Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Implementação da rotina de unfolding para determinação de distribuição de tamanho de grãos esféricos via distribuição de interceptos lineares e de área de seção

Na unfolding method of linear intercept distributions and secction área distribution was implemented for structures with spherical grains. Although the unfolding routine depends on the grain shape, structures with spheroidal grains can also be treated by this routine. Grains of non-spheroidal shape can be treated only as approximation. A software was developed with two parts. The first part calculates the probability matrix. The second part uses this matrix and minimizes the chi-square. The results are presented with any number of size classes as required. The probability matrix was determined by means of the linear intercept and section area distributions created by computer simulation. Using curve fittings the probability matrix for spheres of any sizes could be determined. Two kinds of tests were carried out to prove the efficiency of the Technique. The theoretical tests represent ideal cases. The software was able to exactly find the proposed grain size distribution. In the second test, a structure was simulated in computer and images of its slices were used to produce the corresponding linear intercept the section area distributions. These distributions were then unfolded. This test simulates better reality. The results show deviations from the real size distribution. This deviations are caused by statistic fluctuation. The unfolding of the linear intercept distribution works perfectly, but the unfolding of section area distribution does not work due to a failure in the chi-square minimization. The minimization method uses a matrix inversion routine. The matrix generated by this procedure cannot be inverted. Other minimization method must be used

Diferenciais de rendimentos por gênero: uma análise dos efeitos composição e estrutura salarial no Brasil (1976, 1987, 1996 e 2009)

This study aims to analyze the income differentials by gender in Brazil, in the years 1976, 1987, 1996 and 2009. Specifically, there are two objectives. First, attempt to analyze the importance of the effects of composition and wage structure in the job market. In the second, to verify which socioeconomic variables explain the effects of composition and wage structure in the job market. The information in this study was obtained from the microdata of Pesquisa Nacional por Amostra de Domicílios (PNAD) regarding the respective years. In the first stage of the methodology we used: the index of income distribution Theil-T; the income gap decompositions proposed by Oaxaca (1973) and Blinder (1973); and Firpo et al. (2007). In the second stage we applied the RIF regression method (Recentered Influence Function) of Firpo et al. (2007). The results show that income inequality is higher among men than among women in the country. It was observed that the component of inequality between people of the same gender represented the largest share in the decomposition of income inequality between genders. It was found, in the decomposition of the average income, a downward trend of income gap, but the differential remains favorable to the men. We noticed that the impact of the composition effect in reducing the gap was offset by the positive effect of wage structure. Regarding the distribution quantis, income differential between genres appeared greater at the bottom, in the years 1976, 1987 and 2009; and at the top of the distribution, in 1996 featuring, respectively, the sticky floor and glass ceiling effects in Brazil. As for the decomposition of the RIF, it turns out that the composition effect assisted in the downfall of the income gap between 1976 and 2009, but was offset by the positive effect of the wage structure in quantis 10th, 50th, and 90th. The main socioeconomic variables influenced the drop in income gap were: the composition effect, the manual labor occupations, service sector and low-grade and high school, and the wage structure effect, schooling low and high experience professional and technical occupations and urban centers

Identificação fuzzy-multimodelos para sistemas não lineares

This paper presents a new multi-model technique of dentification in ANFIS for nonlinear systems. In this technique, the structure used is of the fuzzy Takagi-Sugeno of which the consequences are local linear models that represent the system of different points of operation and the precursors are membership functions whose adjustments are realized by the learning phase of the neuro-fuzzy ANFIS technique. The models that represent the system at different points of the operation can be found with linearization techniques like, for example, the Least Squares method that is robust against sounds and of simple application. The fuzzy system is responsible for informing the proportion of each model that should be utilized, using the membership functions. The membership functions can be adjusted by ANFIS with the use of neural network algorithms, like the back propagation error type, in such a way that the models found for each area are correctly interpolated and define an action of each model for possible entries into the system. In multi-models, the definition of action of models is known as metrics and, since this paper is based on ANFIS, it shall be denominated in ANFIS metrics. This way, ANFIS metrics is utilized to interpolate various models, composing a system to be identified. Differing from the traditional ANFIS, the created technique necessarily represents the system in various well defined regions by unaltered models whose pondered activation as per the membership functions. The selection of regions for the application of the Least Squares method is realized manually from the graphic analysis of the system behavior or from the physical characteristics of the plant. This selection serves as a base to initiate the linear model defining technique and generating the initial configuration of the membership functions. The experiments are conducted in a teaching tank, with multiple sections, designed and created to show the characteristics of the technique. The results from this tank illustrate the performance reached by the technique in task of identifying, utilizing configurations of ANFIS, comparing the developed technique with various models of simple metrics and comparing with the NNARX technique, also adapted to identification

