Formulação teórica dos fundamentos da otimização global topográfica com análise de desempenho e aplicações à estabilidade de fases de misturas termodinâmicas

Métodos de otimização que utilizam condições de otimalidade de primeira e/ou segunda ordem são conhecidos por serem eficientes. Comumente, esses métodos iterativos são desenvolvidos e analisados à luz da análise matemática do espaço euclidiano n-dimensional, cuja natureza é de caráter local. Consequentemente, esses métodos levam a algoritmos iterativos que executam apenas as buscas locais. Assim, a aplicação de tais algoritmos para o cálculo de minimizadores globais de uma função não linear,especialmente não-convexas e multimodais, depende fortemente da localização dos pontos de partida. O método de Otimização Global Topográfico é um algoritmo de agrupamento, que utiliza uma abordagem baseada em conceitos elementares da teoria dos grafos, a fim de gerar bons pontos de partida para os métodos de busca local, a partir de pontos distribuídos de modo uniforme no interior da região viável. Este trabalho tem dois objetivos. O primeiro é realizar uma nova abordagem sobre método de Otimização Global Topográfica, onde, pela primeira vez, seus fundamentos são formalmente descritos e suas propriedades básicas são matematicamente comprovadas. Neste contexto, propõe-se uma fórmula semi-empírica para calcular o parâmetro chave deste algoritmo de agrupamento, e, usando um método robusto e eficiente de direções viáveis por pontos-interiores, estendemos o uso do método de Otimização Global Topográfica a problemas com restrições de desigualdade. O segundo objetivo é a aplicação deste método para a análise de estabilidade de fase em misturas termodinâmicas,o qual consiste em determinar se uma dada mistura se apresenta em uma ou mais fases. A solução deste problema de otimização global é necessária para o cálculo do equilíbrio de fases, que é um problema de grande importância em processos da engenharia, como, por exemplo, na separação por destilação, em processos de extração e simulação da recuperação terciária de petróleo, entre outros. Além disso, afim de ter uma avaliação inicial do potencial dessa técnica, primeiro vamos resolver 70 problemas testes, e então comparar o desempenho do método proposto aqui com o solver MIDACO, um poderoso software recentemente introduzido no campo da otimização global.

Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.

Temporal difference models describe higher-order learning in humans.

The ability to use environmental stimuli to predict impending harm is critical for survival. Such predictions should be available as early as they are reliable. In pavlovian conditioning, chains of successively earlier predictors are studied in terms of higher-order relationships, and have inspired computational theories such as temporal difference learning. However, there is at present no adequate neurobiological account of how this learning occurs. Here, in a functional magnetic resonance imaging (fMRI) study of higher-order aversive conditioning, we describe a key computational strategy that humans use to learn predictions about pain. We show that neural activity in the ventral striatum and the anterior insula displays a marked correspondence to the signals for sequential learning predicted by temporal difference models. This result reveals a flexible aversive learning process ideally suited to the changing and uncertain nature of real-world environments. Taken with existing data on reward learning, our results suggest a critical role for the ventral striatum in integrating complex appetitive and aversive predictions to coordinate behaviour.

An investigation of higher-order multi-objective optimisation for 3D aerodynamic shape design

We investigate the performance of different variants of a suitably tailored Tabu Search optimisation algorithm on a higher-order design problem. We consider four objective func- tions to describe the performance of a compressor stator row, subject to a number of equality and inequality constraints. The same design problem has been previously in- vestigated through single-, bi- and three-objective optimisation studies. However, in this study we explore the capabilities of enhanced variants of our Multi-objective Tabu Search (MOTS) optimisation algorithm in the context of detailed 3D aerodynamic shape design. It is shown that with these enhancements to the local search of the MOTS algorithm we can achieve a rapid exploration of complicated design spaces, but there is a trade-off be- tween speed and the quality of the trade-off surface found. Rapidly explored design spaces reveal the extremes of the objective functions, but the compromise optimum areas are not very well explored. However, there are ways to adapt the behaviour of the optimiser and maintain both a very efficient rate of progress towards the global optimum Pareto front and a healthy number of design configurations lying on the trade-off surface and exploring the compromise optimum regions. These compromise solutions almost always represent the best qualitative balance between the objectives under consideration. Such enhancements to the effectiveness of design space exploration make engineering design optimisation with multiple objectives and robustness criteria ever more practicable and attractive for modern advanced engineering design. Finally, new research questions are addressed that highlight the trade-offs between intelligence in optimisation algorithms and acquisition of qualita- tive information through computational engineering design processes that reveal patterns and relations between design parameters and objective functions, but also speed versus optimum quality. © 2012 AIAA.

Finite Element studies on indentation size effect using a higher order strain gradient theory

In this work, a Finite Element implementation of a higher order strain gradient theory (due to Fleck and Hutchinson, 2001) has been used within the framework of large deformation elasto-viscoplasticity to study the indentation of metals with indenters of various geometries. Of particular interest is the indentation size effect (ISE) commonly observed in experiments where the hardness of a range of materials is found to be significantly higher at small depths of indentation but reduce to a lower, constant value at larger depths. That the ISE can be explained by strain gradient plasticity is well known but this work aims to qualitatively compare a gamut of experimental observations on this effect with predictions from a higher order strain gradient theory. Results indicate that many of the experimental observations are qualitatively borne out by our simulations. However, areas exist where conflicting experimental results make assessment of numerical predictions difficult. © 2012 Elsevier Ltd. All rights reserved.

Material point method for coupled hydromechanical problems

This paper describes a new formulation of the material point method (MPM) for solving coupled hydromechanical problems of fluid-saturated soil subjected to large deformation. A soil-pore fluid coupled MPM algorithm based on Biot's mixture theory is proposed for solving hydromechanical interaction problems that include changes in water table location with time. The accuracy of the proposed method is examined by comparing the results of the simulation of a one-dimensional consolidation test with the corresponding analytical solution. A sensitivity analysis of the MPM parameters used in the proposed method is carried out for examining the effect of the number of particles per mesh and mesh size on solution accuracy. For demonstrating the capability of the proposed method, a physical model experiment of a large-scale levee failure by seepage is simulated. The behavior of the levee model with time-dependent changes in water table matches well to the experimental observations. The mechanisms of seepage-induced failure are discussed by examining the pore-water pressures, as well as the effective stresses computed from the simulations © 2013 American Society of Civil Engineers.

a higher-order duration calculus and its completeness

National Natural Science Foundation of China; Public Administration and Civil Service Bureau of Macau SAR; Companhia de Telecomunicacoes de Macau S.A.R.L.; Macau SAR Government Tourist Office