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- Multidimensional scaling visualization of earthquake phenomenaPublication . Lopes, António M.; Machado, J.A.Tenreiro; Pinto, Carla M.A.; Galhano, AlexandraEarthquakes are associated with negative events, such as large number of casualties, destruction of buildings and infrastructures, or emergence of tsunamis. In this paper, we apply the Multidimensional Scaling (MDS) analysis to earthquake data. MDS is a set of techniques that produce spatial or geometric representations of complex objects, such that, objects perceived to be similar/distinct in some sense are placed nearby/distant on the MDS maps. The interpretation of the charts is based on the resulting clusters since MDS produces a different locus for each similarity measure. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analyzed. The events, characterized by their magnitude and spatiotemporal distributions, are divided into groups, either according to the Flinn–Engdahl seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Space-time and Space-frequency correlation indices are proposed to quantify the similarities among events. MDS has the advantage of avoiding sensitivity to the non-uniform spatial distribution of seismic data, resulting from poorly instrumented areas, and is well suited for accessing dynamics of complex systems. 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 behavior of earthquakes.
- Fractional dynamics and MDS visualization of earthquake phenomenaPublication . Lopes, António M.; Machado, J.A.Tenreiro; Pinto, Carla M.A.; Galhano, AlexandraThis 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.
- Cálculo diferencial e integral: exercíciosPublication . Machado, J. A. Tenreiro; Galhano, Alexandra; Ferreira, Flávio; Ferreira, Fernanda A.
- On statistical analysis of biological armsPublication . Galhano, Alexandra; Carvalho, J. L. Martins de; Tenreiro Machado, J. A.The statistical analysis of robot manipulators reveals the limitations of joint-actuated machines. Steming from the results, in this paper we apply the statistical concepts on the study of biological arms. The superior performances of muscle-actuated arms over standard joint-actuated manipulators are demonstrated.
- On the statistical modelling of robot manipulatorsPublication . Galhano, Alexandra; Carvalho, J. L. Martins de; Tenreiro Machado, J. A.A novel approach to the modelling of robot manipulators is presented. Usually, system descriptions are based on a set of differential equations which, due to their nature, lead to very precise results and strategies but, in general, require laborious computations. This motivates the need of alternative methods based on other mathematical concepts. The proposed statistical model gives clear guidelines towards the optimization of the robot performances.
- Kinematic robustness of manipulating systemsPublication . Galhano, Alexandra; Tenreiro Machado, J. A.Present day mechanical manipulators have poor performances when compared with the human arm. In fact, joint-drivem manipulators are not efficient dues to the high actuator requirements imposed by the transients of the operational tasks. Muscle-actuated arms are superior because the anatomic levers adapt the manipulating exigencies to the driving linear actuators. The kinematic analysis of these systems highlights its main properties and constitutes a step towards the design of new mechanical biological-like robotic structures adopting linear actuators replacing the standard rotational joint-driving motor systems.
- WinRob: A program for teaching robot mechanics and controlPublication . Tenreiro Machado, J. A.; Galhano, AlexandraThe paper presents a program for robotics education that runs on standard IBM-PC's under the Microsoft Windows environment. The WinRob package is designed for undergraduate students and emphasis the fundamental aspects of robot modelling and control. The software is self-explanatory and uses menus, dialog boxes with figures and context-dependent on-line help. In this perspective, students are motivated to investigate on the kinematics, dynamics, trajectory planning and control in order to get insight into robotics.
- Computer system evaluation in robot controlPublication . Tenreiro Machado, J. A.; Carvalho, J. L. Martins de; Galhano, AlexandraThe high computational burden posed by mordern control algorithms preclude its industrial application using present day microcomputers. In this paper we evaluate the computational load of different logical and arihmetic operations and the capabilities of several computing systems (software & hardware). This study reveals that real-time limitations can be alleviated through the adoption of general techniques achieve not only a more efficient management of the computational resources but also provide a deeper insight on developments towards future real-time control architectures.
- Fractional Dynamics: A Statistical PerspectivePublication . Tenreiro Machado, J. A.; Galhano, AlexandraFractional calculus is a mathematical paradigm that has been increasingly adopted to describe the dynamics of systems with hereditary characteristics, or that reflect an average of a large population of microelements. In this line of thought, this article analyzes the statistical dynamics of a system composed of a large number of micromechanical masses with backlash and impacts. We conclude that, while individual dynamics of each element has an integer-order nature, the global dynamics reveal the existence of both integer and fractional dynamics.
- Customized direct dynamics of mechanical manipulatorsPublication . Tenreiro Machado, J. A.; Galhano, AlexandraThis paper studies the eficiency of customized Runge-Kutta methods on the evaluation of the direct dynamics of robot manipulators- Customized consists not only on the elimination of unnecessary and redundant calculations but also on the development of efficient integration methods. In this perspective, we investigate numerical algorithms with high order expansion and integration with adaptative step size based on the embedded estimation of the local truncation error.