Application of fractional calculus in engineering

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. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Some applications of fractional calculus in engineering

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, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. 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 FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

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 of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

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.

How market power affects the behaviour of a pumped storage hydro unit in the day-ahead electricity market?

The integration of large amounts of wind energy in power systems raises important operation issues such as the balance between power demand and generation. The pumped storage hydro (PSH) units are seen as one solution for this issue, avoiding the need for wind power curtailments. However, the behavior of a PSH unit might differ considerably when it operates in a liberalized market with some degree of market power. In this regard, a new approach for the optimal daily scheduling of a PSH unit in the day-ahead electricity market was developed and presented in this paper, in which the market power is modeled by a residual inverse demand function with a variable elasticity. The results obtained show that increasing degrees of market power of the PSH unit correspond to decreasing levels of storage and, therefore, the capacity to integrate wind power is considerably reduced under these circumstances.

Os modelos na compreensão dos números racionais fracionários

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Occupational risk in a glass manufacturing industry unit

Risk assessment is one of the main pillars of the framework directive and other directives in respect of health and safety. It is also the basis of an effective management of safety and health as it is essential to reduce work-related accidents and occupational diseases. To survey the hazards eventually present in the workplaces the usual procedures are i) gathering information about tasks/activities, employees, equipment, legislation and standards; ii) observation of the tasks and; iii) quantification of respective risks through the most adequate risk assessment among the methodologies available. From this preliminary evaluation of a welding plant and, from the different measurable parameters, noise was considered the most critical. This paper focus not only the usual way of risk assessment for noise but also another approach that may allow us to identify the technique with which a weld is being performed.

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.

Legionnaires' disease in the renal transplant unit of "Hospital das Clinicas, FMUSP": during a five year period (1988-1993)

Several reports have related Legionella pneumophila with pneumonia in renal transplant patients, however this association has not been systematically documented in Brazil. Therefore this paper reports the incidence, by serologycal assays, of Legionella pneumophila serogroup 1 in these patients during a five year period. For this purpose sera from blood samples of 70 hospitalized patients with pneumonia from the Renal Transplant Unit of Hospital das Clinicas, FMUSP collected at the acute and convalescent phase of infection were submitted to indirect immunofluorescence assay (IFA) to demonstrate anti-Legionella pneumophila serogroup 1 antibodies. Of these 70 patients studied during the period of 1988 to 1993,18 (25.71 %) had significant rises in specific antibody titers for Legionella pneumophila serogroup 1. Incidence was interrupted following Hospital water decontamination procedures, with recurrence of infections after treatment interruption. In this study, the high susceptibility (25.71%) of immunodepressed renal transplant patients to Legionella pneumophila serogroup 1 nosocomial infections is documented. The importance of the implementation and maintenance of water decontamination measures for prophylaxis of the infection is also clearly evident.

Matemática 100 stress: um projeto aberto no IPP

A Era Tecnológica em que nos vemos inseridos, cujos avanços acontecem a uma velocidade vertiginosa exige, por parte das Instituições de Ensino Superior (IES) uma atitude proactiva no sentido de utilização dos muitos recursos disponíveis. Por outro lado, os elementos próprios da sociedade da informação – flexibilidade, formação ao longo da vida, acessibilidade à informação, mobilidade, entre muito outros – atuam como fortes impulsionadores externos para que as IES procurem e analisem novas modalidades formativas. Perante a mobilidade crescente, que se tem revelado massiva, a aprendizagem tende a ser cada vez mais individualizada, visual e prática. A conjugação de várias formas/tipologias de transmissão de conhecimento, de métodos didáticos e mesmo de ambientes e situações de aprendizagem induzem uma melhor adaptação do estudante, que poderá procurar aqueles que melhor vão ao encontro das suas expetativas, isto é, favorecem um processo de ensino-aprendizagem eficiente na perspetiva da forma de aprender de cada um. A definição de políticas estratégicas relacionadas com novas modalidades de ensino/formação tem sido uma preocupação constante na nossa instituição, nomeadamente no domínio do ensino à distância, seja ele e-Learning, b-Learning ou, mais recentemente, “open-Learning”, onde se inserem os MOOC – Massive Open Online Courses (não esquecendo a vertente m-Learning), de acordo com as várias tendências europeias (OECD, 2007) (Comissão Europeia, 2014) e com os objetivos da “Europa 2020”. Neste sentido surge o Projeto Matemática 100 STRESS, integrado no projeto e-IPP | Unidade de e-Learning do Politécnico do Porto que criou a sua plataforma MOOC, abrindo em junho de 2014 o seu primeiro curso – Probabilidades e Combinatória. Pretendemos dar a conhecer este Projeto, e em particular este curso, que envolveu vários docentes de diferentes unidades orgânicas do IPP.

A calculus for modeling and analyzing conversations in service-oriented computing

Dissertação apresentada para a obtenção do Grau de Doutor em Informática pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Congenital cytomegalovirus infection in a neonatal intensive care unit in Brazil evaluated by PCR and association with perinatal aspects

Cytomegalovirus (CMV) infection is the most common congenital infection, affecting 0.4% to 2.3% newborns. Most of them are asymptomatic at birth, but later 10% develop handicaps, mainly neurological disturbances. Our aim was to determine the prevalence of CMV shed in urine of newborns from a neonatal intensive care unit using the polymerase chain reaction (PCR) and correlate positive cases to some perinatal aspects. Urine samples obtained at first week of life were processed according to a PCR protocol. Perinatal data were collected retrospectively from medical records. Twenty of the 292 cases (6.8%) were CMV-DNA positive. There was no statistical difference between newborns with and without CMV congenital infection concerning birth weight (p=0.11), gestational age (p=0.11), Apgar scores in the first and fifth minutes of life (p=0.99 and 0.16), mother's age (p=0.67) and gestational history. Moreover, CMV congenital infection was neither related to gender (p=0.55) nor to low weight (<2,500g) at birth (p=0.13). This high prevalence of CMV congenital infection (6.8%) could be due to the high sensitivity of PCR technique, the low socioeconomic level of studied population or the severe clinical status of these newborns.

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.