Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

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.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Identifying economic periods and crisis with the multidimensional scaling

This paper applied MDS and Fourier transform to analyze different periods of the business cycle. With such purpose, four important stock market indexes (Dow Jones, Nasdaq, NYSE, S&P500) were studied over time. The analysis under the lens of the Fourier transform showed that the indexes have characteristics similar to those of fractional noise. By the other side, the analysis under the MDS lens identified patterns in the stock markets specific to each economic expansion period. Although the identification of patterns characteristic to each expansion period is interesting to practitioners (even if only in a posteriori fashion), further research should explore the meaning of such regularities and target to find a method to estimate future crisis.

Fractional calculus: application in modelling 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.

Scheduling a cutting and treatment stainless steel sheet line with self-management capabilities

With advancement in computer science and information technology, computing systems are becoming increasingly more complex with an increasing number of heterogeneous components. They are thus becoming more difficult to monitor, manage, and maintain. This process has been well known as labor intensive and error prone. In addition, traditional approaches for system management are difficult to keep up with the rapidly changing environments. There is a need for automatic and efficient approaches to monitor and manage complex computing systems. In this paper, we propose an innovative framework for scheduling system management by combining Autonomic Computing (AC) paradigm, Multi-Agent Systems (MAS) and Nature Inspired Optimization Techniques (NIT). Additionally, we consider the resolution of realistic problems. The scheduling of a Cutting and Treatment Stainless Steel Sheet Line will be evaluated. Results show that proposed approach has advantages when compared with other scheduling systems

A multidimensional scaling classification of robotic sensors

This chapter analyzes the signals captured during impacts and vibrations of a mechanical manipulator. Eighteen signals are captured and several metrics are calculated between them, such as the correlation, the mutual information and the entropy. A sensor classification scheme based on the multidimensional scaling technique is presented.

Multidimensional scaling analysis of electricity market prices

This paper studies the impact of energy and stock markets upon electricity markets using Multidimensional Scaling (MDS). Historical values from major energy, stock and electricity markets are adopted. To analyze the data several graphs produced by MDS are presented and discussed. This method is useful to have a deeper insight into the behavior and the correlation of the markets. The results may also guide the construction models, helping electricity markets agents hedging against Market Clearing Price (MCP) volatility and, simultaneously, to achieve better financial results.

Single-objective spreading algorithm

This paper addresses the problem of finding several different solutions with the same optimum performance in single objective real-world engineering problems. In this paper a parallel robot design is proposed. Thereby, this paper presents a genetic algorithm to optimize uni-objective problems with an infinite number of optimal solutions. The algorithm uses the maximin concept and ε-dominance to promote diversity over the admissible space. The performance of the proposed algorithm is analyzed with three well-known test functions and a function obtained from practical real-world engineering optimization problems. A spreading analysis is performed showing that the solutions drawn by the algorithm are well dispersed.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Realization of fractional-order controllers: analysis, synthesis and application to the velocity control of a servo system

The synthesis and application of fractional-order controllers is now an active research field. This article investigates the use of fractional-order PID controllers in the velocity control of an experimental modular servo system. The systern consists of a digital servomechanism and open-architecture software environment for real-time control experiments using MATLAB/Simulink. Different tuning methods will be employed, such as heuristics based on the well-known Ziegler Nichols rules, techniques based on Bode’s ideal transfer function and optimization tuning methods. Experimental responses obtained from the application of the several fractional-order controllers are presented and analyzed. The effectiveness and superior performance of the proposed algorithms are also compared with classical integer-order PID controllers.

A sensor classification strategy for robotic manipulators using multidimensional scaling technique

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. To test the impacts, a flexible beam is clamped to the end-effector of a manipulator that is programmed in a way such that the rod moves against a rigid surface. Eighteen signals are captured and theirs correlation are calculated. A sensor classification scheme based on the multidimensional scaling technique is presented.

Fractional control of legged robots

Fractional calculus (FC) is being used in several distinct areas of science and engineering, being recognized its ability to yield a superior modelling and control in many dynamical systems. This article illustrates the application of FC in the area of robot control. A Fractional Order PDμ controller is proposed for the control of an hexapod robot with 3 dof legs. It is demonstrated the superior performance of the system by using the FC concepts.

Fitness function evaluation through fractional algorithms

This paper proposes a Genetic Algorithm (GA) for the design of combinational logic circuits. The fitness function evaluation is calculated using Fractional Calculus. This approach extends the classical fitness function by including a fractional-order dynamical evaluation. The experiments reveal superior results when comparing with the classical method.