On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Comparação de alguns modelos matemáticos para ajuste à curva de lactação média de um rebanho da raça Caracu

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparação de alguns modelos matemáticos para o ajuste às curvas de lactação individuais de vacas da raça Caracu

Foram ajustadas 7239 curvas de lactação de vacas Caracu, controladas semanalmente entre os anos de 1978 a 1988, pertencentes à Fazenda Chiqueirão, Poços de Caldas, MG. As funções utilizadas foram a linear hiperbólica (FLH), a quadrática logarítmica (FQL), a gama incompleta (FGI) e a polinomial inversa (FPI). Os parâmetros foram estimados por meio de regressões não lineares, usando-se processos iterativos. A verificação da qualidade do ajuste baseou-se no coeficiente de determinação ajustado (R²A), no teste de Durbin-Watson (DW) e nas médias e desvios-padrão estimados para os parâmetros e funções dos parâmetros dos modelos. Para a curva média, os R²A foram superiores a 0,90 para todas as funções. Bons ajustes, baseados nos R²A>0,80 foram obtidos, respectivamente, por 25,2%, 39,1%, 31,1% e 28,4% das lactações ajustadas pelas funções FLH, FQL, FGI e FPI. de acordo com o teste de DW, bons ajustes foram proporcionados para 29,4% das lactações ajustadas pela FLH, 54,9% pela FQL, 34,9% pela FGI e 29,6% pela FPI. Para ambos os critérios, a FQL foi superior às demais funções, indicando grande variação nas formas das curvas de lactação geradas pelos ajustes individuais. Curvas atípicas foram estimadas pelas funções, com picos ocorrendo antes do parto e algumas vezes após o término da lactação. Todas as funções apresentaram problemas quando ajustaram dados individuais.

Electric power systems transient stability analysis by neural networks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Application of a model updating technique for health condition monitoring and damage detection of flexible structures

This paper discusses the application of a damage detection methodology to monitor the location and extent of partial structural damage. The methodology combines, in an iterative way, the model updating technique based on frequency response functions (FRF) with monitoring data aiming at identifying the damage area of the structure. After the updating procedure reaches a good correlation between the models, it compares the parameters of the damage structure with those of the undamaged one to find the deteriorated area. The influence of the FEM mesh size on the evaluation of the extent of the damage has also been discussed. The methodology is applied using real experimental data from a spatial frame structure.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Expert system for hot forging design

Planning hot forging processes is a time-consuming activity with high costs involved because of the trial-and-error iterative methods used to design dies and to choose equipment and process conditions. Some processes demand many months to produce forged parts with controlled shapes, dimensions and microstructure. This paper shows how expert systems can help engineers to reduce the time needed to design precision forged parts and dies from machined parts. The software ADHFD interfacing MS Visual Basic v.5.0 and SolidEdge v.3.0 was used to design flashless hot forged gears, chosen from families of gears. © 1998 Elsevier Science S.A. All rights reserved.

H2 and/or H∞-norm model reduction of uncertain discrete-time systems

This paper addresses the problem of model reduction for uncertain discrete-time systems with convex bounded (polytope type) uncertainty. A reduced order precisely known model is obtained in such a way that the H2 and/or the H∞ guaranteed norm of the error between the original (uncertain) system and the reduced one is minimized. The optimization problems are formulated in terms of coupled (non-convex) LMIs - Linear Matrix Inequalities, being solved through iterative algorithms. Examples illustrate the results.

Constraints implementation for IQML and mode direction-of-arrival estimators

The iterative quadratic maximum likelihood IQML and the method of direction estimation MODE are well known high resolution direction-of-arrival DOA estimation methods. Their solutions lead to an optimization problem with constraints. The usual linear constraint presents a poor performance for certain DOA values. This work proposes a new linear constraint applicable to both DOA methods and compare their performance with two others: unit norm and usual linear constraint. It is shown that the proposed alternative performs better than others constraints. The resulting computational complexity is also investigated.

Identification of synchronous machine parameters using load rejection test data

This work shows a computational methodology for the determination of synchronous machines parameters using load rejection test data. By machine modeling one can obtain the quadrature parameters through a load rejection under an arbitrary reference, reducing the present difficulties. The proposed method is applied to a real machine.

