Controlador integrado baseado em conceito híbrido e controle geométrico para embarcações posicionadas dinamicamente.

O conceito de controle híbrido é aplicado à operação de alívio entre um FPWSO e um navio aliviador. Ambos os navios mantêm suas posições e aproamentos pelo resultado da ação do seu Sistema de Posicionamento Dinâmico (SPD). O alívio dura cerca de 24 horas para ser concluído. Durante este período, o estado de mar pode se alterar e os calados estão sendo constantemente alterados. Um controlador híbrido é projetado para permitir modificacões dos parâmetros de controle/observação se alguma alteração significante do estado de mar e/ou calado das embarcações ocorrer. O principal objetivo dos controladores é manter o posicionamento relativo entre os navios com o intuito de evitar perigosa proximidade ou excesso de tensão no cabo. Com isto em mente, uma nova estratégia de controle que atue integradamente em ambos os navios é proposta baseda em geometria diferencial. Observadores não lineares baseados em passividade são aplicados para estimar a posição, a velocidade e as forças externas de mares calmos até extremos. O critério para troca do controle/observação é baseado na variação do calado e no estado de mar. O calado é assumido conhecido e o estado de mar é estimado pela frequência de pico do espectro do movimento de primeira ordem dos navios. Um modelo de perturbação é proposto para encontrar o número de controladores do sistema híbrido. A equivalência entre o controle geométrico e o controlador baseado em Multiplicadores de Lagrange é demonstrada. Assumindo algumas hipóteses, a equivalência entre os controladores geométrico e o PD é também apresentada. O desempenho da nova estratégia é avaliada por meio de simulações numéricas e comparada a um controlador PD. Os resultados apresentam muito bom desempenho em função do objetivo proposto. A comparação entre a abordagem geométrica e o controlador PD aponta um desempenho muito parecido entre eles.

An autoregressive conditional filtering process to remove intraday seasonal volatility and its application to testing the noisy rational expectations model

We develop a new autoregressive conditional process to capture both the changes and the persistency of the intraday seasonal (U-shape) pattern of volatility in essay 1. Unlike other procedures, this approach allows for the intraday volatility pattern to change over time without the filtering process injecting a spurious pattern of noise into the filtered series. We show that prior deterministic filtering procedures are special cases of the autoregressive conditional filtering process presented here. Lagrange multiplier tests prove that the stochastic seasonal variance component is statistically significant. Specification tests using the correlogram and cross-spectral analyses prove the reliability of the autoregressive conditional filtering process. In essay 2 we develop a new methodology to decompose return variance in order to examine the informativeness embedded in the return series. The variance is decomposed into the information arrival component and the noise factor component. This decomposition methodology differs from previous studies in that both the informational variance and the noise variance are time-varying. Furthermore, the covariance of the informational component and the noisy component is no longer restricted to be zero. The resultant measure of price informativeness is defined as the informational variance divided by the total variance of the returns. The noisy rational expectations model predicts that uninformed traders react to price changes more than informed traders, since uninformed traders cannot distinguish between price changes caused by information arrivals and price changes caused by noise. This hypothesis is tested in essay 3 using intraday data with the intraday seasonal volatility component removed, as based on the procedure in the first essay. The resultant seasonally adjusted variance series is decomposed into components caused by unexpected information arrivals and by noise in order to examine informativeness.

An Autoregressive Conditional Filtering Process to remove Intraday Seasonal Volatility and its Application to Testing the Noisy Rational Expectations Model

We develop a new autoregressive conditional process to capture both the changes and the persistency of the intraday seasonal (U-shape) pattern of volatility in essay 1. Unlike other procedures, this approach allows for the intraday volatility pattern to change over time without the filtering process injecting a spurious pattern of noise into the filtered series. We show that prior deterministic filtering procedures are special cases of the autoregressive conditional filtering process presented here. Lagrange multiplier tests prove that the stochastic seasonal variance component is statistically significant. Specification tests using the correlogram and cross-spectral analyses prove the reliability of the autoregressive conditional filtering process. In essay 2 we develop a new methodology to decompose return variance in order to examine the informativeness embedded in the return series. The variance is decomposed into the information arrival component and the noise factor component. This decomposition methodology differs from previous studies in that both the informational variance and the noise variance are time-varying. Furthermore, the covariance of the informational component and the noisy component is no longer restricted to be zero. The resultant measure of price informativeness is defined as the informational variance divided by the total variance of the returns. The noisy rational expectations model predicts that uninformed traders react to price changes more than informed traders, since uninformed traders cannot distinguish between price changes caused by information arrivals and price changes caused by noise. This hypothesis is tested in essay 3 using intraday data with the intraday seasonal volatility component removed, as based on the procedure in the first essay. The resultant seasonally adjusted variance series is decomposed into components caused by unexpected information arrivals and by noise in order to examine informativeness.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

