• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.463-463
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• 2012

본 연구에서는 유역의 공간적 자기상사성 평가를 통하여 하천유역의 특성을 파악하고자 하였다. 이를 위해 자기상사성 분석의 지표인 허스트지수 및 프랙탈차원을 산정하였다. 허스트지수(h)의 산정은 모형에 있어서 상당히 중요한 부분을 차지한다. 이 지수에 따라 지형의 모양은 서로 상이하게 다루어질 수 있기 때문이다. 허스트지수의 산정은 Hurst가 제시한 방법(허스트지수), Peters의 수정식, Mandebrot와 Wallis의 Pox 도표, 투영면적 및 표면적 비율 방법(면적지수)이 있으며, 본 연구에서는 유역의 공간 자기상성 분석을 위해 면적지수에 의한 방법과 허스트지수에 의한 방법을 적용하였다. 지형자료는 LiDAR 측량 및 하천 횡단측량에 의해 생성된 정밀 DEM을 활용하여 허스트지수 및 프랙탈차원을 산정하였다. 면적지수 및 허스트지수에 의한 프랙탈차원과 평균경사도와의 관계에서 아라천유역은 결정계수 R2값이 94.9 %, 99.5 %로 비교적 결정계수값이 크게 나타났으며, 경사도와 표면적과의 관계에서 결정계수 R2값은 81.8 %로 분석되었다. 이는 면적지수와 허스트지수에 의해 산정된 프랙탈 차원은 유역의 지형특성 인자로 타당성을 갖는 것으로 판단된다.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.85-96
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• 2004

The Resealed range statistical analysis and Hurst exponent which are standard methods to test the chaotic model are used to examine sinusoid pattern. We notice that the Hurst exponent can be used as a measure to examine the time series data that show semi-cyclic trend with noise.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.221-226
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• 2005

우리나라의 애국가(愛國歌), 일본(Kimigayo) 그리고 미국국가(The star-spangled Banner) 등에 대해서 악보가 갖는 고유정보를 카오스적 접근 방법인 근사엔트로피(approximate entropy)와 허스트(Hurst) 지수를 이용하여 각각 음계(scale)의 복잡도(複雜度)와 장기기억속성(長期 記憶 屬性)을 계산하여 비교하였던 바, 애국가가 상대적으로 복잡도에서 가장 높았으며, 세 국가 모두 장기 기억효과가 있는 것으로 나타났는데, 지속적인(persistent) 성향은 일본국가가 가장 컸다.

• Journal of Korea Water Resources Association
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• v.37 no.12
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• pp.993-1007
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• 2004

There are many different techniques for the estimation of the Hurst exponent. However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, resealed range(RR) analysis, modified restated range(MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation(MLE), detrended fluctuations analysis(DFA), and aggregated variance time(AVT)method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then this study discusses the advantages and disadvantages of the techniques and also the limitations of them.

• Journal of Korea Water Resources Association
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• v.44 no.10
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• pp.831-841
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• 2011

In this study, with the assumption that the geographical characteristics of the river basin have selfsimilarity, fractal dimensions are used to quantify the complexity of the terrain. For this, Area exponent and hurst exponent was applied to estimate the fractal dimension by using spatial analysis. The result shows that the value of area exponent and hurst exponent calculated by the fractal dimension are 2.008~2.074 and 2.132~2.268 respectively. Also the $R^2$ of area exponent and hurst exponent are 94.9% and 87.1% respectively too. It shows that the $R^2$ is relatively high. After analyzing the spatial self-similarity parameter, it is shown that traditional urban area's moderate slope geographical characteristic closed to 2D fractal in Ara water way. In addition, the relation between fractal dimension and geographical elements are identified. With these results, fractal dimension is the representative value of basin characteristics.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.9 no.3
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• pp.115-124
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• 1997

We measured the variance of eddy diffusion and associated ‘diffusion coefficients’ in coastal regions of Korea by observing the separation distances among multiple drifters deployed simultaneously at the same initial position. The variance of eddy diffusion was found to be proportional to $t^m$, where t is the time and m is a non-integer scaling exponent between 1.5 and 3.5. The observed scaling exponent of eddy diffusion cannot be reproduced by diffusion models employing constant eddy diffusivity. In this study, we applied fractal theory in simulating exponential increase of variance of eddy diffusion. We employed the fGn(fractional Gaussian noise) as a ‘modified’ random walks corresponding to the oceanic eddy diffusion. The variance of eddy diffusion, which corresponds to the fBm(fractional Brown motion) of our diffusion model, is proportional to $t^{2H}$, where H is Hurst scaling exponent. The temporal increase of the variance. with scaling exponent between 1 and 2, was successfully reproduced by our fractal diffusion model. However, our model cannot reproduce scaling exponent greater than 2. The scaling exponents greater than 2 are associated with the velocity shear of the mean flow.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.172-172
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• 2021