Distribution line models analysis for loss calculation within three-phase three-wire power flow algorithms

Three-phase three-wire power flow algorithms, as any tool for power systems analysis, require reliable impedances and models in order to obtain accurate results. Kron's reduction procedure, which embeds neutral wire influence into phase wires, has shown good results when three-phase three-wire power flow algorithms based on current summation method were used. However, Kron's reduction can harm reliabilities of some algorithms whose iterative processes need loss calculation (power summation method). In this work, three three-phase three-wire power flow algorithms based on power summation method, will be compared with a three-phase four-wire approach based on backward-forward technique and current summation. Two four-wire unbalanced medium-voltage distribution networks will be analyzed and results will be presented and discussed. © 2004 IEEE.

On the determination of epsilon during discriminative GMM training

Discriminative training of Gaussian Mixture Models (GMMs) for speech or speaker recognition purposes is usually based on the gradient descent method, in which the iteration step-size, ε, uses to be defined experimentally. In this letter, we derive an equation to adaptively determine ε, by showing that the second-order Newton-Raphson iterative method to find roots of equations is equivalent to the gradient descent algorithm. © 2010 IEEE.

Medidas de coerência para análise de velocidade na migração em tempo

Métodos iterativos para a análise de velocidade com migração dependem das funções objetivo medirem a horizontalização dos eventos de reflexão em famílias de ponto imagem comum (CIG). A migração em tempo é um método simples de imageamento para avaliar essas funções objetivo. Usando migração em tempo, estudamos a influência da função objetivo nos resultados da análise de velocidade com migração. Propomos duas novas funções objetivo para a análise velocidade com migração: Semblance Diferencial Estendido e o produto do Semblance Clássico com o Semblance Diferencial Estendido. Experimentos numéricos, utilizando os dados Marmousoft, mostram a eficácia das novas funções objetivo em estimar modelos velocidade produzindo eventos horizontalmente alinhados nas famílias de ponto imagem comum.

SPECT (Single photon emission tomography): Gama câmara, reconstrução tomográfica e características funcional

The SPECT (Single Photon Emission Computed Tomography) systems are part of a medical image acquisition technology which has been outstanding, because the resultant images are functional images complementary to those that give anatomic information, such as X-Ray CT, presenting a high diagnostic value. These equipments acquire, in a non-invasive way, images from the interior of the human body through tomographic mapping of radioactive material administered to the patient. The SPECT systems are based on the Gamma Camera detection system, and one of them being set on a rotational gantry is enough to obtain the necessary data for a tomographic image. The images obtained from the SPECT system consist in a group of flat images that describe the radioactive distribution on the patient. The trans-axial cuts are obtained from the tomographic reconstruction techniques. There are analytic and iterative methods to obtain the tomographic reconstruction. The analytic methods are based on the Fourier Cut Theorem (FCT), while the iterative methods search for numeric solutions to solve the equations from the projections. Within the analytic methods, the filtered backprojection (FBP) method maybe is the simplest of all the tomographic reconstruction techniques. This paper's goal is to present the operation of the SPECT system, the Gamma Camera detection system, some tomographic reconstruction techniques and the requisites for the implementation of this system in a Nuclear Medicine service

Sulla progettazione in zona sismica di strutture dotate di dissipatori fluido-viscosi: proposta di una metodologia

