Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Educational in a global environment: non-formal examples of learning practices at the international office

23rd SPACE AGM and Conference from 9 to 12 May 2012 Conference theme: The Role of Professional Higher Education: Responsibility and Reflection Venue: Mikkeli University of Applied Sciences, Mikkeli, Finland

Dynamical analysis of the global warming

Global warming is a major concern nowadays. Weather conditions are changing, and it seems that human activity is one of the main causes. In fact, since the beginning of the industrial revolution, the burning of fossil fuels has increased the nonnatural emissions of carbon dioxide to the atmosphere. Carbon dioxide is a greenhouse gas that absorbs the infrared radiation produced by the reflection of the sunlight on the Earth’s surface, trapping the heat in the atmosphere. Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic, and health aspects of human life. This paper studies the global warming trend in the perspective of dynamical systems and fractional calculus, which is a new standpoint in this context. Worldwide distributed meteorological stations and temperature records for the last 100 years are analysed. It is shown that the application of Fourier transforms and power law trend lines leads to an assertive representation of the global warming dynamics and a simpler analysis of its characteristics.

Power Law Behavior and Self-similarity in Modern Industrial Accidents

Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.

Análise e melhoria de processo de pintura e vulcanização na Continental

A indústria automóvel é um dos setores mais exigentes do mercado global, por este motivo empresas como a Continental Mabor S.A, líderes de mercado, necessitam estar na linha da frente no que toca a programas de melhoria contínua e de uma gestão orientada para um crescimento rentável e sustentado. Nesta perspetiva, este estudo de dissertação tem como objetivo encontrar uma solução para a gestão de stock e FiFo (First in First out) de pneus em verde na supracitada empresa, situada em Lousado, Vila Nova de Famalicão. Este projeto de dissertação iniciou-se com uma análise e diagnóstico do processo produtivo do pneu, entre a Construção e a Vulcanização. Nesta análise, foi possível identificar vários problemas, sendo o mais crítico associado à logística interna de transporte do pneu “em curso”, de fabrico entre as fases do mesmo, Construção e Vulcanização. Devido a condicionantes estruturais e de organização, a logística interna de transporte entre estes dois sectores enfrenta estrangulamentos nos fluxos, a falta de espaço para acomodar o material em curso, problemas organizacionais de controlo e monitorização do processo produtivo, dificuldades de regulação do fluxo e localização dos carros de transporte dos pneus em verde. Face aos problemas detetados ao longo do estudo, foram analisadas várias soluções para a resolução ou minimização dos mesmos. Entre as soluções propostas salientam-se: o alargamento do sistema de transporte por tapetes rolantes GTC (Green Tire Conveying) a todos os módulos de construção. Esta solução diminui o fluxo de carros para a área da construção, descongestionando a zona próxima do sistema de carregamento automático GTAL (Green Tire Automatic Loading) na vulcanização. A implementação dum sistema Wi-Fi RFID, que permite identificar e localizar artigos em curso utilizando etiquetas inteligentes numa rede wireless, conseguindo melhorar a programação de produção e o respetivo sequenciamento. Sabendo também que a Continental se encontra numa fase de expansão, designada Projeto Route 17/20, as soluções propostas tomaram em consideração essa nova realidade futura. Assim, foram estudados e propostos novos layouts para esse atual processo. Nestes novos layouts, procurou-se uma reorganização dos processos de fabrico, bem como um redimensionamento dos espaços de parqueamento de carros de pneus verdes adequado aos volumes produtivos. De igual forma, adequou-se os espaços físicos à possível implementação de um sistema de FiFo de pneus em verde na planta fabril, quando concluída a expansão. Este trabalho de dissertação apresenta como vantagens diretas da sua implementação: gerar a menor perturbação no atual método de trabalho seguido na empresa; previsivelmente aumentar a eficiência do processo produtivo; potenciar o crescimento tecnológico programado pela empresa; e oferecer uma boa relação custo/benefício no investimento necessário. Como apreciação final, pode-se concluir que este estudo foi finalizado com sucesso, visto que as soluções propostas foram apreciadas positivamente pela Administração da Continental Mabor S.A. e estão correntemente a ser avaliadas pelo grupo.

Analysis and visualization of seismic data using mutual information

Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Run-time monitoring in real-time operating systems

Embedded systems are increasingly complex and dynamic, imposing progressively higher developing time and costs. Tuning a particular system for deployment is thus becoming more demanding. Furthermore when considering systems which have to adapt themselves to evolving requirements and changing service requests. In this perspective, run-time monitoring of the system behaviour becomes an important requirement, allowing to dynamically capturing the actual scheduling progress and resource utilization. For this to succeed, operating systems need to expose their internal behaviour and state, making it available to external applications, and a runtime monitoring mechanism must be available. However, such mechanism can impose a burden in the system itself if not wisely used. In this paper we explore this problem and propose a framework, which is intended to provide this run-time mechanism whilst achieving code separation, run-time efficiency and flexibility for the final developer.

Analysis of temperature time-series: embedding dynamics into the MDS method

Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic and health aspects of the human life. Surface temperature time-series characterise Earth as a slow dynamics spatiotemporal system, evidencing long memory behaviour, typical of fractional order systems. Such phenomena are difficult to model and analyse, demanding for alternative approaches. This paper studies the complex correlations between global temperature time-series using the Multidimensional scaling (MDS) approach. MDS provides a graphical representation of the pattern of climatic similarities between regions around the globe. The similarities are quantified through two mathematical indices that correlate the monthly average temperatures observed in meteorological stations, over a given period of time. Furthermore, time dynamics is analysed by performing the MDS analysis over slices sampling the time series. MDS generates maps describing the stations’ locus in the perspective that, if they are perceived to be similar to each other, then they are placed on the map forming clusters. We show that MDS provides an intuitive and useful visual representation of the complex relationships that are present among temperature time-series, which are not perceived on traditional geographic maps. Moreover, MDS avoids sensitivity to the irregular distribution density of the meteorological stations.

Fractional dynamics in financial indexes

The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists. The methods and algorithms that have been explored for the description of physical phenomena become an effective background in the analysis of economical data. In this perspective are applied the classical concepts of signal analysis, Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional dynamical systems.

And I say to myself: “What a fractional world!”

This paper discusses several complex systems in the perspective of fractional dynamics. For prototype systems are considered the cases of deoxyribonucleic acid decoding, financial evolution, earthquakes events, global warming trend, and musical rhythms. The application of the Fourier transform and of the power law trendlines leads to an assertive representation of the dynamics and to a simple comparison of their characteristics. Moreover, the gallery of different systems, both natural and man made, demonstrates the richness of phenomena that can be described and studied with the tools of fractional calculus.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

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.

On similarities in infrared spectra of complex drugs

A chromatographic separation of active ingredients of Combivir, Epivir, Kaletra, Norvir, Prezista, Retrovir, Trivizir, Valcyte, and Viramune is performed on thin layer chromatography. The spectra of these nine drugs were recorded using the Fourier transform infrared spectroscopy. This information is then analyzed by means of the cosine correlation. The comparison of the infrared spectra in the perspective of the adopted similarity measure is possible to visualize with present day computer tools, and the emerging clusters provide additional information about the similarities of the investigated set of complex drugs.