• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.7 s.166
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• pp.1065-1074
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• 1999

This study proposes the analysis and evaluation method of time series ultrasonic signal using the chaotic feature extraction for ultrasonic pattern recognition. Features extracted from time series data using the chaotic time series signal analysis quantitatively welding defects. For this purpose analysis objective in this study is fractal dimension and Lyapunov exponent. Trajectory changes in the strange attractor indicated that even same type of defects carried substantial difference in chaoticity resulting from distance shills such as 0.5 and 1.0 skip distance. Such differences in chaoticity enables the evaluation of unique features of defects in the weld zone. In experiment fractal(correlation) dimension and Lyapunov exponent extracted from 6dB ultrasonic defect signals of weld zone showed chaoticity. In quantitative chaotic feature extraction, feature values(mean values) of 4.2690 and 0.0907 in the case of porosity and 4.2432 and 0.0888 in the case of incomplete penetration were proposed on the basis of fractal dimension and Lyapunov exponent. Proposed chaotic feature extraction in this study enhances ultrasonic pattern recognition results from defect signals of weld zone such as vertical hole.

• Annals of Clinical Neurophysiology
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• v.3 no.1
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• pp.31-36
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• 2001

Background & Objectives : Fractal Dimension(FD) could be an index of correlation between variable parameters in non-linear chaotic signals. We tried to demonstrate that EEG wave is compatible with chaotic waves by measuring the Lyapunov exponent index and compared the difference of FD between variable age groups(teens, 30's, 50's) Methods : We estimated the Lyapunov exponent index and the FD from digital EEG data among five persons in each normal age groups by using the software which is programmed in our laboratory. Statistical analysis was done with SPSS win 8.0. The statistical differences of Lyapunov exponent index and FD between each electrodes and each age groups were done with ANOVA and paired sample t-test. Result : The Lyapunov exponent indexes were larger than 1 in each electrode and age group. There is no statistical difference in FD between each electrodes and each age groups. Except in 30th age group. In this group the FD of right hemisphere is larger than that of left hemisphere. Conclusion : The result of Lyapunov exponent index means EEG wave is a non-linear chaotic signal. And the results of FD suggest that chaotic parameters of right hemisphere is larger than those of left hemisphere at rest at least in younger people. We think that chaotic parameters can be a useful tool in investigating the variable diseases or brain states.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.8
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• pp.1647-1652
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• 2009

Generally the neural network and the fuzzy compensative algorithm are applied to forecast the time series for power demand with a characteristic of non-linear dynamic system, but it has a few prediction errors relatively. It also makes long term forecast difficult for sensitivity on the initial condition. On this paper, we evaluate the chaotic characteristic of electrical power demand with analysis methods of qualitative and quantitative and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction, time series forecast for multi dimension using Lyapunov exponent quantitatively. We compare simulated results with the previous method and verify that the purpose one being more practice and effective than it.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.171-174
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• 2009

Generally the neural network and the fuzzy compensative algorithm are applied to forecast the time series for power demand with a characteristic of non-linear dynamic system, but it has a few prediction errors relatively. It also makes long term forecast difficult for sensitivity on the initial condition. On this paper, we evaluate the chaotic characteristic of electrical power demand with analysis methods of qualitative and quantitative and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction, time series forecast for multi dimension using Lyapunov exponent quantitatively. We compare simulated results with the previous method and verify that the purpose one being more practice and effective than it.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.445-454
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• 2006

We describe a solution to the Ornstein-Uhlenbeck equation $\frac{dI}{dt}-\frac{1}{\tau}$I(t)=cV(t) where V(t) is a constant multiple of a Gaussian white noise. Our solution is based on a discrete set of Gaussian white noise obtained by taking sample points from a sum of single frequency harmonics that have random amplitudes, random frequencies, and random phases. Hence, it is different from the solution by the standard random walk using random numbers generated by the Box-Mueller algorithm. We prove that the power of the signal has the additive property, from which we derive that the Lyapunov characteristic exponent for our solution is positive. This compares with the solution by other methods where the noise is kept to be in an error range so that its Lyapunov exponent is negative.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.2
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• pp.123-129
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• 2010

The purpose of study is to investigate the correlation between the Lyapunov exponent (LE) and the displacement of the center of gravity (DCG) for clarifying walking stability on the treadmill. From fifteen young healthy subjects volunteered, lower extremity joint angles were recorded using a three-dimensional motion capture system with reflective markers. The anteroposterior DCG and the LE were calculated by a commercial software. A linear correlation between LE and DCG (p<0.05) showed that LEs compensated for walking distance on the treadmill walking. However, LEs were found to be independent of self-selected walking speeds by a negligible correlation between LE and the Froude number (p>0.05).

• Journal of Welding and Joining
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• v.28 no.1
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• pp.72-76
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• 2010

Irregular fluctuation of penetration depth in CW single mode fiber laser welding is analyzed statistically and chaotically. Among various chaos theories, one of the basic concept referred as Lyapunov exponent is applied to the analysis to quantify the irregularity of penetration. Especially, maximal Lyapunov exponent (MLE) is known as the representative value indicating chaotic degree of the system dynamics. MLE calculation method of experimental data is applied to longitudinal spiking defect in fiber laser weld. Laser power modulation is suggested as a remedy then the computed MLE value is compared to CW case. It is shown that the adoption of chaos theory, MLE computation, can be used as a measurement standard to prove the validity of the solutions to prevent the unexpected chaotic behavior of weld through this work.

• Journal of information and communication convergence engineering
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• v.9 no.4
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• pp.369-374
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• 2011

Generally the neural network and the Fuzzy compensative algorithms are applied to forecast the time series for power demand with the characteristics of a nonlinear dynamic system, but, relatively, they have a few prediction errors. They also make long term forecasts difficult because of sensitivity to the initial conditions. In this paper, we evaluate the chaotic characteristic of electrical power demand with qualitative and quantitative analysis methods and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction and a time series forecast for multi dimension using Lyapunov Exponent (L.E.) quantitatively. We compare simulated results with previous methods and verify that the present method is more practical and effective than the previous methods. We also obtain the hourly predictability of time series for power demand using the L.E. and evaluate its accuracy.

• Korean Journal of Applied Biomechanics
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• v.31 no.1
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• pp.24-29
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• 2021

Objective: The goal of this study is to calculate and compare the Maximum Lyapunov Exponent (MLE) for the anteroposterior, mediolateral and vertical displacement of the markers attached to bony land marks of the trunk and foot. Method: Ten young and healthy male subjects (age: 26.5±3.27 years, height: 167.44±5.12 cm, and weight 69.5±7.36) participated in the study. Three-dimensional positional coordinate of eight different trunk and foot marker during walking on tread mill were analysed. Results: MLE values for anteroposterior displacement of the marker were found to be significantly different with MLE values for mediolateral and vertical displacement whereas MLE values for mediolateral displacement of the marker shows no significant difference with the MLE values for vertical displacement of the markers at significance level 0.05. Conclusion: Finding of this study suggest that it is essential to consider the displacement in all three direction to examine the real characteristic of a gait signal.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.525-540
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• 2014

The Lyapunov exponent and moment Lyapunov exponents of Hill's equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged $It\hat{o}$ differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.