Substitution-Newton-Raphson method applied to the modeling of a vapour compression refrigeration system using different representations of the thermodynamic properties of R-134a

This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

Dynamic Imaging in Electrical Impedance Tomography of the Human Chest With Online Transition Matrix Identification

One of the electrical impedance tomography objectives is to estimate the electrical resistivity distribution in a domain based only on electrical potential measurements at its boundary generated by an imposed electrical current distribution into the boundary. One of the methods used in dynamic estimation is the Kalman filter. In biomedical applications, the random walk model is frequently used as evolution model and, under this conditions, poor tracking ability of the extended Kalman filter (EKF) is achieved. An analytically developed evolution model is not feasible at this moment. The paper investigates the identification of the evolution model in parallel to the EKF and updating the evolution model with certain periodicity. The evolution model transition matrix is identified using the history of the estimated resistivity distribution obtained by a sensitivity matrix based algorithm and a Newton-Raphson algorithm. To numerically identify the linear evolution model, the Ibrahim time-domain method is used. The investigation is performed by numerical simulations of a domain with time-varying resistivity and by experimental data collected from the boundary of a human chest during normal breathing. The obtained dynamic resistivity values lie within the expected values for the tissues of a human chest. The EKF results suggest that the tracking ability is significantly improved with this approach.

Sobre o procedimento de Zippin para estimar populações de animais

O procedimento de Zippin é uma das técnicas mais precisas para estimar populações de animais, além de fornecer estimativas do erro padrão. Entretanto, a solução das equações de máxima verossimilhança não é algebricamente explícita. Sugere-se um procedimento iterativo utilizando a técnica de Newton Raphson para encontrar as soluções desejadas. Comparações com o procedimento clássico mostram sensíveis diferenças nas estimativas do erro padrão e diferenças menores nos demais parâmetros.

Desenvolvimento e estudo de modelos de FACTS para o trânsito de energia: aplicação ao estudo das condições técnicas de ligação de linhas MAT

Dissertação para obtenção do grau de Mestre em Engenharia Electrotécnica Ramo de Energia

Formulação corrotacional para análise de vigas com elementos finitos

Dissertação apresentada na faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Mecânica

EFFECT – Efficient finite element code

The theme of this dissertation is the finite element method applied to mechanical structures. A new finite element program is developed that, besides executing different types of structural analysis, also allows the calculation of the derivatives of structural performances using the continuum method of design sensitivities analysis, with the purpose of allowing, in combination with the mathematical programming algorithms found in the commercial software MATLAB, to solve structural optimization problems. The program is called EFFECT – Efficient Finite Element Code. The object-oriented programming paradigm and specifically the C ++ programming language are used for program development. The main objective of this dissertation is to design EFFECT so that it can constitute, in this stage of development, the foundation for a program with analysis capacities similar to other open source finite element programs. In this first stage, 6 elements are implemented for linear analysis: 2-dimensional truss (Truss2D), 3-dimensional truss (Truss3D), 2-dimensional beam (Beam2D), 3-dimensional beam (Beam3D), triangular shell element (Shell3Node) and quadrilateral shell element (Shell4Node). The shell elements combine two distinct elements, one for simulating the membrane behavior and the other to simulate the plate bending behavior. The non-linear analysis capability is also developed, combining the corotational formulation with the Newton-Raphson iterative method, but at this stage is only avaiable to solve problems modeled with Beam2D elements subject to large displacements and rotations, called nonlinear geometric problems. The design sensitivity analysis capability is implemented in two elements, Truss2D and Beam2D, where are included the procedures and the analytic expressions for calculating derivatives of displacements, stress and volume performances with respect to 5 different design variables types. Finally, a set of test examples were created to validate the accuracy and consistency of the result obtained from EFFECT, by comparing them with results published in the literature or obtained with the ANSYS commercial finite element code.

