Aplicação de métodos estocásticos na gestão de custos de construção de condutas de saneamento

O trabalho apresentado centra-se na determinação dos custos de construção de condutas de pequenos e médios diâmetros em Polietileno de Alta Densidade (PEAD) para saneamento básico, tendo como base a metodologia descrita no livro Custos de Construção e Exploração – Volume 9 da série Gestão de Sistemas de Saneamento Básico, de Lencastre et al. (1994). Esta metodologia descrita no livro já referenciado, nos procedimentos de gestão de obra, e para tal foram estimados custos unitários de diversos conjuntos de trabalhos. Conforme Lencastre et al (1994), “esses conjuntos são referentes a movimentos de terras, tubagens, acessórios e respetivos órgãos de manobra, pavimentações e estaleiro, estando englobado na parte do estaleiro trabalhos acessórios correspondentes à obra.” Os custos foram obtidos analisando vários orçamentos de obras de saneamento, resultantes de concursos públicos de empreitadas recentemente realizados. Com vista a tornar a utilização desta metodologia numa ferramenta eficaz, foram organizadas folhas de cálculo que possibilitam obter estimativas realistas dos custos de execução de determinada obra em fases anteriores ao desenvolvimento do projeto, designadamente numa fase de preparação do plano diretor de um sistema ou numa fase de elaboração de estudos de viabilidade económico-financeiros, isto é, mesmo antes de existir qualquer pré-dimensionamento dos elementos do sistema. Outra técnica implementada para avaliar os dados de entrada foi a “Análise Robusta de Dados”, Pestana (1992). Esta metodologia permitiu analisar os dados mais detalhadamente antes de se formularem hipóteses para desenvolverem a análise de risco. A ideia principal é o exame bastante flexível dos dados, frequentemente antes mesmo de os comparar a um modelo probabilístico. Assim, e para um largo conjunto de dados, esta técnica possibilitou analisar a disparidade dos valores encontrados para os diversos trabalhos referenciados anteriormente. Com os dados recolhidos, e após o seu tratamento, passou-se à aplicação de uma metodologia de Análise de Risco, através da Simulação de Monte Carlo. Esta análise de risco é feita com recurso a uma ferramenta informática da Palisade, o @Risk, disponível no Departamento de Engenharia Civil. Esta técnica de análise quantitativa de risco permite traduzir a incerteza dos dados de entrada, representada através de distribuições probabilísticas que o software disponibiliza. Assim, para por em prática esta metodologia, recorreu-se às folhas de cálculo que foram realizadas seguindo a abordagem proposta em Lencastre et al (1994). A elaboração e a análise dessas estimativas poderão conduzir à tomada de decisões sobre a viabilidade da ou das obras a realizar, nomeadamente no que diz respeito aos aspetos económicos, permitindo uma análise de decisão fundamentada quanto à realização dos investimentos.

Some pioneers of the applications of fractional calculus

In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Lévy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair.

Fractional calculus analysis of the cosmic microwave background

Cosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.

Condition-Based Diagnosis of Mechatronic Systems Using a Fractional Calculus Approach

While fractional calculus (FC) is as old as integer calculus, its application has been mainly restricted to mathematics. However, many real systems are better described using FC equations than with integer models. FC is a suitable tool for describing systems characterised by their fractal nature, long-term memory and chaotic behaviour. It is a promising methodology for failure analysis and modelling, since the behaviour of a failing system depends on factors that increase the model’s complexity. This paper explores the proficiency of FC in modelling complex behaviour by tuning only a few parameters. This work proposes a novel two-step strategy for diagnosis, first modelling common failure conditions and, second, by comparing these models with real machine signals and using the difference to feed a computational classifier. Our proposal is validated using an electrical motor coupled with a mechanical gear reducer.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Fractional Calculus: Quo Vadimus? (Where Are We Going?)

Discussions under this title were held during a special session in frames of the International Conference “Fractional Differentiation and Applications” (ICFDA ’14) held in Catania (Italy), 23-25 June 2014, see details at http://www.icfda14.dieei.unict.it/. Along with the presentations made during this session, we include here some contributions by the participants sent afterwards and also by few colleagues planning but failed to attend. The intention of this special session was to continue the useful traditions from the first conferences on the Fractional Calculus (FC) topics, to pose open problems, challenging hypotheses and questions “where to go”, to discuss them and try to find ways to resolve.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Response Time Analysis for Fixed-Priority Tasks with Multiple Probabilistic Parameters

Demo presented in 12th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2015). 8 to 12, Jun, 2015. La Roche-en-Ardenne, Belgium. Extended abstract.

Fractional Calculus: Application in modeling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

Short-Circuit Impedance of Power Transformers: the Fractional Order Calculus Approach

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

On the Estimation of the Short-Circuit Impedance of Power Transformers Using Fractional Order Calculus

This paper reports investigation on the estimation of the short circuit impedance of power transformers, using fractional order calculus to analytically study the influence of the diffusion phenomena in the windings. The aim is to better characterize the medium frequency range behavior of leakage inductances of power transformer models, which include terms to represent the magnetic field diffusion process in the windings. Comparisons between calculated and measured values are shown and discussed.

Application of Fractional Calculus in Mechatronics

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of mechanical systems.

6D Visual Odometry with Dense Probabilistic Egomotion Estimation

Proceedings of the International Conference on Computer Vision Theory and Applications, 361-365, 2013, Barcelona, Spain