주된 물관리 시설의 신뢰성 있는 운영 계획의 수립을 위하여 충분한 길이의 유입량을 확보하는 것은 중요하나 현실적으로 제한된 관측 자료만 존재한다. 본 연구에서는 충분한 길이의 유입량을 생성하기 위하여 유입량의 모의 방법론을 제안하고자 한다. 제안하는 모형은 크게 3가지의 방법론을 기반으로 한다. 첫 번째는 연 유입량과 월 유입량의 생성단계로 Wavelet 기반으로 Autoregressive-moving-average(ARMA)을 적용할 것이다. 다음으로 일 유입량의 생성에 있어서 과거 관측값을 기반으로 한 Z-Score-based jittering 방법론을 적용할 것이다. 이렇게 각각 생성된 연 유입량, 월 유입량 그리고 일 유입량을 K-Nearest Nedighbors (K-NN) 방법론을 이용하여 최종 유입량을 결정하고자 한다. 생성된 유입량의 유용성을 판단하기 위하여 본 연구에서는 단기와 장기에서의 시계열의 지속성을 허스트 지수와 상관계수를 사용하여 검증할 것이며 이를 과거 관측치와 비교하고자 한다. 또한 각각의 연, 월, 일별의 기준으로 주요 통계치인 평균과 표준편차를 과거 관측 시계열의 통계치와 비교하여 그 유용성을 판단할 것이다.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.3
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• pp.103-108
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• 2016

In daily life, humans get stress very often. Stress is one of the important factors of healthy life and closely related to the quality of life. Too much stress is known to cause hormone imbalance of our body, and it is observed by the brain and bio signals. Based on this, the relationship between brain signal and stress is explored, and brain signal based stress index is proposed in our work. In this study, an EEG measurement device with 32 channels is adopted. However, only two channels (FP1, FP2) are used to this study considering the applicability of the proposed method in real enveironment, and to compare it with the commercial 2 channel EEG device. Frequency domain features are power of each frequency bands, subtraction, addition, or division by each frequency bands. Features in time domain are hurst exponent, correlation dimension, lyapunov exponent, etc. Total 6 subjects are participated in this experiment with English sentence reading task given. Among several candidate features, ${\frac{{\theta}\;power}{mid\;{\beta}\;power}}$ shows the best test performance (70.8%). For future work, we will confirm the results is consistent in low price EEG device.

• Knowledge Management Research
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• v.22 no.4
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• pp.119-133
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• 2021

As a large amount of data is produced in each industry, a number of time series pattern prediction studies are being conducted to make quick business decisions. However, there is a limit to predicting specific patterns in nonlinear time series data due to the uncertainty inherent in the data, and there are difficulties in making strategic decisions in corporate management. In addition, in recent decades, various studies have been conducted on data such as demand/supply and financial markets that are suitable for industrial purposes to predict time series data of irregular random walk models, but predict specific rules and achieve sustainable corporate objectives There are difficulties. In this study, the prediction results were compared and analyzed using the Chaos analysis method for roulette data and financial market data, and meaningful results were derived. And, this study confirmed that chaos analysis is useful for finding a new method in analyzing time series data. By comparing and analyzing the characteristics of roulette games with the time series of Korean stock index future, it was derived that predictive power can be improved if the trend is confirmed, and it is meaningful in determining whether nonlinear time series data with high uncertainty have a specific pattern.

• Economic and Environmental Geology
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• v.40 no.6
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• pp.739-749
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• 2007

The seismic velocity at the formation varies widely with physical properties in the layers. These features on seismic shot gathers are not capable of reproducing normally by numerical modeling of homogeneous medium, so that we need that of random inhomogeneous medium instead. In this study, we conducted Gaussian autocorrelation function (ACF), exponential autocorrelation function and von Karman autocorrelation function for getting inhomogeneous velocity model and applied a simple geological model. According to the results, von Karman autocorrelation function showed short wavelength to the inhomogeneous velocity medium. For numerical modeling for a gas hydrate, we determined a geological model based on field data set gathered in the East sea. The numerical modeling results showed that the von Karman autocorrelation function could properly describe scattering phenomena in the gas hydrate velocity model which contains an inhomogeneous layer. Besides, bottom-simulating-reflectors and scattered waves which appear at seismic shot gather of the field data showed properly in the inhomogeneous numerical modeling.