Samir A. M. Martins
Universidade Federal de São João del-Rei
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Featured researches published by Samir A. M. Martins.
Systems Science & Control Engineering | 2016
Erivelton Geraldo Nepomuceno; Samir A. M. Martins
ABSTRACT A lower bound error for free-run simulation of the polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous input) is introduced. The ultimate goal of the polynomial NARMAX is to predict an arbitrary number of steps ahead. Free-run simulation is also used to validate the model. Although free-run simulation of the polynomial NARMAX is essential, little attention has been given to the error propagation to round off in digital computers. Our procedure is based on the comparison of two pseudo-orbits produced from two mathematical equivalent models, but different from the point of view of floating point representation. We apply successfully our technique for three identified models of the systems: sine map, Chuas circuit and Duffing–Ueda oscillator. This technique may be used to reject a simulation, if a required precision is greater than the lower bound error, increasing the numerical reliability in free-run simulation of the polynomial NARMAX.
Systems Science & Control Engineering | 2017
Erivelton Geraldo Nepomuceno; Samir A. M. Martins; Gleison Vasconcelos Amaral; R. Riveret
ABSTRACT This paper introduces a class of pseudo-orbits which guarantees the same lower bound error (LBE) for two different natural interval extensions of discrete maps. In previous work, the LBE was investigated along with a simple technique to evaluate numerical accuracy of free-run simulations of polynomial NARMAX or similar discrete maps. Here we prove that it is possible to calculate the LBE for two pseudo-orbits, extending so the results of previous work in which the LBE is valid for only one of the two pseudo-orbits. The main application of this technique is to provide a simple estimation of the LBE. We illustrate our approach with the Logistic Map and Hénon Map. Using double precision, our results show that we ought simulate the Logistic Map and Hénon Map with less than 100 iterations, which is, for instance, far less than the number usually considered as transient to build bifurcation diagrams.
Applied Mathematics and Computation | 2018
Erivelton Geraldo Nepomuceno; Samir A. M. Martins; Bruno C. Silva; Gleison F. V. Amaral; Matjaž Perc
This paper presents a procedure to detect unreliable computer simulations of recursive functions. The proposed method calculates a lower bound error which is derived from two different pseudo-orbits based on interval extensions. The interval extensions are generated by taking into account the associative property of multiplication, which keeps the same error bound. We have tested our approach on the logistic map using many different programming languages and simulation packages, including Matlab, Scilab, Octave, Fortran and C. In all cases, the number of iterates is significantly lower than that considered reliable in the existing literature. We have also used the lower bound error on the logistic map and on the polynomial NARMAX for the Rossler equations to estimate the largest Lyapunov exponent, which determines the critical simulation time that guarantees the reliability of the simulation.
Mathematical Problems in Engineering | 2018
Erivelton Geraldo Nepomuceno; Samir A. M. Martins; Márcio J. Lacerda; Eduardo M. A. M. Mendes
A method to estimate the (positive) largest Lyapunov exponent (LLE) from data using interval extensions is proposed. The method differs from the ones available in the literature in its simplicity since it is only based on three rather simple steps. Firstly, a polynomial NARMAX is used to identify a model from the data under investigation. Secondly, interval extensions, which can be easily extracted from the identified model, are used to calculate the lower bound error. Finally, a simple linear fit to the logarithm of lower bound error is obtained and then the LLE is retrieved from it as the third step. To illustrate the proposed method, the LLE is calculated for the following well-known benchmarks: sine map, Rossler Equations, and Mackey-Glass Equations from identified models given in the literature and also from two identified NARMAX models: a chaotic jerk circuit and the tent map. In the latter, a Gaussian noise has been added to show the robustness of the proposed method.
arXiv: Numerical Analysis | 2016
Bruno C. Silva; F. L. Milani; Erivelton Geraldo Nepomuceno; Samir A. M. Martins; Gleison F. V. Amaral
Computational techniques are extensively applied in nonlinear science. However, while the use of computers for research has been expressive, the evaluation of numerical results does not grow in the same pace. Hammel et al. (Journal of Complexity, 1987, 3(2), 136--145) were pioneers in the numerical reliability field and have proved a theorem that a pseudo-orbit of a logistic map is shadowed by a true orbit within a distance of
International Journal of Bifurcation and Chaos | 2018
Erivelton Geraldo Nepomuceno; M. L. C. Peixoto; Samir A. M. Martins; Heitor Magno Rodrigues Junior; Matjaž Perc
10^{-8}
Applied Mathematics and Computation | 2018
Erivelton Geraldo Nepomuceno; Heitor Magno Rodrigues Junior; Samir A. M. Martins; Matjaž Perc; Mitja Slavinec
for
2017 IEEE World Engineering Education Conference (EDUNINE) | 2017
Pedro H. O. Silva; Erivelton Geraldo Nepomuceno; Alex Vitorino; Samir A. M. Martins
10^{7}
6th International Conference on Nonlinear Science and Complexity | 2016
Wilson Rocha Lacerda Junior; Lucas Giovani Nardo; Vinícius S. Borges; Alisson D. M. Vitor; Samir A. M. Martins
iterates. But the simulation of the logistic map with less than 100 iterates presents an error greater than
Journal of Control, Automation and Electrical Systems | 2013
Samir A. M. Martins; Erivelton Geraldo Nepomuceno; Márcio Falcão Santos Barroso
10^{-8}