Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Presença e influência dos contraiões em filmes automontados

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Física, especialidade de Engenharia de Superfícies, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Modeling of the lung impedance using a fractional order ladder network with constant phase elements

The self similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. The fractal geometry is typically characterized by a recurrent structure. This study investigates the identification of a model for the respiratory tree by means of its electrical equivalent based on intrinsic morphology. Measurements were obtained from seven volunteers, in terms of their respiratory impedance by means of its complex representation for frequencies below 5 Hz. A parametric modeling is then applied to the complex valued data points. Since at low-frequency range the inertance is negligible, each airway branch is modeled by using gamma cell resistance and capacitance, the latter having a fractional-order constant phase element (CPE), which is identified from measurements. In addition, the complex impedance is also approximated by means of a model consisting of a lumped series resistance and a lumped fractional-order capacitance. The results reveal that both models characterize the data well, whereas the averaged CPE values are supraunitary and subunitary for the ladder network and the lumped model, respectively.

Persistence characteristics in financial prices: evidence from the portuguese stock market returns

The objective of this article is to provide additional knowledge to the discussion of long-term memory, leaning over the behavior of the main Portuguese stock index. The first four moments are calculated using time windows of increasing size and sliding time windows of fixed size equal to 50 days and suggest that daily returns are non-ergodic and non-stationary. Seeming that the series is best described by a fractional Brownian motion approach, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA). The findings indicate evidence of long term memory in the form of persistence. This evidence of fractal structure suggests that the market is subject to greater predictability and contradicts the efficient market hypothesis in its weak form. This raises issues regarding theoretical modeling of asset pricing. In addition, we carried out a more localized (in time) study to identify the evolution of the degree of long-term dependency over time using windows 200-days and 400-days. The results show a switching feature in the index, from persistent to anti-persistent, quite evident from 2010.

Urban land use change analysis and modelling: a case study of Setubal-Sesimbra, Portugal

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Introduction to fractional linear systems. Part 1 : continuous-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.

Avaliação da satisfação do utente na comunicação com os profissionais de saúde construção e validação de um instrumento

A satisfação do utente na comunicação com profissionais de saúde é um indicador de qualidade dos serviços ou instituições. Na literatura não encontramos instrumentos padronizados e validados, que avaliem a satisfação do utente na comunicação com os profissionais de saúde. O presente estudo tem como objetivo construir e validar um instrumento para avaliar a satisfação do utente na comunicação com os profissionais de saúde. Desenvolvemos este estudo em três ciclos. Um primeiro, revisão da literatura, para identificar dimensões e itens da comunicação interpessoal na saúde. No segundo ciclo, conduzimos um método de Delphi modificado em três rondas, com recurso à plataforma informática de questionários Survey Monkey, no qual participou um painel de 25 peritos; estabelecemos como critério mínimo de retenção para a ronda seguinte os itens que recebessem 70% do consenso por parte do painel. Após as três rondas, obtivemos um instrumento com seis dimensões comunicacionais (comunicação verbal, comunicação não verbal, empatia, respeito, resolução de problemas e material de apoio), vinte e cinco itens específicos, e mais seis dimensões genéricas, que avaliam cada uma das dimensões. No terceiro ciclo avaliamos as características psicométricas, em termos de sensibilidade, validade do construto e fidelidade, numa amostra de 348 participantes. Os resultados mostram que todas as categorias de resposta estavam representadas em todos os itens. Validade do construto- a análise fatorial identificou uma solução de seis componentes que explicam 71% da variância total. Fiabilidade - os valores da correlação item-total variam entre 0,387 e 0,722, existindo uma correlação positiva moderada a forte. O valor de alfa de Cronbach (α=0,928) indica que a consistência interna é excelente. O instrumento construído apresenta boas propriedades psicométricas. Fica assim disponível uma nova ferramenta para auxiliar na gestão e no processo de planeamento necessários ao incremento da qualidade nos serviços e instituições de saúde.

Long-term memory in financial prices: evidence from the Dutch stock market returns

Prepared for presentation at the Portuguese Finance Network International Conference 2014, Vilamoura, Portugal, June 18-20

Electrical ageing studies of polymeric insulation for power cables (estudo do envelhecimento eléctrico do isolante polimérico de cabos eléctricos

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Física - Física Aplicada pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Analysis of the Respiratory Dynamics During Normal Breathing by Means of Pseudophase Plots and Pressure–Volume Loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure-volume curves and the pseudophase-plane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.