Estágio na empresa SPECMAN para a prática de técnicas de controlo da condição

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

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Analysis of stock market indices with multidimensional scaling and wavelets

Stock market indices SMIs are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling MDS . Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

A fractional approach to the Fermi-Pasta-Ulam problem

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.

Caracterização dinâmica de um edifício existente de betão armado através de ensaios de vibração ambiental

Dissertação de natureza Científica para obtenção do grau de Mestre em Engenharia Civil

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

Fractional dynamics in liquid manipulation

This paper presents a fractional calculus perspective in the study of signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs off-line and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system and the trajectory planning to be used in reducing or eliminating the effect of vibrations.

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.

A sensor classification strategy for robotic manipulators

In practice the robotic manipulators present some degree of unwanted vibrations. The advent of lightweight arm manipulators, mainly in the aerospace industry, where weight is an important issue, leads to the problem of intense vibrations. On the other hand, robots interacting with the environment often generate impacts that propagate through the mechanical structure and produce also vibrations. In order to analyze these phenomena a robot signal acquisition system was developed. The manipulator motion produces vibrations, either from the structural modes or from endeffector impacts. The instrumentation system acquires signals from several sensors that capture the joint positions, mass accelerations, forces and moments, and electrical currents in the motors. Afterwards, an analysis package, running off-line, reads the data recorded by the acquisition system and extracts the signal characteristics. Due to the multiplicity of sensors, the data obtained can be redundant because the same type of information may be seen by two or more sensors. Because of the price of the sensors, this aspect can be considered in order to reduce the cost of the system. On the other hand, the placement of the sensors is an important issue in order to obtain the suitable signals of the vibration phenomenon. Moreover, the study of these issues can help in the design optimization of the acquisition system. In this line of thought a sensor classification scheme is presented. Several authors have addressed the subject of the sensor classification scheme. White (White, 1987) presents a flexible and comprehensive categorizing scheme that is useful for describing and comparing sensors. The author organizes the sensors according to several aspects: measurands, technological aspects, detection means, conversion phenomena, sensor materials and fields of application. Michahelles and Schiele (Michahelles & Schiele, 2003) systematize the use of sensor technology. They identified several dimensions of sensing that represent the sensing goals for physical interaction. A conceptual framework is introduced that allows categorizing existing sensors and evaluates their utility in various applications. This framework not only guides application designers for choosing meaningful sensor subsets, but also can inspire new systems and leads to the evaluation of existing applications. Today’s technology offers a wide variety of sensors. In order to use all the data from the diversity of sensors a framework of integration is needed. Sensor fusion, fuzzy logic, and neural networks are often mentioned when dealing with problem of combing information from several sensors to get a more general picture of a given situation. The study of data fusion has been receiving considerable attention (Esteban et al., 2005; Luo & Kay, 1990). A survey of the state of the art in sensor fusion for robotics can be found in (Hackett & Shah, 1990). Henderson and Shilcrat (Henderson & Shilcrat, 1984) introduced the concept of logic sensor that defines an abstract specification of the sensors to integrate in a multisensor system. The recent developments of micro electro mechanical sensors (MEMS) with unwired communication capabilities allow a sensor network with interesting capacity. This technology was applied in several applications (Arampatzis & Manesis, 2005), including robotics. Cheekiralla and Engels (Cheekiralla & Engels, 2005) propose a classification of the unwired sensor networks according to its functionalities and properties. This paper presents a development of a sensor classification scheme based on the frequency spectrum of the signals and on a statistical metrics. Bearing these ideas in mind, this paper is organized as follows. Section 2 describes briefly the robotic system enhanced with the instrumentation setup. Section 3 presents the experimental results. Finally, section 4 draws the main conclusions and points out future work.

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.

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.

Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Generalized models from Beta(p,2) densities with strong allee effect: dynamical approach

A dynamical approach to study the behaviour of generalized populational growth models from Bets(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.