• 한국정밀공학회지
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• 제16권1호통권94호
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• pp.141-149
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• 1999

어느 한 계가 양수의 발산지수(Lyapunov exponent)를 가질 때 이 계는 카오스계로 분류되며 그 동특성은 예측이 불가능해 진다. 감쇠 기계계(소산계)에서는 위상공간(phase space)의 초기 부피가 시간에 따라 수축한다. 발산 지수들의 합은 음수이며 그 기계계의 감쇠와 관련되며, 따라서 발산지수들의 합은 감쇠의 변화를 감시하는데 사용되어질 수 있다. 그러나 그 감쇠변화를 감시하기 위해서는 발산지수를 계산하는데 사용하는 신호(data) 부분(segment)이 짧아야 한다. 이는 문제점을 야기시키는데 그 이유는 발산지수가 아주 많은 양의 발산률(divergence rate)의 평균으로서 구해지기 때문이다. 이 문제를 극복하기 위해서, 본 저자는 '순간발산지수(Instantaneous Lyapunov Exponent)'를 도입하였으며, 이 순간발산지수들의 합이 어떻게 기계계의 감쇠와 관련되어지는 가에 대하여 기술하였다. 미분방적식과 시계열(time series)을 이용한 컴퓨터 시뮬레이션은 '순간발산지수들의 합'의 중요성을 입증하였다. 그러나 시계열(또는 실험신호)로 부터의 정확한 순간발산지수를 측정하기는 매우 힘들기 때문에 '부분발산지수(Short term averaged Lyapunov Exponent)'를 또한 도입하였다.

• 한국생산제조학회지
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• 제9권2호
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• pp.45-51
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• 2000

This study proposes that analysis and evaluation method of time series ultrasonic signal using the chaotic feature extrac-tion for degradation extent. Features extracted from time series data using the chaotic time series signal analyze quantitatively material degradation extent. For this purpose analysis objective in this study if fractal dimension lyapunov exponent and 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 syste, In experiment fractal(correlation) dimensions and lyapunov experiments showed values of mean 3.837-4.211 and 0.054-0.078 in case of degradation material The proposed chaotic feature extraction in this study can enhances ultrasonic pattern recognition results from degrada-tion signals.

• Journal of Welding and Joining
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• 제16권6호
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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)

• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.371-381
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• 2017

국내에서 부동산 경매 낙찰가율 데이터를 활용한 Chaos 분석 연구는 전무하다. 부동산 경매분야의 데이터가 충분히 누적됨에 따라 부동산 경매 낙찰가율 시계열 분석의 의미가 커지게 되었다. 본 연구에서는 Hurst 지수, 상관차원, maximum Lyapunov 지수, 이 3가지 Chaos 분석기법을 활용하여 낙찰가율의 비선형 결정론적 동역학계적 특성을 확인하고, Chaos 분석을 통하여 얻은 결과와 실무 데이터를 비교하여, 함의를 도출한다. 높은 Hurst 지수에 따르는 추세와, maximum Lyapunov 지수의 측정을 통한 지속성, 그리고 상관차원 분석의 결과에 따라 time lag가 개시결정일에서 낙찰일, 배당요구종기일에서 낙찰일까지와 일치하는 점으로부터, Chaos 분석이 낙찰가율의 움직임을 예측하는데 유용함을 확인할 수 있었다.

• Annals of Clinical Neurophysiology
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• 제8권2호
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• pp.135-145
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• 2006

Background: Parkinson's disease is movement disorder due to dopaminergic deficiency. It has been noted that cognitive dysfunction also presented on Parkinson's disease patients. But, it is not clear whether such a cognitive dysfunction was a dopaminergic dysfunction or cholinergic dysfunction. Using linear and non-linear analyses, we analysed the effect of cognitive and motor symptom on EEG change. Methods: EEGs were recorded from patients with Parkinson's disease and essential tremor, and normal controls during rest. We calculated the power spectrum, correlation dimension and Lyapunov exponent by using 'Complexity'program. The power spectrum, correlation dimension, and Lyapunov exponent were compared between Parkinson's disease patients and essential tremor patients. Results: Theta power was increased in Parkinson's disease patient group. Correlation dimension was increased in Parkinson's disease patients. Positive correlation was noted between MMSE and correlation dimension, and negative correlation was noted between MMSE and Lyapunov exponent. Lyapunov exponent was decreased in Parkinson's disease patient. Conclusions: We conclude that the state of Parkinson's disease patient is characterized by increased correlation dimension and decreased Lyapunov exponent.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.87-100
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• 2000

In this paper, we try to approach chasos with numerical method. After investigating nonlinear dynamcis (chaos) theory, we introduce Lyapunov exponent as chaos\`s index. To look into the existence of chaos in 2-dimensional difference equation we computes Lypunov exponent and examine the various behaviors of solutions by difurcation map.

• 한국정밀공학회지
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• 제15권12호
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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.

• Journal of the Korean Data and Information Science Society
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• 제23권3호
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• pp.595-604
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• 2012

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefore, Lyapunov exponents can decide whether an orbit is chaos or not. To measure the sensitive dependence on initial conditions for nonsmooth dynamical systems, the calculation of Lyapunov exponent plays a key role, but in a theoretical point of view or based on the definition of Lyapunov exponents, Lyapunov exponents of nonsmooth orbit could not be calculated easily, because the Jacobian derivative at some point in the orbit may not exists. We use an algorithmic calculation method for computing Lyapunov exponents using time series for a two dimensional piecewise smooth dynamic system.

• 대한산업공학회지
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• 제22권1호
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• pp.65-82
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• 1996

This paper proposes a sequential procedure which can be used to determine a truncation point and run length to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state behavior. It is based on the idea of Lyapunov exponent in chaos theory. The performance measures considered are relative bias, coverage, estimated relative half-width of the confidence interval, and mean amount of deleted data.

• Ocean and Polar Research
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• 제28권4호
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• pp.459-465
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• 2006

Ambient noise as a background noise in the ocean has been well known for its the various and irregular signal characteristics. Generally, these signals we treated as noise and they are analyzed through stochastical level if they don't include definite sinusoidal signals. This study is to see how ocean ambient noise can be analyzed by the chaotic analysis technique. The chaotic analysis is carried out with underwater ambient noise obtained in areas near the Korean Peninsula. The calculated physical parameters of time series signal are as follows: histogram, self-correlation coefficient, delay time, frequency spectrum, sonogram, return map, embedding dimension, correlation dimension, Lyapunov exponent, etc. We investigate the chaotic pattern of noises from these parameters. From the embedding dimensions of underwater noises, the assesment of underwater noise by chaotic analysis shows similar results if they don't include a definite sinusoidal signal. However, the values of Lyapunov exponent (divergence exponent) are smaller than that of random noise signal. As a result we confirm the possibility of classification of underwater noise using Lyapunov analysis.