de não negatividade em algumas variáveis, e trabalhamos na resolução de tal reformulação por meio de estratégias de pontos interiores. Em particular, definimos dois algoritmos e provamos a convergência local de tais algoritmos sob hipóteses usuais. O primeiro algoritmo é baseado no método de Newton, e o segundo, no método tensorial de Chebyshev. O algoritmo baseado no método de Chebyshev pode ser visto como um método do tipo preditor-corretor. Tal algoritmo, quando aplicado a problemas em que as funções envolvidas são afins, e com escolhas adequadas dos parâmetros, torna-se o bem conhecido algoritmo preditor-corretor de Mehrotra. Também apresentamos resultados numéricos que ilustram a competitividade de ambas as propostas. / Abstract: In this work we reformulate the generalized nonlinear complementarity problem (GNCP) in polyhedral cones as a nonlinear system with nonnegativity in some variables and propose the resolution of such reformulation through interior-point methods. In particular we define two algorithms and prove the local convergence of these algorithms under standard assumptions. The first algorithm is based on Newton's method and the second, on the Chebyshev's tensorial method. The algorithm based on Chebyshev's method may be considered a predictor-corrector one. Such algorithm, when applied to problems for which the functions are affine, and the parameters are properly chosen, turns into the well-known Mehrotra's predictor corrector algorithm. We also present numerical results that illustrate the competitiveness of both proposals. / Doutorado / Otimização / Doutor em Matemática Aplicada

In this thesis, we present the use of logistic regression method to develop a credit scoring modelusing the raw data of 4447 customers of a bank. The data of customers is collected under 14independent explanatory variables and 1 default indicator. The objective of this thesis is toidentify optimal coefficients. In order to clean data, the raw data set was put through variousdata calibration techniques such as Kurtosis, Skewness, Winsorization to eliminate outliers.On this winsorized dataset, LOGIT analysis is applied in two rounds with multiple statisticaltests. These tests aim to estimate the significance of each independent variable and modelfitness. The optimal coefficients can be used to obtain the credit scores for new customers witha new data set and rank them according to their credit risk.

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