H. M. Rodrigues Junior, M. L. C. Peixoto, E. G. Nepomuceno
In this work we use intersection of different pseudo-orbits obtained by interval extensions to reduce the bounds of the exact solution provided by the toolbox Intlab. The method is applied on the logistic map.
B. C. Silva, F. L. Milani, E. G. Nepomuceno et al.
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 $10^{-8}$ for $10^{7}$ iterates. But the simulation of the logistic map with less than 100 iterates presents an error greater than $10^{-8}$ in a modern computer, performing a test based on the concept of multiple pseudo-orbits and symbolic computing.
M. L. C. Peixoto, E. G. Nepomuceno, H. M. Rodrigues et al.
Differences between computer simulation of dynamical systems and laboratory experiments are common in teaching and research in engineering. Normally, numerical inaccuracy and the non-ideal behaviour of the devices involved in the experiment are the most common explanations. With the application of interval analysis, it is possible to incorporate the numerical and parametric uncertainties in the simulation, allowing a better understanding of the play between simulation and experiment. This article presents a case study in which an step input is applied to an RLC circuit. Using the toolbox Intlab for Matlab, it was possible to present a computer simulation with the range that encompasses the experimental results . Comparison of simulation with experimental data show the success of the technique and indicates a potential content to be delivered to undergraduate engineering courses.
P. H. O. Silva, A. S. Cerqueira, E. G. Nepomuceno
The classification of time series is essential for extracting meaningful insights and aiding decision-making in engineering domains. Parametric modeling techniques like NARX are invaluable for comprehending intricate processes, such as environmental time series, owing to their easily interpretable and transparent structures. This article introduces a classification algorithm, Logistic-NARX Multinomial, which merges the NARX methodology with logistic regression. This approach not only produces interpretable models but also effectively tackles challenges associated with multiclass classification. Furthermore, this study introduces an innovative methodology tailored for the railway sector, offering a tool by employing NARX models to interpret the multitude of features derived from onboard sensors. This solution provides profound insights through feature importance analysis, enabling informed decision-making regarding safety and maintenance.
W. R. Lacerda Junior, S. A. M. Martins, E. G. Nepomuceno
This work presents a new meta-heuristic approach to select the structure of polynomial NARX models for regression and classification problems. The method takes into account the complexity of the model and the contribution of each term to build parsimonious models by proposing a new cost function formulation. The robustness of the new algorithm is tested on several simulated and experimental system with different nonlinear characteristics. The obtained results show that the proposed algorithm is capable of identifying the correct model, for cases where the proper model structure is known, and determine parsimonious models for experimental data even for those systems for which traditional and contemporary methods habitually fails. The new algorithm is validated over classical methods such as the FROLS and recent randomized approaches.
P. H. O. Silva, A. S. Cerqueira, E. G. Nepomuceno
This work presents a novel technique that integrates the methodologies of machine learning and system identification to solve multiclass problems. Such an approach allows to extract and select sets of representative features with reduced dimensionality, as well as predicts categorical outputs. The efficiency of the method was tested by running case studies investigated in machine learning, obtaining better absolute results when compared with classical classification algorithms.
R. C. Gonzalez, E. G. Nepomuceno
The increase in data traffic on the internet has significantly increased the relevance of data and image encryption. Among the techniques most used in cryptography, chaotic systems have received great attention due to their easy implementation. However, it has recently been observed that these systems can lose their chaotic properties due to the finite precision of computers. In this work, we intend to investigate flexible computing tools, particularly interval analysis, to reduce this problem. We opted for the Lorenz System, as it is one of the few systems whose chaoticity is proven analytically. The results of this study, based on the correlation and entropy indexes, were superior to other studies published in the recent literature.
M. Teixeira, N. P. Basilio, D. L. Firmo et al.
Chaotic systems have been investigated in several areas of engineering. In control theory, such systems have instigated the emergence of new techniques as well, have been used as a source of noise generation. The application of chaotic systems as pseudo-random numbers has also been widely employed in cryptography. One of the central aspects of these applications in high performance situations, such as those involving a large amount of data (Big Data), is the response of these systems in a short period of time. Despite the great advances in the design of chaotic systems in analog circuits, it is perceived less attention in the optimized design of these systems in the digital domain. In this work, the polarized fixed point representation is applied to reduce the number of digital elements. Using this approach, it was possible to significantly reduce the number of logic gates in the subtraction operation. When compared to other works in the literature, it has been viable to reduce by 50 \% the number of elements per bit of the digital representation of the tent map. The chaoticity was evidenced with the calculation of the Lyapunov exponent. Histogram, entropy and autocorrelation tests were used satisfactorily to evaluate the randomness of the represented system.
T. A. Santos, E. P. Magalhaes, D. R. Fiorio et al.
This paper investigates the use of dynamical chaotic systems to encrypt and exchange images between different devices. Two devices were used to simulate the Cubic Map, having the same set of initial conditions, to generate an encryption key. Although both devices are floating-point compliant, the simulations, and consequently the encryption key, turned out to differ from one another. This indicates that many existing chaos-based encryption schemes are just special cases of computational arithmetic properties, in which some characteristics in the construction of the devices coincided. A method to mitigate such flaw was also presented.
L. G. Nardo, A. M. Lima, E. G. Nepomuceno et al.
It is known that chaotic systems have widely been used in cryptography. Generally, floating point simulations are used to generate pseudo-random sequence of numbers. Although, it is possible to find some works on the degradation of chaotic systems due to finite precision of digital computers, little attention has been paid to exploit this limitation to formulate efficient process for image encode. This article proposes a novel image encryption method using natural interval extensions. The sequence of arithmetic operations is different in each natural interval extension. This is what we need to produce two different sequences; the difference between these sequences is used to generate the lower bound error, which has been shown to present satisfactory pseudo-random properties. The approach has been successfully tested using the Chua's circuit as the chaotic system. The secret key has presented good properties for encrypting the Lena image.