• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.4
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• pp.478-485
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• 1999

The purpose of this paper was the determination of the relationship between the chaotic charateristics and various levels of brain activities. Assuming that EEG(eletroencephalogram), which is generated by a nonlinear electiecal behavior of billions of neurons in the brain, has chaotic characteristics, it was confirmed by frequency spectrum analysis, log frequency spectrum analysis, correlation dimension analysis and Lyapunov exponents analysis. Chaotic characteristics are related to the degree of brain activity. The slope of log frequency spectrum increased and the correlation dimension decreased with respect to the brain activities, while the lagrest Lyapunov exponent has some rough correlation.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.49 no.3
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• pp.169-176
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• 2000

The partial discharge(PD) signal, may seems to be stochastic and merely random, was investigated using the method to discern between chaos and random signal, e.g. correlation integral, Lyapunov characteristic exponents and etc. For the purpose of obtaining experimental data, partial discharge detecting system via computer aided acoustic sensor, detect PD signal from the insulating system, was used. While this method is very different from typical statistical analysis from the point of view of a nonlinear analysis, it can provide better interpretable criterion according to the time evolution with a degradation process in the same type insulating system.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.161-164
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• 1995

Nonlinear analysis of various phenomena has been developed with improvement of computer. The characteristics form nonlinear analysis are available in monitoring and diagnosis state of system. There are many nonlinear property in cutting process, but nonlinear signals have been considered as noise. In this study, nonlinear analysis technique is applied and it will be verified that cutting force is chaos by calculating Lyapunov exponents,fractal dimension and embedding dimension. The relation between characteristic parameter calculated form sensor signal and various cutting condition is investigated.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1999.05a
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• pp.165-168
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• 1999

The chaotic characteristics of partial discharge(PD), may seems to be stochastic and merely random, were investigated using the method to discern between chaos and random signal, e.g. correlation integral, Lyapunov characteristic exponents and etc. For the purpose of obtaining experimental data, computer aided partial discharge detecting system was used. While this method is very different from typical statistical analysis from the point of view of a nonlinear analysis, it can provide better interpretable criterion according to the time evolution with a degradation process in the same type insulating system.

• The Journal of Natural Sciences
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• v.6 no.1
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• pp.79-87
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• 1993

In the map of period-doubling bifurcation, stable fixed points bifurcate to $2^n$ fixed points, and in the chaotic region, the chaotic bands merge to 1/$2^n$ bands. In a typical map, the chaotic bands expand to a broad chaotic band during the merging process, so called crisis. In this paper, interior crises appearing during the merging process will be discussed by using our map and will be analyzed the characteristics of the phenomenon by obtaining the Lyapunov Exponents.

• Journal of Welding and Joining
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• v.16 no.6
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• pp.86-96
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• 1998

This study proposes the analysis method of time series ultrasonic signal using the chaotic feature extraction for degradation extent evaluation. Features extracted from time series data using the chaotic time series signal analyze quantitatively degradation extent. For this purpose, analysis objective in this study is fractal dimension, lyapunov exponent, strange attractor on hyperspace. The lyapunov exponent is a measure of the rate at which nearby trajectories in phase space diverge. Chaotic trajectories have at least one positive lyapunov exponent. The fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal correlation) dimensions, lyapunov exponents, energy variation showed values of 2.217∼2.411, 0.097∼ 0.146, 1.601∼1.476 voltage according to degardation extent. The proposed chaotic feature extraction in this study can enhances precision ate of degradation extent evaluation from degradation extent results of the degraded materials (SA508 CL.3)

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.327-335
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• 2018

In this paper, we present the construction of natural invariant measures so called SRB(Sinai-Ruelle-Bowen) measures by the properties of geometric t-potential and Bowen's equation for the hyperbolic attractors.

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1249-1260
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• 2003

This present work focuses on the influence of nonlinearities associated with impact on the rocking behavior of a rigid body block subjected to a two-dimensional excitation in the horizontal and vertical directions. The nonlinearities in rocking system are found to be strongly dependent on the impact between the block and the base that abruptly reduces the kinetic energy. In this study, the rocking systems of the two types are considered : The first is an undamped rocking system model that disregards the energy dissipation during the impact and the second is a damped rocking system, which incorporates energy dissipation during the impact. The response analysis is carried out by a numerical method using a non-dimensional rocking equation in which the variations in the excitation levels are considered. Chaos responses are observed over a wide range of parameter values, and particularly in the case of large vertical displacements, the chaotic characteristics are observed in the time histories, Poincare sections, the power spectral density and the largest Lyapunov exponents of the rocking responses. Complex behavior characteristics of rocking responses are illustrated by the Poincare sections.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.380-388
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• 1994

Study on the chaotic stirring has been performed numerically and experimentally for a shallow rectangular tank accompanying a vortex shedding. The model is composed of a rectangular tank with a vertical plate with a length half the width of the tank. The tank is subject to a horizontal sinusoidal oscillation. The chaotic stirring was analysed by Poincare sections, unstable manifolds and Lyapunov exponents. As Reynolds number is increased the stirring effect is decreased due to the growth of a regular regions near the lower surface of the tank. In the other hand decrease of Reynolds number gives a weaker vortex shedding resulting in the poorer stirring effect. It was also found that the Lyapunov exponent is the highest at the dimensionless period of 1.3-1.5, which seems to be the best condition for the efficient stirring. The experimental visualization for the deformation of materials exhibits the striation pattern similar to the unstable manifold obtained numerically.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.12
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• pp.226-235
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• 1998

This study proposes the analysis and evaluation of method of time series of ultrasonic signal using the chaotic feature extraction for ultrasonic pattern recognition. The features are extracted from time series data for analysis of weld defects quantitatively. For this purpose, analysis objectives in this study are fractal dimension, Lyapunov exponent, and strange attractor on hyperspace. The Lyapunov exponent is a measure of rate in which phase space diverges nearby trajectories. Chaotic trajectories have at least one positive Lyapunov exponent, and the fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal(correlation) dimensions and Lyapunov exponents show the mean value of 4.663, and 0.093 relatively in case of learning, while the mean value of 4.926, and 0.090 in case of testing in slag inclusion(weld defects) are shown. Therefore, the proposed chaotic feature extraction can be enhancement of precision rate for ultrasonic pattern recognition in defecting signals of weld zone, such as slag inclusion.