• International Journal of Fuzzy Logic and Intelligent Systems
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• v.1 no.1
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• pp.104-112
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• 2001

Simply, Nonlinear dynamics theory means the complicated and noise-like phenomena originated form nonlinearity involved in deterministic dynamical system. An almost all the natural signals have nonlinear property. However, there exist few analysis software tool or package for a research and development of applications. We develop nonlinear time series analysis simulator is to provide a common and useful tool for this purpose and to promote research and development of nonlinear dynamics theory. This simulator is consists of the following four modules such as generation module, preprocessing module, analysis module and ICA module. In this paper, we applied to Electroencephalograph (EEG), as it turned out, our simulator is able to analyze nonlinear time series. Besides, we could get the useful results using the various parameters. These results are used to diagnostic the brain diseases.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.145-149
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• 1987

The input-output relation for nonlinear systems can be explicitly represented by the Voltera functional series and it is characterized by the Volterra Kernels. A block diagram reduction method is introduced to determine the Volterra Kernels for the nonlinear systems represented by nonlinear differential equations. Degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• 한국데이터정보과학회:학술대회논문집
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• 2004.04a
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• pp.91-101
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• 2004

The turbulent flow is of fundamental interest because the conservation equations for thermodynamics, mass and momentum are linked together. This turbulent flow consists of some coherent time- and space-organized vortical structures. Research has already shown that some dynamic systems and experimental models still cannot provide a good nonlinear analysis of turbulent time series. In the real turbulent flow, very complicated nonlinear behaviors, which are affected by many vague factors are present. In this paper, a kernel-based machine for fuzzy nonlinear regression analysis is proposed to predict the nonlinear time series of turbulent flows. In order to show the practicality and usefulness of this model, we present an example of predicting the near-wall turbulence time series as a verifiable model and compare with fuzzy piecewise regression. The results of practical applications show that the proposed method is appropriate and appears to be useful in nonlinear analysis and in fuzzy environments to predict the turbulence time series.

• Structural Engineering and Mechanics
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• v.54 no.2
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• pp.221-237
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• 2015

An integrated method is proposed for structural nonlinear damage detection based on time series analysis and the higher statistical moments of structural responses in this study. It combines the time series analysis, the higher statistical moments of AR model residual errors and the fuzzy c-means (FCM) clustering techniques. A few comprehensive damage indexes are developed in the arithmetic and geometric mean of the higher statistical moments, and are classified by using the FCM clustering method to achieve nonlinear damage detection. A series of the measured response data, downloaded from the web site of the Los Alamos National Laboratory (LANL) USA, from a three-storey building structure considering the environmental variety as well as different nonlinear damage cases, are analyzed and used to assess the performance of the new nonlinear damage detection method. The effectiveness and robustness of the new proposed method are finally analyzed and concluded.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.315-321
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• 1988

The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1B
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• pp.37-45
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• 2011

We studied noise influence on nonlinear chaotic system by using Logistic data series which is known as a typical nonlinear chaotic system. We regenerated Logistic data series by the method of adding noise according to noise level. And, we performed some analyses such as phase space reconstruction, correlation dimension, BDS statistics, and DVS Algorithms which are known as the methods of nonlinear deterministic or chaotic analysis. If we see the results of analysis, the characteristics of data series are gradually changed from nonlinear chaotic data series to random stochastic data series according to increasing noise level. We applied Low Pass Filter (LPF) and Kalman Filter techniques for the investigation of removing effect of the added noise to data series. Typical nonparametric method cannot distinguish nonlinear random series but the BDS statistic can distinguish the nonlinear randomness of the time series. Therefore this study used the BDS statistic which is well known as nonlinear statistical method for the investigation of randomness of time series for the effect of removing noise of data series. We found that Kalman filter is better method to remove the noise of chaotic data series even for high noise level.

• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.187-199
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• 2000

In this paper, we deal with the asymptotic properties of the least absolute deviation estimators in the nonlinear time series regression model. For the sinusodial model which frequently appears in a time series analysis, we study the strong consistency and asymptotic normality of least absolute deviation estimators. And using the derived limiting distributions we show that the least absolute deviation estimators is more efficient than the least squared estimators when the error distribution of the model has heavy tails.

• Journal of Mechanical Science and Technology
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• v.20 no.7
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• pp.950-960
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• 2006

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.

• Smart Structures and Systems
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• v.26 no.1
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• pp.23-33
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• 2020

Majority of the damage in engineering structures is nonlinear. Damage sensitive features (DSFs) extracted by traditional methods from linear time series models cannot effectively handle nonlinearity induced by structural damage. A new DSF is proposed based on vector space cosine similarity (VSCS), which combines K-means cluster analysis and Bayesian discrimination to detect nonlinear structural damage. A reference autoregressive moving average (ARMA) model is built based on measured acceleration data. This study first considers an existing DSF, residual standard deviation (RSD). The DSF is further advanced using the VSCS, and then the advanced VSCS is classified using K-means cluster analysis and Bayes discriminant analysis, respectively. The performance of the proposed approach is then verified using experimental data from a three-story shear building structure, and compared with the results of existing RSD. It is demonstrated that combining the linear ARMA model and the advanced VSCS, with cluster analysis and Bayes discriminant analysis, respectively, is an effective approach for detection of nonlinear damage. This approach improves the reliability and accuracy of the nonlinear damage detection using the linear model and significantly reduces the computational cost. The results indicate that the proposed approach is potential to be a promising damage detection technique.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.857-860
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• 1993

In this paper, we apply the self generating neuro fuzzy model (SGNFM) to the dimension analysis of the chaotic time series. Firstly, we formulate a nonlinear time series identification problem with nonlinear autoregressive (NARMAX) model. Secondly, we propose an identification algorithm using SGNFM. We apply this method to the estimation of embedding dimension for chaotic time series, since the embedding dimension plays an essential role for the identification and the prediction of chaotic time series. In this estimation method, identification problems with gradually increasing embedding dimension are solved, and the identified result is used for computing correlation coefficients between the predicted time series and the observed one. We apply this method to the dimension estimation of a chaotic pulsation in a finger's capillary vessels.