Um ambiente computacional para modelagem simbólica de sistemas físicos lineares

Este trabalho propõe um ambiente computacional aplicado ao ensino de sistemas de controle, denominado de ModSym. O software implementa uma interface gráfica para a modelagem de sistemas físicos lineares e mostra, passo a passo, o processamento necessário à obtenção de modelos matemáticos para esses sistemas. Um sistema físico pode ser representado, no software, de três formas diferentes. O sistema pode ser representado por um diagrama gráfico a partir de elementos dos domínios elétrico, mecânico translacional, mecânico rotacional e hidráulico. Pode também ser representado a partir de grafos de ligação ou de diagramas de fluxo de sinal. Uma vez representado o sistema, o ModSym possibilita o cálculo de funções de transferência do sistema na forma simbólica, utilizando a regra de Mason. O software calcula também funções de transferência na forma numérica e funções de sensibilidade paramétrica. O trabalho propõe ainda um algoritmo para obter o diagrama de fluxo de sinal de um sistema físico baseado no seu grafo de ligação. Este algoritmo e a metodologia de análise de sistemas conhecida por Network Method permitiram a utilização da regra de Mason no cálculo de funções de transferência dos sistemas modelados no software

Controle preditivo robusto baseado em desigualdades matriciais lineares aplicado a um sistema de tanques acoplados

This work deals with an on-line control strategy based on Robust Model Predictive Control (RMPC) technique applied in a real coupled tanks system. This process consists of two coupled tanks and a pump to feed the liquid to the system. The control objective (regulator problem) is to keep the tanks levels in the considered operation point even in the presence of disturbance. The RMPC is a technique that allows explicit incorporation of the plant uncertainty in the problem formulation. The goal is to design, at each time step, a state-feedback control law that minimizes a 'worst-case' infinite horizon objective function, subject to constraint in the control. The existence of a feedback control law satisfying the input constraints is reduced to a convex optimization over linear matrix inequalities (LMIs) problem. It is shown in this work that for the plant uncertainty described by the polytope, the feasible receding horizon state feedback control design is robustly stabilizing. The software implementation of the RMPC is made using Scilab, and its communication with Coupled Tanks Systems is done through the OLE for Process Control (OPC) industrial protocol

Técnicas inteligentes hídridas para o controle de sistemas não lineares

A neuro-fuzzy system consists of two or more control techniques in only one structure. The main characteristic of this structure is joining one or more good aspects from each technique to make a hybrid controller. This controller can be based in Fuzzy systems, artificial Neural Networks, Genetics Algorithms or rein forced learning techniques. Neuro-fuzzy systems have been shown as a promising technique in industrial applications. Two models of neuro-fuzzy systems were developed, an ANFIS model and a NEFCON model. Both models were applied to control a ball and beam system and they had their results and needed changes commented. Choose of inputs to controllers and the algorithms used to learning, among other information about the hybrid systems, were commented. The results show the changes in structure after learning and the conditions to use each one controller based on theirs characteristics

Separação cega de fontes lineares e não lineares usando algoritmo genético, redes neurais artificiais RBF e negentropia de Rényi como medida de independência

Conventional methods to solve the problem of blind source separation nonlinear, in general, using series of restrictions to obtain the solution, often leading to an imperfect separation of the original sources and high computational cost. In this paper, we propose an alternative measure of independence based on information theory and uses the tools of artificial intelligence to solve problems of blind source separation linear and nonlinear later. In the linear model applies genetic algorithms and Rényi of negentropy as a measure of independence to find a separation matrix from linear mixtures of signals using linear form of waves, audio and images. A comparison with two types of algorithms for Independent Component Analysis widespread in the literature. Subsequently, we use the same measure of independence, as the cost function in the genetic algorithm to recover source signals were mixed by nonlinear functions from an artificial neural network of radial base type. Genetic algorithms are powerful tools for global search, and therefore well suited for use in problems of blind source separation. Tests and analysis are through computer simulations

Espectro das ondas de spin lineares e não-lineares em multicamadas magnéticas anisotrópicas

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Coeficientes de incidência do dengue e sua relação com os diferenciais intra-urbanos segundo condições de vida no município do Natal, Rio Grande do Norte