Theoretical study of the second-order vibrational Stark effect

The behaviour of the harmonic infrared frequency of diatomic molecules subjected to moderate static uniform electric fields is analysed. The potential energy expression has been developed as a function of a static uniform electric field, which brings about a formulation describing the frequency versus field strength curve. With the help of the first and second derivatives of the expressions obtained, which correspond to the first- and second-order Stark effects, it was possible to find the maxima of the frequency versus field strength curves for a series of molecules using a Newton-Raphson search. A method is proposed which requires only the calculation of a few energy derivatives at a particular value of the field strength. At the same time, the expression for the dependence of the interatomic distance on the electric field strength is derived and the minimum of this curve is found for the same species. Derived expressions and numerical results are discussed and compared with other studi

Modelagem numérica para o processo da evaporação da água do solo

Foram realizados vários ensaios laboratoriais para avaliar o desempenho de um modelo numérico em simular o processo unidimensional da evaporação da água do solo. Este modelo foi desenvolvido a partir da linearização da equação de Richards no espaço e do uso da técnica iterativa de Newton-Raphson, para resolver essa equação não-linear no tempo, e leva em conta o fluxo de vapor dentro do perfil de solo e a taxa de evaporação na sua superfície. Os resultados mostraram que o modelo foi capaz de simular satisfatoriamente o processo, tanto em meios porosos homogêneos quanto estratificados

Programa de ajuste multiparamétrico de curvas de titulação potenciométricas de ácidos húmicos

Tendo em vista a dificuldade de determinação dos pontos de inflexão na curva de titulação potenciométrica de ácidos húmicos, por metodologias tradicionais, foi desenvolvido foi desenvolvido um programa na linguagem Delphi para ajuste multiparamétrico de dados de titulação potenciométrica. Para isso um processo iterativo para estimar as raízes de um polinômio, com base no método de Newton-Raphson, foi utilizado. Os dados das titulações potenciométricas de ácidos húmicos usados nas regressões foram obtidos em um sistema automatizado de titulação potenciométrica. O programa desenvolvido na linguagem Delphi permite maior versatilidade e facilidade de operação, com uma interação mais amigável com o usuário. As curvas de titulação potenciométricas ajustadas sobrepuseram-se quase que totalmente às curvas experimentais. Os valores de pKa e as percentagens de grupos tituláveis dos ácidos húmicos, parâmetros ajustáveis na regressão multiparamétrica, apresentaram valores comparáveis com dados da literatura.

Aplicação de métodos numéricos para estimativa de variáveis psicrométricas

O ar atmosférico é formado por uma composição de ar seco e vapor d'água, cujos valores da quantidade de vapor, em termos quantitativos, são variáveis em função dos elementos climáticos, tais como: temperatura e pressão. Portanto, para estimar os valores de umidade relativa do ar, são necessárias informações completas de séries de dados de temperatura do ar (Tar), pressão atual de vapor (e a) e temperatura de bulbo úmido (Tu). O trabalho apresenta como objetivo a elaboração de rotina computacional para encontrar valores da temperatura do termômetro de bulbo úmido (Tu) em função de outras variáveis, para uma série de dados obtidos, mediante a aplicação de métodos numéricos (Método de Newton-Raphson e Método da Secante), para fins de complementação de uma série de dados diários para Piracicaba - SP. Verificou-se que os métodos numéricos de Newton-Raphson e da Secante apresentaram bom desempenho na simulação dos resultados, porém o método da Secante apresentou-se como o melhor para encontrar os valores de Tu, mediante a resolução numérica da equação psicrométrica.

Modeling a Network of Heat Exchangers

This research work addresses the problem of building a mathematical model for the given system of heat exchangers and to determine the temperatures, pressures and velocities at the intermediate positions. Such model could be used in nding an optimal design for such a superstructure. To limit the size and computing time a reduced network model was used. The method can be generalized to larger network structures. A mathematical model which includes a system of non-linear equations has been built and solved according to the Newton-Raphson algorithm. The results obtained by the proposed mathematical model were compared with the results obtained by the Paterson approximation and Chen's Approximation. Results of this research work in collaboration with a current ongoing research at the department will optimize the valve positions and hence, minimize the pumping cost and maximize the heat transfer of the system of heat exchangers.