Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Elements of a methodology to assess the alignment of core-values in collaborative networks

Collaborative networks are typically formed by heterogeneous and autonomous entities, and thus it is natural that each member has its own set of core-values. Since these values somehow drive the behaviour of the involved entities, the ability to quickly identify partners with compatible or common core-values represents an important element for the success of collaborative networks. However, tools to assess or measure the level of alignment of core-values are lacking. Since the concept of 'alignment' in this context is still ill-defined and shows a multifaceted nature, three perspectives are discussed. The first one uses a causal maps approach in order to capture, structure, and represent the influence relationships among core-values. This representation provides the basis to measure the alignment in terms of the structural similarity and influence among value systems. The second perspective considers the compatibility and incompatibility among core-values in order to define the alignment level. Under this perspective we propose a fuzzy inference system to estimate the alignment level, since this approach allows dealing with variables that are vaguely defined, and whose inter-relationships are difficult to define. Another advantage provided by this method is the possibility to incorporate expert human judgment in the definition of the alignment level. The last perspective uses a belief Bayesian network method, and was selected in order to assess the alignment level based on members' past behaviour. An example of application is presented where the details of each method are discussed.

Cyclic deformation of bidisperse two-dimensional foams

In-plane deformation of foams was studied experimentally by subjecting bidisperse foams to cycles of traction and compression at a prescribed rate. Each foam contained bubbles of two sizes with given area ratio and one of three initial arrangements: sorted perpendicular to the axis of deformation (iso-strain), sorted parallel to the axis of deformation (iso-stress), or randomly mixed. Image analysis was used to measure the characteristics of the foams, including the number of edges separating small from large bubbles N-sl, the perimeter (surface energy), the distribution of the number of sides of the bubbles, and the topological disorder mu(2)(N). Foams that were initially mixed were found to remain mixed after the deformation. The response of sorted foams, however, depended on the initial geometry, including the area fraction of small bubbles and the total number of bubbles. For a given experiment we found that (i) the perimeter of a sorted foam varied little; (ii) each foam tended towards a mixed state, measured through the saturation of N-sl; and (iii) the topological disorder mu(2)(N) increased up to an "equilibrium" value. The results of different experiments showed that (i) the change in disorder, Delta mu(2)(N), decreased with the area fraction of small bubbles under iso-strain, but was independent of it under iso-stress; and (ii) Delta mu(2)(N) increased with Delta N-sl under iso-strain, but was again independent of it under iso-stress. We offer explanations for these effects in terms of elementary topological processes induced by the deformations that occur at the bubble scale.

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Application of adaptive neuro-fuzzy inference for wind power short-term forecasting

The increased integration of wind power into the electric grid, as nowadays occurs in Portugal, poses new challenges due to its intermittency and volatility. Hence, good forecasting tools play a key role in tackling these challenges. In this paper, an adaptive neuro-fuzzy inference approach is proposed for short-term wind power forecasting. Results from a real-world case study are presented. A thorough comparison is carried out, taking into account the results obtained with other approaches. Numerical results are presented and conclusions are duly drawn. (C) 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Arrow plot and CA maps on microarray preprocessing methods

Microarray allow to monitoring simultaneously thousands of genes, where the abundance of the transcripts under a same experimental condition at the same time can be quantified. Among various available array technologies, double channel cDNA microarray experiments have arisen in numerous technical protocols associated to genomic studies, which is the focus of this work. Microarray experiments involve many steps and each one can affect the quality of raw data. Background correction and normalization are preprocessing techniques to clean and correct the raw data when undesirable fluctuations arise from technical factors. Several recent studies showed that there is no preprocessing strategy that outperforms others in all circumstances and thus it seems difficult to provide general recommendations. In this work, it is proposed to use exploratory techniques to visualize the effects of preprocessing methods on statistical analysis of cancer two-channel microarray data sets, where the cancer types (classes) are known. For selecting differential expressed genes the arrow plot was used and the graph of profiles resultant from the correspondence analysis for visualizing the results. It was used 6 background methods and 6 normalization methods, performing 36 pre-processing methods and it was analyzed in a published cDNA microarray database (Liver) available at http://genome-www5.stanford.edu/ which microarrays were already classified by cancer type. All statistical analyses were performed using the R statistical software.

Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

Controladores linguísticos Fuzzy

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Fuzzy clustering applied to a demand response model in a smart grid contingency scenario

This paper focus on a demand response model analysis in a smart grid context considering a contingency scenario. A fuzzy clustering technique is applied on the developed demand response model and an analysis is performed for the contingency scenario. Model considerations and architecture are described. The demand response developed model aims to support consumers decisions regarding their consumption needs and possible economic benefits.

Fuzzy, integer and fractional-order control: Application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Assessing the behaviour of RC beams subject to significant gravity loads under cyclic loads

Gravity loads can affect a reinforced concrete structure's response to seismic actions, however, traditional procedures for testing the beam behaviour do not take this effect into consideration. An experimental campaign was carried out in order to assess the influence of the gravity load on RC beam connection to the column subjected to cyclic loading. The experiments included the imposition of a conventional quasi-static test protocol based on the imposition of a reverse cyclic displacement history and of an alternative cyclic test procedure starting from the gravity load effects. The test results are presented, compared and analysed in this paper. The imposition of a cyclic test procedure that included the gravity loads effects on the RC beam ends reproduces the demands on the beams' critical zones more realistically than the traditional procedure. The consideration of the vertical load effects in the test procedure led to an accumulation of negative (hogging) deformation. This phenomenon is sustained with the behaviour of a portal frame system under cyclic loads subject to a significant level of the vertical load, leading to the formation of unidirectional plastic hinges. In addition, the hysteretic behaviour of the RC beam ends tested was simulated numerically using the nonlinear structural analysis software - OpenSees. The beam-column model simulates the global element behaviour very well, as there is a reasonable approximation to the hysteretic loops obtained experimentally. (C) 2013 Elsevier Ltd. All rights reserved.

Fuzzy clustering applied to a demand response model in a smatr grid contingency scenario

This paper focus on a demand response model analysis in a smart grid context considering a contingency scenario. A fuzzy clustering technique is applied on the developed demand response model and an analysis is performed for the contingency scenario. Model considerations and architecture are described. The demand response developed model aims to support consumers decisions regarding their consumption needs and possible economic benefits.

Fuzzy, integer and fractional-order control: application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Fuzzy linguistic controllers applied to decouple control loop effects

A fuzzy linguistic controller has been developed and implemented with the aim to cope with interactions between control loops due to coupling effects. To access the performance of the proposed approach several experiments have also been conducted using the classical PID controllers in the control loops. A mixing process has been used as test bed of all controllers experimented and the corresponding dynamic model has been derived. The successful results achieved with the fuzzy linguistic controllers suggests that they can be an alternative to classical controllers when in the presence of process plants where automatic control as to cope with coupling effects between control loops. © 2014 IEEE.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.