This study sprang from the hypothesis that spatial variations in the morbidity rate for dengue fever within the municipality of Natal are related to intra-city socioeconomic and environmental variations. The objective of the project was to classify the different suburbs of Natal according to their living conditions and establish if there was any correlation between this classification and the incidence rate for dengue fever, with the aim of enabling public health planners to better control this disease. Data on population density, access to safe drinking water, rubbish collection, sewage disposal facilities, income level, education and the incidence of dengue fever during the years 2001 and 2003 was drawn from the Brazilian Demographic Census 2000 and from the Reportable Disease Notification System -SINAN. The study is presented here in the form of two papers, corresponding to the types of analysis performed: a classification of the urban districts into quartiles according to the living conditions which exist there, in the first article; and the incidence of dengue fever in each of these quartiles, in the second. By applying factorial analysis to the chosen socioeconomic and environmental indicators for the year 2000, a compound index of living condition (ICV) was obtained. On the basis of this index, it was possible to classify the urban districts into quartiles. On undertaking this grouping (paper 1), a heterogeneous distribution of living conditions was found across the city. As to the incidence rate for dengue fever (paper 2), it was discovered that the quartile identified as having the best living conditions presented incidence rates of 15.62 and 15.24 per 1000 inhabitants respectively in the years 2001 and 2003; whereas the quartile representing worst living conditions showed incidence rates of 25.10 and 10.32 for the comparable periods. The results suggest that dengue fever occurs in all social classes, and that its incidence is not related in any evident way to the chosen formula for living conditions

Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares

The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the general dependence of the Lagrangian that describes this kind of theories. From this Lagrangian and in the background of classical field theory, we derive the general dispersion relation that photons must obey in terms of a background field and the NLED properties. It is important to note that, in order to achieve this result, an aproximation has been made in order to allow the separation of the total electromagnetic field into a strong background electromagnetic field and a perturbation. Once the dispersion relation is in hand, the usual Bose-Einstein statistical procedure is followed through which the thermodynamical properties, energy density and pressure relations are obtained. An important result of this work is the fact that equation of state remains identical to the one obtained under EM. Then, two examples are made where the thermodynamic properties are explicitly derived in the context of two NLED, Born-Infelds and a quadratic approximation. The choice of the first one is due to the vast appearance in literature and, the second one, because it is a first order approximation of a large class of NLED. Ultimately, both are chosen because of their simplicity. Finally, the results are compared to EM and interpreted, suggesting possible tests to verify the internal consistency of NLED and motivating further developement into the formalism s quantum case

Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Diferenciais de mortalidade adulta por nível de escolaridade no Brasil e regiões

The study of mortality by various differentials has been an important tool to guide public health policies, due to better describing the events of deaths in a population. This research aims to seek disparities in mortality according to educational level, sex and adulthood in large Brazilian regions and consequently for Brazil as a whole. A vast literature has shown that people with more education tend to have lower risk of death. Studies on inequalities in mortality by level of education in Brazil are still very specific and has still known very little about Brazil about mortality according to educational level, due to lack of information about the well-filled school in the records of deaths arising from the Mortality Information System (MIS) of the Ministry of Health. This data source has shown improvement in the coverage of sub reports in the last decade, however, it has still perceived negligence in completing the question regarding schooling of death (about 30% of registered deaths in 2010 to Brazil, Given this scenario, this work contributes to the national literature on the behavior of adult mortality differentials having as proposed, using data from the new variable mortality of the 2010 Census (CD 2010), assuming the characteristics of education of the head the household for deaths occurring in the same. It is therefore considered that the probability of mortality is homogeneous within the household. Events of deaths were corrected only for the records come from households where the head possessed levels of schooling and Instruction Elementary Education No Incomplete and Primary Education and Secondary Education Complete Incomplete through the Generations Extinct Adjusted method. With deaths already corrected, probabilities of death were calculated between 15 and 60 years life, as well as tables by sex and level of education to all regions of Brazil. No que se refere às probabilidades de morte por idade, nas idades entre 15 e 60 anos as maiores probabilidades seguem um gradiente, maior probabilidade para os menos escolarizados. Results corroborate the literature, the more educated the population is, the greater the life expectancy. In all Brazilian regions, life expectancy of the female population is greater than that of men at all levels of schooling. With respect to probabilities of death by age between the ages of 15 and 60 years the most likely follow a gradient, most likely to the least educated. At older ages (from 70 years), this behavior has presented another pattern, the lowest level of education has the lowest odds in the regions, North, Northeast, South and Midwest, except in the Southeast region

Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Contribuição ao estudo de treliças não lineares considerando efeitos térmicos

This work presents the numerical analysis of nonlinear trusses summited to thermomechanical actions with Finite Element Method (FEM). The proposed formulation is so-called positional FEM and it is based on the minimum potential energy theorem written according to nodal positions, instead of displacements. The study herein presented considers the effects of geometric and material nonlinearities. Related to dynamic problems, a comparison between different time integration algorithms is performed. The formulation is extended to impact problems between trusses and rigid wall, where the nodal positions are constrained considering nullpenetration condition. In addition, it is presented a thermodynamically consistent formulation, based on the first and second law of thermodynamics and the Helmholtz free-energy for analyzing dynamic problems of truss structures with thermoelastic and thermoplastic behavior. The numerical results of the proposed formulation are compared with examples found in the literature.