The main goal of this paper is to analyse the sensitivity of a vector convex optimization problem according to variations in the right-hand side. We measure the quantitative behavior of a certain set of Pareto optimal points characterized to become minimum when the objective function is composed with a positive function. Its behavior is analysed quantitatively using the circatangent derivative for set-valued maps. Particularly, it is shown that the sensitivity is closely related to a Lagrange multiplier solution of a dual program.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

Development of a numerical platform for the modeling and optimal control of liquid metal flows

The main purpose of this work is to develop a numerical platform for the turbulence modeling and optimal control of liquid metal flows. Thanks to their interesting thermal properties, liquid metals are widely studied as coolants for heat transfer applications in the nuclear context. However, due to their low Prandtl numbers, the standard turbulence models commonly used for coolants as air or water are inadequate. Advanced turbulence models able to capture the anisotropy in the flow and heat transfer are then necessary. In this thesis, a new anisotropic four-parameter turbulence model is presented and validated. The proposed model is based on explicit algebraic models and solves four additional transport equations for dynamical and thermal turbulent variables. For the validation of the model, several flow configurations are considered for different Reynolds and Prandtl numbers, namely fully developed flows in a plane channel and cylindrical pipe, and forced and mixed convection in a backward-facing step geometry. Since buoyancy effects cannot be neglected in liquid metals-cooled fast reactors, the second aim of this work is to provide mathematical and numerical tools for the simulation and optimization of liquid metals in mixed and natural convection. Optimal control problems for turbulent buoyant flows are studied and analyzed with the Lagrange multipliers method. Numerical algorithms for optimal control problems are integrated into the numerical platform and several simulations are performed to show the robustness, consistency, and feasibility of the method.

Assessing the fit of unidimensional IRT models for binary data under model misspecification

Model misspecification affects the classical test statistics used to assess the fit of the Item Response Theory (IRT) models. Robust tests have been derived under model misspecification, as the Generalized Lagrange Multiplier and Hausman tests, but their use has not been largely explored in the IRT framework. In the first part of the thesis, we introduce the Generalized Lagrange Multiplier test to detect differential item response functioning in IRT models for binary data under model misspecification. By means of a simulation study and a real data analysis, we compare its performance with the classical Lagrange Multiplier test, computed using the Hessian and the cross-product matrix, and the Generalized Jackknife Score test. The power of these tests is computed empirically and asymptotically. The misspecifications considered are local dependence among items and non-normal distribution of the latent variable. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the performance of the tests deteriorates. None of the tests considered show an overall superior performance than the others. In the second part of the thesis, we extend the Generalized Hausman test to detect non-normality of the latent variable distribution. To build the test, we consider a seminonparametric-IRT model, that assumes a more flexible latent variable distribution. By means of a simulation study and two real applications, we compare the performance of the Generalized Hausman test with the M2 limited information goodness-of-fit test and the Likelihood-Ratio test. Additionally, the information criteria are computed. The Generalized Hausman test has a better performance than the Likelihood-Ratio test in terms of Type I error rates and the M2 test in terms of power. The performance of the Generalized Hausman test and the information criteria deteriorates when the sample size is small and with a few items.

A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations

We introduce a second order in time modified Lagrange--Galerkin (MLG) method for the time dependent incompressible Navier--Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the $P2/P1$ Taylor--Hood element are used.

Superefficiency and Multiplier Adjustment in Data Envelopment Analysis

Copyright © 2013 Springer Netherlands.

Multiplier adjustment in data envelopment analysis

V Congreso de Eficiencia y Productividad EFIUCO, Córdoba, 19-20 Mayo 2011.

Economic optimization method to design telescope irrigation of multiples outlets

In this study is presented an economic optimization method to design telescope irrigation laterals (multidiameter) with regular spaced outlets. The proposed analytical hydraulic solution was validated by means of a pipeline composed of three different diameters. The minimum acquisition cost of the telescope pipeline was determined by an ideal arrangement of lengths and respective diameters for each one of the three segments. The mathematical optimization method based on the Lagrange multipliers provides a strategy for finding the maximum or minimum of a function subject to certain constraints. In this case, the objective function describes the acquisition cost of pipes, and the constraints are determined from hydraulic parameters as length of irrigation laterals and total head loss permitted. The developed analytical solution provides the ideal combination of each pipe segment length and respective diameter, resulting in a decreased of the acquisition cost.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.