CHAPTER 1:FLUID-VISCOUS DAMPERS In this chapter the fluid-viscous dampers are introduced. The first section is focused on the technical characteristics of these devices, their mechanical behavior and the latest evolution of the technology whose they are equipped. In the second section we report the definitions and the guide lines about the design of these devices included in some international codes. In the third section the results of some experimental tests carried out by some authors on the response of these devices to external forces are discussed. On this purpose we report some technical schedules that are usually enclosed to the devices now available on the international market. In the third section we show also some analytic models proposed by various authors, which are able to describe efficiently the physical behavior of the fluid-viscous dampers. In the last section we propose some cases of application of these devices on existing structures and on new-construction structures. We show also some cases in which these devices have been revealed good for aims that lies outside the reduction of seismic actions on the structures. CHAPTER 2:DESIGN METHODS PROPOSED IN LITERATURE In this chapter the more widespread design methods proposed in literature for structures equipped by fluid-viscous dampers are introduced. In the first part the response of sdf systems in the case of harmonic external force is studied, in the last part the response in the case of random external force is discussed. In the first section the equations of motion in the case of an elastic-linear sdf system equipped with a non-linear fluid-viscous damper undergoing a harmonic force are introduced. This differential problem is analytically quite complex and it’s not possible to be solved in a closed form. Therefore some authors have proposed approximate solution methods. The more widespread methods are based on equivalence principles between a non-linear device and an equivalent linear one. Operating in this way it is possible to define an equivalent damping ratio and the problem becomes linear; the solution of the equivalent problem is well-known. In the following section two techniques of linearization, proposed by some authors in literature, are described: the first technique is based on the equivalence of the energy dissipated by the two devices and the second one is based on the equivalence of power consumption. After that we compare these two techniques by studying the response of a sdf system undergoing a harmonic force. By introducing the equivalent damping ratio we can write the equation of motion of the non-linear differential problem in an implicit form, by dividing, as usual, for the mass of the system. In this way, we get a reduction of the number of variables, by introducing the natural frequency of the system. The equation of motion written in this form has two important properties: the response is linear dependent on the amplitude of the external force and the response is dependent on the ratio of the frequency of the external harmonic force and the natural frequency of the system only, and not on their single values. All these considerations, in the last section, are extended to the case of a random external force. CHAPTER 3: DESIGN METHOD PROPOSED In this chapter the theoretical basis of the design method proposed are introduced. The need to propose a new design method for structures equipped with fluid-viscous dampers arises from the observation that the methods reported in literature are always iterative, because the response affects some parameters included in the equation of motion (such as the equivalent damping ratio). In the first section the dimensionless parameterε is introduced. This parameter has been obtained from the definition of equivalent damping ratio. The implicit form of the equation of motion is written by introducing the parameter ε, instead of the equivalent damping ratio. This new implicit equation of motions has not any terms affected by the response, so that once ε is known the response can be evaluated directly. In the second section it is discussed how the parameter ε affects some characteristics of the response: drift, velocity and base shear. All the results described till this point have been obtained by keeping the non-linearity of the behavior of the dampers. In order to get a linear formulation of the problem, that is possible to solve by using the well-known methods of the dynamics of structures, as we did before for the iterative methods by introducing the equivalent damping ratio, it is shown how the equivalent damping ratio can be evaluated from knowing the value of ε. Operating in this way, once the parameter ε is known, it is quite easy to estimate the equivalent damping ratio and to proceed with a classic linear analysis. In the last section it is shown how the parameter ε could be taken as reference for the evaluation of the convenience of using non-linear dampers instead of linear ones on the basis of the type of external force and the characteristics of the system. CHAPTER 4: MULTI-DEGREE OF FREEDOM SYSTEMS In this chapter the design methods of a elastic-linear mdf system equipped with non-linear fluidviscous dampers are introduced. It has already been shown that, in the sdf systems, the response of the structure can be evaluated through the estimation of the equivalent damping ratio (ξsd) assuming the behavior of the structure elastic-linear. We would to mention that some adjusting coefficients, to be applied to the equivalent damping ratio in order to consider the actual behavior of the structure (that is non-linear), have already been proposed in literature; such coefficients are usually expressed in terms of ductility, but their treatment is over the aims of this thesis and we does not go into further. The method usually proposed in literature is based on energy equivalence: even though this procedure has solid theoretical basis, it must necessary include some iterative process, because the expression of the equivalent damping ratio contains a term of the response. This procedure has been introduced primarily by Ramirez, Constantinou et al. in 2000. This procedure is reported in the first section and it is defined “Iterative Method”. Following the guide lines about sdf systems reported in the previous chapters, it is introduced a procedure for the assessment of the parameter ε in the case of mdf systems. Operating in this way the evaluation of the equivalent damping ratio (ξsd) can be done directly without implementing iterative processes. This procedure is defined “Direct Method” and it is reported in the second section. In the third section the two methods are analyzed by studying 4 cases of two moment-resisting steel frames undergoing real accelerogramms: the response of the system calculated by using the two methods is compared with the numerical response obtained from the software called SAP2000-NL, CSI product. In the last section a procedure to create spectra of the equivalent damping ratio, affected by the parameter ε and the natural period of the system for a fixed value of exponent α, starting from the elasticresponse spectra provided by any international code, is introduced.