• Honam Mathematical Journal
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• v.34 no.2
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• pp.219-230
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• 2012

In the paper, a symbolic construction is considered to define generalized Cantor-like sets. Lower and upper bounds for the correlation dimension of the sets with a regular condition are obtained with respect to a probability Borel measure. Especially, for some special cases of the sets, the exact formulas of the correlation dimension are established and we show that the correlation dimension and the Hausdorff dimension of some of them are the same. Finally, we find a condition which guarantees the positive correlation dimension of the generalized Cantor-like sets.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.134-139
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• 2004

The correlation dimension of a nonlinear method for the diagnosis on the clearance of rotating machinery is introduced in this paper. The correlation dimension can provide some intrinsic information of an underlying dynamic system by reconstructing measured scalar time series. Vibration signals measured from a rotor with different operating conditions are analyzed using the correlation dimension. The results show that the correlation dimension method can identify the magnitude of the clearance of a rotor and the lubricating condition.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.7 s.100
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• pp.781-787
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• 2005

The correlation dimension can provide some intrinsic Information of an underlying dynamic system by reconstructing measured nonlinear time series. The vibration signals measured from a rotor with different clearance sizes between shaft and bushing were analyzed using the correlation dimension. The results showed that the correlation dimension can identify the size of the clearance of a rotor and the lubricating condition, which can not be analyzed by frequency spectrum or wavelet. The magnitude of the correlation dimension became smaller as the clearance larger and as the lubrication condition better.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.95-102
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• 2001

We consider a Cantor set with overlaps Λ in R$^1$. We calculate its correlation dimension with respect to the push-down measure on Λ comparing with its similarity dimension.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.1
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• pp.115-122
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• 1999

In this paper, we confirmed that a speech signal is a chaos signal, and in order to use it as a speaker recognition parameter, analyzed chaos dimension. In order to raise speaker identification and pattern recognition, by making up the strange attractor involving an individual's vocal tract characteristics very well and applying fuzzy membership function to correlation dimension, we proposed fuzzy correlation dimension. By estimating the correlation of the points making up an attractor are limited according space dimension value, fuzzy correlation dimension absorbed the variation of the reference pattern attractor and test pattern attractor. Concerning fuzzy correlation dimension, by estimating the distance according to the average value of discrimination error per each speaker and reference pattern, investigated the validity of speaker recognition parameter.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1844-1847
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• 1997

Assuming that EEG(electroencephalogram), which is generated by a nonlinear electrical of billions of neurons in the brain, has chaotic characteristics, it is confirmend by frequency spectrum analysis, log frequency spectrum analysis, correlation dimension analysis and Lyapunov exponents analysis. Some chaotic characteristics are related to the degree of brain activity. The slope of log frequency spectrum increases and the correlation dimension decreasess with respect to the activities, while the largest Lyapunov exponent has only a rough correlation.

• The Journal of the Acoustical Society of Korea
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• v.16 no.4
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• pp.42-48
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• 1997

This paper has apparaised ability of speaker recognition and speech recognition using correlation dimension and Lyapunov dimension. In this method, speech was regarded the cahos that the random signal is appeared in determinisitic raising system. we deduced exact correlation dimension and Lyapunov dimension with searching important orbit from AR model power spectrum when reconstruct strange attractor using Taken's embedding theory. We considered a usefulness of speech recognition and speaker recognition using correlation dimension and Lyapunov dimension that characterized reconstruction attractor. As a result of consideration, which were of use more the speaker recognition than speech recognition, and in case of speaker recognition using Lyapunov dimension were much recognition rate more than speaker recognitions using correlation dimension.

• Korean Institute of Interior Design Journal
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• no.11
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• pp.20-25
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• 1997

The purpose of this study is to find out the correlation between Truth(道) and dimension through the understanding of architectural point of value in the aspect of correlation between modern western thoughts and the thoughts of Truth and also through the reading of what kind of composite trend of the Truth can be seen in a Korea traditional house. This stduy takes the following procedure with reference books and traditional house that we have. 1) Making foundation for this study by finding out the fundamental meaning of the thoughts of Truth through the comparing and analyzing between modern western thoughts and the thoughts of Truth. 2) Reviewing the understanding of dimension in the thoughts of Truth. 3) Traslation of the organic correlation through the analysis of composition, placement and characteristics of dimension in a real present traditional Korea house. 4) Finding out the meaning of each dimension through the adaptation of the fundamental rules of nature of Jane(藏:store), Sang(生:life), Jang(長:long), Su(收obtain) to the dimension composite of a traditional house and concluding that the cyclical process in the oriental thoughts could be made.

• The Journal of the Society of Korean Medicine Diagnostics
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• v.11 no.2
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• pp.84-95
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• 2007

Background and Purpose: We have studied the trends of EEG signals in the voluntary breathing condition by applying the fractal analysis. According to chaos theory, irregularity of EEG signals can result from low dimensional deterministic chaos. A principal parameter to quantify the degree of Chaotic nonlinear dynamics is correlation dimension. The aim of this study was to analyze correlation between the correlation dimension of EEG and HRV(heart rate variability). We have studied the trends of EEG signals in the voluntary breathing condition by applying the fractal analysis. Methods: EEG raw data were measured by moving windows during 15 minutes. Then, the correlation dimension(D2) was calculated by each 40-seconds-segment in 15 minutes data, totally 36 segments. 8 channels EEG study on the Fp, F, T, P was carried out in 30 subjects. Results and Conclusion: Correlation analysis of HRV was calculated with deterministic non-linear data and stochastic non-linear data. 1. Ch1(Fp1), Ch4(F3), Ch4(F4) is positive correlated with In LF. 2. Ch1(Fp1), Ch3(F3) is positive correlated with In TF.

• Journal of The Korean Society of Agricultural Engineers
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• v.54 no.2
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• pp.127-135
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• 2012

The processes of chemical and physical weathering occur simultaneously. The objective of this study was to estimate the degree weathered using fractal dimension through comparison with chemical characteristic of soil samples from Pohang (PH) and Kimpo (KP). Comparing chemical characteristics with fractal dimension, $SiO_2$, $Na_2O$, $K_2O$ content decreased and loss of ignition increased as fractal dimension increased. And fractal dimension showed high correlation with CWI while ATI, STI CIW, PI, CIA and RR demonstrated different degrees of correlation with fractal dimension. The tendency of the changes in oxide content and chemical weathering index with increasing fractal dimension appeared to be similar with the chemical changes due to weathering. Therefore, fractal dimension could be a good indicator representing the extent of weathering and chemical changes.